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Unknown: Research on the what's
going on out there, and then
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bringing that to you as well as,
of course, my opinion, every
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month. So that is a big purpose,
just to be able to the to
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gather, network, collaborate, be
with like minded people. And so
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here we are, right here, feel
free to use the chat to talk to
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each other, which is really one
of the benefits of being here
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today. You can, in a moment,
we'll see where people are from
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and what grade levels you teach.
But the other main purpose of
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Saturday math, and this has
always been the case in the
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eight years that we've done
Saturday math is the bottom
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line. If students have number
sense, we can take off with
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whatever initiative and
resources are thrown at us. So
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the overall goal that has always
been on Saturday, math is
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improving. Number Sense, that is
our foundation. So I'm going to
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put number sense here. There's a
secondary goal. And over the
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last couple of months, we've
launched an initiative called
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math testing secrets that we
have an entire course for now
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that we're very, very proud of,
but in that testing secrets, we
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say that there are two barriers
to increasing test scores. And
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the barriers are students having
a lack of number sense, but also
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a lack of notation. And there
are some of my favorite
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notations that have scaled
student achievement that we use,
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that are not explicitly stated
in the standards, but are very
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much related to the standards.
Some of you can probably guess
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one of my favorite notations.
Should I have you? Guess I
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should have you. Guess what's
one of my favorite notations
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that relates to a task that is
the utmost of importance for
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understanding numbers and having
number sense and improving
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number sense? Natalie, of course
you have you are always
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transplanted here to give us the
exact answer notation of square
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root. We have no idea how
essential notation of square
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root is. That's the one I'm
going to land on today. There
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are other notations that are
absolutely essential, because
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part of what is the difference
between a student passing an end
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of year math test and almost
passing an end of year math
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test, most often, is the
notation that is used and the
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lack of understanding of that
notation. Now I'm coming out of
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the gate talking a lot about
testing as if like testing is
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the be all, end all. Well, no,
it's not. If you all know me,
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you know it's not. But we want
our cake, and we want to be able
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to eat it too. So I want kids to
have great, rich, complex,
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accessible math experiences in
the classroom on a daily basis.
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That's what I advocate for. I
empower teachers to create these
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experiences for students,
because I cannot personally
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create these experiences for
every student out there in
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United States, but with your
help, I can do that. So my main
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goal and mission and vision is
to empower and inspire teachers
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and teach teachers how to create
these rich, complex, accessible
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math experiences that target all
students, and especially
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students that struggle and
students with disabilities.
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Having said that, if we're going
to do that in an effective way,
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the test scores should show it
so and I mean, that's what we're
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judged on. We're judged on the
test scores. So why not have a
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goal of these kids can, and I
know these kids can, because if
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any of you know me, you know
that we have taken cohorts of
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students from 27% passing one
year to the next year 65%
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passing. We've taken cohorts
from 65% passing to 86% passing.
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We've taken cohorts of students
from exhibiting bell curve
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results, meaning bell curve,
this is 50th percentile. So
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average is 50th really from 40th
to 60th percentile on bell curve
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on a true standardized test. Now
I have to get on my soapbox for
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just a minute.
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So. We have for years, even from
the time that I was in school,
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we've used very high rated,
credible standardized testing
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companies that this is all they
do. And I'm going to give two
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examples of those, the Iowa
battery and the Terra Nova.
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Okay, I don't know if you have
heard of those, or know those,
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or whatever. Those are true
standardized tests. They're
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they're competitive companies.
They're two different companies.
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But the Iowa and Terra Nova, I
have an immense amount of
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respect for an immense amount of
respect, the same amount of
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respect I have for the A C T and
S A T, again, a c t and s a t2,
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totally different companies, two
totally different platforms,
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competing interests, whatever.
But it's always good to have
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both. And I don't have, you
know, a preference one way or
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another. I think we can use both
of them to our advantage. But
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the Iowa and Terra Nova used to
be the be all, end all, a
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district would pick one of them,
and either every year or every
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three years or every other year,
students would take this
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standardized test. And the
reason that I loved how
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standardized it was is it is
national, like it didn't matter
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if you were in Pennsylvania or
Arizona or whatever it was,
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usually one of those two
options. And what the Iowa and
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Terra Nova did was, yes, it gave
you an achievement percentile,
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not a percent, not a passing.
There's no passing. It gave you,
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it gave students a score based
on percentile for achievement.
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So there were subject
achievement, pieces of it, and
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if students scored anywhere
between the 40th and 60th
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percentile, spot on average,
spot on average, fantastic,
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which is why. And I'll just give
you an example from the state of
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Ohio, which is why in reading.
Now we have what are called
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rimps in reading, their
individual plans for reading,
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even if kids that are not
special ed, not on IEP, but
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school districts were able to
pick and choose what what
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percentile ranking was the
maximum for students that have
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deficits. Too many school
districts picked 40/40
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percentile. The problem is 40 is
right at the bottom of average.
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So we're doing a lot of extra
work for these kids. And what
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was happening in schools? What
is happening in schools is some
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of those kids that are like 32nd
to 40th percentile, we're
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creating these plans for them,
but they have been passing their
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reading on the state test. So
there's this disconnect. The
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reason is, I believe we've gone
down a very, very skewed road
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for data. So I just want to
enlighten us this morning on
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what data we're using and how
we're using data, and how the
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data has shifted to become much
more ineffective in recent
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years. So Iowa, TerraNova, I the
results of these things used to
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be outstanding, spot on for
kids. Okay, now the reason I
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bring this up is I'm trying to
show you in cohorts that have
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used the model that we present
in all of our sessions, is we've
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been able to scale exponentially
the achievement of students, not
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just their achievement, but
their test score results. So
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when we look at percentile
rankings, when we were using
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Iowa TerraNova, we had a cohort
of students that no one in this
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certain cohort scored below the
70th percentile. I mean, we
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literally broke the bell curve
with one of our cohorts.
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Absolutely crazy. The other
thing I want to say about Iowa
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and Terra Nova is a really
important piece of them was the
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cognitive ability test. So you
would get a cognitive ability
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students would get a cognitive
ability score, which was like,
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IQ score, okay, and on that
cognitive ability score, 100
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spot on average, but really
average went from 90 to 110
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and this cognitive ability score
scoring high enough. Staff would
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accurately determine gifted
brains and accurately determine
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students, you know, our 70s kids
that had severe brain
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disconnects, and this is what
we've used forever and ever and
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ever now. Okay, so let me make
two points on this. One point on
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this is we have scaled math
achievement using part of what
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I'm going to tell you today,
because going back, I'm talking
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about the big overarching
purpose of Saturday, math is
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improving number sense. We know
that with testing, we want to
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improve notation sense, and I
just want to show you some of
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the things that we've been able
to do, because a big purpose of
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Saturday math is to empower and
inspire us to go back and when
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we know better, we do better, so
that we can all be equipped to
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scale math achievement in these
same ways. So I wanted to share
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some of that data with you. So
that's one piece. Is the purpose
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of Saturday math, and it really
starts with number sense, but
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dwindles down to these other
things. And since we're in
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testing season, I want to bring
bring those things to light.
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Now, here's the other point. I
wasn't even going to talk about
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this today. I think I've been
really fired up about it. I was
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going to jump right into our
content. Remember, I said that
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we're going to, well, I mean, I
kind of did, but now I'm
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derailed. I'm just totally
derailed because I don't know if
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any of you have seen some of the
news media about I ready, so I'm
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not going to go into that
deeply, but what I am going to
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say about this is, over the
years, we have states not we
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states have disapproved some of
our testing entities and
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disapproved some of our textbook
companies and disapproved and
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disapproved and disapproved, and
for some of us, things that were
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working very well for us, and
then re approved, created a re
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approval list of some things
that I think are just pure
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trash. Now I say that and you're
like, Okay, where's your data?
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Let me go back to sort of this
is not necessarily Saturday
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math, but one of the biggest
overarching leads for scaling
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math achievement, and that is
shifting, shifting. And we
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started to make this shift in
about the I'm going to say 20,
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2015 2016 2017 then I think we
were moving in the right
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direction. Covid came, and then
everything went out the window.
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I don't even know what happened
with decision makers like I
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don't know if, if they're
desperate or if I don't even
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know, but what we have been
moving toward ever since minds
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on math started this mission in
2011 what we have been moving
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toward is shifting math
instruction to exactly how the
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brain learns and decision makers
and states are saying they're
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doing this through the science
of reading, which there's a lot
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of merit to the science of
reading. I I'm not a literacy
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expert. I'm not an expert there,
but here's where our downfall is
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going to happen, and this is,
this is my prediction, and this
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is what's going to and this is
why I want you all to be
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educated on this before it comes
in and and takes over and swoops
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in. The science of math.
Learning is not parallel to the
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science of reading learning.
Reading is a skill that must be
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explicitly taught it is not
innate, intuitive inborn, but
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number sense is the exact
opposite, that we are born with
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a certain level of understanding
of number. Number Sense is
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intuitive, ingrained inborn. It
is a natural sense of the
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magnitude of numbers, magnitude
meaning how large and small
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numbers are.
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And so number sense cannot be
explicitly taught, but number
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sense can be. Dramatically
improved through experiences. So
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I want to catch us and educate
us before some of these shifts
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come into place, so we as
educators can be knowledgeable
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enough to ask the right
questions based on the correct
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current research of how the
brain learns and how the brain
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learns certain things. So
notation, notation must be
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explicitly taught. Kids aren't
just going to discover what a
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square root is. So there,
notation is explicit, very much
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parallel to science of reading
number sense is not so when I
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share with you on Saturday
sessions How to Improve number
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sense, this all falls into a
bigger picture of how the brain
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actually learns mathematics, and
there are two different types of
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instruction and learning
outcomes. One we call
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conceptual, which is the number
sense piece, which students must
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experience and figure out on
their own. But we must have
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powerful instructional delivery
methods to be able to make that
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happen. That's what we focus on,
on Saturday, math. And then
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there are procedural,
algorithmic math ability,
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notation, instructional delivery
methods that are very
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traditional, okay, so we need
both, but these are competing
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interests, because the more
procedure and algorithm based we
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are in our classrooms, the less
this conceptual can improve. But
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the more and more and more we
work to improve the conceptual,
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the notation declines. So what
we do in all of our programs is
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find that right teeter totter
balance of being able to improve
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both because they are competing
interests and they do require a
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different instructional
delivery. Wasn't going to go
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into all that today, but I'm
glad that I did, because now we
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have it all pieced in in one
section here. My purpose of
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saying all that, though, was to
talk about the purpose of
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Saturday math, and it's always
been to improve number sense,
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and that's exactly what we're
going to be doing today as well.
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Alright, before I move on,
though, that was, that was a lot
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a lot. Whoo, that was a lot, a
lot. Okay, unmute, if you have
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other thoughts, questions,
comments, etc. And I'll review
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the chat, because I know some of
you have been chatting in the
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chatting.
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Well, I had in the chat a neat
story from an experience with my
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kids this week. Please. Yes, it
actually goes along with
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everything, how the brain learns
number, sense and notation were
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an absolute value. And so they
were working on their lesson of
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the day, and they were comparing
some absolute values. And it was
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absolute value of negative 24
compared to absolute value of
225
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positive 24 greater than, less
than or equal. So I'm walking
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around the room and observing,
you know what they're writing.
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And so many, of course, said the
absolute value of positive 24
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was greater. And I knew you know
exactly what they were thinking.
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But because, you know, I've been
with Jonily for so long, I just
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each kid I touch base with, I
either said something like, Tell
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me about that. Or, how did you
get that answer? Or tell me how
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you know that's true something
to that effect, and they know
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enough that they don't assume
they're wrong when I say
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something like that. I just want
to know how they got there. So
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they all just launch into the
explanation, and every single
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one of them goes, Oh, they're
equal every single kid, every
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time. So I did this across both
of my classes that day, probably
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in total, 16 to 20 kids that
had, you know, the wrong answer.
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But when I stopped them and
paused them and didn't say, Oh,
240
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you're wrong. How would you fix
that? But how did you get that?
241
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Tell me about that, they
launched into their explanation.
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They all self corrected the
answer. And it really got me
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thinking about, like, state
testing in two weeks. I was
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like, you guys, you all knew the
answer. You all knew it. I
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didn't even I didn't say
anything. But how did you know,
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tell me about that? What did you
think about that? And you all
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got the right answer. So my
like, takeaway and message to
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them was like, you know more
math than you think you do, we
249
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have to slow because we've been
talking a lot about taking your
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time on the test and like, it's
not taking time for the sake of
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taking time. But I was like, I
want you to slow down your
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brain. Have my voice in your
head if you need to prompt
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yourself to say, How do I know?
Or how did I get that answer?
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Like, take your gut reaction.
Like. Course, 24 is bigger, but
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take that gut reaction and
really evaluate the problem, and
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you'll they're they self
corrected. But I'm like, what if
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they did that five times? That's
like, a whole level on a test,
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five questions where your gut
answer, and then you stop and
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think about it. So I'm like,
That's the brain science. I
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think, like, stop and think
about it. And they know so much,
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but they just have to, so I'm
trying to get my voice in their
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head, which is weird, but it was
just a really neat experience.
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Like 16 to 20 kids, literally.
And they all, Oh, they're equal.
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I'm like, okay, so what a time,
you
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know, but I have to give a good
background on our friend,
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Natalie, Krista, Amy, Sarah
Neal, that's here Kirk. Where is
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Kirk today? Oh, man, I really
needed Kirk here today. It's
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okay. So I want to share with
all of you. And then we have, we
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have Lisa, Sarah W we have
Daphne, we have Janet. We have
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so the reason I'm naming these
names is this doesn't just
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happen like especially by coming
to Saturday maths. So we have it
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minds on math, a math teacher
mastermind group, which these
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names that I've mentioned are
either currently a part of that
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or have been a part of it. The
math teacher mastermind group
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launches into a math
certification group. So Natalie,
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Krista, Amy, Sarah, are all some
of our certified coaches that
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have been implementing this for
years, like years Natalie, not
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as many years as others, because
Natalie got to be a student
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teacher for one of our certified
coaches. So Natalie had an
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accelerated learning experience
of this type of implementation.
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And the reason that I say all of
this is it doesn't happen with
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one Saturday math or one math
teacher mastermind or one
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implementation. It takes a good
345, solid years of interacting
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with this on Saturday maths, on
math teacher masterminds on June
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events, on certification
programs, on, you know, all of
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these things that we offer. And
the reason I said April 24 mark
287
00:22:23,960 --> 00:22:27,860
your calendars for April 24 in
the evening. April 24 in the
288
00:22:27,920 --> 00:22:34,520
evening, we are having our next
webinar. And this next webinar
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00:22:34,520 --> 00:22:39,080
is going to outline a bundle
package of all of our programs
290
00:22:39,080 --> 00:22:45,040
for 2026 2027 so you can get all
of our programs that we're
291
00:22:45,040 --> 00:22:49,120
launching, that we launch every
year in a bundle at a very
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00:22:49,120 --> 00:22:53,020
discounted rate. I'll send you
information on that webinar. The
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00:22:53,020 --> 00:22:56,020
registration isn't out yet, but
the reason that I say that is
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it's all about interactions over
time. And what I want to say
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about Natalie and her group is
it's been about interactions
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over time, all year. It's not
just about the February, March
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testing season. If she just
started this mindset and culture
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in February, there is no way her
kids would have been there. But
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this was launched in August,
what we call the first 15 at the
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beginning of the school year, so
that kids by this time of year
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are ready. They're just ready
for this. And I also want to say
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I mentioned a lot of these
names, crystal as well. We had a
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big field trip, a teacher field
trip. I wasn't even going to
304
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mention this today, but I have
to, because it was just it was
305
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so powerful, it was so amazing,
it was so enlightening and such
306
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a an impactful experience for me
that I want to share it today
307
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and have a few of you share if
you were on the field trip with
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US. So last month in March, we
had a teacher field trip. There
309
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were nine teachers that traveled
to Central Ohio, to my school
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district on one day and got to
see my Algebra Two and algebra
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one classes. Got to watch me
teach. Then I arranged me
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00:24:18,480 --> 00:24:22,100
teaching a class at in fourth
grade and second grade at our
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00:24:22,100 --> 00:24:27,260
elementary school. So all nine
people shadowed me all day,
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watched me teach the same exact
task to every class that day.
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And so the people that were
there that day, and I don't want
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to forget anybody. Natalie West,
Christie Ewing, Amy Garrison,
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00:24:41,300 --> 00:24:47,080
Christy Flynn, Crystal Davis,
Kirk was there that day. We had
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two other people that were there
that day from another school.
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They're not here this morning.
We had another Natalie and
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Jessica.
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I know I'm going to forget
somebody. I don't mean to forget
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00:24:59,500 --> 00:25:03,240
anybody. It let me know if I'm
forgetting anybody. Anyway, all
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of us observed in the morning at
the high school, and then the
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00:25:06,900 --> 00:25:10,380
afternoon the elementary I
taught all of the classes, and
325
00:25:10,380 --> 00:25:14,520
then we had some reflection time
and thought time, and it was in
326
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March. So I have worked with a
lot of these kids and have
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00:25:18,300 --> 00:25:21,440
trained a lot of these kids. So
what you were seeing in a lot of
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these kids are kids that have
had this model all year, but
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00:25:25,760 --> 00:25:29,060
came in with some severe
deficits. All of the classes I
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teach are inclusion classes, so
there's IEP students in every
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class that I teach. I don't have
any advanced classes. I don't
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have any advanced so when you
look at these types of scores,
333
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it's just bad. But what we saw
on field trip day is you
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wouldn't be able to tell that by
March, and it's really
335
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spectacular to see. Well, then
the next day, Kirk and I got to
336
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go to Natalie West school and
watch Miss Natalie, and then we
337
00:26:01,980 --> 00:26:06,180
got to go to Krista Ewing school
and watch Miss Krista. And I'm
338
00:26:06,180 --> 00:26:12,660
telling you people right now on
record that Natalie and Krista
339
00:26:12,720 --> 00:26:22,580
teach the model better than I
do. You guys, mind blowing. So I
340
00:26:22,580 --> 00:26:24,800
want to give you some
background, especially maybe if
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you're here today for the first
time, you don't know any of us.
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00:26:27,500 --> 00:26:30,920
You don't know any of this. I
want to give you some of those
343
00:26:30,920 --> 00:26:36,260
pieces. But Would anyone like to
share your takeaways from the
344
00:26:36,260 --> 00:26:40,880
field trip experience with us
now, and I'm go back and look at
345
00:26:40,880 --> 00:26:43,900
comments so unmute and let us
know what your takeaways were
346
00:26:43,900 --> 00:26:45,400
from that experience.
347
00:26:49,359 --> 00:26:58,899
Mine was, can you hear me? Yes.
Crystal, crystal. Okay, so my
348
00:26:58,899 --> 00:27:03,299
takeaway was and I shared this
with you or with the group, was
349
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that no matter what grade A
student is in, they can use
350
00:27:11,639 --> 00:27:22,459
their brains to think past just
solving a problem, and you can
351
00:27:22,459 --> 00:27:28,939
take the exact same model and
apply it at every level. And I
352
00:27:28,939 --> 00:27:30,679
thought that was amazing.
353
00:27:31,760 --> 00:27:36,020
And I'm so glad that you all got
to see that that day. And I
354
00:27:36,020 --> 00:27:40,040
think that is more powerful than
just seeing it at the high
355
00:27:40,040 --> 00:27:43,840
school level, or because it's
then you know, what does this
356
00:27:43,840 --> 00:27:46,720
look like in first grade? What
does this look like in seventh
357
00:27:46,720 --> 00:27:52,240
grade? And same task, same
instructional delivery model.
358
00:27:52,600 --> 00:27:55,780
Now I tweak the way that I
interact with kids because of
359
00:27:55,780 --> 00:28:00,220
the grade level, and you you all
got to see those nuances. But
360
00:28:00,400 --> 00:28:04,500
crystal, you said it
beautifully, and I don't think
361
00:28:04,500 --> 00:28:10,140
you can understand it until you
actually see it or hear it. So
362
00:28:10,140 --> 00:28:14,220
if you have not had a chance to
come and observe any of us, or
363
00:28:14,220 --> 00:28:17,340
you all have not had a chance
for me to come and teach it in
364
00:28:17,340 --> 00:28:24,020
your classroom, or the cheapest,
easiest way. If you all have not
365
00:28:24,020 --> 00:28:27,800
had an opportunity to listen to
my audio files of me teaching
366
00:28:27,800 --> 00:28:31,580
these things with students, you
need to make that happen,
367
00:28:32,480 --> 00:28:38,120
because I can tell you all this.
I can I can say all this. I can
368
00:28:38,120 --> 00:28:42,520
tell you. The people on here can
tell you, but that hits
369
00:28:42,520 --> 00:28:49,120
different when you actually hear
it done to students. So it was,
370
00:28:49,120 --> 00:28:53,080
it was just a beautiful
experience those two days. Any
371
00:28:53,140 --> 00:28:57,520
other takeaways from your
experience being in all of those
372
00:28:57,520 --> 00:28:58,240
classrooms?
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00:28:58,240 --> 00:29:03,000
Krista, yeah, the one thing that
impressed me, particularly with
374
00:29:03,000 --> 00:29:07,440
the high schoolers, because I
I'm sixth grade, they allowed,
375
00:29:07,440 --> 00:29:11,040
like the culture that was built
through the methods that are
376
00:29:11,040 --> 00:29:16,080
being used, they allowed, like
all of these strangers to just
377
00:29:16,080 --> 00:29:19,500
come up and we were asking them
questions, and It didn't throw
378
00:29:19,500 --> 00:29:24,200
them off, and they responded to
us, and that's what and it was
379
00:29:24,200 --> 00:29:27,200
the true of every class that we
went to. We were just kind of
380
00:29:27,200 --> 00:29:31,700
all fanned out, looked at their
work, asked these kids
381
00:29:31,700 --> 00:29:35,240
questions, and they didn't know
us from anybody, and they were
382
00:29:35,240 --> 00:29:38,360
just engaged and willing to
share their thinking with us.
383
00:29:38,660 --> 00:29:41,200
And that kind of culture is
something that you have to build
384
00:29:41,200 --> 00:29:44,800
from day one. And it was just
impressive the way that they
385
00:29:44,800 --> 00:29:47,560
just kind of acclimated to us as
well,
386
00:29:48,640 --> 00:29:51,760
and that is really unique. And I
wasn't sure that that they were
387
00:29:51,760 --> 00:29:54,400
going to be able to perform that
way. These are kids that
388
00:29:54,400 --> 00:29:58,060
struggle. They have high anxiety
for math. They've come with a
389
00:29:58,060 --> 00:30:01,440
lot of baggage from you. You
know, and I'm not trying to
390
00:30:01,440 --> 00:30:06,780
blame but from some ineffective
instructional practices, they've
391
00:30:06,780 --> 00:30:12,300
been jaded, and I don't blame
them. And I want to go back to
392
00:30:12,300 --> 00:30:17,940
what crystal said. It's about
going past the solving because,
393
00:30:18,000 --> 00:30:20,960
as I've said in our testing
secrets launch this year. Let me
394
00:30:20,960 --> 00:30:24,020
take a picture of this so I can
erase it. But going back to
395
00:30:24,860 --> 00:30:30,320
solving. Solving is not
learning. Solving is not
396
00:30:30,320 --> 00:30:35,060
learning. And if my emphasis in
my classroom was solving, Krista
397
00:30:35,060 --> 00:30:38,480
and everybody would not have
been able to experience the math
398
00:30:38,480 --> 00:30:42,280
and hearing that was happening.
So what is the opposite of
399
00:30:42,280 --> 00:30:51,220
solving? It is thinking,
reasoning and sense making. This
400
00:30:51,280 --> 00:30:55,120
is the climate and culture that
is going to scale math
401
00:30:55,120 --> 00:30:58,960
achievement. It's going to
decrease anxiety, it's going to
402
00:30:58,960 --> 00:31:03,600
increase confidence, and it's
going to improve test scores. A
403
00:31:03,600 --> 00:31:07,680
focus on thinking, reasoning and
sense making will always lead to
404
00:31:07,680 --> 00:31:11,040
solving, but we don't have to
push solving. It will happen
405
00:31:11,040 --> 00:31:15,300
organically and naturally. And
that's what Krista is talking
406
00:31:15,300 --> 00:31:19,560
about, that she observed, and I
wasn't sure, like I see it in my
407
00:31:19,560 --> 00:31:24,380
students every day I didn't in
August, September, October, it
408
00:31:24,380 --> 00:31:29,900
was like pulling wisdom teeth in
these classes. Awful. I'm like,
409
00:31:29,900 --> 00:31:32,360
there is no way I'm going to be
able to create this culture with
410
00:31:32,360 --> 00:31:36,680
high school students that I
mean, look at how many years
411
00:31:37,040 --> 00:31:40,180
they have not had these type of
experiences. How am I going to
412
00:31:40,180 --> 00:31:44,980
do this by October, November,
they started to thrive and
413
00:31:44,980 --> 00:31:49,300
really come out of their shell.
So for even me to see my
414
00:31:49,300 --> 00:31:53,560
students very vulnerable and
taking risks in front of nine
415
00:31:53,560 --> 00:32:00,520
adults, math and earring with
them, heck yeah, heck yeah. And
416
00:32:00,520 --> 00:32:04,816
I keep saying math and earring.
