WEBVTT
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Good day, folks, and welcome to another edition of Inside Santa Fe Public Schools Podcast.
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I am Joe Abeta, and today with us is the STEM coordinator for Santa Fe Public Schools, Arturo Duhan.
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How are you doing, Arturo?
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Doing well, Joe.
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How about you?
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I'm doing good, good, good.
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Thank you for joining us today.
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Um, so you're here today because the school is starting a new math curriculum.
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Is that right?
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That is correct.
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Um we are we are excited to implement uh what is going to be our new math instructional material.
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Um and and this one promises to to kind of like shift the framework that we we usually have going on in the classrooms, okay um, to something that is more discovery approached.
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Okay.
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So that's awesome.
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And and so what was the I guess what was the purpose of it?
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Was it something that you your office kind of said, hey, we need to we need to make math a little bit more easier or more uh understanding to our students.
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How can we do that?
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Is that what was that the purpose?
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Was it because we weren't getting the results that we wanted with the previous one?
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Yeah, definitely.
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So so last year we had conversations with uh principals from all of our all of our schools in the district.
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Uh-huh.
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And one of the recurring things that would come up was um our teach our students, our students don't have that deep understanding of the mathematical concept.
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And so we had we had principals from uh Capital High School where they would say, uh our students are awesome, however, when they engage with geometry, when they engage with with um algebra concepts, uh we feel that there are foundational skills missing there.
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And so uh that was like the beginning of of a journey.
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Um last year we also had our math, our math adoption, um, our math instructional material adoption.
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Uh-huh.
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And and the committee that came together was which was comprised of uh um uh general education teachers, um uh district staff, coaches, um, principals, they they um they kind of came together to share what their vision of how of what would be considered high quality math instruction.
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Okay.
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What what would that look like?
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What what is it that we've seen that works in in the classroom?
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And so um uh Santa Fe Public School's um math vision was developed.
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Okay.
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That vision was basically what drove the adoption committee.
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Um, they used that lens when they would look at the different instructional material that was offered.
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And and there there were there were like three or four instructional materials that that kind of like align with that vision.
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Okay.
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Um, but really at the end of the day, it was this this one instructional material that that really um gathered all those aspects of that vision in in a well-rounded uh uh material.
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That seems like a a huge task, man, and a huge responsibility on on the committee, right?
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That did that, right?
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To get together the task force that got in together.
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So I I would assume then that like because you want to be careful about what you're bringing in, and there was just like a lot of, I'm sure, sessions of like, why why can't we use this one?
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Why should we use this one?
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Um how did I mean how long did it take for you guys to it took you guys over a year to figure this out to get the to get the right one?
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Or how what was the process like?
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Well, the the process was um there um the public education department has like a list of approved material.
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So so uh many vendors go through through the through the PED, and then the PED kind of like does the the the first part of that work, right?
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And so they they say, okay, these this list of uh high quality instructional materials are actually considered high quality instructional materials.
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Okay.
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And so we go from that list and and teachers look at different aspects of the of the material.
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Uh um how uh what what resources does it offer?
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Um what uh supports the that do teachers get with the instructional material?
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Does it have a digital component?
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Uh does it have activities uh in or or material that families can get so that they can support students?
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And after they look at the ones that that kind of check off all these boxes, yeah, then they they got a chance of test driving it.
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So some teachers uh uh got to teach an actual lesson from from the one from the materials that they were considering.
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And and that was a game changer because they they thought that at first, oh, this material is is great, but when they would actually teach the lesson, they found that there were some things missing.
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Yeah, that's other instructional material that they were ready to discard once they taught the lesson.
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It was like, oh, wait a minute.
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Um, this really felt differently in a good sense.
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Um, so they went through all of that.
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Um, we they they made the recommendation, and that was sent to uh Dr.
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Griffin, our our superintendent, and and ult and she made the ultimately the decision.
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What was the one thing that stuck out from the teachers with this new program that they really liked?
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So one of the things that stuck out was um was the how the instructional material prioritizes developing conceptual understanding.