If you don't have the making
417
00:32:04,816 --> 00:32:08,536
math and ears book, go to
Amazon. Get it today. Making
418
00:32:08,536 --> 00:32:12,976
math and ears, this is for
teachers and students, improving
419
00:32:12,976 --> 00:32:16,876
the conceptual understanding of
mathematics for the teacher and
420
00:32:16,876 --> 00:32:20,300
the student. Many different case
studies in here of students and
421
00:32:20,300 --> 00:32:24,080
teachers and their journeys and
how they've transformed to
422
00:32:24,080 --> 00:32:26,780
creating these types of
environments and being in these
423
00:32:26,780 --> 00:32:30,680
types of environments, in math
classrooms everywhere. So yeah,
424
00:32:30,680 --> 00:32:33,800
get your book. Go to Amazon, get
your book, making math and ears,
425
00:32:34,100 --> 00:32:38,420
and it's really going to kind of
lay out the foundation of the
426
00:32:38,420 --> 00:32:42,160
difference between this
conceptual and procedural. So
427
00:32:42,160 --> 00:32:47,800
notation goes along with what we
call math ability solving, Okay,
428
00:32:48,100 --> 00:32:51,880
number sense is this conceptual
thinking, reasoning and sense
429
00:32:51,880 --> 00:32:55,600
making? Now, I know what you're
all wondering right now is,
430
00:32:55,600 --> 00:33:06,240
well, shoot, how do we create
this in our classrooms? Saturday
431
00:33:06,240 --> 00:33:10,020
math gives you pieces of that,
but what you really want to do
432
00:33:10,260 --> 00:33:14,160
is go through one of our courses
or programs so that you get that
433
00:33:14,160 --> 00:33:17,340
streamlined effect of what do I
do? First, second, third. But
434
00:33:17,340 --> 00:33:19,860
I'm not saying don't come to
Saturday math, because you're
435
00:33:19,860 --> 00:33:22,580
going to get bits and pieces of
everything Saturday, math is
436
00:33:22,580 --> 00:33:28,280
much more non linear and very
like, you know, interactive,
437
00:33:28,280 --> 00:33:33,680
moving around. This is the big
question that we have been
438
00:33:33,680 --> 00:33:39,200
trying to move in this mission
before we talk about the how,
439
00:33:39,200 --> 00:33:42,220
though, and this is part of the
content I wanted to teach today,
440
00:33:42,820 --> 00:33:46,300
before we talk about the how, we
really have to talk about the
441
00:33:46,300 --> 00:33:52,240
when. And this goes back to
textbook companies. Some of
442
00:33:52,240 --> 00:33:57,520
these new approved, not
improved, but these new approved
443
00:33:57,520 --> 00:34:04,500
textbook companies, the when and
the structure of the year and
444
00:34:04,500 --> 00:34:07,740
how the content is delivered.
And when the content is
445
00:34:07,740 --> 00:34:11,340
delivered is the complete
opposite of how the brain learns
446
00:34:11,340 --> 00:34:16,140
mathematics. So what are some of
our common instructional fails?
447
00:34:17,220 --> 00:34:20,120
Some of our common instructional
fails are teaching one thing at
448
00:34:20,120 --> 00:34:27,140
a time like a textbook is set
up, focusing on solving. That's
449
00:34:27,140 --> 00:34:28,040
another fail,
450
00:34:30,440 --> 00:34:35,240
treating all standards equal,
that's another fail, finishing
451
00:34:35,300 --> 00:34:38,720
everything. We haven't talked
about that yet today, finishing
452
00:34:38,780 --> 00:34:43,420
everything so answering every
question, solving every problem
453
00:34:43,420 --> 00:34:48,340
that is a fail. We've got to let
things linger. One of the
454
00:34:48,340 --> 00:34:51,820
biggest ways that we can improve
math achievement is to let
455
00:34:51,820 --> 00:34:57,040
things linger. Ask questions and
give problems that we don't
456
00:34:57,040 --> 00:35:03,120
finalize, because what. In the
brain is the subconscious
457
00:35:03,300 --> 00:35:06,600
continues to think about that.
There's this cognitive
458
00:35:06,600 --> 00:35:10,680
dissonance that we've never
really tied the bow on. We
459
00:35:10,740 --> 00:35:15,780
believe, we really believe, as a
country and as a culture, that
460
00:35:15,780 --> 00:35:20,660
we have to finish every problem.
And I'm telling you that that is
461
00:35:20,660 --> 00:35:25,160
one of the worst ways to try to
improve math achievement, we
462
00:35:25,160 --> 00:35:28,400
have to let some things linger
so that the subconscious brain
463
00:35:28,460 --> 00:35:35,120
activates and continues to think
reason and sense make without
464
00:35:35,240 --> 00:35:40,540
the human being even knowing
it's happening. And that is
465
00:35:40,540 --> 00:35:44,860
probably the greatest fail of
some of our textbook companies.
466
00:35:45,760 --> 00:35:51,880
So how do we shift some of these
fails into fixes? That is to
467
00:35:51,880 --> 00:35:54,760
look at the when, and I'm going
to show you this on a document
468
00:35:54,760 --> 00:36:01,620
that I created. But before we
even do that, before we even
469
00:36:01,800 --> 00:36:05,580
figure out how to do this, we
have to figure out, okay, when
470
00:36:05,580 --> 00:36:09,720
what's the structure of the
year, and before we even do
471
00:36:09,840 --> 00:36:14,340
that, uh Oh, someone's asking a
question about what curriculum.
472
00:36:14,460 --> 00:36:20,760
Oh no. Oh no. Janet, you're
poking me, aren't you? You're
473
00:36:20,760 --> 00:36:27,140
getting me fired up. Janet, all
right, before all of that, we
474
00:36:27,200 --> 00:36:37,760
have to ask ourselves, What the
What is, what is absolutely
475
00:36:37,760 --> 00:36:45,160
essential, and what is essential
has to be exposed in 15 day
476
00:36:45,160 --> 00:36:49,420
cycles throughout the year. So
Janet, to answer your question,
477
00:36:49,420 --> 00:36:52,000
what curriculum would you
recommend that does go with the
478
00:36:52,000 --> 00:36:57,340
brain research and is approved?
None of them. Now, I'm not
479
00:36:57,340 --> 00:37:01,140
saying that you can't adopt
things. Okay, I'm not saying
480
00:37:01,140 --> 00:37:04,740
because every single textbook
resource, every single
481
00:37:04,740 --> 00:37:09,000
curriculum resource, can be put
in this model, every one of
482
00:37:09,000 --> 00:37:14,280
them, every single one of them,
but we have to be able to be
483
00:37:14,340 --> 00:37:19,440
flexible and adapt how we use
our resources. So these are the
484
00:37:19,440 --> 00:37:25,580
three biggest questions in our
bigger program of delivery, the
485
00:37:25,580 --> 00:37:32,000
what the essentials, the when?
When do the essentials come up
486
00:37:32,000 --> 00:37:36,140
throughout the year, and it's in
cycles of 15 days, and then the
487
00:37:36,140 --> 00:37:40,360
how is in the instructional
delivery process that is going
488
00:37:40,360 --> 00:37:43,300
to have an impact on not only
student achievement, but
489
00:37:44,020 --> 00:37:50,200
confidence and and, yeah. I
mean, amplify fantastic. I love
490
00:37:50,200 --> 00:37:54,220
and hate every curriculum
resource. So I will say amplify
491
00:37:54,280 --> 00:37:58,780
is is very good. Is very good in
its pieces. I think the one
492
00:37:58,780 --> 00:38:05,820
thing that amplify, duh. Doesn't
have, but actually it does, but
493
00:38:05,820 --> 00:38:09,360
it's kind of hidden. Is the what
and the when? I think there's a
494
00:38:09,360 --> 00:38:15,720
lot of great house in amplify
and, yeah, so I'll just go from
495
00:38:15,720 --> 00:38:19,620
there. Okay, you all came to
learn something today, though,
496
00:38:19,620 --> 00:38:23,420
but I'm really glad that I kind
of gave all that foundation,
497
00:38:23,420 --> 00:38:27,080
because I think all of that's
important to continue to empower
498
00:38:27,080 --> 00:38:31,280
us to think differently about
math education. Scores across
499
00:38:31,280 --> 00:38:35,120
the country are dismal. They
keep declining. We've never had
500
00:38:35,120 --> 00:38:40,780
major improvements as a country,
and we keep trying things that
501
00:38:40,780 --> 00:38:44,200
are not only not working, but
are working worse than what
502
00:38:44,200 --> 00:38:52,480
we've done before. Oh boy. Okay.
What a downer. What a downer. I
503
00:38:52,480 --> 00:38:55,480
don't mean to be a downer. Let
me share my screen, because I'm
504
00:38:55,480 --> 00:38:59,800
going to Okay.
505
00:39:01,720 --> 00:39:05,340
So these are the notes that I
created for today that I'm going
506
00:39:05,340 --> 00:39:08,520
to work off of. And when I
follow up email for you, I'm
507
00:39:08,520 --> 00:39:11,400
going to send you the PDF
version of these notes so that
508
00:39:11,400 --> 00:39:15,000
you have these. This is what I
basically just did on the
509
00:39:15,000 --> 00:39:19,920
whiteboard that was intentional.
But when I talk about the what,
510
00:39:20,640 --> 00:39:24,680
the essentials, you know, it
comes down to my F words. Love
511
00:39:24,680 --> 00:39:30,020
me some F words. So many F
words, okay, but the essential
512
00:39:30,020 --> 00:39:33,680
math concepts that are going to
build both of these number sense
513
00:39:33,680 --> 00:39:37,400
and notation are factors,
fraction and function. What do I
514
00:39:37,400 --> 00:39:41,080
mean by that? I don't mean we do
a factors unit, a fraction unit
515
00:39:41,080 --> 00:39:46,660
and a function unit. So what I
mean by this is these are the
516
00:39:46,660 --> 00:39:50,860
three key concepts that should
be a part of every 15 day cycle
517
00:39:51,100 --> 00:39:55,060
we should always be teaching
through factors, through
518
00:39:55,060 --> 00:39:59,560
fraction, through function. And
what Crystal was talking about
519
00:39:59,740 --> 00:40:04,140
is. Is seeing this effect at
every grade level. So if you're
520
00:40:04,140 --> 00:40:06,600
a first grade teacher, Amy
garrison is a first grade
521
00:40:06,600 --> 00:40:11,340
teacher. Amy is constantly
teaching through factors,
522
00:40:11,340 --> 00:40:14,400
fraction and function, even
though the word factor doesn't
523
00:40:14,400 --> 00:40:20,160
necessarily come until fourth
grade in the standards, factors
524
00:40:20,160 --> 00:40:27,260
are making arrays. So if I have
24 blocks and I make an array, I
525
00:40:27,260 --> 00:40:31,520
could make an array that is six
tall, four long or eight tall,
526
00:40:31,520 --> 00:40:37,460
three long. Those numbers are
factors. Kids don't know it, but
527
00:40:37,460 --> 00:40:42,880
making rectangles is one of our
go to experiences for students
528
00:40:43,240 --> 00:40:46,600
that not only improve number
sense but math achievement. So
529
00:40:46,600 --> 00:40:50,320
even as a first grade teacher,
you are teaching through these
530
00:40:50,320 --> 00:40:55,060
three things. So our job as
teachers is to learn what
531
00:40:55,060 --> 00:40:58,720
factors, fraction and function
look like at every single grade
532
00:40:58,720 --> 00:41:03,060
level, and what the progression
is from one grade level to next.
533
00:41:03,660 --> 00:41:08,100
And what we do at minds on math
is, and let me go ahead and draw
534
00:41:08,100 --> 00:41:16,500
this in. What we do at minds on
math is we create reference
535
00:41:16,560 --> 00:41:21,980
tasks. We call them the Dirty
Dozen. There are 12 reference
536
00:41:21,980 --> 00:41:26,720
tasks that associate with
factors fraction and function.
537
00:41:26,720 --> 00:41:29,720
So if you're looking for lessons
in your classroom to do, to
538
00:41:30,380 --> 00:41:35,900
teach through these essential
concepts, we have 12 reference
539
00:41:35,900 --> 00:41:39,500
tasks. The 12 reference tasks
are exactly the same for every
540
00:41:39,500 --> 00:41:44,200
single grade level, exactly the
same. There are some differences
541
00:41:44,200 --> 00:41:48,280
at kindergarten and at algebra
one, depending, you know, very,
542
00:41:48,280 --> 00:41:53,560
very minor differences and
variations. But the reason we
543
00:41:53,680 --> 00:41:57,940
bring everything down into
reference tasks is these are
544
00:41:58,660 --> 00:42:03,840
grab and go like these are not
theory. They're not they're very
545
00:42:03,840 --> 00:42:08,400
practical steps to do lessons in
your classrooms. And they are
546
00:42:08,400 --> 00:42:13,320
not a one and done situation, a
reference task like making
547
00:42:13,320 --> 00:42:16,740
rectangles in first grade looks
like making a raise with 24
548
00:42:16,920 --> 00:42:20,972
blocks and then how tall? How
long are those blocks? What that
549
00:42:20,972 --> 00:42:24,452
looks like in fourth grade are,
what are all the rectangles I
550
00:42:24,452 --> 00:42:27,212
can create? Well, actually go to
third grade. In third grade,
551
00:42:27,212 --> 00:42:30,092
what that looks like is, what
are all the rectangles I can
552
00:42:30,092 --> 00:42:36,692
create with an area of 24 but
different perimeters in fourth
553
00:42:36,692 --> 00:42:39,752
grade? What are all the
rectangles I can create with
554
00:42:39,752 --> 00:42:45,040
area 24 and the up level
question to that is, what are
555
00:42:45,040 --> 00:42:49,180
the factors of 24 because they
are the length and what they are
556
00:42:49,180 --> 00:42:52,300
the dimensions of the rectangles
I can create. See, we're using
557
00:42:52,300 --> 00:42:55,300
that same task, and we're
targeting our standards, but
558
00:42:55,300 --> 00:42:59,140
what we're doing is we're front
loading this progression,
559
00:42:59,440 --> 00:43:02,820
because as early as first grade,
kids are learning about factors.
560
00:43:02,820 --> 00:43:07,500
One of our other tasks is a
locker problem. This is an act
561
00:43:07,500 --> 00:43:13,080
it out hands on, concrete,
conceptual situation that kids
562
00:43:13,080 --> 00:43:16,860
experience, that even at first
grade, they start to learn the
563
00:43:16,860 --> 00:43:19,200
factors of a number. But we
don't call it factors of a
564
00:43:19,200 --> 00:43:23,060
number. We call it which
students touch. Locker, 24, oh,
565
00:43:23,060 --> 00:43:25,820
student eight, does, three,
does, four, does, six does.
566
00:43:26,300 --> 00:43:28,760
Through these reference and
these reference tasks are not
567
00:43:28,760 --> 00:43:32,600
one and done. So when I talk
about these 15 day cycles, some
568
00:43:32,600 --> 00:43:37,520
of these reference tasks come
back every 15 days, and then we
569
00:43:37,520 --> 00:43:42,880
up level them. So kids are
getting interactions over time.
570
00:43:42,880 --> 00:43:45,340
They're getting more
interactions with the same thing
571
00:43:45,400 --> 00:43:50,320
at more grade levels through
these reference tasks, targeting
572
00:43:50,500 --> 00:43:52,060
factors, fraction and function.
573
00:43:53,920 --> 00:44:00,540
So that's sort of the framework,
and it answers the what. Now
574
00:44:00,540 --> 00:44:03,480
there are other pieces in this
what, but it just comes down to
575
00:44:03,480 --> 00:44:06,720
those three things, factors,
fraction and function. If you
576
00:44:06,720 --> 00:44:11,640
study the College Board, College
Board is a c t or not. I totally
577
00:44:11,640 --> 00:44:15,000
said that wrong, totally so I'm
ridiculous. Got a c t on the
578
00:44:15,000 --> 00:44:19,260
brain. College Board is not a C
T. College Board s, a T. If you
579
00:44:19,260 --> 00:44:23,900
study that, there was a
published book called math
580
00:44:23,900 --> 00:44:28,100
vertical teams. Oh my gosh, way,
way back in the early 2000s I
581
00:44:28,100 --> 00:44:32,360
believe in this book that the
College Board published. College
582
00:44:32,360 --> 00:44:36,980
Board is the S, A, T people. In
the book math vertical teams
583
00:44:36,980 --> 00:44:39,080
that the College Board
published, they said there are
584
00:44:39,080 --> 00:44:43,540
three things for students to be
successful in AP Calculus, and
585
00:44:43,600 --> 00:44:48,700
it is rate function and
accumulation that very much
586
00:44:49,000 --> 00:44:55,060
relates to factors fraction and
function. If you study what
587
00:44:55,060 --> 00:44:58,960
algebra, two teachers say that
students need to be successful.
588
00:44:59,680 --> 00:45:06,960
They. Say radicals, that's
factors. They say equations,
589
00:45:06,960 --> 00:45:11,580
that's function, or systems of
equations that's function. They
590
00:45:11,580 --> 00:45:16,500
say graphing, which is number,
line, factors and fraction. They
591
00:45:16,500 --> 00:45:23,360
so everything that we are
reading or studying or hearing
592
00:45:23,360 --> 00:45:29,120
about high school to higher ed
comes down to these same things.
593
00:45:29,660 --> 00:45:35,060
And if you study math tests, A,
C, T, S, A, T, end of course,
594
00:45:35,060 --> 00:45:40,040
exams, grade level tests at each
state you study the national
595
00:45:40,040 --> 00:45:45,940
tests, nape, look at the Tims
report, study GRE, I've been
596
00:45:45,940 --> 00:45:50,980
studying as fab, so the the test
that kids have to take, going
597
00:45:50,980 --> 00:45:54,400
into the army, going into the
service. So I've learned more
598
00:45:54,400 --> 00:45:58,540
about asfab This year, because I
teach high school students, and
599
00:45:58,540 --> 00:46:02,400
I have some students that need
to pass the math. And so I've
600
00:46:02,400 --> 00:46:07,680
been creating these it's all the
same. It's all the same themes.
601
00:46:07,740 --> 00:46:11,220
It all comes down to the same
things. So no matter what
602
00:46:11,220 --> 00:46:14,520
textbook you adopt, no matter
what how the curriculum changes,
603
00:46:14,520 --> 00:46:17,700
no matter how the standards
change, there are certain
604
00:46:17,700 --> 00:46:22,220
mathematics that are ingrained
in the foundation that are
605
00:46:22,220 --> 00:46:26,240
priceless and timeless, they're
never going to change, and
606
00:46:26,240 --> 00:46:30,560
that's what we based all of our
programs off of. So no matter
607
00:46:30,560 --> 00:46:34,040
what comes and goes, no matter
what's approved or disapproved,
608
00:46:34,520 --> 00:46:38,000
these certain essentials are
always going to be there, no
609
00:46:38,000 --> 00:46:42,400
matter what. If everything's
important, nothing's important.
610
00:46:42,400 --> 00:46:46,720
Nothing's important, and we have
defined what is absolutely
611
00:46:46,720 --> 00:46:52,000
important. Now I'm not today
going to talk about the when I
612
00:46:52,000 --> 00:46:54,880
set it up, to talk about this
today, which is, how do we
613
00:46:54,880 --> 00:46:58,300
structure our school year? How
do we separate it, and how do
614
00:46:58,300 --> 00:47:02,520
these 15 day cycles occur? I'm
not going to teach on that today
615
00:47:02,580 --> 00:47:05,760
unless we have some time at the
end. Because here's what I want
616
00:47:05,760 --> 00:47:11,160
to teach on today. I want to
teach on a practical example of
617
00:47:11,220 --> 00:47:15,300
everything that I've just talked
about, and that is this
618
00:47:15,360 --> 00:47:23,060
equation. This equation. It I
pulled it right off of our state
619
00:47:23,060 --> 00:47:26,540
test for algebra one. Pulled it
right off our state test for
620
00:47:26,540 --> 00:47:32,420
algebra one. None of my students
last week, when I gave this on a
621
00:47:32,420 --> 00:47:36,560
practice test, none of my
students got the correct answer.
622
00:47:37,220 --> 00:47:40,340
And these are my students that
have been ingrained in this
623
00:47:40,760 --> 00:47:45,280
model all year. So this is
concerning. So what do we do
624
00:47:45,280 --> 00:47:48,040
about it? That's what I want to
answer right now. What do we do
625
00:47:48,040 --> 00:47:53,200
about it? Well, I didn't start
these equations early enough
626
00:47:53,200 --> 00:47:57,220
this year. We have another task
called Jesse and Kay. I started
627
00:47:57,220 --> 00:48:01,800
Jesse and Kay much earlier in
the year. I did not do enough
628
00:48:01,800 --> 00:48:05,760
fractional pieces for Jesse and
Kay. Now, if you guys don't know
629
00:48:05,760 --> 00:48:08,280
what I'm talking about for Jesse
and Kay, don't worry about that.
630
00:48:08,280 --> 00:48:12,360
Just ignore what I just said. If
you know Jesse and Kay, just
631
00:48:12,360 --> 00:48:16,860
know that I made the mistake. I
did not do enough fractional
632
00:48:18,360 --> 00:48:22,340
examples or variations of Jesse
and Kay, and I'm seeing that
633
00:48:22,340 --> 00:48:28,400
now. So live and learn. So I
want us to look at this
634
00:48:28,400 --> 00:48:32,900
equation, whether you know Jesse
and Kay or not, whether you know
635
00:48:32,900 --> 00:48:36,320
quick dots or not, whether you
know that counting is essential
636
00:48:36,320 --> 00:48:39,740
or not. It doesn't matter what
you know or don't know about
637
00:48:39,740 --> 00:48:46,120
this equation. I want you in the
chat right now to do two things.
638
00:48:46,660 --> 00:48:53,680
I want you to type in what grade
levels you connect with, what
639
00:48:53,680 --> 00:48:59,380
grade levels you connect with,
and what you see and notice
640
00:48:59,440 --> 00:49:02,880
about this equation. So you're
going to do two things right
641
00:49:02,880 --> 00:49:06,900
now. In the chat, I want you to
type in what grade levels you
642
00:49:06,900 --> 00:49:09,960
connect with, so what grade
levels you teach or coach or
643
00:49:09,960 --> 00:49:13,260
whatever, or you know, if you're
a principal or curriculum
644
00:49:13,260 --> 00:49:18,960
person, what grade levels you're
in charge of, and what you see
645
00:49:18,960 --> 00:49:22,400
and notice about this equation.
646
00:49:29,420 --> 00:49:35,660
What can you tell me about? Tell
me about this equation, and what
647
00:49:35,660 --> 00:49:37,520
do you see and notice?
648
00:49:51,808 --> 00:49:53,428
Okay, let me look at the chat
here.
649
00:50:01,376 --> 00:50:05,036
Lot of fifth grade teachers.
Hey, I know why you're here.
650
00:50:05,396 --> 00:50:09,596
Hey, the fifth grade test
everywhere, the hardest one I'm
651
00:50:09,596 --> 00:50:13,976
telling you. You guys know this.
There's reasons why the fifth
652
00:50:13,976 --> 00:50:18,416
grade test is most difficult for
students, and we have solutions
653
00:50:18,416 --> 00:50:27,740
on how to fix that too. You a
good this is excellent. Oh,
654
00:50:27,740 --> 00:50:32,060
okay, one half and 1/4 Yeah,
there are two x's. There's an X
655
00:50:32,060 --> 00:50:35,960
on each side. We see variables,
fractions, lots of operations,
656
00:50:35,960 --> 00:50:40,420
hidden symbols, notes, oh my
gosh. You see why kids struggle
657
00:50:40,420 --> 00:50:43,480
with coefficients. Yeah, you've
got to have the ability to work
658
00:50:43,480 --> 00:50:47,020
with fractions. I mean, kids are
going to look at this on the
659
00:50:47,020 --> 00:50:50,200
test and be like, nope, skip
next question. Just because
660
00:50:50,200 --> 00:50:57,340
there's a fraction, there are
constants and variables unlike
661
00:50:57,340 --> 00:51:03,720
denominators. Yeah. Amy, really
good point you would, you would
662
00:51:03,720 --> 00:51:08,340
cover up those x's with smiley
face emojis, yep, and just say
663
00:51:08,340 --> 00:51:11,940
the these are the the numbers we
got to try to figure out, Yep,
664
00:51:11,940 --> 00:51:17,880
perfect constants and
coefficients. The, yeah, the mix
665
00:51:17,880 --> 00:51:23,300
number, the mix number. That was
weird for me, too. And then I
666
00:51:23,300 --> 00:51:26,120
went back to previous years test
release questions, and I'm like,
667
00:51:26,120 --> 00:51:30,260
there's a few of these with the
mixed number in it. There's a
668
00:51:30,260 --> 00:51:37,640
lot of these in fifth grade. Lot
of these in fifth grade. Yeah,
669
00:51:37,640 --> 00:51:40,840
the x being the X being a
multiplication symbol, and not a
670
00:51:40,840 --> 00:51:47,860
bit having no concept that it's
an unknown. Yep, yep. I mean,
671
00:51:47,860 --> 00:51:58,300
there's so much to lose with
this question. Yeah, okay, so my
672
00:51:58,360 --> 00:52:00,940
Okay, let me stop for a moment.
We're going to come back to this
673
00:52:00,940 --> 00:52:04,440
and I'm going to walk us through
instructionally, what we do with
674
00:52:04,440 --> 00:52:09,540
this. Instructionally, what we
do with this in algebra one
675
00:52:09,540 --> 00:52:15,240
knowing my test is in a week and
a half. Instructionally, what do
676
00:52:15,240 --> 00:52:20,780
we do with this at third grade?
Because this is like perfect
677
00:52:20,780 --> 00:52:25,460
third grade, not equation
solving, but like third grade
678
00:52:25,460 --> 00:52:29,420
content. I'm going to show you
that in a moment. But go ahead
679
00:52:29,420 --> 00:52:35,120
and unmute and talk to me about
instructionally, how do we deal
680
00:52:35,120 --> 00:52:40,720
with how do we improve? How do
we use this example in a
681
00:52:40,720 --> 00:52:46,480
conceptual way to improve number
sense and to help students think
682
00:52:46,480 --> 00:52:53,200
reason and sense make and not
solve. You've probably never
683
00:52:53,200 --> 00:52:56,320
thought about equations this
way, but unmute and talk to me.