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And one might ask, well, what is that?
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Yeah.
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So to give a a very um uh practical example, um, if I were to ask you, hey Joe, um at which grade level do you think that a student learns the standard algorithm for adding and subtracting?
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And by that I mean, you know, when when you have like a uh two-digit um um uh um you you have two digits and two digits, and you add the ones first, the ones in the in the digits and the ones column, and then if you if you go over 10, you carry over to the tens column and you add which grade level do you think that should be taught?
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Well, if I'm thinking of my old man self of when I I learned, I would have to think I would think that my deepest memory would be probably first grade.
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We dabbled in it, I would think, but that was back in 76.
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Okay, okay.
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So I'm thinking first grade, but now kids are a little more complex and they're there there's more accessibility to technology and information.
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So maybe kindergarten, maybe kindergarten.
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Okay, so according to Common Core, that is a fourth grade standard.
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Oh wow, yeah, okay, okay.
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So um common core establishes that students should not be exposed to the standard algorithm for adding and subtracting until they reach fourth grade.
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Wow.
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And okay, and and it's it's um it's not uncommon that answer that you just provided, because even um teachers across the nation, when they are asked uh that same question, they say first grade, second grade, and then when they are given the answer, they're like, whoa, whoa, whoa, no, wait a minute.
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I have a son in second grade, and that's exactly what my son is is getting.
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That my son is getting uh um um homework or worksheets where they are uh you know practicing adding using the standard algorithm.
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And when you look at the instructional material, well, no wonder why why teachers are doing that.
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The instructional material is is is leading the students and teachers to using the standard algorithm for adding and subtracting.
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Common core, well, common core, but uh common core is founded on research.
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Yeah.
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Um all the research says that from kindergarten all the way up to fourth grade, students need to um, what I said, they need to develop conceptual understanding.
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And what does that mean?
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So um some examples will be um if students students need to structure number, right?
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Uh they need to know how much is um uh three and five.
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And and getting the right answer is not the the ultimate uh uh objective.
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Students can go uh one, two, three.
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You know, we I've seen first grade students that that that do precisely that.
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Yeah, they they first let's say if they're going to add uh I don't know five and and three.
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They go one, two, three, four, five, and then they count again.
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One, two, three, four, five, six, seven, eight.
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And then they do a third count.
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One, two, three, four, five, six, seven, eight, eight.
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Yeah.
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They got to the correct answer, but uh the where they are in in their learning is completely different from a student that goes five, six, seven, eight, eight, which is what we call counting on.
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The student built the five, knows that here are five, but there they the student doesn't have to reassure that there are five elements here and just goes and goes one, two, three, that's eight.
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So those are two widely different approaches.
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Well, it's interesting too.
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I mean, uh, you know, comparing to like memorization, right?
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That we would go home and do uh uh five plus three is eight and write it twenty times and just memorize it without any concept of what five plus three is that equals eight, correct?
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Right, not understanding why it is that, why is it that, other than I memorize that, and when that comes up, I know that it's eight.
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Not because I of quantity or right or thinking of it in my mind that it's now a quantity of eight.
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I just know that five plus three is eight because that's what I wrote down 20, you know, 20 or 50 times in a row, and I I know that, correct?
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Yeah, and funny that you mentioned that because you know what have we always heard, right?
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Like, like, you know, when we talk about multiplication, if you memorize your multiplication fact, that was a great example of that.
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Yeah, you should be good, right?
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Yeah.
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Um uh I've actually screened seventh graders uh here in our district, and and I ask them uh a simple uh multiplication task, like uh what does it say there?
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And then they read it six times four.
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And how much is six times four?
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And they go, well, 24.
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But then I ask them, how do you know that?
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And they go, Well, uh, because I memorized it.
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Uh also it kind of rhymes.
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I'm like, okay.
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And then I I put in front of them a six by four array and another image that has six dots and four dots.
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And then I ask them, uh, which of these two represents six times four?