684
00:52:56,620 --> 00:53:01,260
How would you what are your
ideas of using this equation. It
685
00:53:01,260 --> 00:53:05,640
looks very traditional, very
notation ish, how would we use
686
00:53:05,640 --> 00:53:11,460
this in a conceptual, contextual
way such that kids are thinking,
687
00:53:11,460 --> 00:53:14,100
reasoning and sense, making and
improving number sense at the
688
00:53:14,100 --> 00:53:18,720
same time? So there's a way to
notationally, procedurally,
689
00:53:18,720 --> 00:53:23,540
algorithmically, there's a way
to solve this equation. But if
690
00:53:23,540 --> 00:53:25,880
that's the only thing
instructionally we ever do with
691
00:53:25,880 --> 00:53:30,200
this, we're never going to make
major gains. So what would we do
692
00:53:30,200 --> 00:53:35,360
instructionally, conceptually,
to teach this? Talk to me.
693
00:53:36,860 --> 00:53:40,660
So the first thing I would just
ask is, and I learned this from
694
00:53:40,660 --> 00:53:43,660
you, Jonily. Is, what do you
notice?
695
00:53:45,220 --> 00:53:53,980
Beautiful? Notice, what can you
tell me? And then this is, this
696
00:53:53,980 --> 00:53:56,980
is what's scary, because they're
going to tell us things that we
697
00:53:56,980 --> 00:54:00,720
weren't expecting, and then we
have to responsive teach on
698
00:54:00,720 --> 00:54:08,220
that. Do you see? So here's what
I want you to think about. When
699
00:54:08,220 --> 00:54:11,520
you use the tell me about what
do you notice? What do you see?
700
00:54:12,600 --> 00:54:20,100
Do not have an expectation for
yourself to teach on it. That's
701
00:54:20,100 --> 00:54:24,200
why we want to let things
linger. We want to ask those
702
00:54:24,200 --> 00:54:28,580
prompts. Document, even in
writing, on a poster paper, on
703
00:54:28,580 --> 00:54:34,040
the board, document, what kids
are seeing and noticing respond
704
00:54:34,040 --> 00:54:37,640
with that is brilliant, and that
is interesting. I love the way
705
00:54:37,640 --> 00:54:42,160
your brain thinks. Ooh, I've not
thought about it that way. We're
706
00:54:42,160 --> 00:54:47,860
celebrating the thinking that's
the only responsive teaching
707
00:54:47,860 --> 00:54:54,100
we're doing on the day that we
give it. And then after we do
708
00:54:54,100 --> 00:55:00,420
that for about seven minutes or
so, maybe 10 minutes, we. We
709
00:55:00,420 --> 00:55:03,720
then put that away, we move on
to what our regular lesson is of
710
00:55:03,720 --> 00:55:09,180
the day. Then we have time as a
teacher to create the responsive
711
00:55:09,180 --> 00:55:13,320
lesson based on their responses.
Don't try to do it in the same
712
00:55:13,320 --> 00:55:16,560
lesson or class period. That's
what freaks us out, and that's
713
00:55:16,560 --> 00:55:19,140
why some of us are afraid to
implement some of these
714
00:55:19,140 --> 00:55:22,460
strategies. Is we think we have
to then create the responsive
715
00:55:22,460 --> 00:55:27,560
lesson on the spot. We don't let
all that linger. Don't even come
716
00:55:27,560 --> 00:55:32,840
back to it the next day. Wait a
week to come back to it. Email
717
00:55:32,840 --> 00:55:36,260
me and say, here's a picture of
their responses. What do I do
718
00:55:36,260 --> 00:55:40,220
next? I mean, that's the
interactions I'm talking about
719
00:55:40,220 --> 00:55:43,840
with with this transformation
that we're trying to make
720
00:55:43,840 --> 00:55:50,440
instructionally, and then what?
Now and then, what? So what do
721
00:55:50,440 --> 00:55:54,880
we do then, when we start to
teach later, how would you teach
722
00:55:54,880 --> 00:55:55,420
this?
723
00:56:00,640 --> 00:56:04,380
With my third graders, I would
probably ask them, Do you think
724
00:56:04,380 --> 00:56:07,620
it's going to be a whole number?
Do you think it's going to be a
725
00:56:07,620 --> 00:56:12,000
fraction? I would you know, do
you think it's greater than,
726
00:56:12,000 --> 00:56:16,020
less than or equal to a certain
number within the equation? Just
727
00:56:16,020 --> 00:56:20,960
to get their kind of general
understanding of things, yeah,
728
00:56:21,200 --> 00:56:24,920
that's really a different way to
do estimation.
729
00:56:26,360 --> 00:56:30,320
That's a really great, powerful
twist on estimation. Love it.
730
00:56:30,320 --> 00:56:35,360
What else would you do? Yeah,
good. Krista. Krista even brings
731
00:56:35,360 --> 00:56:40,040
in a good sentence starter,
question starter, how does how
732
00:56:40,040 --> 00:56:44,080
does the right side relate to
the left side? Beautiful
733
00:56:44,080 --> 00:56:46,360
prompting. What else would you
do? You're
734
00:56:55,420 --> 00:56:58,420
probably afraid to say of what,
what you would do. Think I'm
735
00:56:58,660 --> 00:57:02,880
going to judge you or something.
Don't be afraid. Don't be
736
00:57:02,880 --> 00:57:05,700
afraid, guys, I use algebra
tiles,
737
00:57:07,080 --> 00:57:09,300
Janet Lane: interesting stuff
like this, so I've always tried
738
00:57:09,300 --> 00:57:13,680
to encourage my kids to draw it.
We we've been trying the same
739
00:57:13,680 --> 00:57:16,860
problem. And thanks to you, I'm
not, like, totally losing it
740
00:57:17,160 --> 00:57:20,420
because I gave a I've been given
a practice OST tip question
741
00:57:20,420 --> 00:57:25,760
today, and like, my test is
Monday, and yesterday they those
742
00:57:25,820 --> 00:57:28,940
one prompt. Two thirds of my
classes got it completely wrong.
743
00:57:28,940 --> 00:57:33,020
And I'm like, Ah. So I took a
deep breath, and I was like, All
744
00:57:33,020 --> 00:57:35,660
right, tell me how you got that
answer. And then, and I'm like,
745
00:57:35,660 --> 00:57:38,660
tell me what you know. And so it
was so interesting, because once
746
00:57:38,660 --> 00:57:42,580
they I said, Tell me about I got
thinking, and I'm like, gosh,
747
00:57:42,580 --> 00:57:46,420
you guys knew this. So, so my
thing is, is we were doing this
748
00:57:46,420 --> 00:57:50,020
like incentive that they they
take the test, and I look at
749
00:57:50,020 --> 00:57:53,620
their answer papers, like with
their work, and if they do it
750
00:57:53,620 --> 00:57:57,760
their way, and then do it my way
with other strategies, then they
751
00:57:57,760 --> 00:58:00,940
get to go to this extra recess.
So that's kind of cool for
752
00:58:01,360 --> 00:58:04,980
seventh graders. But the push is
the thinking. So we've been
753
00:58:04,980 --> 00:58:08,520
doing, you know, like you said,
Stop. What do you notice? What
754
00:58:08,520 --> 00:58:11,700
did you wander? Then answer. And
I've been withholding their
755
00:58:11,700 --> 00:58:16,620
calculators to say, Okay, think
about this first. Yeah, now you
756
00:58:16,620 --> 00:58:19,980
can have calculator, because
beautiful. Grab the calculator.
757
00:58:19,980 --> 00:58:23,360
Go. I'm like, You didn't even
think about that, guys. So
758
00:58:23,420 --> 00:58:27,800
that's what I'm trying to like,
you said, sit and think, but I
759
00:58:27,800 --> 00:58:30,380
would have them draw a picture,
and what do they see when they
760
00:58:30,380 --> 00:58:30,980
draw the picture?
761
00:58:31,340 --> 00:58:35,660
Unknown: Beautiful. Janet makes
a good point. That was little
762
00:58:35,660 --> 00:58:40,180
bit of a hidden message in
there. And that is all year, if,
763
00:58:40,180 --> 00:58:43,780
if students experiences every
day in our classrooms is
764
00:58:43,780 --> 00:58:47,980
solving, solving, solving,
solving, solving, solving, we're
765
00:58:47,980 --> 00:58:53,440
training them to not think. See
if we have less emphasis on
766
00:58:53,440 --> 00:58:57,760
solving all year. If our
emphasis, if our lessons are
767
00:58:57,760 --> 00:59:00,240
structured every day for
thinking, reasoning and sense
768
00:59:00,240 --> 00:59:02,520
making, and that's what we
prioritize, and that's what we
769
00:59:02,520 --> 00:59:06,840
celebrate, then we're going to
change their habit. They're not
770
00:59:06,840 --> 00:59:10,140
going to be able to help it, but
to look at a test question and
771
00:59:10,140 --> 00:59:12,960
think reason and sense make
before they solve. Because
772
00:59:12,960 --> 00:59:17,940
that's the culture and climate
every day. And I can tell this,
773
00:59:17,940 --> 00:59:20,540
we have a brand new fourth grade
teacher in our elementary
774
00:59:20,540 --> 00:59:25,160
school, and she is phenomenal.
She came to our June event last
775
00:59:25,160 --> 00:59:29,360
year. She's fresh out of
college. She started teaching
776
00:59:29,360 --> 00:59:32,000
fourth grade this year. I didn't
get to work with her a lot, but
777
00:59:32,000 --> 00:59:34,160
she came to the June event, and
we have another like
778
00:59:34,160 --> 00:59:36,680
intervention coach at the
elementary that's been
779
00:59:36,800 --> 00:59:39,140
supporting her, because I
haven't been able to do that
780
00:59:39,380 --> 00:59:42,280
well, I've been in her room a
few times just in the last
781
00:59:42,280 --> 00:59:45,340
month, Her room was one of the
rooms we went in when we had the
782
00:59:45,340 --> 00:59:50,020
teacher field trip. And I can
tell her kids have been trained
783
00:59:50,020 --> 00:59:53,980
by her really beautifully,
because I see her kids doing,
784
00:59:53,980 --> 00:59:57,640
thinking, reasoning and sense
making. So when I went in just
785
00:59:57,640 --> 01:00:00,720
on Thursday this week, because I
went back twice this. Last week,
786
01:00:00,960 --> 01:00:05,400
when I went in Thursday, I gave
them a question, and we talked
787
01:00:05,400 --> 01:00:09,420
about, pretend this popped up on
your computer, on your test, and
788
01:00:09,660 --> 01:00:13,500
this is fourth graders. What are
you going to do first? And
789
01:00:13,500 --> 01:00:15,960
they're like, we're going to
look at that piece of it. We're
790
01:00:15,960 --> 01:00:18,960
going to ask ourselves, what do
we see? What do we notice? And
791
01:00:18,960 --> 01:00:23,120
what do we wonder? Okay, now
whether they do this or not is
792
01:00:23,300 --> 01:00:27,080
one thing, but the fact that
they can at least articulate it
793
01:00:28,100 --> 01:00:33,320
is going to train their brain to
look at mathematics in that way,
794
01:00:34,160 --> 01:00:39,260
not as a solving exercise, but
as a thinking exercise. And then
795
01:00:39,260 --> 01:00:41,920
one of the outcomes is we're
going to get a solution
796
01:00:41,920 --> 01:00:46,960
eventually, but we've got to
make sense of it first before we
797
01:00:46,960 --> 01:00:51,220
try to solve anything. And so
you talk about effective Test
798
01:00:51,220 --> 01:00:56,680
Prep. That's effective test
prep, other thoughts, comments,
799
01:00:56,680 --> 01:00:57,580
questions.
800
01:00:58,900 --> 01:01:02,160
I've been doing that this week
with test questions where we
801
01:01:02,160 --> 01:01:05,100
haven't, I haven't given them or
worked through an answer on any
802
01:01:05,100 --> 01:01:07,860
of them. It's just, this is,
what comes up, what are you
803
01:01:07,860 --> 01:01:10,260
going to do? How are you going
to attack it? What's important?
804
01:01:10,260 --> 01:01:13,620
What kind of strategy? What does
the model look like? And then if
805
01:01:13,620 --> 01:01:16,320
they decide, I'll give them
candy, if they come to me with
806
01:01:16,320 --> 01:01:18,360
the answer by the end of the
day, because some of them can't
807
01:01:18,360 --> 01:01:21,860
help themselves, but we haven't,
you know, solved any problems.
808
01:01:21,860 --> 01:01:24,980
We've just been, like, attacking
them and like, getting to that
809
01:01:24,980 --> 01:01:27,500
understanding part. So, yeah,
810
01:01:28,520 --> 01:01:31,100
I know we're just crossing our
fingers at this point, Janet,
811
01:01:31,160 --> 01:01:33,980
I'll be saying a little prayer
for you guys on Monday morning.
812
01:01:33,980 --> 01:01:38,480
Wow, that's, that's like, in two
days. Okay, fantastic. Um, and,
813
01:01:38,480 --> 01:01:43,000
yeah, fantastic. Yeah, really
great prompt. How can you start
814
01:01:43,300 --> 01:01:49,840
look the same? Yeah. Okay, so
this is really good, because you
815
01:01:49,840 --> 01:01:57,460
guys know me. These are some of
my favorite early grade I don't
816
01:01:57,460 --> 01:02:01,440
want to draw, I want to type.
These are some of my early grade
817
01:02:01,440 --> 01:02:07,080
equations that I even give to my
secondary kids. We have
818
01:02:07,080 --> 01:02:12,180
something like, let me get
bigger here. We might have
819
01:02:12,180 --> 01:02:16,260
something like, oh, shoot, I'm
going to this is going to be a
820
01:02:16,260 --> 01:02:24,200
bad one. Okay, hold on, let me
think. Let me think. Three plus
821
01:02:24,380 --> 01:02:30,860
eight equals blank plus
822
01:02:36,020 --> 01:02:46,240
five. Okay, okay, so this is
something that I do specifically
823
01:02:46,420 --> 01:02:54,760
at the earlier grades to promote
unknowns equivalents. This is
824
01:02:54,760 --> 01:02:58,360
more of a thinking, reasoning
and sense making prompt than it
825
01:02:58,360 --> 01:03:03,000
is a solving prompt. I know if
kids have been trained to solve
826
01:03:03,360 --> 01:03:07,200
or reason, and those are
competing interests. I know if
827
01:03:07,200 --> 01:03:10,440
kids, like in a fourth grade
classroom, have been trained to
828
01:03:10,440 --> 01:03:18,120
solve or to reason by giving
this prompt. And if kids put,
829
01:03:19,680 --> 01:03:27,440
I'll draw. Now, if kids put what
is that? If kids put 11 here, I
830
01:03:27,440 --> 01:03:35,420
know that their instruction has
been highly solving. The
831
01:03:35,420 --> 01:03:40,040
priority is solving. I know that
that they believe that the equal
832
01:03:40,040 --> 01:03:44,620
sign is an answer getting
symbol. They do not understand
833
01:03:44,620 --> 01:03:49,720
equivalence and representation
and balance and same as and they
834
01:03:49,720 --> 01:03:54,640
don't understand that these are
two different situations, two
835
01:03:54,640 --> 01:04:00,600
different situations that need
to be exactly the same. They
836
01:04:00,600 --> 01:04:05,460
don't they don't have any idea.
Same as that's really what
837
01:04:05,520 --> 01:04:08,880
equivalence is. So if we want to
promote thinking, reasoning and
838
01:04:08,880 --> 01:04:12,900
sense making with equations, we
need to talk more equivalence
839
01:04:13,140 --> 01:04:21,860
and balancing and structure than
we do solving. So this does not
840
01:04:21,860 --> 01:04:26,720
create an equal. This does not
create the same thing on both
841
01:04:26,720 --> 01:04:32,540
sides. So one of the things that
I do is I give this equation, do
842
01:04:32,540 --> 01:04:39,080
a tell me about then I give this
one, because this is kind of a
843
01:04:39,080 --> 01:04:42,520
precursor to understanding
what's happening in the other
844
01:04:42,940 --> 01:04:49,120
Yeah, very good. Great. Great
comment there, yep, Amy, you
845
01:04:49,120 --> 01:04:52,360
good. You good. Did I give you
good takeaway today for your
846
01:04:52,660 --> 01:04:59,800
Yeah? See, see, Amy, good. When
we read that in class, we always
847
01:04:59,800 --> 01:05:04,620
say. Three plus eight is the
same as blank plus five. See,
848
01:05:04,620 --> 01:05:09,780
yeah, Amy and Amy teaches first
grade. Yep, Amy's always wants
849
01:05:09,780 --> 01:05:14,820
us to get to those numbers. Now,
let me go back to this. Let me
850
01:05:15,600 --> 01:05:22,940
non draw. Let me get okay now,
because I'm in a desperate
851
01:05:22,940 --> 01:05:28,700
attempt to make sure my kids do
know how to solve here's what I
852
01:05:28,700 --> 01:05:32,900
did yesterday, because I'm like
you guys, you know how to do
853
01:05:33,020 --> 01:05:37,340
this. Because if I give them, if
I give my kids equations like
854
01:05:37,340 --> 01:05:41,560
this, they're not putting 11
okay, if I give kids equations
855
01:05:41,560 --> 01:05:44,020
just like this with variables on
both sides that don't have
856
01:05:44,020 --> 01:05:49,360
fractions, they can solve and be
accurate 98% of the time. So
857
01:05:49,960 --> 01:05:53,200
this is frustrating, that they
just freak, that they totally
858
01:05:53,200 --> 01:05:58,540
freak. So this is what I did
yesterday. I did the traditional
859
01:05:58,540 --> 01:06:00,960
This is algebra one. They're
going to take the algebra one
860
01:06:00,960 --> 01:06:04,860
course. And I'm like, what would
you do? Like, if these, if there
861
01:06:04,860 --> 01:06:07,140
weren't fractions, and they're
like, Oh, we would take away
862
01:06:07,140 --> 01:06:09,720
three from both sides. I'm like,
Okay, well, then why can't you
863
01:06:09,720 --> 01:06:13,680
do that? They're like, well, we
can. Like, well, then do it.
864
01:06:13,680 --> 01:06:16,680
Like, what the freak are you
doing? I think I said that to
865
01:06:16,680 --> 01:06:24,020
them. Now this is important.
When we take away three from
866
01:06:24,020 --> 01:06:29,480
both sides, I always say to my
kids, what's the point? What's
867
01:06:29,480 --> 01:06:33,800
the purpose of that? What did we
want to try to do? They're like,
868
01:06:33,800 --> 01:06:37,280
well, we wanted to to remove
this three. We wanted to, like,
869
01:06:37,280 --> 01:06:41,020
move it to the we wanted to
remove it. How do we remove a
870
01:06:41,020 --> 01:06:48,040
plus three. What goal do we want
to get? To remove it? Well, for
871
01:06:48,040 --> 01:06:54,160
a plus three, we want to get to
a zero. This goes back to and
872
01:06:54,160 --> 01:06:58,480
I've taught on this numerous
times, the importance of zeros
873
01:06:58,480 --> 01:07:02,700
and ones, the importance of
zeros and ones. So if I want to
874
01:07:02,760 --> 01:07:08,640
get rid of eliminate a plus
three, I have to make a zero. I
875
01:07:08,640 --> 01:07:16,320
have to make a zero. Now if I
have 3x and I want to eliminate
876
01:07:16,320 --> 01:07:24,920
a times three, I have to make a
one. So there's a train. There's
877
01:07:24,920 --> 01:07:27,620
many trainings that I do, that I
talk about the importance of
878
01:07:27,620 --> 01:07:33,320
zeros and ones in mathematics.
So here, let's say the half
879
01:07:33,320 --> 01:07:35,720
wasn't there, 13 minus 310,
880
01:07:37,400 --> 01:07:45,100
and a half. Okay, so what's the
same as what's the same as now?
881
01:07:45,400 --> 01:07:50,020
So we've got x over here equals
10 and a half
882
01:07:55,060 --> 01:08:03,060
plus 1/4 X. Here was another
problem I gave my kids last
883
01:08:03,060 --> 01:08:17,280
week. I said y equals x over
four plus seven. Okay. And I
884
01:08:17,280 --> 01:08:19,980
said, What's the slope? Now my
kids know that y equals mx plus
885
01:08:19,980 --> 01:08:22,760
b is a linear function degree
one. They know they know it
886
01:08:22,760 --> 01:08:25,880
makes a line. They know that
when x is zero, you have a y
887
01:08:25,880 --> 01:08:28,580
intercept, so it's going to
cross the y axis at seven.
888
01:08:28,580 --> 01:08:32,720
That's the 07 point. But this
trips them up because of the way
889
01:08:32,720 --> 01:08:37,700
this is written. The way that
this is written, they want the
890
01:08:37,700 --> 01:08:45,760
slope m to be one because the
coefficient of x looks like it's
891
01:08:45,760 --> 01:08:49,660
one, but it's not. So you have
to understand the different
892
01:08:49,660 --> 01:08:57,100
representations that this
actually means this. So because
893
01:08:57,100 --> 01:09:01,560
I had done this problem earlier
in the week, I brought this back
894
01:09:01,560 --> 01:09:05,820
and connected it to this. So the
more connections we can make to
895
01:09:05,820 --> 01:09:09,480
other types of problems, the
better associations they're
896
01:09:09,480 --> 01:09:13,260
going to make as well. So now
we're boiled down to this, and
897
01:09:13,260 --> 01:09:18,240
then my kids are like, Oh, well,
we need to get the x's, okay.
898
01:09:18,480 --> 01:09:22,880
Now what they wanted to do here
with the plus 1/4 X, they wanted
899
01:09:22,880 --> 01:09:27,320
to multiply by four, which is
great if I wanted to get a one.
900
01:09:28,520 --> 01:09:32,000
Now I did the multiplying by
four, and I entertained them
901
01:09:32,000 --> 01:09:35,240
with that. And then I said,
okay, then we get 4x and we get
902
01:09:35,240 --> 01:09:37,940
this multiplied by four. And
then over here, what do we get?
903
01:09:37,940 --> 01:09:39,920
And they're like, Well, that
went away. No, it didn't,
904
01:09:39,920 --> 01:09:44,080
because 1/4 times four is one.
Now I have 1x over here. Now I
905
01:09:44,080 --> 01:09:48,280
have 4x here and but it's okay.
We don't have to go backwards.
906
01:09:48,400 --> 01:09:52,240
We can multiply everything by
four, and it's just fine. That's
907
01:09:52,240 --> 01:09:59,440
legal, but we could have done
something else that is going to
908
01:09:59,440 --> 01:10:04,680
put our. X's together. Okay, so
if we think of this as our
909
01:10:04,680 --> 01:10:07,860
chunk, and we want to remove
this chunk, we have a plus
910
01:10:07,860 --> 01:10:11,040
chunk. Again, we have how do we
get rid of a plus chunk? We
911
01:10:11,040 --> 01:10:15,360
minus the chunk. Okay, now I'm
being very traditional here,
912
01:10:15,360 --> 01:10:17,640
blah blah, but I want to make
this point, and then I'm going
913
01:10:17,640 --> 01:10:21,740
to stop with this traditional
nonsense. Here's the point I
914
01:10:21,740 --> 01:10:26,960
want to make. Now, my kids know
that this is not zero. Many
915
01:10:26,960 --> 01:10:31,640
algebra one students think that
this is zero minus a fourth. And
916
01:10:31,640 --> 01:10:33,980
I'm like, but how many x's
what's the coefficient? It's not
917
01:10:33,980 --> 01:10:37,640
written. It's one. You actually
have 1x now this goes back to
918
01:10:37,640 --> 01:10:41,560
what Janet was talking about,
because if you use algebra
919
01:10:41,560 --> 01:10:49,120
tiles, these x terms are green
rectangles. A green rectangle,
920
01:10:49,120 --> 01:10:55,240
Algebra tile has a height of x
and a length of one. We call the
921
01:10:55,300 --> 01:11:01,440
area of this. We call the name
of this green rectangle x. So if
922
01:11:01,440 --> 01:11:07,620
I want to represent 3x i would
need this x, and I would need
923
01:11:07,620 --> 01:11:10,260
three of them. Now I could draw
three rectangles, but I teach my
924
01:11:10,260 --> 01:11:13,740
kids to shorthand this. There
are three rectangles. That's
925
01:11:13,740 --> 01:11:22,640
what 3x look like. So over here
I have 1x so I just have one of
926
01:11:22,640 --> 01:11:28,880
these here, which shows that you
have the coefficient of one and
927
01:11:28,880 --> 01:11:32,180
not zero, because there actually
is one. There is a green
928
01:11:32,180 --> 01:11:36,920
rectangle over here. Oh, I don't
even have a whole green
929
01:11:36,920 --> 01:11:41,740
rectangle. I have a fourth. I
didn't draw that very well, but
930
01:11:41,740 --> 01:11:45,820
you get the idea. Okay, so this
is, this is how much I have of
931
01:11:45,820 --> 01:11:49,540
that rectangle, or that paper
strip, or whatever it is that
932
01:11:49,540 --> 01:11:52,660
we're using that gives that
conceptual, concrete,
933
01:11:52,660 --> 01:12:00,900
situational, contextual visual
to this equation. Now I'm going
934
01:12:00,900 --> 01:12:05,640
to go ahead and stop here,
because my kids also were
935
01:12:05,640 --> 01:12:09,120
successful once they know that
was one minus 1/4 is three
936
01:12:09,120 --> 01:12:11,220
fourths. Now I'm not going to go
any further with that
937
01:12:11,220 --> 01:12:19,860
traditional, because here's what
I want to do. Let me I want I
938
01:12:19,860 --> 01:12:25,400
just Oh my gosh. Okay, fine,
I'll do it this way. Okay, let's
939
01:12:25,400 --> 01:12:33,260
go down here and start over.
Okay. Now what my students in
940
01:12:33,260 --> 01:12:36,500
first grade, third grade, fourth
grade, sixth grade, eighth
941
01:12:36,500 --> 01:12:40,460
grade, algebra, what my students
know at every grade level is
942
01:12:41,900 --> 01:12:48,100
equations. Are Jesse and K
money. So this side of the
943
01:12:48,100 --> 01:12:51,280
equation is Jesse's money.
944
01:12:55,000 --> 01:12:59,380
And so this side of the equation
says that Jesse starts with $3
945
01:13:00,040 --> 01:13:03,120
and I know that that's the
starting number for Jesse,
946
01:13:03,600 --> 01:13:07,380
because that's when x is zero.
That's on day zero, when x is
947
01:13:07,440 --> 01:13:13,680
zero. Jesse has $3 that is also
y intercept. The y intercept of
948
01:13:13,680 --> 01:13:18,960
Jesse's linear function is
three, because a y intercept
949
01:13:18,960 --> 01:13:22,220
happens when x is zero. Now I'm
not telling third graders this,
950
01:13:22,400 --> 01:13:30,620
but I'm telling you this because
you can use x as this is, and
951
01:13:30,620 --> 01:13:39,080
you can notate it however you
want. This can be how much money
952
01:13:39,080 --> 01:13:44,920
Jesse or Kay gets or loses every
day. And that could just be
953
01:13:45,220 --> 01:13:49,000
your, you know, emoji number,
whatever you want to call it,
954
01:13:49,420 --> 01:13:53,500
the number that doesn't have
that variable or unknown. That's
955
01:13:53,500 --> 01:13:57,280
called a constant, and that's
the starting it's plus three. So
956
01:13:57,280 --> 01:14:02,580
Jesse starts with $3, a day. And
then how many of these were
957
01:14:02,580 --> 01:14:12,000
there? There were one. So Jesse
gets $1 she earns $1 every day.
958
01:14:12,660 --> 01:14:16,740
Now you could say that this is
the rate, and talk about rate
959
01:14:16,740 --> 01:14:21,380
speed, 60 miles per hour, but
you don't have to. You can just
960
01:14:21,380 --> 01:14:24,920
say that the way that this is
notated, that means, because
961
01:14:24,920 --> 01:14:29,480
there's 1x that Jesse's going to
get $1 a day. So on day zero,
962
01:14:29,480 --> 01:14:35,360
Jesse has $3 day one, Jesse has
$4 day two, Jesse has $5 day
963
01:14:35,360 --> 01:14:42,100
three, Jesse has $6 this is the
model and mindset of instruction
964
01:14:42,100 --> 01:14:49,540
in Singapore. What they do in
Singapore is they give typical
965
01:14:49,540 --> 01:14:53,980
algebra one questions to
elementary students, but they
966
01:14:53,980 --> 01:15:00,840
frame it in a context that
allows access for. Graders,
967
01:15:00,900 --> 01:15:06,360
third graders to do an equation
like this, but in a different
968
01:15:06,360 --> 01:15:11,100
way that's going to target the
standards at elementary now we
969
01:15:11,100 --> 01:15:14,160
at minds on math. We add a
different level to that. We
970
01:15:14,580 --> 01:15:18,420
reference task it, we
contextualize it as a Jesse and
971
01:15:18,420 --> 01:15:24,320
K problem. So now, if I go over
here, let me do a different
972
01:15:24,320 --> 01:15:28,640
color, and I'll save this and
I'll send you these notes. If
973
01:15:28,820 --> 01:15:36,740
this is Kay's money situation,
what's K starting? Number K
974
01:15:36,740 --> 01:15:43,180
starts with 13 and a half
dollars. Now what we might say
975
01:15:43,240 --> 01:15:55,540
is, oh, that is $13.50 if kids
want to do it that way. Okay, so
976
01:15:55,720 --> 01:15:59,980
K starts with $13.50 now what I
could do at this point is ask my
977
01:15:59,980 --> 01:16:03,720
students, what math questions
can we create? And so some of
978
01:16:03,720 --> 01:16:07,920
those might be, who starts with
more money? Who gets more money?
979
01:16:07,920 --> 01:16:11,340
Who loses money? Who this? Who
that? Okay, how much money does
980
01:16:11,340 --> 01:16:15,000
Jesse have on day 100 how much
money does Kay have on day 100
981
01:16:17,160 --> 01:16:21,980
so if I line this up, when this
number is zero, when this is
982
01:16:21,980 --> 01:16:26,720
zero, when this is not there,
when the 1/4 whatever, no days
983
01:16:26,720 --> 01:16:32,000
have gained any money yet. This
is Day Zero. I start to line up
984
01:16:33,800 --> 01:16:39,200
this relationship here. So now
this, this one is is harder. K
985
01:16:39,200 --> 01:16:43,660
is harder, I admit So on day
one, we need to know how much
986
01:16:43,660 --> 01:16:49,540
money K has. But how much money
is K gaining or losing every
987
01:16:49,540 --> 01:16:55,300
day? Well, K is gaining money.
So k is gaining money a fourth
988
01:16:55,360 --> 01:17:01,740
of $1 every day, a fourth of $1
every day. Well, how much money
989
01:17:01,740 --> 01:17:05,460
is that every day? Okay, well,
that's a we can leave it in
990
01:17:05,460 --> 01:17:12,300
fraction, or we could say, Kay's
getting 25 cents. Come on. I'm
991
01:17:12,300 --> 01:17:17,400
trying to do this with my just
mouse pad. Come on. Jay Z, make
992
01:17:17,400 --> 01:17:18,540
a two. Okay.
993
01:17:22,739 --> 01:17:29,359
Okay. So k is gaining 25 cents a
quarter every day. Now, if you
994
01:17:29,359 --> 01:17:31,999
teach second graders, third
graders, and you're trying to
995
01:17:31,999 --> 01:17:35,959
get them to understand money,
what a better way to do money
996
01:17:36,079 --> 01:17:39,679
than to embed it in a situation
that is very algebraic thinking,
997
01:17:39,679 --> 01:17:47,439
very skip counting. Ish, very
rate infused that is is grounded
998
01:17:47,439 --> 01:17:50,919
in unknowns and equivalents,
like look at how many birds
999
01:17:50,919 --> 01:17:53,919
you're killing with one stone.
Not that I advocate for killing
1000
01:17:53,919 --> 01:17:57,579
birds, but I advocate for
efficiency of instruction. I
1001
01:17:57,579 --> 01:18:02,339
advocate for using one example,
one situation to teach lots of
1002
01:18:02,339 --> 01:18:06,299
different standards. And when
crystal said, I saw the impact
1003
01:18:06,359 --> 01:18:09,839
of the same task, the same
thing, no matter what it is
1004
01:18:09,959 --> 01:18:12,599
being done at every grade level,
and being effective and
1005
01:18:12,599 --> 01:18:18,299
powerful, this is what crystal
is talking about. So on day one,
1006
01:18:18,599 --> 01:18:22,999
on day zero, if Kay had $13.50
and we get 25 cents more, then
1007
01:18:22,999 --> 01:18:29,179
we have $13.75 and let me know
if I make a mistake
1008
01:18:29,179 --> 01:18:32,359
mathematically, because I do
that a lot. On day two, how much
1009
01:18:32,359 --> 01:18:37,159
money does K have? Well, we add
another 25 cents, $14 on day
1010
01:18:37,159 --> 01:18:43,179
three, how much money does K
have? $14.25 or I could write 14
1011
01:18:43,179 --> 01:18:46,059
and a fourth. I can go back and
forth on variations of
1012
01:18:46,059 --> 01:18:50,859
representation. Doesn't matter.
Okay. Now, after we're doing
1013
01:18:50,859 --> 01:18:55,419
this together as a class, I'm
going to then ask again, say my
1014
01:18:55,419 --> 01:19:00,219
favorite words, tell me about
what you see. What do you see?
1015
01:19:00,459 --> 01:19:04,619
What do you notice? Make sense
of it again. We're going to
1016
01:19:04,619 --> 01:19:08,219
stop. And we started to, kind of
like do some solving and
1017
01:19:08,219 --> 01:19:11,819
counting. And so every time we
start to move to solving and
1018
01:19:11,819 --> 01:19:15,299
answer getting we, as the
instructor, need to back up and
1019
01:19:15,299 --> 01:19:17,939
say, Wait a minute. How do I
bring it back to thinking,
1020
01:19:17,939 --> 01:19:20,959
reasoning and sense making? So I
get this started, and then I
1021
01:19:20,959 --> 01:19:25,159
say, tell me about what do you
see, what do you notice in the
1022
01:19:25,159 --> 01:19:29,599
chat right now, I want all of
you to type in, what do you see
1023
01:19:29,599 --> 01:19:33,439
and notice about what just
happened. So type that in the
1024
01:19:33,439 --> 01:19:37,939
chat. Tell me about this
structure. Tell me about these
1025
01:19:37,939 --> 01:19:42,399
numbers. What do you see and
what do you notice about what
1026
01:19:42,399 --> 01:19:43,599
just happened?
1027
01:19:46,120 --> 01:19:51,220
What are your thoughts? Come on
now. Chat it up.
1028
01:20:07,840 --> 01:20:13,840
Oh, nice, both sides are
increasing at the same rate.
1029
01:20:17,260 --> 01:20:20,540
Good, yep.
1030
01:20:29,899 --> 01:20:32,719
Another thing I ask my students
as they're thinking reasoning
1031
01:20:32,719 --> 01:20:37,159
and sense making is, what other
math questions could we ask?
1032
01:20:39,979 --> 01:20:46,119
Nice j is increasing faster than
k, even though K began greater.
1033
01:20:46,119 --> 01:20:51,279
So what does that mean? What
does it all mean? Basil,
1034
01:21:02,939 --> 01:21:08,219
a nice Yep, will Jay end up with
more at some point and when?
1035
01:21:08,219 --> 01:21:10,019
Crystal, yeah, this is amazing.
1036
01:21:20,520 --> 01:21:28,280
Oh, yeah, okay, okay. Now here's
where your default instruction
1037
01:21:28,280 --> 01:21:33,200
is going to kick in. If you do
this in your classroom, and you
1038
01:21:33,200 --> 01:21:38,060
get to this point, your default
because you have habitual,
1039
01:21:38,060 --> 01:21:41,380
traditional instruction, what's
going to happen now is you're
1040
01:21:41,380 --> 01:21:43,780
going to have you're going to
have kids keep extending, and
1041
01:21:43,780 --> 01:21:47,260
you're going to have them answer
these questions. What I'm
1042
01:21:47,260 --> 01:21:53,740
telling you is, don't, when you
get to this point in your
1043
01:21:53,740 --> 01:21:57,400
instruction, in your class,
you're going to be like, Okay,
1044
01:21:58,360 --> 01:22:02,280
that was so beautiful today. I'm
so proud of you guys. We
1045
01:22:02,280 --> 01:22:05,580
realized a lot of different
things. We're going to put that
1046
01:22:05,580 --> 01:22:10,080
away. And I want you to take out
yesterday's homework that has
1047
01:22:10,080 --> 01:22:12,660
nothing to do with this. Okay, I
want you to go on to your
1048
01:22:12,660 --> 01:22:16,860
regular lesson now that if you
leave here with nothing else
1049
01:22:16,860 --> 01:22:20,360
today, I want you to hear me on
this. You're going to be like,
1050
01:22:20,420 --> 01:22:23,480
Oh, but the kids want to finish.
Well, the kids want to keep
1051
01:22:23,480 --> 01:22:27,320
going. I finally got them
focused and engaged, then cut it
1052
01:22:27,320 --> 01:22:27,800
off.
1053
01:22:29,659 --> 01:22:36,079
There are brain reasons for
this. There are cognitive
1054
01:22:36,079 --> 01:22:37,519
reasons for this.
1055
01:22:39,199 --> 01:22:42,579
We are shaping the brain, and we
are shaping the mathematical
1056
01:22:42,579 --> 01:22:47,319
mind. So right now, as soon as
you have the kids in the palm of
1057
01:22:47,319 --> 01:22:50,019
your hands, as soon as you have
them right where you want them,
1058
01:22:50,319 --> 01:22:53,199
you're going to stop and you're
going to be like, Okay, we're
1059
01:22:53,199 --> 01:22:56,139
going to put this away, and
we're going to go on to our
1060
01:22:56,139 --> 01:22:58,779
lesson of the day. Now you're
going to have kids still working
1061
01:22:58,779 --> 01:23:03,119
on it and trying to hide it.
Don't call them out. Just ignore
1062
01:23:03,119 --> 01:23:06,539
it. You're going to have kids
still talking about it. You're
1063
01:23:06,539 --> 01:23:10,679
going to have kids going, Oh,
but I know where they're going
1064
01:23:10,679 --> 01:23:20,179
to go do math without you asking
them to do math. How amazing is
1065
01:23:20,179 --> 01:23:24,019
that they're going to talk about
this at lunch. They're going to
1066
01:23:24,019 --> 01:23:27,799
come in the next day with the
answer, and when they give you
1067
01:23:27,799 --> 01:23:31,399
answers, you're going to be
like, That's interesting, you
1068
01:23:31,399 --> 01:23:34,339
know what? Let's start adding
that to an answer list. Let's
1069
01:23:34,339 --> 01:23:37,099
start documenting that. We'll
come back to this next week. But
1070
01:23:37,099 --> 01:23:43,299
let's celebrate what they're
doing, but do not confirm or
1071
01:23:43,299 --> 01:23:47,739
deny their answers. There are
some responses that are going to
1072
01:23:47,739 --> 01:23:51,819
negate all of the work that
you've done. You want to let
1073
01:23:51,819 --> 01:24:00,359
this linger. See, I'm going to
let this linger. You're going to
1074
01:24:00,359 --> 01:24:03,899
let this Lisa, beautiful,
beautiful, because that's what
1075
01:24:03,899 --> 01:24:09,239
we end up doing with Jesse and
Kay, is we graph Jesse's system
1076
01:24:09,239 --> 01:24:12,419
of equations. That's what this
is. We graph Jesse's function,
1077
01:24:12,479 --> 01:24:16,499
we graph K's function, and
that's just good practice in
1078
01:24:16,499 --> 01:24:21,799
slope, intercept, like boom. And
then we start asking, are we
1079
01:24:21,799 --> 01:24:25,339
going to have parallel lines or
non parallel lines? Parallel
1080
01:24:25,339 --> 01:24:28,279
lines, same slope? No solution.
We don't have the same slope
1081
01:24:28,279 --> 01:24:30,439
here. So we are going to
probably have a solution
1082
01:24:30,439 --> 01:24:32,779
somewhere. What is that
solution? Is the solution going
1083
01:24:32,779 --> 01:24:35,299
to be in the future or in the
past or in the negatives? And
1084
01:24:35,299 --> 01:24:40,039
what is this so much, so much we
can do at algebra one and Lisa,
1085
01:24:40,099 --> 01:24:44,559
imagine if your seventh grade,
sixth grade, fifth grade, fourth
1086
01:24:44,559 --> 01:24:47,139
grade, third grade, second
grade, first grade. Teachers in
1087
01:24:47,139 --> 01:24:51,639
your building did Jesse and K
every year in lots of
1088
01:24:51,639 --> 01:24:55,479
variations. So by the time kids
came to you in algebra one
1089
01:24:56,199 --> 01:25:01,139
they've already had a lot of
this mentality. Mm. Can you
1090
01:25:01,139 --> 01:25:05,999
imagine what that would look
like? It's really beautiful
1091
01:25:06,239 --> 01:25:09,479
because the cohorts I got rid of
the data here, but the cohorts
1092
01:25:09,479 --> 01:25:12,119
where we've seen this extreme
data, that's what we've been
1093
01:25:12,119 --> 01:25:19,199
doing in schools, and we've
earned 1520, 30, 40% higher test
1094
01:25:19,199 --> 01:25:25,939
score rates by doing exactly
this. All right, friends, it is
1095
01:25:25,939 --> 01:25:29,059
almost 11. Here's what I want to
hear right now. Type it in the
1096
01:25:29,059 --> 01:25:34,759
chat or unmute. What were your
takeaways from today? What were
1097
01:25:34,759 --> 01:25:38,239
your ahas? What are you going to
take away from today? What did
1098
01:25:38,239 --> 01:25:42,039
you learn from today? What
solidified your learning. So
1099
01:25:42,039 --> 01:25:45,159
what are your takeaways? Unmute
or type them in the chat or
1100
01:25:45,159 --> 01:25:46,299
both. Go ahead,
1101
01:25:51,520 --> 01:25:55,960
I just have something about the
field trip. Yeah, I'm going to
1102
01:25:55,960 --> 01:25:58,840
bring in another reference
reference task, but the painted
1103
01:25:58,840 --> 01:26:04,200
cube, so I had my the block that
you were in with came back on
1104
01:26:04,260 --> 01:26:09,000
from spring break, okay? And one
of their first questions to me
1105
01:26:09,060 --> 01:26:14,100
was, Hey, are we ever going to
do that cube problem again? And
1106
01:26:14,160 --> 01:26:17,340
not only that, but then my other
block that they kind of
1107
01:26:17,340 --> 01:26:21,140
intermingle with was like, Hey,
I heard that you did this cute
1108
01:26:21,140 --> 01:26:24,260
problem, like, are we ever going
to have a chance to do that
1109
01:26:24,260 --> 01:26:27,080
again? So, you know, they've
been talking about it. It's just
1110
01:26:27,500 --> 01:26:28,280
interesting.
1111
01:26:28,640 --> 01:26:35,000
That's cool. That is cool.
Lingering is so powerful. Let it
1112
01:26:35,000 --> 01:26:39,860
linger. Other takeaways, Hannah
says, Teach based on thinking
1113
01:26:39,860 --> 01:26:42,760
more than salt, yeah, beautiful
other takeaways.
1114
01:26:57,520 --> 01:27:00,600
Yep, thinking, reasoning and
sense making is the key and only
1115
01:27:01,200 --> 01:27:06,120
that's not on the kids, that's
not on the kids, that is on our
1116
01:27:06,120 --> 01:27:10,620
instructional facilitation and
delivery. So if kids don't have
1117
01:27:10,620 --> 01:27:13,800
thinking, reasoning and sense
making, if they don't persevere,
1118
01:27:13,800 --> 01:27:18,120
if they don't initiate, that's
on us, not on them, we have not
1119
01:27:18,120 --> 01:27:23,120
created the environment, culture
and habits for them to default
1120
01:27:23,120 --> 01:27:26,720
to thinking, reasoning and sense
making. A lot of times, I hear
1121
01:27:26,720 --> 01:27:29,180
these kids, they just don't
start. They don't know where to
1122
01:27:29,180 --> 01:27:32,660
begin. They don't they're so
helpless. They're done. They
1123
01:27:32,660 --> 01:27:36,860
didn't do that to themselves.
Because toddlers don't have any
1124
01:27:36,860 --> 01:27:40,580
of that. They toddlers don't
have any of that effectiveness.
1125
01:27:41,900 --> 01:27:47,380
School. Has created that in our
students that's on us, guys
1126
01:27:47,740 --> 01:27:51,940
that's on us. Get students
brains thinking, leave them
1127
01:27:51,940 --> 01:27:55,360
hanging. Yeah, that's important.
Focus factors, fractions
1128
01:27:55,360 --> 01:27:58,720
function, and we have more
explicit, streamlined approaches
1129
01:27:58,720 --> 01:28:01,980
to being able to focus on those.
Yep, very good takeaways.
1130
01:28:01,980 --> 01:28:06,300
Balance between procedures.
Yeah, just do it like, just jump
1131
01:28:06,300 --> 01:28:09,480
in. Don't be like, you don't
know what's going to happen. As
1132
01:28:09,480 --> 01:28:12,960
a teacher, I know that's scary,
but I've given you the out. Once
1133
01:28:12,960 --> 01:28:15,180
you get to a point where you
don't know what to say and do
1134
01:28:15,180 --> 01:28:17,760
next, and you feel yourself
defaulting to telling and
1135
01:28:17,760 --> 01:28:20,840
teaching, then you want to stop
and be like, Hey, we're gonna
1136
01:28:20,840 --> 01:28:26,000
finish that another day,
insisting that my students pre
1137
01:28:26,000 --> 01:28:29,600
read, understand, yeah, yeah.
What is it asking think, reason
1138
01:28:29,600 --> 01:28:33,740
and sense, making new way to
word, make rectangles now. Okay,
1139
01:28:33,740 --> 01:28:36,320
good, good. Amy, yeah, and
you're going back to third
1140
01:28:36,320 --> 01:28:40,100
grade. Awesome. Oh, that seems
like it's going well, that's
1141
01:28:40,100 --> 01:28:44,860
excellent. Wonderful. Okay, you
guys, I've got a pretty hard
1142
01:28:44,860 --> 01:28:48,880
stop today. Usually we stay on
and I give you some more time,
1143
01:28:48,880 --> 01:28:51,520
and then, like all of you, end
up staying for like another
1144
01:28:51,520 --> 01:28:54,100
hour. I can't do that today. I
have a hard stop time today.
1145
01:28:54,580 --> 01:28:59,260
Although I love you, I love you
so much. Mark down, April 24
1146
01:28:59,800 --> 01:29:05,760
there will be the next webinar,
a webinar with upsell. Saturday
1147
01:29:05,760 --> 01:29:08,580
maths. I usually don't have any
upsell. I mean, this is just
1148
01:29:08,640 --> 01:29:12,180
real organic like Saturday math
is free. There's nothing I'm
1149
01:29:12,180 --> 01:29:16,260
selling to you. But on April 24
there will be an upsell, and it
1150
01:29:16,260 --> 01:29:19,140
will be a bundled package of
what you can jump into for the
1151
01:29:19,140 --> 01:29:24,020
2026 2027 school year. I really
want you to be here on April 24
1152
01:29:24,320 --> 01:29:26,600
but I can't give you any link
right now. Nothing is up for
1153
01:29:26,600 --> 01:29:29,660
registration yet. It'll be
coming up later this week. So I
1154
01:29:29,660 --> 01:29:33,260
will send you the information
for the April 24 webinar this
1155
01:29:33,260 --> 01:29:36,680
week. Once I have the link, I'll
follow up and send you the notes
1156
01:29:36,680 --> 01:29:39,980
from today, the PDF notes from
today. And I want to thank all
1157
01:29:39,980 --> 01:29:42,460
of you for being here and
spending your Saturday morning
1158
01:29:42,460 --> 01:29:45,040
with us. We will have another
Saturday math in May, and you
1159
01:29:45,040 --> 01:29:48,400
will definitely get that
information. Also love you guys.
1160
01:29:48,400 --> 01:29:53,200
Bye, bye. Good luck with
testing. Enjoy the final 30 some
1161
01:29:53,200 --> 01:29:56,740
days of school and have a great
summer, but hope to see you in
1162
01:29:56,740 --> 01:29:57,880
May. Bye, everybody. You.
00:00:00,332 --> 00:00:03,512
Unknown: Research on the what's
going on out there, and then
2
00:00:03,512 --> 00:00:07,892
bringing that to you as well as,
of course, my opinion, every
3
00:00:07,892 --> 00:00:12,872
month. So that is a big purpose,
just to be able to the to
4
00:00:12,872 --> 00:00:18,992
gather, network, collaborate, be
with like minded people. And so
5
00:00:18,992 --> 00:00:23,480
here we are, right here, feel
free to use the chat to talk to
6
00:00:23,480 --> 00:00:29,420
each other, which is really one
of the benefits of being here
7
00:00:29,420 --> 00:00:33,020
today. You can, in a moment,
we'll see where people are from
8
00:00:33,020 --> 00:00:38,000
and what grade levels you teach.
But the other main purpose of
9
00:00:38,000 --> 00:00:41,080
Saturday math, and this has
always been the case in the
10
00:00:41,140 --> 00:00:46,300
eight years that we've done
Saturday math is the bottom
11
00:00:46,300 --> 00:00:50,620
line. If students have number
sense, we can take off with
12
00:00:50,620 --> 00:00:56,380
whatever initiative and
resources are thrown at us. So
13
00:00:56,380 --> 00:01:01,260
the overall goal that has always
been on Saturday, math is
14
00:01:01,500 --> 00:01:05,880
improving. Number Sense, that is
our foundation. So I'm going to
15
00:01:05,880 --> 00:01:13,320
put number sense here. There's a
secondary goal. And over the
16
00:01:13,320 --> 00:01:16,200
last couple of months, we've
launched an initiative called
17
00:01:16,200 --> 00:01:20,600
math testing secrets that we
have an entire course for now
18
00:01:20,600 --> 00:01:24,980
that we're very, very proud of,
but in that testing secrets, we
19
00:01:25,040 --> 00:01:30,560
say that there are two barriers
to increasing test scores. And
20
00:01:30,560 --> 00:01:36,560
the barriers are students having
a lack of number sense, but also
21
00:01:36,800 --> 00:01:44,500
a lack of notation. And there
are some of my favorite
22
00:01:44,500 --> 00:01:50,740
notations that have scaled
student achievement that we use,
23
00:01:51,280 --> 00:01:54,400
that are not explicitly stated
in the standards, but are very
24
00:01:54,400 --> 00:01:58,300
much related to the standards.
Some of you can probably guess
25
00:01:58,300 --> 00:02:02,160
one of my favorite notations.