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And I have students that point to the six dots and four dots instead of pointing to the six by four array.
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So that's what we mean by conceptual understanding.
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Gotcha, gotcha.
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So, so going back, teachers like this curriculum because it teaches the algorithm or it leads up to it as far as like it it teaches in a different way where kids now can really understand the mechanics of what it is.
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Right.
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Right.
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So, so the standard algorithm and and you know how to follow um uh you know like a step-by-step, uh, that is what we call uh procedural fluency.
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Okay.
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So this instructional material builds that procedural fluency, all right, but on a foundation of conceptual understanding.
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Gotcha.
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So we are going to get to that, we're going to get to the algorithm, but um working those foundational skills is essential so that when they get to the algorithm, they are like, oh yeah, I know exactly how why that works.
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It's because they have soaked up all of that.
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And what that does is hopefully is what we're hoping is that so they they they find that, they understand it.
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So then when they get to more complicated, complex mathematics, it's easier for them to understand.
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Right.
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To give you a very practical example, um, I've seen uh students where they have they they go into fractions, right?
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And so they have uh seven eighths plus a half.
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Now, um if if if I were to give you that, or if I were to do that myself, you know, with our mathematical background, how we were taught back then, those are two fractions that have different denominators.
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Yes.
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So I I mean, if I go back to to my teaching, I know that when I have two fractions that have different denominators, I have to find first a common denominator, a common denominator.
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And so I'm I'm there thinking, okay, so which are the multiples of eight?
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And then where am I going to match multiples of two and eight?
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And and I've seen students that immediately tell me, uh, well, that's a hole and and three eighths.
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And I'm like, how do you know that?
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Well, because seven eights, within seven eighths, there's a half, which is four eighths.
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So that's a half.
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A half and a half make a hole.
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And what I have left from that seven eighths is three.
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So that's a hole in three eighths.
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And I'm like, well, yeah, that is exactly correct.
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Yeah.
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They then they didn't use an algorithm, they just use their understanding of multiple of um of factors, of of uh, uh, partitions of of these different numbers, and they are actually more efficient than going to the algorithm.
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Wow.
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Yeah, that that's incredible.
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That's something that it's interesting that you know, we think math has changed, right?
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I mean, I've had kids and uh my kids they're they're both really good at math, but the thing is is there's only a certain point that I could help them out, is because you know, you only you're taught a different way and they're taught a different way, and you're thinking, wow, this is pretty insane.
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The way the they called it the new math, right?
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Yeah.
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So now which is not new, by the way.
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It's not this is research from the 60s.
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Correct.
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So no, no, no.
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I gotcha.
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So so now we have this new math curriculum that's gonna be when is this gonna be implemented?
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So that was implemented on day one of the school year.
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Okay.
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Um, we teachers have already started using it.
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Um, I have had we had an email that came from one of our teachers here at Aspen.
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And and and I just love the quote because when we were when we were looking at the instructional material and all the components that come with it, we're like, okay, um we want to we're going to we we're going to purchase this part of the other structural material, but not not this one.
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And we would see the the vendor like, hmm, like what?
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Well, it's it's kind of like if you're going to if you're going to buy the mozzarella, right?
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Okay.
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And then you tell me, but uh I don't want the the the hood on the mozzarati, or I don't want the but the bumper in the mozzarati.
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If you're going to buy the mozzarati, you need to buy the whole thing, right?
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Yeah, yeah.
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Because that that is how you're going to uh be driving that vehicle.
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And and it's and and it's that that just stuck stuck to me.
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And it's funny that the the teacher over at Aspen said, this is like driving a Ferrari.
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So I don't know what we have with vehicles.
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Uh this is like driving a Ferrari because last year it was like driving a Volkswagen.
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Yeah, I've never driven a Volkswagen, but uh, but I guess I I get the idea, right?
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Is that this really feels like we are cruising along nicely.
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When is this gonna be introduced?
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Is it introduced right away in kindergarten and then works up its way?
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Is it right away that these that uh our students are gonna be getting this?