Should I have you? Guess I
26
00:02:02,160 --> 00:02:05,640
should have you. Guess what's
one of my favorite notations
27
00:02:05,640 --> 00:02:12,300
that relates to a task that is
the utmost of importance for
28
00:02:12,300 --> 00:02:15,660
understanding numbers and having
number sense and improving
29
00:02:15,660 --> 00:02:20,400
number sense? Natalie, of course
you have you are always
30
00:02:20,400 --> 00:02:28,520
transplanted here to give us the
exact answer notation of square
31
00:02:28,520 --> 00:02:33,680
root. We have no idea how
essential notation of square
32
00:02:33,680 --> 00:02:37,940
root is. That's the one I'm
going to land on today. There
33
00:02:37,940 --> 00:02:41,260
are other notations that are
absolutely essential, because
34
00:02:41,260 --> 00:02:46,300
part of what is the difference
between a student passing an end
35
00:02:46,300 --> 00:02:50,080
of year math test and almost
passing an end of year math
36
00:02:50,080 --> 00:02:55,120
test, most often, is the
notation that is used and the
37
00:02:55,120 --> 00:02:59,140
lack of understanding of that
notation. Now I'm coming out of
38
00:02:59,140 --> 00:03:02,400
the gate talking a lot about
testing as if like testing is
39
00:03:02,400 --> 00:03:06,720
the be all, end all. Well, no,
it's not. If you all know me,
40
00:03:06,720 --> 00:03:10,920
you know it's not. But we want
our cake, and we want to be able
41
00:03:10,920 --> 00:03:16,680
to eat it too. So I want kids to
have great, rich, complex,
42
00:03:17,220 --> 00:03:21,320
accessible math experiences in
the classroom on a daily basis.
43
00:03:21,320 --> 00:03:25,760
That's what I advocate for. I
empower teachers to create these
44
00:03:25,820 --> 00:03:29,180
experiences for students,
because I cannot personally
45
00:03:29,240 --> 00:03:32,720
create these experiences for
every student out there in
46
00:03:32,720 --> 00:03:37,460
United States, but with your
help, I can do that. So my main
47
00:03:37,460 --> 00:03:41,200
goal and mission and vision is
to empower and inspire teachers
48
00:03:41,500 --> 00:03:45,580
and teach teachers how to create
these rich, complex, accessible
49
00:03:45,580 --> 00:03:49,180
math experiences that target all
students, and especially
50
00:03:49,180 --> 00:03:52,300
students that struggle and
students with disabilities.
51
00:03:53,500 --> 00:04:00,720
Having said that, if we're going
to do that in an effective way,
52
00:04:01,200 --> 00:04:06,540
the test scores should show it
so and I mean, that's what we're
53
00:04:06,540 --> 00:04:10,200
judged on. We're judged on the
test scores. So why not have a
54
00:04:10,200 --> 00:04:16,680
goal of these kids can, and I
know these kids can, because if
55
00:04:16,740 --> 00:04:20,600
any of you know me, you know
that we have taken cohorts of
56
00:04:20,600 --> 00:04:27,620
students from 27% passing one
year to the next year 65%
57
00:04:28,520 --> 00:04:34,880
passing. We've taken cohorts
from 65% passing to 86% passing.
58
00:04:35,540 --> 00:04:42,580
We've taken cohorts of students
from exhibiting bell curve
59
00:04:42,580 --> 00:04:49,000
results, meaning bell curve,
this is 50th percentile. So
60
00:04:49,000 --> 00:04:54,580
average is 50th really from 40th
to 60th percentile on bell curve
61
00:04:54,940 --> 00:04:58,180
on a true standardized test. Now
I have to get on my soapbox for
62
00:04:58,180 --> 00:04:58,780
just a minute.
63
00:04:58,780 --> 00:05:07,140
So. We have for years, even from
the time that I was in school,
64
00:05:07,680 --> 00:05:14,580
we've used very high rated,
credible standardized testing
65
00:05:14,580 --> 00:05:19,680
companies that this is all they
do. And I'm going to give two
66
00:05:19,680 --> 00:05:24,680
examples of those, the Iowa
battery and the Terra Nova.
67
00:05:25,400 --> 00:05:28,280
Okay, I don't know if you have
heard of those, or know those,
68
00:05:28,280 --> 00:05:33,800
or whatever. Those are true
standardized tests. They're
69
00:05:34,040 --> 00:05:36,980
they're competitive companies.
They're two different companies.
70
00:05:37,520 --> 00:05:41,860
But the Iowa and Terra Nova, I
have an immense amount of
71
00:05:41,860 --> 00:05:46,420
respect for an immense amount of
respect, the same amount of
72
00:05:46,420 --> 00:05:50,620
respect I have for the A C T and
S A T, again, a c t and s a t2,
73
00:05:51,040 --> 00:05:54,280
totally different companies, two
totally different platforms,
74
00:05:54,760 --> 00:05:58,180
competing interests, whatever.
But it's always good to have
75
00:05:58,240 --> 00:06:02,580
both. And I don't have, you
know, a preference one way or
76
00:06:02,580 --> 00:06:07,440
another. I think we can use both
of them to our advantage. But
77
00:06:07,440 --> 00:06:11,400
the Iowa and Terra Nova used to
be the be all, end all, a
78
00:06:11,400 --> 00:06:16,860
district would pick one of them,
and either every year or every
79
00:06:16,860 --> 00:06:19,860
three years or every other year,
students would take this
80
00:06:19,860 --> 00:06:23,540
standardized test. And the
reason that I loved how
81
00:06:23,540 --> 00:06:28,820
standardized it was is it is
national, like it didn't matter
82
00:06:28,820 --> 00:06:34,580
if you were in Pennsylvania or
Arizona or whatever it was,
83
00:06:34,580 --> 00:06:38,360
usually one of those two
options. And what the Iowa and
84
00:06:38,360 --> 00:06:44,920
Terra Nova did was, yes, it gave
you an achievement percentile,
85
00:06:45,340 --> 00:06:50,800
not a percent, not a passing.
There's no passing. It gave you,
86
00:06:50,860 --> 00:06:59,380
it gave students a score based
on percentile for achievement.
87
00:06:59,500 --> 00:07:03,840
So there were subject
achievement, pieces of it, and
88
00:07:03,840 --> 00:07:07,380
if students scored anywhere
between the 40th and 60th
89
00:07:07,380 --> 00:07:14,520
percentile, spot on average,
spot on average, fantastic,
90
00:07:15,120 --> 00:07:18,300
which is why. And I'll just give
you an example from the state of
91
00:07:18,300 --> 00:07:22,700
Ohio, which is why in reading.
Now we have what are called
92
00:07:22,700 --> 00:07:26,480
rimps in reading, their
individual plans for reading,
93
00:07:26,900 --> 00:07:31,280
even if kids that are not
special ed, not on IEP, but
94
00:07:31,340 --> 00:07:36,560
school districts were able to
pick and choose what what
95
00:07:36,560 --> 00:07:43,120
percentile ranking was the
maximum for students that have
96
00:07:43,120 --> 00:07:46,840
deficits. Too many school
districts picked 40/40
97
00:07:47,680 --> 00:07:52,900
percentile. The problem is 40 is
right at the bottom of average.
98
00:07:53,080 --> 00:07:56,860
So we're doing a lot of extra
work for these kids. And what
99
00:07:56,860 --> 00:08:00,720
was happening in schools? What
is happening in schools is some
100
00:08:00,720 --> 00:08:05,820
of those kids that are like 32nd
to 40th percentile, we're
101
00:08:05,820 --> 00:08:10,320
creating these plans for them,
but they have been passing their
102
00:08:10,320 --> 00:08:14,640
reading on the state test. So
there's this disconnect. The
103
00:08:14,640 --> 00:08:19,500
reason is, I believe we've gone
down a very, very skewed road
104
00:08:19,500 --> 00:08:22,820
for data. So I just want to
enlighten us this morning on
105
00:08:22,880 --> 00:08:25,880
what data we're using and how
we're using data, and how the
106
00:08:25,880 --> 00:08:30,560
data has shifted to become much
more ineffective in recent
107
00:08:30,560 --> 00:08:37,400
years. So Iowa, TerraNova, I the
results of these things used to
108
00:08:37,400 --> 00:08:42,820
be outstanding, spot on for
kids. Okay, now the reason I
109
00:08:42,820 --> 00:08:47,440
bring this up is I'm trying to
show you in cohorts that have
110
00:08:47,440 --> 00:08:52,240
used the model that we present
in all of our sessions, is we've
111
00:08:52,240 --> 00:08:56,980
been able to scale exponentially
the achievement of students, not
112
00:08:56,980 --> 00:09:00,480
just their achievement, but
their test score results. So
113
00:09:00,720 --> 00:09:04,440
when we look at percentile
rankings, when we were using
114
00:09:04,500 --> 00:09:12,600
Iowa TerraNova, we had a cohort
of students that no one in this
115
00:09:12,600 --> 00:09:18,840
certain cohort scored below the
70th percentile. I mean, we
116
00:09:18,840 --> 00:09:21,440
literally broke the bell curve
with one of our cohorts.
117
00:09:21,860 --> 00:09:25,340
Absolutely crazy. The other
thing I want to say about Iowa
118
00:09:25,340 --> 00:09:30,260
and Terra Nova is a really
important piece of them was the
119
00:09:30,260 --> 00:09:35,180
cognitive ability test. So you
would get a cognitive ability
120
00:09:35,600 --> 00:09:42,040
students would get a cognitive
ability score, which was like,
121
00:09:42,100 --> 00:09:48,400
IQ score, okay, and on that
cognitive ability score, 100
122
00:09:49,780 --> 00:09:54,280
spot on average, but really
average went from 90 to 110
123
00:09:55,960 --> 00:10:01,500
and this cognitive ability score
scoring high enough. Staff would
124
00:10:01,740 --> 00:10:07,860
accurately determine gifted
brains and accurately determine
125
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students, you know, our 70s kids
that had severe brain
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disconnects, and this is what
we've used forever and ever and
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ever now. Okay, so let me make
two points on this. One point on
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this is we have scaled math
achievement using part of what
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I'm going to tell you today,
because going back, I'm talking
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about the big overarching
purpose of Saturday, math is
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improving number sense. We know
that with testing, we want to
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improve notation sense, and I
just want to show you some of
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the things that we've been able
to do, because a big purpose of
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Saturday math is to empower and
inspire us to go back and when
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we know better, we do better, so
that we can all be equipped to
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scale math achievement in these
same ways. So I wanted to share
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some of that data with you. So
that's one piece. Is the purpose
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of Saturday math, and it really
starts with number sense, but
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dwindles down to these other
things. And since we're in
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testing season, I want to bring
bring those things to light.
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Now, here's the other point. I
wasn't even going to talk about
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this today. I think I've been
really fired up about it. I was
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going to jump right into our
content. Remember, I said that
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we're going to, well, I mean, I
kind of did, but now I'm
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derailed. I'm just totally
derailed because I don't know if
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any of you have seen some of the
news media about I ready, so I'm
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not going to go into that
deeply, but what I am going to
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say about this is, over the
years, we have states not we
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states have disapproved some of
our testing entities and
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disapproved some of our textbook
companies and disapproved and
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disapproved and disapproved, and
for some of us, things that were
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working very well for us, and
then re approved, created a re
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approval list of some things
that I think are just pure
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trash. Now I say that and you're
like, Okay, where's your data?
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Let me go back to sort of this
is not necessarily Saturday
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math, but one of the biggest
overarching leads for scaling
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math achievement, and that is
shifting, shifting. And we
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started to make this shift in
about the I'm going to say 20,
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2015 2016 2017 then I think we
were moving in the right
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direction. Covid came, and then
everything went out the window.
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I don't even know what happened
with decision makers like I
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don't know if, if they're
desperate or if I don't even
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know, but what we have been
moving toward ever since minds
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on math started this mission in
2011 what we have been moving
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toward is shifting math
instruction to exactly how the
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brain learns and decision makers
and states are saying they're
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doing this through the science
of reading, which there's a lot
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of merit to the science of
reading. I I'm not a literacy
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expert. I'm not an expert there,
but here's where our downfall is
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going to happen, and this is,
this is my prediction, and this
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is what's going to and this is
why I want you all to be
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educated on this before it comes
in and and takes over and swoops
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in. The science of math.
Learning is not parallel to the
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science of reading learning.
Reading is a skill that must be
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explicitly taught it is not
innate, intuitive inborn, but
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number sense is the exact
opposite, that we are born with
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a certain level of understanding
of number. Number Sense is
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intuitive, ingrained inborn. It
is a natural sense of the
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magnitude of numbers, magnitude
meaning how large and small
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numbers are.
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And so number sense cannot be
explicitly taught, but number
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sense can be. Dramatically
improved through experiences. So
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I want to catch us and educate
us before some of these shifts
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come into place, so we as
educators can be knowledgeable
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enough to ask the right
questions based on the correct
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current research of how the
brain learns and how the brain
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learns certain things. So
notation, notation must be
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explicitly taught. Kids aren't
just going to discover what a
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square root is. So there,
notation is explicit, very much
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parallel to science of reading
number sense is not so when I
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share with you on Saturday
sessions How to Improve number
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sense, this all falls into a
bigger picture of how the brain
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actually learns mathematics, and
there are two different types of
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instruction and learning
outcomes. One we call
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conceptual, which is the number
sense piece, which students must
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experience and figure out on
their own. But we must have
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powerful instructional delivery
methods to be able to make that
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happen. That's what we focus on,
on Saturday, math. And then
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there are procedural,
algorithmic math ability,
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notation, instructional delivery
methods that are very
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traditional, okay, so we need
both, but these are competing
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interests, because the more
procedure and algorithm based we
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are in our classrooms, the less
this conceptual can improve. But
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the more and more and more we
work to improve the conceptual,
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the notation declines. So what
we do in all of our programs is
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find that right teeter totter
balance of being able to improve
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both because they are competing
interests and they do require a
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different instructional
delivery. Wasn't going to go
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into all that today, but I'm
glad that I did, because now we
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have it all pieced in in one
section here. My purpose of
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saying all that, though, was to
talk about the purpose of
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Saturday math, and it's always
been to improve number sense,
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and that's exactly what we're
going to be doing today as well.
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Alright, before I move on,
though, that was, that was a lot
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a lot. Whoo, that was a lot, a
lot. Okay, unmute, if you have
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other thoughts, questions,
comments, etc. And I'll review
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the chat, because I know some of
you have been chatting in the
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chatting.
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Well, I had in the chat a neat
story from an experience with my
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kids this week. Please. Yes, it
actually goes along with
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everything, how the brain learns
number, sense and notation were
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an absolute value. And so they
were working on their lesson of
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the day, and they were comparing
some absolute values. And it was
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absolute value of negative 24
compared to absolute value of
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positive 24 greater than, less
than or equal. So I'm walking
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around the room and observing,
you know what they're writing.
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And so many, of course, said the
absolute value of positive 24
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was greater. And I knew you know
exactly what they were thinking.
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But because, you know, I've been
with Jonily for so long, I just
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each kid I touch base with, I
either said something like, Tell
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me about that. Or, how did you
get that answer? Or tell me how
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you know that's true something
to that effect, and they know
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enough that they don't assume
they're wrong when I say
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something like that. I just want
to know how they got there. So
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they all just launch into the
explanation, and every single
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one of them goes, Oh, they're
equal every single kid, every
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time. So I did this across both
of my classes that day, probably
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in total, 16 to 20 kids that
had, you know, the wrong answer.
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But when I stopped them and
paused them and didn't say, Oh,
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you're wrong. How would you fix
that? But how did you get that?
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Tell me about that, they
launched into their explanation.
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They all self corrected the
answer. And it really got me
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thinking about, like, state
testing in two weeks. I was
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like, you guys, you all knew the
answer. You all knew it. I
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didn't even I didn't say
anything. But how did you know,
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tell me about that? What did you
think about that? And you all
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got the right answer. So my
like, takeaway and message to
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them was like, you know more
math than you think you do, we
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have to slow because we've been
talking a lot about taking your
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time on the test and like, it's
not taking time for the sake of
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taking time. But I was like, I
want you to slow down your
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brain. Have my voice in your
head if you need to prompt
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yourself to say, How do I know?
Or how did I get that answer?
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Like, take your gut reaction.
Like. Course, 24 is bigger, but
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take that gut reaction and
really evaluate the problem, and
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you'll they're they self
corrected. But I'm like, what if
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they did that five times? That's
like, a whole level on a test,
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five questions where your gut
answer, and then you stop and
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think about it. So I'm like,
That's the brain science. I
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think, like, stop and think
about it. And they know so much,
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but they just have to, so I'm
trying to get my voice in their
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head, which is weird, but it was
just a really neat experience.
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Like 16 to 20 kids, literally.
And they all, Oh, they're equal.
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I'm like, okay, so what a time,
you
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know, but I have to give a good
background on our friend,
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Natalie, Krista, Amy, Sarah
Neal, that's here Kirk. Where is
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Kirk today? Oh, man, I really
needed Kirk here today. It's
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okay. So I want to share with
all of you. And then we have, we
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have Lisa, Sarah W we have
Daphne, we have Janet. We have
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so the reason I'm naming these
names is this doesn't just
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happen like especially by coming
to Saturday maths. So we have it
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minds on math, a math teacher
mastermind group, which these
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names that I've mentioned are
either currently a part of that
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or have been a part of it. The
math teacher mastermind group
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launches into a math
certification group. So Natalie,
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Krista, Amy, Sarah, are all some
of our certified coaches that
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have been implementing this for
years, like years Natalie, not
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as many years as others, because
Natalie got to be a student
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teacher for one of our certified
coaches. So Natalie had an
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accelerated learning experience
of this type of implementation.
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And the reason that I say all of
this is it doesn't happen with
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one Saturday math or one math
teacher mastermind or one
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implementation. It takes a good
345, solid years of interacting
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with this on Saturday maths, on
math teacher masterminds on June
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events, on certification
programs, on, you know, all of
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these things that we offer. And
the reason I said April 24 mark
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your calendars for April 24 in
the evening. April 24 in the
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evening, we are having our next
webinar. And this next webinar
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is going to outline a bundle
package of all of our programs
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for 2026 2027 so you can get all
of our programs that we're
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launching, that we launch every
year in a bundle at a very
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discounted rate. I'll send you
information on that webinar. The
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00:22:53,020 --> 00:22:56,020
registration isn't out yet, but
the reason that I say that is
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it's all about interactions over
time. And what I want to say
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about Natalie and her group is
it's been about interactions
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over time, all year. It's not
just about the February, March
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testing season. If she just
started this mindset and culture
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in February, there is no way her
kids would have been there. But
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this was launched in August,
what we call the first 15 at the
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beginning of the school year, so
that kids by this time of year
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are ready. They're just ready
for this. And I also want to say
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I mentioned a lot of these
names, crystal as well. We had a
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big field trip, a teacher field
trip. I wasn't even going to
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mention this today, but I have
to, because it was just it was
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so powerful, it was so amazing,
it was so enlightening and such
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a an impactful experience for me
that I want to share it today
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and have a few of you share if
you were on the field trip with
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US. So last month in March, we
had a teacher field trip. There
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were nine teachers that traveled
to Central Ohio, to my school
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district on one day and got to
see my Algebra Two and algebra
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one classes. Got to watch me
teach. Then I arranged me
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teaching a class at in fourth
grade and second grade at our
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00:24:22,100 --> 00:24:27,260
elementary school. So all nine
people shadowed me all day,
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watched me teach the same exact
task to every class that day.
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And so the people that were
there that day, and I don't want
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00:24:36,860 --> 00:24:40,580
to forget anybody. Natalie West,
Christie Ewing, Amy Garrison,
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00:24:41,300 --> 00:24:47,080
Christy Flynn, Crystal Davis,
Kirk was there that day. We had
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00:24:47,080 --> 00:24:49,660
two other people that were there
that day from another school.
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They're not here this morning.
We had another Natalie and
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Jessica.
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I know I'm going to forget
somebody. I don't mean to forget
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00:24:59,500 --> 00:25:03,240
anybody. It let me know if I'm
forgetting anybody. Anyway, all
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of us observed in the morning at
the high school, and then the
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00:25:06,900 --> 00:25:10,380
afternoon the elementary I
taught all of the classes, and
325
00:25:10,380 --> 00:25:14,520
then we had some reflection time
and thought time, and it was in
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March. So I have worked with a
lot of these kids and have
327
00:25:18,300 --> 00:25:21,440
trained a lot of these kids. So
what you were seeing in a lot of
328
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these kids are kids that have
had this model all year, but
329
00:25:25,760 --> 00:25:29,060
came in with some severe
deficits. All of the classes I
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teach are inclusion classes, so
there's IEP students in every
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class that I teach. I don't have
any advanced classes. I don't
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00:25:35,720 --> 00:25:40,040
have any advanced so when you
look at these types of scores,
333
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it's just bad. But what we saw
on field trip day is you
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00:25:46,300 --> 00:25:51,100
wouldn't be able to tell that by
March, and it's really
335
00:25:51,100 --> 00:25:56,740
spectacular to see. Well, then
the next day, Kirk and I got to
336
00:25:56,740 --> 00:26:01,980
go to Natalie West school and
watch Miss Natalie, and then we
337
00:26:01,980 --> 00:26:06,180
got to go to Krista Ewing school
and watch Miss Krista. And I'm
338
00:26:06,180 --> 00:26:12,660
telling you people right now on
record that Natalie and Krista
339
00:26:12,720 --> 00:26:22,580
teach the model better than I
do. You guys, mind blowing. So I
340
00:26:22,580 --> 00:26:24,800
want to give you some
background, especially maybe if
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00:26:24,800 --> 00:26:27,500
you're here today for the first
time, you don't know any of us.
342
00:26:27,500 --> 00:26:30,920
You don't know any of this. I
want to give you some of those
343
00:26:30,920 --> 00:26:36,260
pieces. But Would anyone like to
share your takeaways from the
344
00:26:36,260 --> 00:26:40,880
field trip experience with us
now, and I'm go back and look at
345
00:26:40,880 --> 00:26:43,900
comments so unmute and let us
know what your takeaways were
346
00:26:43,900 --> 00:26:45,400
from that experience.
347
00:26:49,359 --> 00:26:58,899
Mine was, can you hear me? Yes.
Crystal, crystal. Okay, so my
348
00:26:58,899 --> 00:27:03,299
takeaway was and I shared this
with you or with the group, was
349
00:27:03,299 --> 00:27:11,579
that no matter what grade A
student is in, they can use
350
00:27:11,639 --> 00:27:22,459
their brains to think past just
solving a problem, and you can
351
00:27:22,459 --> 00:27:28,939
take the exact same model and
apply it at every level. And I
352
00:27:28,939 --> 00:27:30,679
thought that was amazing.
353
00:27:31,760 --> 00:27:36,020
And I'm so glad that you all got
to see that that day. And I
354
00:27:36,020 --> 00:27:40,040
think that is more powerful than
just seeing it at the high
355
00:27:40,040 --> 00:27:43,840
school level, or because it's
then you know, what does this
356
00:27:43,840 --> 00:27:46,720
look like in first grade? What
does this look like in seventh
357
00:27:46,720 --> 00:27:52,240
grade? And same task, same
instructional delivery model.
358
00:27:52,600 --> 00:27:55,780
Now I tweak the way that I
interact with kids because of
359
00:27:55,780 --> 00:28:00,220
the grade level, and you you all
got to see those nuances. But
360
00:28:00,400 --> 00:28:04,500
crystal, you said it
beautifully, and I don't think
361
00:28:04,500 --> 00:28:10,140
you can understand it until you
actually see it or hear it. So
362
00:28:10,140 --> 00:28:14,220
if you have not had a chance to
come and observe any of us, or
363
00:28:14,220 --> 00:28:17,340
you all have not had a chance
for me to come and teach it in
364
00:28:17,340 --> 00:28:24,020
your classroom, or the cheapest,
easiest way. If you all have not
365
00:28:24,020 --> 00:28:27,800
had an opportunity to listen to
my audio files of me teaching
366
00:28:27,800 --> 00:28:31,580
these things with students, you
need to make that happen,
367
00:28:32,480 --> 00:28:38,120
because I can tell you all this.
I can I can say all this. I can
368
00:28:38,120 --> 00:28:42,520
tell you. The people on here can
tell you, but that hits
369
00:28:42,520 --> 00:28:49,120
different when you actually hear
it done to students. So it was,
370
00:28:49,120 --> 00:28:53,080
it was just a beautiful
experience those two days. Any
371
00:28:53,140 --> 00:28:57,520
other takeaways from your
experience being in all of those
372
00:28:57,520 --> 00:28:58,240
classrooms?
373
00:28:58,240 --> 00:29:03,000
Krista, yeah, the one thing that
impressed me, particularly with
374
00:29:03,000 --> 00:29:07,440
the high schoolers, because I
I'm sixth grade, they allowed,
375
00:29:07,440 --> 00:29:11,040
like the culture that was built
through the methods that are
376
00:29:11,040 --> 00:29:16,080
being used, they allowed, like
all of these strangers to just
377
00:29:16,080 --> 00:29:19,500
come up and we were asking them
questions, and It didn't throw
378
00:29:19,500 --> 00:29:24,200
them off, and they responded to
us, and that's what and it was
379
00:29:24,200 --> 00:29:27,200
the true of every class that we
went to. We were just kind of
380
00:29:27,200 --> 00:29:31,700
all fanned out, looked at their
work, asked these kids
381
00:29:31,700 --> 00:29:35,240
questions, and they didn't know
us from anybody, and they were
382
00:29:35,240 --> 00:29:38,360
just engaged and willing to
share their thinking with us.
383
00:29:38,660 --> 00:29:41,200
And that kind of culture is
something that you have to build
384
00:29:41,200 --> 00:29:44,800
from day one. And it was just
impressive the way that they
385
00:29:44,800 --> 00:29:47,560
just kind of acclimated to us as
well,
386
00:29:48,640 --> 00:29:51,760
and that is really unique. And I
wasn't sure that that they were
387
00:29:51,760 --> 00:29:54,400
going to be able to perform that
way. These are kids that
388
00:29:54,400 --> 00:29:58,060
struggle. They have high anxiety
for math. They've come with a
389
00:29:58,060 --> 00:30:01,440
lot of baggage from you. You
know, and I'm not trying to
390
00:30:01,440 --> 00:30:06,780
blame but from some ineffective
instructional practices, they've
391
00:30:06,780 --> 00:30:12,300
been jaded, and I don't blame
them. And I want to go back to
392
00:30:12,300 --> 00:30:17,940
what crystal said. It's about
going past the solving because,
393
00:30:18,000 --> 00:30:20,960
as I've said in our testing
secrets launch this year. Let me
394
00:30:20,960 --> 00:30:24,020
take a picture of this so I can
erase it. But going back to
395
00:30:24,860 --> 00:30:30,320
solving. Solving is not
learning. Solving is not
396
00:30:30,320 --> 00:30:35,060
learning. And if my emphasis in
my classroom was solving, Krista
397
00:30:35,060 --> 00:30:38,480
and everybody would not have
been able to experience the math
398
00:30:38,480 --> 00:30:42,280
and hearing that was happening.
So what is the opposite of
399
00:30:42,280 --> 00:30:51,220
solving? It is thinking,
reasoning and sense making. This
400
00:30:51,280 --> 00:30:55,120
is the climate and culture that
is going to scale math
401
00:30:55,120 --> 00:30:58,960
achievement. It's going to
decrease anxiety, it's going to
402
00:30:58,960 --> 00:31:03,600
increase confidence, and it's
going to improve test scores. A
403
00:31:03,600 --> 00:31:07,680
focus on thinking, reasoning and
sense making will always lead to
404
00:31:07,680 --> 00:31:11,040
solving, but we don't have to
push solving. It will happen
405
00:31:11,040 --> 00:31:15,300
organically and naturally. And
that's what Krista is talking
406
00:31:15,300 --> 00:31:19,560
about, that she observed, and I
wasn't sure, like I see it in my
407
00:31:19,560 --> 00:31:24,380
students every day I didn't in
August, September, October, it
408
00:31:24,380 --> 00:31:29,900
was like pulling wisdom teeth in
these classes. Awful. I'm like,
409
00:31:29,900 --> 00:31:32,360
there is no way I'm going to be
able to create this culture with
410
00:31:32,360 --> 00:31:36,680
high school students that I
mean, look at how many years
411
00:31:37,040 --> 00:31:40,180
they have not had these type of
experiences. How am I going to
412
00:31:40,180 --> 00:31:44,980
do this by October, November,
they started to thrive and
413
00:31:44,980 --> 00:31:49,300
really come out of their shell.
So for even me to see my
414
00:31:49,300 --> 00:31:53,560
students very vulnerable and
taking risks in front of nine
415
00:31:53,560 --> 00:32:00,520
adults, math and earring with
them, heck yeah, heck yeah. And
416
00:32:00,520 --> 00:32:04,816
I keep saying math and earring.
If you don't have the making
417
00:32:04,816 --> 00:32:08,536
math and ears book, go to
Amazon. Get it today. Making
418
00:32:08,536 --> 00:32:12,976
math and ears, this is for
teachers and students, improving
419
00:32:12,976 --> 00:32:16,876
the conceptual understanding of
mathematics for the teacher and
420
00:32:16,876 --> 00:32:20,300
the student. Many different case
studies in here of students and
421
00:32:20,300 --> 00:32:24,080
teachers and their journeys and
how they've transformed to
422
00:32:24,080 --> 00:32:26,780
creating these types of
environments and being in these
423
00:32:26,780 --> 00:32:30,680
types of environments, in math
classrooms everywhere. So yeah,
424
00:32:30,680 --> 00:32:33,800
get your book. Go to Amazon, get
your book, making math and ears,
425
00:32:34,100 --> 00:32:38,420
and it's really going to kind of
lay out the foundation of the
426
00:32:38,420 --> 00:32:42,160
difference between this
conceptual and procedural. So
427
00:32:42,160 --> 00:32:47,800
notation goes along with what we
call math ability solving, Okay,
428
00:32:48,100 --> 00:32:51,880
number sense is this conceptual
thinking, reasoning and sense
429
00:32:51,880 --> 00:32:55,600
making? Now, I know what you're
all wondering right now is,
430
00:32:55,600 --> 00:33:06,240
well, shoot, how do we create
this in our classrooms? Saturday
431
00:33:06,240 --> 00:33:10,020
math gives you pieces of that,
but what you really want to do
432
00:33:10,260 --> 00:33:14,160
is go through one of our courses
or programs so that you get that
433
00:33:14,160 --> 00:33:17,340
streamlined effect of what do I
do? First, second, third. But
434
00:33:17,340 --> 00:33:19,860
I'm not saying don't come to
Saturday math, because you're
435
00:33:19,860 --> 00:33:22,580
going to get bits and pieces of
everything Saturday, math is
436
00:33:22,580 --> 00:33:28,280
much more non linear and very
like, you know, interactive,
437
00:33:28,280 --> 00:33:33,680
moving around. This is the big
question that we have been
438
00:33:33,680 --> 00:33:39,200
trying to move in this mission
before we talk about the how,
439
00:33:39,200 --> 00:33:42,220
though, and this is part of the
content I wanted to teach today,
440
00:33:42,820 --> 00:33:46,300
before we talk about the how, we
really have to talk about the
441
00:33:46,300 --> 00:33:52,240
when. And this goes back to
textbook companies. Some of
442
00:33:52,240 --> 00:33:57,520
these new approved, not
improved, but these new approved
443
00:33:57,520 --> 00:34:04,500
textbook companies, the when and
the structure of the year and
444
00:34:04,500 --> 00:34:07,740
how the content is delivered.
And when the content is
445
00:34:07,740 --> 00:34:11,340
delivered is the complete
opposite of how the brain learns
446
00:34:11,340 --> 00:34:16,140
mathematics. So what are some of
our common instructional fails?
447
00:34:17,220 --> 00:34:20,120
Some of our common instructional
fails are teaching one thing at
448
00:34:20,120 --> 00:34:27,140
a time like a textbook is set
up, focusing on solving. That's
449
00:34:27,140 --> 00:34:28,040
another fail,
450
00:34:30,440 --> 00:34:35,240
treating all standards equal,
that's another fail, finishing
451
00:34:35,300 --> 00:34:38,720
everything. We haven't talked
about that yet today, finishing
452
00:34:38,780 --> 00:34:43,420
everything so answering every
question, solving every problem
453
00:34:43,420 --> 00:34:48,340
that is a fail. We've got to let
things linger. One of the
454
00:34:48,340 --> 00:34:51,820
biggest ways that we can improve
math achievement is to let
455
00:34:51,820 --> 00:34:57,040
things linger. Ask questions and
give problems that we don't
456
00:34:57,040 --> 00:35:03,120
finalize, because what. In the
brain is the subconscious
457
00:35:03,300 --> 00:35:06,600
continues to think about that.
There's this cognitive
458
00:35:06,600 --> 00:35:10,680
dissonance that we've never
really tied the bow on. We
459
00:35:10,740 --> 00:35:15,780
believe, we really believe, as a
country and as a culture, that
460
00:35:15,780 --> 00:35:20,660
we have to finish every problem.
And I'm telling you that that is
461
00:35:20,660 --> 00:35:25,160
one of the worst ways to try to
improve math achievement, we
462
00:35:25,160 --> 00:35:28,400
have to let some things linger
so that the subconscious brain
463
00:35:28,460 --> 00:35:35,120
activates and continues to think
reason and sense make without
464
00:35:35,240 --> 00:35:40,540
the human being even knowing
it's happening. And that is
465
00:35:40,540 --> 00:35:44,860
probably the greatest fail of
some of our textbook companies.
466
00:35:45,760 --> 00:35:51,880
So how do we shift some of these
fails into fixes? That is to
467
00:35:51,880 --> 00:35:54,760
look at the when, and I'm going
to show you this on a document
468
00:35:54,760 --> 00:36:01,620
that I created. But before we
even do that, before we even
469
00:36:01,800 --> 00:36:05,580
figure out how to do this, we
have to figure out, okay, when
470
00:36:05,580 --> 00:36:09,720
what's the structure of the
year, and before we even do
471
00:36:09,840 --> 00:36:14,340
that, uh Oh, someone's asking a
question about what curriculum.
472
00:36:14,460 --> 00:36:20,760
Oh no. Oh no. Janet, you're
poking me, aren't you? You're
473
00:36:20,760 --> 00:36:27,140
getting me fired up. Janet, all
right, before all of that, we
474
00:36:27,200 --> 00:36:37,760
have to ask ourselves, What the
What is, what is absolutely
475
00:36:37,760 --> 00:36:45,160
essential, and what is essential
has to be exposed in 15 day
476
00:36:45,160 --> 00:36:49,420
cycles throughout the year. So
Janet, to answer your question,
477
00:36:49,420 --> 00:36:52,000
what curriculum would you
recommend that does go with the
478
00:36:52,000 --> 00:36:57,340
brain research and is approved?
None of them. Now, I'm not
479
00:36:57,340 --> 00:37:01,140
saying that you can't adopt
things. Okay, I'm not saying
480
00:37:01,140 --> 00:37:04,740
because every single textbook
resource, every single
481
00:37:04,740 --> 00:37:09,000
curriculum resource, can be put
in this model, every one of
482
00:37:09,000 --> 00:37:14,280
them, every single one of them,
but we have to be able to be
483
00:37:14,340 --> 00:37:19,440
flexible and adapt how we use
our resources. So these are the
484
00:37:19,440 --> 00:37:25,580
three biggest questions in our
bigger program of delivery, the
485
00:37:25,580 --> 00:37:32,000
what the essentials, the when?
When do the essentials come up
486
00:37:32,000 --> 00:37:36,140
throughout the year, and it's in
cycles of 15 days, and then the
487
00:37:36,140 --> 00:37:40,360
how is in the instructional
delivery process that is going
488
00:37:40,360 --> 00:37:43,300
to have an impact on not only
student achievement, but
489
00:37:44,020 --> 00:37:50,200
confidence and and, yeah. I
mean, amplify fantastic. I love
490
00:37:50,200 --> 00:37:54,220
and hate every curriculum
resource. So I will say amplify
491
00:37:54,280 --> 00:37:58,780
is is very good. Is very good in
its pieces. I think the one
492
00:37:58,780 --> 00:38:05,820
thing that amplify, duh. Doesn't
have, but actually it does, but
493
00:38:05,820 --> 00:38:09,360
it's kind of hidden. Is the what
and the when? I think there's a
494
00:38:09,360 --> 00:38:15,720
lot of great house in amplify
and, yeah, so I'll just go from
495
00:38:15,720 --> 00:38:19,620
there. Okay, you all came to
learn something today, though,
496
00:38:19,620 --> 00:38:23,420
but I'm really glad that I kind
of gave all that foundation,
497
00:38:23,420 --> 00:38:27,080
because I think all of that's
important to continue to empower
498
00:38:27,080 --> 00:38:31,280
us to think differently about
math education. Scores across
499
00:38:31,280 --> 00:38:35,120
the country are dismal. They
keep declining. We've never had
500
00:38:35,120 --> 00:38:40,780
major improvements as a country,
and we keep trying things that
501
00:38:40,780 --> 00:38:44,200
are not only not working, but
are working worse than what
502
00:38:44,200 --> 00:38:52,480
we've done before. Oh boy. Okay.
What a downer. What a downer. I
503
00:38:52,480 --> 00:38:55,480
don't mean to be a downer. Let
me share my screen, because I'm
504
00:38:55,480 --> 00:38:59,800
going to Okay.
505
00:39:01,720 --> 00:39:05,340
So these are the notes that I
created for today that I'm going
506
00:39:05,340 --> 00:39:08,520
to work off of. And when I
follow up email for you, I'm
507
00:39:08,520 --> 00:39:11,400
going to send you the PDF
version of these notes so that
508
00:39:11,400 --> 00:39:15,000
you have these. This is what I
basically just did on the
509
00:39:15,000 --> 00:39:19,920
whiteboard that was intentional.
But when I talk about the what,
510
00:39:20,640 --> 00:39:24,680
the essentials, you know, it
comes down to my F words. Love
511
00:39:24,680 --> 00:39:30,020
me some F words. So many F
words, okay, but the essential
512
00:39:30,020 --> 00:39:33,680
math concepts that are going to
build both of these number sense
513
00:39:33,680 --> 00:39:37,400
and notation are factors,
fraction and function. What do I
514
00:39:37,400 --> 00:39:41,080
mean by that? I don't mean we do
a factors unit, a fraction unit
515
00:39:41,080 --> 00:39:46,660
and a function unit. So what I
mean by this is these are the
516
00:39:46,660 --> 00:39:50,860
three key concepts that should
be a part of every 15 day cycle
517
00:39:51,100 --> 00:39:55,060
we should always be teaching
through factors, through
518
00:39:55,060 --> 00:39:59,560
fraction, through function. And
what Crystal was talking about
519
00:39:59,740 --> 00:40:04,140
is. Is seeing this effect at
every grade level. So if you're
520
00:40:04,140 --> 00:40:06,600
a first grade teacher, Amy
garrison is a first grade
521
00:40:06,600 --> 00:40:11,340
teacher. Amy is constantly
teaching through factors,
522
00:40:11,340 --> 00:40:14,400
fraction and function, even
though the word factor doesn't
523
00:40:14,400 --> 00:40:20,160
necessarily come until fourth
grade in the standards, factors
524
00:40:20,160 --> 00:40:27,260
are making arrays. So if I have
24 blocks and I make an array, I
525
00:40:27,260 --> 00:40:31,520
could make an array that is six
tall, four long or eight tall,
526
00:40:31,520 --> 00:40:37,460
three long. Those numbers are
factors. Kids don't know it, but
527
00:40:37,460 --> 00:40:42,880
making rectangles is one of our
go to experiences for students
528
00:40:43,240 --> 00:40:46,600
that not only improve number
sense but math achievement. So
529
00:40:46,600 --> 00:40:50,320
even as a first grade teacher,
you are teaching through these
530
00:40:50,320 --> 00:40:55,060
three things. So our job as
teachers is to learn what
531
00:40:55,060 --> 00:40:58,720
factors, fraction and function
look like at every single grade
532
00:40:58,720 --> 00:41:03,060
level, and what the progression
is from one grade level to next.
533
00:41:03,660 --> 00:41:08,100
And what we do at minds on math
is, and let me go ahead and draw
534
00:41:08,100 --> 00:41:16,500
this in. What we do at minds on
math is we create reference
535
00:41:16,560 --> 00:41:21,980
tasks. We call them the Dirty
Dozen. There are 12 reference
536
00:41:21,980 --> 00:41:26,720
tasks that associate with
factors fraction and function.
537
00:41:26,720 --> 00:41:29,720
So if you're looking for lessons
in your classroom to do, to
538
00:41:30,380 --> 00:41:35,900
teach through these essential
concepts, we have 12 reference
539
00:41:35,900 --> 00:41:39,500
tasks. The 12 reference tasks
are exactly the same for every
540
00:41:39,500 --> 00:41:44,200
single grade level, exactly the
same. There are some differences
541
00:41:44,200 --> 00:41:48,280
at kindergarten and at algebra
one, depending, you know, very,
542
00:41:48,280 --> 00:41:53,560
very minor differences and
variations. But the reason we
543
00:41:53,680 --> 00:41:57,940
bring everything down into
reference tasks is these are
544
00:41:58,660 --> 00:42:03,840
grab and go like these are not
theory. They're not they're very
545
00:42:03,840 --> 00:42:08,400
practical steps to do lessons in
your classrooms. And they are
546
00:42:08,400 --> 00:42:13,320
not a one and done situation, a
reference task like making
547
00:42:13,320 --> 00:42:16,740
rectangles in first grade looks
like making a raise with 24
548
00:42:16,920 --> 00:42:20,972
blocks and then how tall? How
long are those blocks? What that
549
00:42:20,972 --> 00:42:24,452
looks like in fourth grade are,
what are all the rectangles I
550
00:42:24,452 --> 00:42:27,212
can create? Well, actually go to
third grade. In third grade,
551
00:42:27,212 --> 00:42:30,092
what that looks like is, what
are all the rectangles I can
552
00:42:30,092 --> 00:42:36,692
create with an area of 24 but
different perimeters in fourth
553
00:42:36,692 --> 00:42:39,752
grade? What are all the
rectangles I can create with
554
00:42:39,752 --> 00:42:45,040
area 24 and the up level
question to that is, what are
555
00:42:45,040 --> 00:42:49,180
the factors of 24 because they
are the length and what they are
556
00:42:49,180 --> 00:42:52,300
the dimensions of the rectangles
I can create. See, we're using
557
00:42:52,300 --> 00:42:55,300
that same task, and we're
targeting our standards, but
558
00:42:55,300 --> 00:42:59,140
what we're doing is we're front
loading this progression,
559
00:42:59,440 --> 00:43:02,820
because as early as first grade,
kids are learning about factors.
560
00:43:02,820 --> 00:43:07,500
One of our other tasks is a
locker problem. This is an act
561
00:43:07,500 --> 00:43:13,080
it out hands on, concrete,
conceptual situation that kids
562
00:43:13,080 --> 00:43:16,860
experience, that even at first
grade, they start to learn the
563
00:43:16,860 --> 00:43:19,200
factors of a number. But we
don't call it factors of a
564
00:43:19,200 --> 00:43:23,060
number. We call it which
students touch. Locker, 24, oh,
565
00:43:23,060 --> 00:43:25,820
student eight, does, three,
does, four, does, six does.
566
00:43:26,300 --> 00:43:28,760
Through these reference and
these reference tasks are not
567
00:43:28,760 --> 00:43:32,600
one and done. So when I talk
about these 15 day cycles, some
568
00:43:32,600 --> 00:43:37,520
of these reference tasks come
back every 15 days, and then we
569
00:43:37,520 --> 00:43:42,880
up level them. So kids are
getting interactions over time.
570
00:43:42,880 --> 00:43:45,340
They're getting more
interactions with the same thing
571
00:43:45,400 --> 00:43:50,320
at more grade levels through
these reference tasks, targeting
572
00:43:50,500 --> 00:43:52,060
factors, fraction and function.
573
00:43:53,920 --> 00:44:00,540
So that's sort of the framework,
and it answers the what. Now
574
00:44:00,540 --> 00:44:03,480
there are other pieces in this
what, but it just comes down to
575
00:44:03,480 --> 00:44:06,720
those three things, factors,
fraction and function. If you
576
00:44:06,720 --> 00:44:11,640
study the College Board, College
Board is a c t or not. I totally
577
00:44:11,640 --> 00:44:15,000
said that wrong, totally so I'm
ridiculous. Got a c t on the
578
00:44:15,000 --> 00:44:19,260
brain. College Board is not a C
T. College Board s, a T. If you
579
00:44:19,260 --> 00:44:23,900
study that, there was a
published book called math
580
00:44:23,900 --> 00:44:28,100
vertical teams. Oh my gosh, way,
way back in the early 2000s I
581
00:44:28,100 --> 00:44:32,360
believe in this book that the
College Board published. College
582
00:44:32,360 --> 00:44:36,980
Board is the S, A, T people. In
the book math vertical teams
583
00:44:36,980 --> 00:44:39,080
that the College Board
published, they said there are
584
00:44:39,080 --> 00:44:43,540
three things for students to be
successful in AP Calculus, and
585
00:44:43,600 --> 00:44:48,700
it is rate function and
accumulation that very much
586
00:44:49,000 --> 00:44:55,060
relates to factors fraction and
function. If you study what
587
00:44:55,060 --> 00:44:58,960
algebra, two teachers say that
students need to be successful.
588
00:44:59,680 --> 00:45:06,960
They. Say radicals, that's
factors. They say equations,
589
00:45:06,960 --> 00:45:11,580
that's function, or systems of
equations that's function. They
590
00:45:11,580 --> 00:45:16,500
say graphing, which is number,
line, factors and fraction. They
591
00:45:16,500 --> 00:45:23,360
so everything that we are
reading or studying or hearing
592
00:45:23,360 --> 00:45:29,120
about high school to higher ed
comes down to these same things.
593
00:45:29,660 --> 00:45:35,060
And if you study math tests, A,
C, T, S, A, T, end of course,
594
00:45:35,060 --> 00:45:40,040
exams, grade level tests at each
state you study the national
595
00:45:40,040 --> 00:45:45,940
tests, nape, look at the Tims
report, study GRE, I've been
596
00:45:45,940 --> 00:45:50,980
studying as fab, so the the test
that kids have to take, going
597
00:45:50,980 --> 00:45:54,400
into the army, going into the
service. So I've learned more
598
00:45:54,400 --> 00:45:58,540
about asfab This year, because I
teach high school students, and
599
00:45:58,540 --> 00:46:02,400
I have some students that need
to pass the math. And so I've
600
00:46:02,400 --> 00:46:07,680
been creating these it's all the
same. It's all the same themes.
601
00:46:07,740 --> 00:46:11,220
It all comes down to the same
things. So no matter what
602
00:46:11,220 --> 00:46:14,520
textbook you adopt, no matter
what how the curriculum changes,
603
00:46:14,520 --> 00:46:17,700
no matter how the standards
change, there are certain
604
00:46:17,700 --> 00:46:22,220
mathematics that are ingrained
in the foundation that are
605
00:46:22,220 --> 00:46:26,240
priceless and timeless, they're
never going to change, and
606
00:46:26,240 --> 00:46:30,560
that's what we based all of our
programs off of. So no matter
607
00:46:30,560 --> 00:46:34,040
what comes and goes, no matter
what's approved or disapproved,
608
00:46:34,520 --> 00:46:38,000
these certain essentials are
always going to be there, no
609
00:46:38,000 --> 00:46:42,400
matter what. If everything's
important, nothing's important.
610
00:46:42,400 --> 00:46:46,720
Nothing's important, and we have
defined what is absolutely
611
00:46:46,720 --> 00:46:52,000
important. Now I'm not today
going to talk about the when I
612
00:46:52,000 --> 00:46:54,880
set it up, to talk about this
today, which is, how do we
613
00:46:54,880 --> 00:46:58,300
structure our school year? How
do we separate it, and how do
614
00:46:58,300 --> 00:47:02,520
these 15 day cycles occur? I'm
not going to teach on that today
615
00:47:02,580 --> 00:47:05,760
unless we have some time at the
end. Because here's what I want
616
00:47:05,760 --> 00:47:11,160
to teach on today. I want to
teach on a practical example of
617
00:47:11,220 --> 00:47:15,300
everything that I've just talked
about, and that is this
618
00:47:15,360 --> 00:47:23,060
equation. This equation. It I
pulled it right off of our state
619
00:47:23,060 --> 00:47:26,540
test for algebra one. Pulled it
right off our state test for
620
00:47:26,540 --> 00:47:32,420
algebra one. None of my students
last week, when I gave this on a
621
00:47:32,420 --> 00:47:36,560
practice test, none of my
students got the correct answer.
622
00:47:37,220 --> 00:47:40,340
And these are my students that
have been ingrained in this
623
00:47:40,760 --> 00:47:45,280
model all year. So this is
concerning. So what do we do
624
00:47:45,280 --> 00:47:48,040
about it? That's what I want to
answer right now. What do we do
625
00:47:48,040 --> 00:47:53,200
about it? Well, I didn't start
these equations early enough
626
00:47:53,200 --> 00:47:57,220
this year. We have another task
called Jesse and Kay. I started
627
00:47:57,220 --> 00:48:01,800
Jesse and Kay much earlier in
the year. I did not do enough
628
00:48:01,800 --> 00:48:05,760
fractional pieces for Jesse and
Kay. Now, if you guys don't know
629
00:48:05,760 --> 00:48:08,280
what I'm talking about for Jesse
and Kay, don't worry about that.
630
00:48:08,280 --> 00:48:12,360
Just ignore what I just said. If
you know Jesse and Kay, just
631
00:48:12,360 --> 00:48:16,860
know that I made the mistake. I
did not do enough fractional
632
00:48:18,360 --> 00:48:22,340
examples or variations of Jesse
and Kay, and I'm seeing that
633
00:48:22,340 --> 00:48:28,400
now. So live and learn. So I
want us to look at this
634
00:48:28,400 --> 00:48:32,900
equation, whether you know Jesse
and Kay or not, whether you know
635
00:48:32,900 --> 00:48:36,320
quick dots or not, whether you
know that counting is essential
636
00:48:36,320 --> 00:48:39,740
or not. It doesn't matter what
you know or don't know about
637
00:48:39,740 --> 00:48:46,120
this equation. I want you in the
chat right now to do two things.
638
00:48:46,660 --> 00:48:53,680
I want you to type in what grade
levels you connect with, what
639
00:48:53,680 --> 00:48:59,380
grade levels you connect with,
and what you see and notice
640
00:48:59,440 --> 00:49:02,880
about this equation. So you're
going to do two things right
641
00:49:02,880 --> 00:49:06,900
now. In the chat, I want you to
type in what grade levels you
642
00:49:06,900 --> 00:49:09,960
connect with, so what grade
levels you teach or coach or
643
00:49:09,960 --> 00:49:13,260
whatever, or you know, if you're
a principal or curriculum
644
00:49:13,260 --> 00:49:18,960
person, what grade levels you're
in charge of, and what you see
645
00:49:18,960 --> 00:49:22,400
and notice about this equation.
646
00:49:29,420 --> 00:49:35,660
What can you tell me about? Tell
me about this equation, and what
647
00:49:35,660 --> 00:49:37,520
do you see and notice?
648
00:49:51,808 --> 00:49:53,428
Okay, let me look at the chat
here.
649
00:50:01,376 --> 00:50:05,036
Lot of fifth grade teachers.
Hey, I know why you're here.
650
00:50:05,396 --> 00:50:09,596
Hey, the fifth grade test
everywhere, the hardest one I'm
651
00:50:09,596 --> 00:50:13,976
telling you. You guys know this.