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Yes.
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So right now, all K through eight um uh grade levels have IM as their instructional material.
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Um there is um there the the first unit in every single grade level is uh building a math community.
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So one of the one of the that's another thing that teachers like very much about it, which is um, you know, when you hear people saying, Well, I'm not a math person.
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And uh and and I remember uh my colleague Peter McGwain saying, Well, I tell him, Well, I'm not a reading person.
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Then everybody looks at me, we are like, Well, what do you mean you're not a reading person?
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Well, that's how we should feel about people when they say, Oh, I'm not a math person.
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No, we are all math, but because that is a thing.
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Um uh Imagine Learning's uh illustrative mathematics starts off with that component, how to develop a math identity.
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And that is the first unit in every uh single grade level because uh we know the need to create that that environment in our classrooms, right?
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We are all mathematicians, we are all math people, and we have something valuable to to contribute and and and to bring on on and put on the table.
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So it's interesting.
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I I think it's great because you what you're doing is you're creating, if you want to think of your brain as a as a computer with a bunch of connections, you're creating a strong foundation of connections, right?
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Yeah that lay that are able to uh handle eventually more and more data and to be able to process it, but you've already established the foundation, the connection uh foundation of the way the brain works, right?
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And so then when you get to a certain point and you start having to figure out the more complicated problems, you go, oh yeah, well, I already I already have the network inside my brain right now to be able to do that.
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Yeah, that is completely correct.
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And thank you for saying that because that that is one of the most one that is one of the quotes that I most like about John Pi J, which is like, you know, like a very important uh uh individual in the education world.
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Uh and and there is a quote that he has.
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Um I I'm obviously going to kind of like uh quote uh John Piaget all wrong, but but basically the idea is that he says when you prematurely expose a student to something that they could have uh invented on their own, then you uh deprive that student from understanding the concept completely.
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Yeah.
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And and his the the whole approach in education is that um uh going back to John Piaget, that we have different uh types of knowledge, and then one is the logical mathematical and the other one is the social.
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Uh, he says that the logical mathematical, you should never show the student uh your thinking because all of us develop our own schemas.
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Yeah.
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How you understand the concept is going to be completely different from how I understand the concept, and that is okay.
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We have we have different strategies and different approaches to resolving a particular problem.
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When will you guys know that there's uh as far as like when are you expecting like your first um results where you can establish a benchmark of like, hey, this is really taking on.
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How how long are you are you thinking it will take?
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Three years.
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Okay.
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Three years.
00:20:18.079 --> 00:20:25.039
Um I am has been implemented in other states, um, places like New York, California.
00:20:25.200 --> 00:20:25.519
Okay.
00:20:25.839 --> 00:20:58.640
Uh, and and and it's and it's always a struggle because going from a a gradual release approach where I teach you the concepts, we do it together, and then you do it on your own, the famous I do, you do, we do, uh I inflips that that that approach to to how math should be taught, whereas the student engages with the mathematical concept, the I do the the you do, and then works together with their with their peers uh through the standards of mathematical practice is kind of like okay, how did you solve it?
00:20:58.720 --> 00:20:59.759
Well, I solved it this well.
00:20:59.839 --> 00:21:03.279
I I had no idea that there was another strategy to that.
00:21:03.440 --> 00:21:24.160
And and and then I am concludes with with the synthesis, where okay, now that all of you had a chance to engage with a mathematical concept, some of you um uh came to some some conjectures, others uh were awesome enough to to generalize the the the pattern or the the uh or the mathematical concept.
00:21:24.319 --> 00:21:34.079
Um and that that approach of the teacher being more of a facilitator rather than this the sage on the stage is a huge shift.
00:21:34.240 --> 00:21:39.839
Um many many educators, including myself, we were used to the other model.
00:21:40.319 --> 00:21:42.880
Um, so it takes some time.
00:21:43.039 --> 00:21:50.240
And what we've seen in and uh where I am has been implemented in other parts of the United States, it's precisely that.