There's reasons why the fifth
652
00:50:13,976 --> 00:50:18,416
grade test is most difficult for
students, and we have solutions
653
00:50:18,416 --> 00:50:27,740
on how to fix that too. You a
good this is excellent. Oh,
654
00:50:27,740 --> 00:50:32,060
okay, one half and 1/4 Yeah,
there are two x's. There's an X
655
00:50:32,060 --> 00:50:35,960
on each side. We see variables,
fractions, lots of operations,
656
00:50:35,960 --> 00:50:40,420
hidden symbols, notes, oh my
gosh. You see why kids struggle
657
00:50:40,420 --> 00:50:43,480
with coefficients. Yeah, you've
got to have the ability to work
658
00:50:43,480 --> 00:50:47,020
with fractions. I mean, kids are
going to look at this on the
659
00:50:47,020 --> 00:50:50,200
test and be like, nope, skip
next question. Just because
660
00:50:50,200 --> 00:50:57,340
there's a fraction, there are
constants and variables unlike
661
00:50:57,340 --> 00:51:03,720
denominators. Yeah. Amy, really
good point you would, you would
662
00:51:03,720 --> 00:51:08,340
cover up those x's with smiley
face emojis, yep, and just say
663
00:51:08,340 --> 00:51:11,940
the these are the the numbers we
got to try to figure out, Yep,
664
00:51:11,940 --> 00:51:17,880
perfect constants and
coefficients. The, yeah, the mix
665
00:51:17,880 --> 00:51:23,300
number, the mix number. That was
weird for me, too. And then I
666
00:51:23,300 --> 00:51:26,120
went back to previous years test
release questions, and I'm like,
667
00:51:26,120 --> 00:51:30,260
there's a few of these with the
mixed number in it. There's a
668
00:51:30,260 --> 00:51:37,640
lot of these in fifth grade. Lot
of these in fifth grade. Yeah,
669
00:51:37,640 --> 00:51:40,840
the x being the X being a
multiplication symbol, and not a
670
00:51:40,840 --> 00:51:47,860
bit having no concept that it's
an unknown. Yep, yep. I mean,
671
00:51:47,860 --> 00:51:58,300
there's so much to lose with
this question. Yeah, okay, so my
672
00:51:58,360 --> 00:52:00,940
Okay, let me stop for a moment.
We're going to come back to this
673
00:52:00,940 --> 00:52:04,440
and I'm going to walk us through
instructionally, what we do with
674
00:52:04,440 --> 00:52:09,540
this. Instructionally, what we
do with this in algebra one
675
00:52:09,540 --> 00:52:15,240
knowing my test is in a week and
a half. Instructionally, what do
676
00:52:15,240 --> 00:52:20,780
we do with this at third grade?
Because this is like perfect
677
00:52:20,780 --> 00:52:25,460
third grade, not equation
solving, but like third grade
678
00:52:25,460 --> 00:52:29,420
content. I'm going to show you
that in a moment. But go ahead
679
00:52:29,420 --> 00:52:35,120
and unmute and talk to me about
instructionally, how do we deal
680
00:52:35,120 --> 00:52:40,720
with how do we improve? How do
we use this example in a
681
00:52:40,720 --> 00:52:46,480
conceptual way to improve number
sense and to help students think
682
00:52:46,480 --> 00:52:53,200
reason and sense make and not
solve. You've probably never
683
00:52:53,200 --> 00:52:56,320
thought about equations this
way, but unmute and talk to me.
684
00:52:56,620 --> 00:53:01,260
How would you what are your
ideas of using this equation. It
685
00:53:01,260 --> 00:53:05,640
looks very traditional, very
notation ish, how would we use
686
00:53:05,640 --> 00:53:11,460
this in a conceptual, contextual
way such that kids are thinking,
687
00:53:11,460 --> 00:53:14,100
reasoning and sense, making and
improving number sense at the
688
00:53:14,100 --> 00:53:18,720
same time? So there's a way to
notationally, procedurally,
689
00:53:18,720 --> 00:53:23,540
algorithmically, there's a way
to solve this equation. But if
690
00:53:23,540 --> 00:53:25,880
that's the only thing
instructionally we ever do with
691
00:53:25,880 --> 00:53:30,200
this, we're never going to make
major gains. So what would we do
692
00:53:30,200 --> 00:53:35,360
instructionally, conceptually,
to teach this? Talk to me.
693
00:53:36,860 --> 00:53:40,660
So the first thing I would just
ask is, and I learned this from
694
00:53:40,660 --> 00:53:43,660
you, Jonily. Is, what do you
notice?
695
00:53:45,220 --> 00:53:53,980
Beautiful? Notice, what can you
tell me? And then this is, this
696
00:53:53,980 --> 00:53:56,980
is what's scary, because they're
going to tell us things that we
697
00:53:56,980 --> 00:54:00,720
weren't expecting, and then we
have to responsive teach on
698
00:54:00,720 --> 00:54:08,220
that. Do you see? So here's what
I want you to think about. When
699
00:54:08,220 --> 00:54:11,520
you use the tell me about what
do you notice? What do you see?
700
00:54:12,600 --> 00:54:20,100
Do not have an expectation for
yourself to teach on it. That's
701
00:54:20,100 --> 00:54:24,200
why we want to let things
linger. We want to ask those
702
00:54:24,200 --> 00:54:28,580
prompts. Document, even in
writing, on a poster paper, on
703
00:54:28,580 --> 00:54:34,040
the board, document, what kids
are seeing and noticing respond
704
00:54:34,040 --> 00:54:37,640
with that is brilliant, and that
is interesting. I love the way
705
00:54:37,640 --> 00:54:42,160
your brain thinks. Ooh, I've not
thought about it that way. We're
706
00:54:42,160 --> 00:54:47,860
celebrating the thinking that's
the only responsive teaching
707
00:54:47,860 --> 00:54:54,100
we're doing on the day that we
give it. And then after we do
708
00:54:54,100 --> 00:55:00,420
that for about seven minutes or
so, maybe 10 minutes, we. We
709
00:55:00,420 --> 00:55:03,720
then put that away, we move on
to what our regular lesson is of
710
00:55:03,720 --> 00:55:09,180
the day. Then we have time as a
teacher to create the responsive
711
00:55:09,180 --> 00:55:13,320
lesson based on their responses.
Don't try to do it in the same
712
00:55:13,320 --> 00:55:16,560
lesson or class period. That's
what freaks us out, and that's
713
00:55:16,560 --> 00:55:19,140
why some of us are afraid to
implement some of these
714
00:55:19,140 --> 00:55:22,460
strategies. Is we think we have
to then create the responsive
715
00:55:22,460 --> 00:55:27,560
lesson on the spot. We don't let
all that linger. Don't even come
716
00:55:27,560 --> 00:55:32,840
back to it the next day. Wait a
week to come back to it. Email
717
00:55:32,840 --> 00:55:36,260
me and say, here's a picture of
their responses. What do I do
718
00:55:36,260 --> 00:55:40,220
next? I mean, that's the
interactions I'm talking about
719
00:55:40,220 --> 00:55:43,840
with with this transformation
that we're trying to make
720
00:55:43,840 --> 00:55:50,440
instructionally, and then what?
Now and then, what? So what do
721
00:55:50,440 --> 00:55:54,880
we do then, when we start to
teach later, how would you teach
722
00:55:54,880 --> 00:55:55,420
this?
723
00:56:00,640 --> 00:56:04,380
With my third graders, I would
probably ask them, Do you think
724
00:56:04,380 --> 00:56:07,620
it's going to be a whole number?
Do you think it's going to be a
725
00:56:07,620 --> 00:56:12,000
fraction? I would you know, do
you think it's greater than,
726
00:56:12,000 --> 00:56:16,020
less than or equal to a certain
number within the equation? Just
727
00:56:16,020 --> 00:56:20,960
to get their kind of general
understanding of things, yeah,
728
00:56:21,200 --> 00:56:24,920
that's really a different way to
do estimation.
729
00:56:26,360 --> 00:56:30,320
That's a really great, powerful
twist on estimation. Love it.
730
00:56:30,320 --> 00:56:35,360
What else would you do? Yeah,
good. Krista. Krista even brings
731
00:56:35,360 --> 00:56:40,040
in a good sentence starter,
question starter, how does how
732
00:56:40,040 --> 00:56:44,080
does the right side relate to
the left side? Beautiful
733
00:56:44,080 --> 00:56:46,360
prompting. What else would you
do? You're
734
00:56:55,420 --> 00:56:58,420
probably afraid to say of what,
what you would do. Think I'm
735
00:56:58,660 --> 00:57:02,880
going to judge you or something.
Don't be afraid. Don't be
736
00:57:02,880 --> 00:57:05,700
afraid, guys, I use algebra
tiles,
737
00:57:07,080 --> 00:57:09,300
Janet Lane: interesting stuff
like this, so I've always tried
738
00:57:09,300 --> 00:57:13,680
to encourage my kids to draw it.
We we've been trying the same
739
00:57:13,680 --> 00:57:16,860
problem. And thanks to you, I'm
not, like, totally losing it
740
00:57:17,160 --> 00:57:20,420
because I gave a I've been given
a practice OST tip question
741
00:57:20,420 --> 00:57:25,760
today, and like, my test is
Monday, and yesterday they those
742
00:57:25,820 --> 00:57:28,940
one prompt. Two thirds of my
classes got it completely wrong.
743
00:57:28,940 --> 00:57:33,020
And I'm like, Ah. So I took a
deep breath, and I was like, All
744
00:57:33,020 --> 00:57:35,660
right, tell me how you got that
answer. And then, and I'm like,
745
00:57:35,660 --> 00:57:38,660
tell me what you know. And so it
was so interesting, because once
746
00:57:38,660 --> 00:57:42,580
they I said, Tell me about I got
thinking, and I'm like, gosh,
747
00:57:42,580 --> 00:57:46,420
you guys knew this. So, so my
thing is, is we were doing this
748
00:57:46,420 --> 00:57:50,020
like incentive that they they
take the test, and I look at
749
00:57:50,020 --> 00:57:53,620
their answer papers, like with
their work, and if they do it
750
00:57:53,620 --> 00:57:57,760
their way, and then do it my way
with other strategies, then they
751
00:57:57,760 --> 00:58:00,940
get to go to this extra recess.
So that's kind of cool for
752
00:58:01,360 --> 00:58:04,980
seventh graders. But the push is
the thinking. So we've been
753
00:58:04,980 --> 00:58:08,520
doing, you know, like you said,
Stop. What do you notice? What
754
00:58:08,520 --> 00:58:11,700
did you wander? Then answer. And
I've been withholding their
755
00:58:11,700 --> 00:58:16,620
calculators to say, Okay, think
about this first. Yeah, now you
756
00:58:16,620 --> 00:58:19,980
can have calculator, because
beautiful. Grab the calculator.
757
00:58:19,980 --> 00:58:23,360
Go. I'm like, You didn't even
think about that, guys. So
758
00:58:23,420 --> 00:58:27,800
that's what I'm trying to like,
you said, sit and think, but I
759
00:58:27,800 --> 00:58:30,380
would have them draw a picture,
and what do they see when they
760
00:58:30,380 --> 00:58:30,980
draw the picture?
761
00:58:31,340 --> 00:58:35,660
Unknown: Beautiful. Janet makes
a good point. That was little
762
00:58:35,660 --> 00:58:40,180
bit of a hidden message in
there. And that is all year, if,
763
00:58:40,180 --> 00:58:43,780
if students experiences every
day in our classrooms is
764
00:58:43,780 --> 00:58:47,980
solving, solving, solving,
solving, solving, solving, we're
765
00:58:47,980 --> 00:58:53,440
training them to not think. See
if we have less emphasis on
766
00:58:53,440 --> 00:58:57,760
solving all year. If our
emphasis, if our lessons are
767
00:58:57,760 --> 00:59:00,240
structured every day for
thinking, reasoning and sense
768
00:59:00,240 --> 00:59:02,520
making, and that's what we
prioritize, and that's what we
769
00:59:02,520 --> 00:59:06,840
celebrate, then we're going to
change their habit. They're not
770
00:59:06,840 --> 00:59:10,140
going to be able to help it, but
to look at a test question and
771
00:59:10,140 --> 00:59:12,960
think reason and sense make
before they solve. Because
772
00:59:12,960 --> 00:59:17,940
that's the culture and climate
every day. And I can tell this,
773
00:59:17,940 --> 00:59:20,540
we have a brand new fourth grade
teacher in our elementary
774
00:59:20,540 --> 00:59:25,160
school, and she is phenomenal.
She came to our June event last
775
00:59:25,160 --> 00:59:29,360
year. She's fresh out of
college. She started teaching
776
00:59:29,360 --> 00:59:32,000
fourth grade this year. I didn't
get to work with her a lot, but
777
00:59:32,000 --> 00:59:34,160
she came to the June event, and
we have another like
778
00:59:34,160 --> 00:59:36,680
intervention coach at the
elementary that's been
779
00:59:36,800 --> 00:59:39,140
supporting her, because I
haven't been able to do that
780
00:59:39,380 --> 00:59:42,280
well, I've been in her room a
few times just in the last
781
00:59:42,280 --> 00:59:45,340
month, Her room was one of the
rooms we went in when we had the
782
00:59:45,340 --> 00:59:50,020
teacher field trip. And I can
tell her kids have been trained
783
00:59:50,020 --> 00:59:53,980
by her really beautifully,
because I see her kids doing,
784
00:59:53,980 --> 00:59:57,640
thinking, reasoning and sense
making. So when I went in just
785
00:59:57,640 --> 01:00:00,720
on Thursday this week, because I
went back twice this. Last week,
786
01:00:00,960 --> 01:00:05,400
when I went in Thursday, I gave
them a question, and we talked
787
01:00:05,400 --> 01:00:09,420
about, pretend this popped up on
your computer, on your test, and
788
01:00:09,660 --> 01:00:13,500
this is fourth graders. What are
you going to do first? And
789
01:00:13,500 --> 01:00:15,960
they're like, we're going to
look at that piece of it. We're
790
01:00:15,960 --> 01:00:18,960
going to ask ourselves, what do
we see? What do we notice? And
791
01:00:18,960 --> 01:00:23,120
what do we wonder? Okay, now
whether they do this or not is
792
01:00:23,300 --> 01:00:27,080
one thing, but the fact that
they can at least articulate it
793
01:00:28,100 --> 01:00:33,320
is going to train their brain to
look at mathematics in that way,
794
01:00:34,160 --> 01:00:39,260
not as a solving exercise, but
as a thinking exercise. And then
795
01:00:39,260 --> 01:00:41,920
one of the outcomes is we're
going to get a solution
796
01:00:41,920 --> 01:00:46,960
eventually, but we've got to
make sense of it first before we
797
01:00:46,960 --> 01:00:51,220
try to solve anything. And so
you talk about effective Test
798
01:00:51,220 --> 01:00:56,680
Prep. That's effective test
prep, other thoughts, comments,
799
01:00:56,680 --> 01:00:57,580
questions.
800
01:00:58,900 --> 01:01:02,160
I've been doing that this week
with test questions where we
801
01:01:02,160 --> 01:01:05,100
haven't, I haven't given them or
worked through an answer on any
802
01:01:05,100 --> 01:01:07,860
of them. It's just, this is,
what comes up, what are you
803
01:01:07,860 --> 01:01:10,260
going to do? How are you going
to attack it? What's important?
804
01:01:10,260 --> 01:01:13,620
What kind of strategy? What does
the model look like? And then if
805
01:01:13,620 --> 01:01:16,320
they decide, I'll give them
candy, if they come to me with
806
01:01:16,320 --> 01:01:18,360
the answer by the end of the
day, because some of them can't
807
01:01:18,360 --> 01:01:21,860
help themselves, but we haven't,
you know, solved any problems.
808
01:01:21,860 --> 01:01:24,980
We've just been, like, attacking
them and like, getting to that
809
01:01:24,980 --> 01:01:27,500
understanding part. So, yeah,
810
01:01:28,520 --> 01:01:31,100
I know we're just crossing our
fingers at this point, Janet,
811
01:01:31,160 --> 01:01:33,980
I'll be saying a little prayer
for you guys on Monday morning.
812
01:01:33,980 --> 01:01:38,480
Wow, that's, that's like, in two
days. Okay, fantastic. Um, and,
813
01:01:38,480 --> 01:01:43,000
yeah, fantastic. Yeah, really
great prompt. How can you start
814
01:01:43,300 --> 01:01:49,840
look the same? Yeah. Okay, so
this is really good, because you
815
01:01:49,840 --> 01:01:57,460
guys know me. These are some of
my favorite early grade I don't
816
01:01:57,460 --> 01:02:01,440
want to draw, I want to type.
These are some of my early grade
817
01:02:01,440 --> 01:02:07,080
equations that I even give to my
secondary kids. We have
818
01:02:07,080 --> 01:02:12,180
something like, let me get
bigger here. We might have
819
01:02:12,180 --> 01:02:16,260
something like, oh, shoot, I'm
going to this is going to be a
820
01:02:16,260 --> 01:02:24,200
bad one. Okay, hold on, let me
think. Let me think. Three plus
821
01:02:24,380 --> 01:02:30,860
eight equals blank plus
822
01:02:36,020 --> 01:02:46,240
five. Okay, okay, so this is
something that I do specifically
823
01:02:46,420 --> 01:02:54,760
at the earlier grades to promote
unknowns equivalents. This is
824
01:02:54,760 --> 01:02:58,360
more of a thinking, reasoning
and sense making prompt than it
825
01:02:58,360 --> 01:03:03,000
is a solving prompt. I know if
kids have been trained to solve
826
01:03:03,360 --> 01:03:07,200
or reason, and those are
competing interests. I know if
827
01:03:07,200 --> 01:03:10,440
kids, like in a fourth grade
classroom, have been trained to
828
01:03:10,440 --> 01:03:18,120
solve or to reason by giving
this prompt. And if kids put,
829
01:03:19,680 --> 01:03:27,440
I'll draw. Now, if kids put what
is that? If kids put 11 here, I
830
01:03:27,440 --> 01:03:35,420
know that their instruction has
been highly solving. The
831
01:03:35,420 --> 01:03:40,040
priority is solving. I know that
that they believe that the equal
832
01:03:40,040 --> 01:03:44,620
sign is an answer getting
symbol. They do not understand
833
01:03:44,620 --> 01:03:49,720
equivalence and representation
and balance and same as and they
834
01:03:49,720 --> 01:03:54,640
don't understand that these are
two different situations, two
835
01:03:54,640 --> 01:04:00,600
different situations that need
to be exactly the same. They
836
01:04:00,600 --> 01:04:05,460
don't they don't have any idea.
Same as that's really what
837
01:04:05,520 --> 01:04:08,880
equivalence is. So if we want to
promote thinking, reasoning and
838
01:04:08,880 --> 01:04:12,900
sense making with equations, we
need to talk more equivalence
839
01:04:13,140 --> 01:04:21,860
and balancing and structure than
we do solving. So this does not
840
01:04:21,860 --> 01:04:26,720
create an equal. This does not
create the same thing on both
841
01:04:26,720 --> 01:04:32,540
sides. So one of the things that
I do is I give this equation, do
842
01:04:32,540 --> 01:04:39,080
a tell me about then I give this
one, because this is kind of a
843
01:04:39,080 --> 01:04:42,520
precursor to understanding
what's happening in the other
844
01:04:42,940 --> 01:04:49,120
Yeah, very good. Great. Great
comment there, yep, Amy, you
845
01:04:49,120 --> 01:04:52,360
good. You good. Did I give you
good takeaway today for your
846
01:04:52,660 --> 01:04:59,800
Yeah? See, see, Amy, good. When
we read that in class, we always
847
01:04:59,800 --> 01:05:04,620
say. Three plus eight is the
same as blank plus five. See,
848
01:05:04,620 --> 01:05:09,780
yeah, Amy and Amy teaches first
grade. Yep, Amy's always wants
849
01:05:09,780 --> 01:05:14,820
us to get to those numbers. Now,
let me go back to this. Let me
850
01:05:15,600 --> 01:05:22,940
non draw. Let me get okay now,
because I'm in a desperate
851
01:05:22,940 --> 01:05:28,700
attempt to make sure my kids do
know how to solve here's what I
852
01:05:28,700 --> 01:05:32,900
did yesterday, because I'm like
you guys, you know how to do
853
01:05:33,020 --> 01:05:37,340
this. Because if I give them, if
I give my kids equations like
854
01:05:37,340 --> 01:05:41,560
this, they're not putting 11
okay, if I give kids equations
855
01:05:41,560 --> 01:05:44,020
just like this with variables on
both sides that don't have
856
01:05:44,020 --> 01:05:49,360
fractions, they can solve and be
accurate 98% of the time. So
857
01:05:49,960 --> 01:05:53,200
this is frustrating, that they
just freak, that they totally
858
01:05:53,200 --> 01:05:58,540
freak. So this is what I did
yesterday. I did the traditional
859
01:05:58,540 --> 01:06:00,960
This is algebra one. They're
going to take the algebra one
860
01:06:00,960 --> 01:06:04,860
course. And I'm like, what would
you do? Like, if these, if there
861
01:06:04,860 --> 01:06:07,140
weren't fractions, and they're
like, Oh, we would take away
862
01:06:07,140 --> 01:06:09,720
three from both sides. I'm like,
Okay, well, then why can't you
863
01:06:09,720 --> 01:06:13,680
do that? They're like, well, we
can. Like, well, then do it.
864
01:06:13,680 --> 01:06:16,680
Like, what the freak are you
doing? I think I said that to
865
01:06:16,680 --> 01:06:24,020
them. Now this is important.
When we take away three from
866
01:06:24,020 --> 01:06:29,480
both sides, I always say to my
kids, what's the point? What's
867
01:06:29,480 --> 01:06:33,800
the purpose of that? What did we
want to try to do? They're like,
868
01:06:33,800 --> 01:06:37,280
well, we wanted to to remove
this three. We wanted to, like,
869
01:06:37,280 --> 01:06:41,020
move it to the we wanted to
remove it. How do we remove a
870
01:06:41,020 --> 01:06:48,040
plus three. What goal do we want
to get? To remove it? Well, for
871
01:06:48,040 --> 01:06:54,160
a plus three, we want to get to
a zero. This goes back to and
872
01:06:54,160 --> 01:06:58,480
I've taught on this numerous
times, the importance of zeros
873
01:06:58,480 --> 01:07:02,700
and ones, the importance of
zeros and ones. So if I want to
874
01:07:02,760 --> 01:07:08,640
get rid of eliminate a plus
three, I have to make a zero. I
875
01:07:08,640 --> 01:07:16,320
have to make a zero. Now if I
have 3x and I want to eliminate
876
01:07:16,320 --> 01:07:24,920
a times three, I have to make a
one. So there's a train. There's
877
01:07:24,920 --> 01:07:27,620
many trainings that I do, that I
talk about the importance of
878
01:07:27,620 --> 01:07:33,320
zeros and ones in mathematics.
So here, let's say the half
879
01:07:33,320 --> 01:07:35,720
wasn't there, 13 minus 310,
880
01:07:37,400 --> 01:07:45,100
and a half. Okay, so what's the
same as what's the same as now?
881
01:07:45,400 --> 01:07:50,020
So we've got x over here equals
10 and a half
882
01:07:55,060 --> 01:08:03,060
plus 1/4 X. Here was another
problem I gave my kids last
883
01:08:03,060 --> 01:08:17,280
week. I said y equals x over
four plus seven. Okay. And I
884
01:08:17,280 --> 01:08:19,980
said, What's the slope? Now my
kids know that y equals mx plus
885
01:08:19,980 --> 01:08:22,760
b is a linear function degree
one. They know they know it
886
01:08:22,760 --> 01:08:25,880
makes a line. They know that
when x is zero, you have a y
887
01:08:25,880 --> 01:08:28,580
intercept, so it's going to
cross the y axis at seven.
888
01:08:28,580 --> 01:08:32,720
That's the 07 point. But this
trips them up because of the way
889
01:08:32,720 --> 01:08:37,700
this is written. The way that
this is written, they want the
890
01:08:37,700 --> 01:08:45,760
slope m to be one because the
coefficient of x looks like it's
891
01:08:45,760 --> 01:08:49,660
one, but it's not. So you have
to understand the different
892
01:08:49,660 --> 01:08:57,100
representations that this
actually means this. So because
893
01:08:57,100 --> 01:09:01,560
I had done this problem earlier
in the week, I brought this back
894
01:09:01,560 --> 01:09:05,820
and connected it to this. So the
more connections we can make to
895
01:09:05,820 --> 01:09:09,480
other types of problems, the
better associations they're
896
01:09:09,480 --> 01:09:13,260
going to make as well. So now
we're boiled down to this, and
897
01:09:13,260 --> 01:09:18,240
then my kids are like, Oh, well,
we need to get the x's, okay.
898
01:09:18,480 --> 01:09:22,880
Now what they wanted to do here
with the plus 1/4 X, they wanted
899
01:09:22,880 --> 01:09:27,320
to multiply by four, which is
great if I wanted to get a one.
900
01:09:28,520 --> 01:09:32,000
Now I did the multiplying by
four, and I entertained them
901
01:09:32,000 --> 01:09:35,240
with that. And then I said,
okay, then we get 4x and we get
902
01:09:35,240 --> 01:09:37,940
this multiplied by four. And
then over here, what do we get?
903
01:09:37,940 --> 01:09:39,920
And they're like, Well, that
went away. No, it didn't,
904
01:09:39,920 --> 01:09:44,080
because 1/4 times four is one.
Now I have 1x over here. Now I
905
01:09:44,080 --> 01:09:48,280
have 4x here and but it's okay.
We don't have to go backwards.
906
01:09:48,400 --> 01:09:52,240
We can multiply everything by
four, and it's just fine. That's
907
01:09:52,240 --> 01:09:59,440
legal, but we could have done
something else that is going to
908
01:09:59,440 --> 01:10:04,680
put our. X's together. Okay, so
if we think of this as our
909
01:10:04,680 --> 01:10:07,860
chunk, and we want to remove
this chunk, we have a plus
910
01:10:07,860 --> 01:10:11,040
chunk. Again, we have how do we
get rid of a plus chunk? We
911
01:10:11,040 --> 01:10:15,360
minus the chunk. Okay, now I'm
being very traditional here,
912
01:10:15,360 --> 01:10:17,640
blah blah, but I want to make
this point, and then I'm going
913
01:10:17,640 --> 01:10:21,740
to stop with this traditional
nonsense. Here's the point I
914
01:10:21,740 --> 01:10:26,960
want to make. Now, my kids know
that this is not zero. Many
915
01:10:26,960 --> 01:10:31,640
algebra one students think that
this is zero minus a fourth. And
916
01:10:31,640 --> 01:10:33,980
I'm like, but how many x's
what's the coefficient? It's not
917
01:10:33,980 --> 01:10:37,640
written. It's one. You actually
have 1x now this goes back to
918
01:10:37,640 --> 01:10:41,560
what Janet was talking about,
because if you use algebra
919
01:10:41,560 --> 01:10:49,120
tiles, these x terms are green
rectangles. A green rectangle,
920
01:10:49,120 --> 01:10:55,240
Algebra tile has a height of x
and a length of one. We call the
921
01:10:55,300 --> 01:11:01,440
area of this. We call the name
of this green rectangle x. So if
922
01:11:01,440 --> 01:11:07,620
I want to represent 3x i would
need this x, and I would need
923
01:11:07,620 --> 01:11:10,260
three of them. Now I could draw
three rectangles, but I teach my
924
01:11:10,260 --> 01:11:13,740
kids to shorthand this. There
are three rectangles. That's
925
01:11:13,740 --> 01:11:22,640
what 3x look like. So over here
I have 1x so I just have one of
926
01:11:22,640 --> 01:11:28,880
these here, which shows that you
have the coefficient of one and
927
01:11:28,880 --> 01:11:32,180
not zero, because there actually
is one. There is a green
928
01:11:32,180 --> 01:11:36,920
rectangle over here. Oh, I don't
even have a whole green
929
01:11:36,920 --> 01:11:41,740
rectangle. I have a fourth. I
didn't draw that very well, but
930
01:11:41,740 --> 01:11:45,820
you get the idea. Okay, so this
is, this is how much I have of
931
01:11:45,820 --> 01:11:49,540
that rectangle, or that paper
strip, or whatever it is that
932
01:11:49,540 --> 01:11:52,660
we're using that gives that
conceptual, concrete,
933
01:11:52,660 --> 01:12:00,900
situational, contextual visual
to this equation. Now I'm going
934
01:12:00,900 --> 01:12:05,640
to go ahead and stop here,
because my kids also were
935
01:12:05,640 --> 01:12:09,120
successful once they know that
was one minus 1/4 is three
936
01:12:09,120 --> 01:12:11,220
fourths. Now I'm not going to go
any further with that
937
01:12:11,220 --> 01:12:19,860
traditional, because here's what
I want to do. Let me I want I
938
01:12:19,860 --> 01:12:25,400
just Oh my gosh. Okay, fine,
I'll do it this way. Okay, let's
939
01:12:25,400 --> 01:12:33,260
go down here and start over.
Okay. Now what my students in
940
01:12:33,260 --> 01:12:36,500
first grade, third grade, fourth
grade, sixth grade, eighth
941
01:12:36,500 --> 01:12:40,460
grade, algebra, what my students
know at every grade level is
942
01:12:41,900 --> 01:12:48,100
equations. Are Jesse and K
money. So this side of the
943
01:12:48,100 --> 01:12:51,280
equation is Jesse's money.
944
01:12:55,000 --> 01:12:59,380
And so this side of the equation
says that Jesse starts with $3
945
01:13:00,040 --> 01:13:03,120
and I know that that's the
starting number for Jesse,
946
01:13:03,600 --> 01:13:07,380
because that's when x is zero.
That's on day zero, when x is
947
01:13:07,440 --> 01:13:13,680
zero. Jesse has $3 that is also
y intercept. The y intercept of
948
01:13:13,680 --> 01:13:18,960
Jesse's linear function is
three, because a y intercept
949
01:13:18,960 --> 01:13:22,220
happens when x is zero. Now I'm
not telling third graders this,
950
01:13:22,400 --> 01:13:30,620
but I'm telling you this because
you can use x as this is, and
951
01:13:30,620 --> 01:13:39,080
you can notate it however you
want. This can be how much money
952
01:13:39,080 --> 01:13:44,920
Jesse or Kay gets or loses every
day. And that could just be
953
01:13:45,220 --> 01:13:49,000
your, you know, emoji number,
whatever you want to call it,
954
01:13:49,420 --> 01:13:53,500
the number that doesn't have
that variable or unknown. That's
955
01:13:53,500 --> 01:13:57,280
called a constant, and that's
the starting it's plus three. So
956
01:13:57,280 --> 01:14:02,580
Jesse starts with $3, a day. And
then how many of these were
957
01:14:02,580 --> 01:14:12,000
there? There were one. So Jesse
gets $1 she earns $1 every day.
958
01:14:12,660 --> 01:14:16,740
Now you could say that this is
the rate, and talk about rate
959
01:14:16,740 --> 01:14:21,380
speed, 60 miles per hour, but
you don't have to. You can just
960
01:14:21,380 --> 01:14:24,920
say that the way that this is
notated, that means, because
961
01:14:24,920 --> 01:14:29,480
there's 1x that Jesse's going to
get $1 a day. So on day zero,
962
01:14:29,480 --> 01:14:35,360
Jesse has $3 day one, Jesse has
$4 day two, Jesse has $5 day
963
01:14:35,360 --> 01:14:42,100
three, Jesse has $6 this is the
model and mindset of instruction
964
01:14:42,100 --> 01:14:49,540
in Singapore. What they do in
Singapore is they give typical
965
01:14:49,540 --> 01:14:53,980
algebra one questions to
elementary students, but they
966
01:14:53,980 --> 01:15:00,840
frame it in a context that
allows access for. Graders,
967
01:15:00,900 --> 01:15:06,360
third graders to do an equation
like this, but in a different
968
01:15:06,360 --> 01:15:11,100
way that's going to target the
standards at elementary now we
969
01:15:11,100 --> 01:15:14,160
at minds on math. We add a
different level to that. We
970
01:15:14,580 --> 01:15:18,420
reference task it, we
contextualize it as a Jesse and
971
01:15:18,420 --> 01:15:24,320
K problem. So now, if I go over
here, let me do a different
972
01:15:24,320 --> 01:15:28,640
color, and I'll save this and
I'll send you these notes. If
973
01:15:28,820 --> 01:15:36,740
this is Kay's money situation,
what's K starting? Number K
974
01:15:36,740 --> 01:15:43,180
starts with 13 and a half
dollars. Now what we might say
975
01:15:43,240 --> 01:15:55,540
is, oh, that is $13.50 if kids
want to do it that way. Okay, so
976
01:15:55,720 --> 01:15:59,980
K starts with $13.50 now what I
could do at this point is ask my
977
01:15:59,980 --> 01:16:03,720
students, what math questions
can we create? And so some of
978
01:16:03,720 --> 01:16:07,920
those might be, who starts with
more money? Who gets more money?
979
01:16:07,920 --> 01:16:11,340
Who loses money? Who this? Who
that? Okay, how much money does
980
01:16:11,340 --> 01:16:15,000
Jesse have on day 100 how much
money does Kay have on day 100
981
01:16:17,160 --> 01:16:21,980
so if I line this up, when this
number is zero, when this is
982
01:16:21,980 --> 01:16:26,720
zero, when this is not there,
when the 1/4 whatever, no days
983
01:16:26,720 --> 01:16:32,000
have gained any money yet. This
is Day Zero. I start to line up
984
01:16:33,800 --> 01:16:39,200
this relationship here. So now
this, this one is is harder. K
985
01:16:39,200 --> 01:16:43,660
is harder, I admit So on day
one, we need to know how much
986
01:16:43,660 --> 01:16:49,540
money K has. But how much money
is K gaining or losing every
987
01:16:49,540 --> 01:16:55,300
day? Well, K is gaining money.
So k is gaining money a fourth
988
01:16:55,360 --> 01:17:01,740
of $1 every day, a fourth of $1
every day. Well, how much money
989
01:17:01,740 --> 01:17:05,460
is that every day? Okay, well,
that's a we can leave it in
990
01:17:05,460 --> 01:17:12,300
fraction, or we could say, Kay's
getting 25 cents. Come on. I'm
991
01:17:12,300 --> 01:17:17,400
trying to do this with my just
mouse pad. Come on. Jay Z, make
992
01:17:17,400 --> 01:17:18,540
a two. Okay.
993
01:17:22,739 --> 01:17:29,359
Okay. So k is gaining 25 cents a
quarter every day. Now, if you
994
01:17:29,359 --> 01:17:31,999
teach second graders, third
graders, and you're trying to
995
01:17:31,999 --> 01:17:35,959
get them to understand money,
what a better way to do money
996
01:17:36,079 --> 01:17:39,679
than to embed it in a situation
that is very algebraic thinking,
997
01:17:39,679 --> 01:17:47,439
very skip counting. Ish, very
rate infused that is is grounded
998
01:17:47,439 --> 01:17:50,919
in unknowns and equivalents,
like look at how many birds
999
01:17:50,919 --> 01:17:53,919
you're killing with one stone.
Not that I advocate for killing
1000
01:17:53,919 --> 01:17:57,579
birds, but I advocate for
efficiency of instruction. I
1001
01:17:57,579 --> 01:18:02,339
advocate for using one example,
one situation to teach lots of
1002
01:18:02,339 --> 01:18:06,299
different standards. And when
crystal said, I saw the impact
1003
01:18:06,359 --> 01:18:09,839
of the same task, the same
thing, no matter what it is
1004
01:18:09,959 --> 01:18:12,599
being done at every grade level,
and being effective and
1005
01:18:12,599 --> 01:18:18,299
powerful, this is what crystal
is talking about. So on day one,
1006
01:18:18,599 --> 01:18:22,999
on day zero, if Kay had $13.50
and we get 25 cents more, then
1007
01:18:22,999 --> 01:18:29,179
we have $13.75 and let me know
if I make a mistake
1008
01:18:29,179 --> 01:18:32,359
mathematically, because I do
that a lot. On day two, how much
1009
01:18:32,359 --> 01:18:37,159
money does K have? Well, we add
another 25 cents, $14 on day
1010
01:18:37,159 --> 01:18:43,179
three, how much money does K
have? $14.25 or I could write 14
1011
01:18:43,179 --> 01:18:46,059
and a fourth. I can go back and
forth on variations of
1012
01:18:46,059 --> 01:18:50,859
representation. Doesn't matter.
Okay. Now, after we're doing
1013
01:18:50,859 --> 01:18:55,419
this together as a class, I'm
going to then ask again, say my
1014
01:18:55,419 --> 01:19:00,219
favorite words, tell me about
what you see. What do you see?
1015
01:19:00,459 --> 01:19:04,619
What do you notice? Make sense
of it again. We're going to
1016
01:19:04,619 --> 01:19:08,219
stop. And we started to, kind of
like do some solving and
1017
01:19:08,219 --> 01:19:11,819
counting. And so every time we
start to move to solving and
1018
01:19:11,819 --> 01:19:15,299
answer getting we, as the
instructor, need to back up and
1019
01:19:15,299 --> 01:19:17,939
say, Wait a minute. How do I
bring it back to thinking,
1020
01:19:17,939 --> 01:19:20,959
reasoning and sense making? So I
get this started, and then I
1021
01:19:20,959 --> 01:19:25,159
say, tell me about what do you
see, what do you notice in the
1022
01:19:25,159 --> 01:19:29,599
chat right now, I want all of
you to type in, what do you see
1023
01:19:29,599 --> 01:19:33,439
and notice about what just
happened. So type that in the
1024
01:19:33,439 --> 01:19:37,939
chat. Tell me about this
structure. Tell me about these
1025
01:19:37,939 --> 01:19:42,399
numbers. What do you see and
what do you notice about what
1026
01:19:42,399 --> 01:19:43,599
just happened?
1027
01:19:46,120 --> 01:19:51,220
What are your thoughts? Come on
now. Chat it up.
1028
01:20:07,840 --> 01:20:13,840
Oh, nice, both sides are
increasing at the same rate.
1029
01:20:17,260 --> 01:20:20,540
Good, yep.
1030
01:20:29,899 --> 01:20:32,719
Another thing I ask my students
as they're thinking reasoning
1031
01:20:32,719 --> 01:20:37,159
and sense making is, what other
math questions could we ask?
1032
01:20:39,979 --> 01:20:46,119
Nice j is increasing faster than
k, even though K began greater.
1033
01:20:46,119 --> 01:20:51,279
So what does that mean? What
does it all mean? Basil,
1034
01:21:02,939 --> 01:21:08,219
a nice Yep, will Jay end up with
more at some point and when?
1035
01:21:08,219 --> 01:21:10,019
Crystal, yeah, this is amazing.
1036
01:21:20,520 --> 01:21:28,280
Oh, yeah, okay, okay. Now here's
where your default instruction
1037
01:21:28,280 --> 01:21:33,200
is going to kick in. If you do
this in your classroom, and you
1038
01:21:33,200 --> 01:21:38,060
get to this point, your default
because you have habitual,
1039
01:21:38,060 --> 01:21:41,380
traditional instruction, what's
going to happen now is you're
1040
01:21:41,380 --> 01:21:43,780
going to have you're going to
have kids keep extending, and
1041
01:21:43,780 --> 01:21:47,260
you're going to have them answer
these questions. What I'm
1042
01:21:47,260 --> 01:21:53,740
telling you is, don't, when you
get to this point in your
1043
01:21:53,740 --> 01:21:57,400
instruction, in your class,
you're going to be like, Okay,
1044
01:21:58,360 --> 01:22:02,280
that was so beautiful today. I'm
so proud of you guys. We
1045
01:22:02,280 --> 01:22:05,580
realized a lot of different
things. We're going to put that
1046
01:22:05,580 --> 01:22:10,080
away. And I want you to take out
yesterday's homework that has
1047
01:22:10,080 --> 01:22:12,660
nothing to do with this. Okay, I
want you to go on to your
1048
01:22:12,660 --> 01:22:16,860
regular lesson now that if you
leave here with nothing else
1049
01:22:16,860 --> 01:22:20,360
today, I want you to hear me on
this. You're going to be like,
1050
01:22:20,420 --> 01:22:23,480
Oh, but the kids want to finish.
Well, the kids want to keep
1051
01:22:23,480 --> 01:22:27,320
going. I finally got them
focused and engaged, then cut it
1052
01:22:27,320 --> 01:22:27,800
off.
1053
01:22:29,659 --> 01:22:36,079
There are brain reasons for
this. There are cognitive
1054
01:22:36,079 --> 01:22:37,519
reasons for this.
1055
01:22:39,199 --> 01:22:42,579
We are shaping the brain, and we
are shaping the mathematical
1056
01:22:42,579 --> 01:22:47,319
mind. So right now, as soon as
you have the kids in the palm of
1057
01:22:47,319 --> 01:22:50,019
your hands, as soon as you have
them right where you want them,
1058
01:22:50,319 --> 01:22:53,199
you're going to stop and you're
going to be like, Okay, we're
1059
01:22:53,199 --> 01:22:56,139
going to put this away, and
we're going to go on to our
1060
01:22:56,139 --> 01:22:58,779
lesson of the day. Now you're
going to have kids still working
1061
01:22:58,779 --> 01:23:03,119
on it and trying to hide it.
Don't call them out. Just ignore
1062
01:23:03,119 --> 01:23:06,539
it. You're going to have kids
still talking about it. You're
1063
01:23:06,539 --> 01:23:10,679
going to have kids going, Oh,
but I know where they're going
1064
01:23:10,679 --> 01:23:20,179
to go do math without you asking
them to do math. How amazing is
1065
01:23:20,179 --> 01:23:24,019
that they're going to talk about
this at lunch. They're going to
1066
01:23:24,019 --> 01:23:27,799
come in the next day with the
answer, and when they give you
1067
01:23:27,799 --> 01:23:31,399
answers, you're going to be
like, That's interesting, you
1068
01:23:31,399 --> 01:23:34,339
know what? Let's start adding
that to an answer list. Let's
1069
01:23:34,339 --> 01:23:37,099
start documenting that. We'll
come back to this next week. But
1070
01:23:37,099 --> 01:23:43,299
let's celebrate what they're
doing, but do not confirm or
1071
01:23:43,299 --> 01:23:47,739
deny their answers. There are
some responses that are going to
1072
01:23:47,739 --> 01:23:51,819
negate all of the work that
you've done. You want to let
1073
01:23:51,819 --> 01:24:00,359
this linger. See, I'm going to
let this linger. You're going to
1074
01:24:00,359 --> 01:24:03,899
let this Lisa, beautiful,
beautiful, because that's what
1075
01:24:03,899 --> 01:24:09,239
we end up doing with Jesse and
Kay, is we graph Jesse's system
1076
01:24:09,239 --> 01:24:12,419
of equations. That's what this
is. We graph Jesse's function,
1077
01:24:12,479 --> 01:24:16,499
we graph K's function, and
that's just good practice in
1078
01:24:16,499 --> 01:24:21,799
slope, intercept, like boom. And
then we start asking, are we
1079
01:24:21,799 --> 01:24:25,339
going to have parallel lines or
non parallel lines? Parallel
1080
01:24:25,339 --> 01:24:28,279
lines, same slope? No solution.
We don't have the same slope
1081
01:24:28,279 --> 01:24:30,439
here. So we are going to
probably have a solution
1082
01:24:30,439 --> 01:24:32,779
somewhere. What is that
solution? Is the solution going
1083
01:24:32,779 --> 01:24:35,299
to be in the future or in the
past or in the negatives? And
1084
01:24:35,299 --> 01:24:40,039
what is this so much, so much we
can do at algebra one and Lisa,
1085
01:24:40,099 --> 01:24:44,559
imagine if your seventh grade,
sixth grade, fifth grade, fourth
1086
01:24:44,559 --> 01:24:47,139
grade, third grade, second
grade, first grade. Teachers in
1087
01:24:47,139 --> 01:24:51,639
your building did Jesse and K
every year in lots of
1088
01:24:51,639 --> 01:24:55,479
variations. So by the time kids
came to you in algebra one
1089
01:24:56,199 --> 01:25:01,139
they've already had a lot of
this mentality. Mm. Can you
1090
01:25:01,139 --> 01:25:05,999
imagine what that would look
like? It's really beautiful
1091
01:25:06,239 --> 01:25:09,479
because the cohorts I got rid of
the data here, but the cohorts
1092
01:25:09,479 --> 01:25:12,119
where we've seen this extreme
data, that's what we've been
1093
01:25:12,119 --> 01:25:19,199
doing in schools, and we've
earned 1520, 30, 40% higher test
1094
01:25:19,199 --> 01:25:25,939
score rates by doing exactly
this. All right, friends, it is
1095
01:25:25,939 --> 01:25:29,059
almost 11. Here's what I want to
hear right now. Type it in the
1096
01:25:29,059 --> 01:25:34,759
chat or unmute. What were your
takeaways from today? What were
1097
01:25:34,759 --> 01:25:38,239
your ahas? What are you going to
take away from today? What did
1098
01:25:38,239 --> 01:25:42,039
you learn from today? What
solidified your learning. So
1099
01:25:42,039 --> 01:25:45,159
what are your takeaways? Unmute
or type them in the chat or
1100
01:25:45,159 --> 01:25:46,299
both. Go ahead,
1101
01:25:51,520 --> 01:25:55,960
I just have something about the
field trip. Yeah, I'm going to
1102
01:25:55,960 --> 01:25:58,840
bring in another reference
reference task, but the painted
1103
01:25:58,840 --> 01:26:04,200
cube, so I had my the block that
you were in with came back on
1104
01:26:04,260 --> 01:26:09,000
from spring break, okay? And one
of their first questions to me
1105
01:26:09,060 --> 01:26:14,100
was, Hey, are we ever going to
do that cube problem again? And
1106
01:26:14,160 --> 01:26:17,340
not only that, but then my other
block that they kind of
1107
01:26:17,340 --> 01:26:21,140
intermingle with was like, Hey,
I heard that you did this cute
1108
01:26:21,140 --> 01:26:24,260
problem, like, are we ever going
to have a chance to do that
1109
01:26:24,260 --> 01:26:27,080
again? So, you know, they've
been talking about it. It's just
1110
01:26:27,500 --> 01:26:28,280
interesting.
1111
01:26:28,640 --> 01:26:35,000
That's cool. That is cool.
Lingering is so powerful. Let it
1112
01:26:35,000 --> 01:26:39,860
linger. Other takeaways, Hannah
says, Teach based on thinking
1113
01:26:39,860 --> 01:26:42,760
more than salt, yeah, beautiful
other takeaways.
1114
01:26:57,520 --> 01:27:00,600
Yep, thinking, reasoning and
sense making is the key and only
1115
01:27:01,200 --> 01:27:06,120
that's not on the kids, that's
not on the kids, that is on our
1116
01:27:06,120 --> 01:27:10,620
instructional facilitation and
delivery. So if kids don't have
1117
01:27:10,620 --> 01:27:13,800
thinking, reasoning and sense
making, if they don't persevere,
1118
01:27:13,800 --> 01:27:18,120
if they don't initiate, that's
on us, not on them, we have not
1119
01:27:18,120 --> 01:27:23,120
created the environment, culture
and habits for them to default
1120
01:27:23,120 --> 01:27:26,720
to thinking, reasoning and sense
making. A lot of times, I hear
1121
01:27:26,720 --> 01:27:29,180
these kids, they just don't
start. They don't know where to
1122
01:27:29,180 --> 01:27:32,660
begin. They don't they're so
helpless. They're done. They
1123
01:27:32,660 --> 01:27:36,860
didn't do that to themselves.
Because toddlers don't have any
1124
01:27:36,860 --> 01:27:40,580
of that. They toddlers don't
have any of that effectiveness.
1125
01:27:41,900 --> 01:27:47,380
School. Has created that in our
students that's on us, guys
1126
01:27:47,740 --> 01:27:51,940
that's on us. Get students
brains thinking, leave them
1127
01:27:51,940 --> 01:27:55,360
hanging. Yeah, that's important.
Focus factors, fractions
1128
01:27:55,360 --> 01:27:58,720
function, and we have more
explicit, streamlined approaches
1129
01:27:58,720 --> 01:28:01,980
to being able to focus on those.
Yep, very good takeaways.
1130
01:28:01,980 --> 01:28:06,300
Balance between procedures.
Yeah, just do it like, just jump
1131
01:28:06,300 --> 01:28:09,480
in. Don't be like, you don't
know what's going to happen. As
1132
01:28:09,480 --> 01:28:12,960
a teacher, I know that's scary,
but I've given you the out. Once
1133
01:28:12,960 --> 01:28:15,180
you get to a point where you
don't know what to say and do
1134
01:28:15,180 --> 01:28:17,760
next, and you feel yourself
defaulting to telling and
1135
01:28:17,760 --> 01:28:20,840
teaching, then you want to stop
and be like, Hey, we're gonna
1136
01:28:20,840 --> 01:28:26,000
finish that another day,
insisting that my students pre
1137
01:28:26,000 --> 01:28:29,600
read, understand, yeah, yeah.
What is it asking think, reason
1138
01:28:29,600 --> 01:28:33,740
and sense, making new way to
word, make rectangles now. Okay,
1139
01:28:33,740 --> 01:28:36,320
good, good. Amy, yeah, and
you're going back to third
1140
01:28:36,320 --> 01:28:40,100
grade. Awesome. Oh, that seems
like it's going well, that's
1141
01:28:40,100 --> 01:28:44,860
excellent. Wonderful. Okay, you
guys, I've got a pretty hard
1142
01:28:44,860 --> 01:28:48,880
stop today. Usually we stay on
and I give you some more time,
1143
01:28:48,880 --> 01:28:51,520
and then, like all of you, end
up staying for like another
1144
01:28:51,520 --> 01:28:54,100
hour. I can't do that today. I
have a hard stop time today.
1145
01:28:54,580 --> 01:28:59,260
Although I love you, I love you
so much. Mark down, April 24
1146
01:28:59,800 --> 01:29:05,760
there will be the next webinar,
a webinar with upsell. Saturday
1147
01:29:05,760 --> 01:29:08,580
maths. I usually don't have any
upsell. I mean, this is just
1148
01:29:08,640 --> 01:29:12,180
real organic like Saturday math
is free. There's nothing I'm
1149
01:29:12,180 --> 01:29:16,260
selling to you. But on April 24
there will be an upsell, and it
1150
01:29:16,260 --> 01:29:19,140
will be a bundled package of
what you can jump into for the
1151
01:29:19,140 --> 01:29:24,020
2026 2027 school year. I really
want you to be here on April 24
1152
01:29:24,320 --> 01:29:26,600
but I can't give you any link
right now. Nothing is up for
1153
01:29:26,600 --> 01:29:29,660
registration yet. It'll be
coming up later this week. So I
1154
01:29:29,660 --> 01:29:33,260
will send you the information
for the April 24 webinar this
1155
01:29:33,260 --> 01:29:36,680
week. Once I have the link, I'll
follow up and send you the notes
1156
01:29:36,680 --> 01:29:39,980
from today, the PDF notes from
today. And I want to thank all
1157
01:29:39,980 --> 01:29:42,460
of you for being here and
spending your Saturday morning
1158
01:29:42,460 --> 01:29:45,040
with us. We will have another
Saturday math in May, and you
1159
01:29:45,040 --> 01:29:48,400
will definitely get that
information. Also love you guys.
1160
01:29:48,400 --> 01:29:53,200
Bye, bye. Good luck with
testing. Enjoy the final 30 some
1161
01:29:53,200 --> 01:29:56,740
days of school and have a great
summer, but hope to see you in
1162
01:29:56,740 --> 01:29:57,880
May. Bye, everybody. You.