00:21:50.400 --> 00:21:59.680
It takes three years for teachers to make the shift, know the resource, and and and find ways of making the the lesson.
00:22:00.400 --> 00:22:01.759
Theirs, their own style.
00:22:02.000 --> 00:22:10.079
And obviously, because uh PET has approved it, and then we took it on that these other states have been successful in their endeavors, right?
00:22:10.160 --> 00:22:11.359
With this with IM?
00:22:11.839 --> 00:22:12.799
Definitely.
00:22:13.039 --> 00:22:17.039
Um, it is it is many things have to come together.
00:22:17.200 --> 00:22:19.759
Um and and and the pet knows it.
00:22:19.839 --> 00:22:30.720
Um, we've seen we've the public education department has looked at states that have made significant growth in their mathematics um um learning.
00:22:30.960 --> 00:22:33.119
And we look at states like Alabama.
00:22:33.440 --> 00:22:37.920
Alabama was pretty much where where New Mexico is right now, yeah.
00:22:38.240 --> 00:22:44.480
Uh, and we saw basically what their their their blueprint to proficiency is, right?
00:22:44.640 --> 00:22:46.400
Or their pathway to proficiency.
00:22:46.559 --> 00:22:46.880
Yeah.
00:22:47.119 --> 00:23:04.720
And and it was a combination of passing legislation that um would kind of dig uh show what is has been what has been effective as far as as far as math teaching, uh, what does the research say?
00:23:04.960 --> 00:23:07.119
What has been proven to work?
00:23:07.440 --> 00:23:13.519
And it's a matter of adopting that and and then that trickling down to to districts.
00:23:13.920 --> 00:23:28.720
But ultimately, as you and I know and many teachers know, um we need to have teacher buy because what the teacher decides to to do in the classroom with the student is ultimately what's what's really going to happen.
00:23:29.039 --> 00:23:33.119
And and this year we we have been telling educators, hey, you know what?
00:23:33.279 --> 00:23:37.920
This year, uh don't expect to have everything mastered, right?
00:23:38.160 --> 00:23:39.680
There are going to be many questions.
00:23:39.839 --> 00:23:46.960
There are going to be many instances where you're like, I don't know if if I'm doing things uh correctly, and that is okay.
00:23:47.119 --> 00:23:47.759
That is fine.
00:23:47.920 --> 00:23:49.519
Uh it's going to take some time.
00:23:49.680 --> 00:23:50.000
Yeah.
00:23:50.160 --> 00:23:55.599
And and and we know that it's going to take some time, and we we are confident that we are going to get there.
00:23:55.839 --> 00:23:56.480
That's awesome.
00:23:56.640 --> 00:23:57.759
That's great.
00:23:58.240 --> 00:24:14.160
So, Arturo, uh, if folks want to do a little bit more research on it, where can they, is there some place they can go where they can find more, you know, the the parents or guardians that are out there right now listening, watching our podcast right now, is there a place where they can go and look more in on uh on Imagine I Am?
00:24:14.559 --> 00:24:14.799
Right.
00:24:14.960 --> 00:24:16.640
They can go to Imagine I Am.
00:24:16.960 --> 00:24:20.640
Uh, they can uh they can just Google illustrative mathematics.
00:24:20.720 --> 00:24:23.200
What is what is uh the the research behind it?
00:24:23.359 --> 00:24:28.160
There is there is a lot of information out there that is accessible to the public.
00:24:28.480 --> 00:24:50.400
But specifically for Santa Fe Public Schools, um, we are we are currently developing um um communications that are going to help uh staff and parents kind of like not only get a sense of what I am is, but how can I support my student at home, right?
00:24:50.480 --> 00:24:55.599
Um I don't want to do something that's going to kind of short circuit the the whole thing.
00:24:55.839 --> 00:25:03.200
How how can I best support my student in in with this new instructional material with this new quote unquote approach to mathematics?
00:25:03.359 --> 00:25:06.000
And and yeah, that is that is that is coming out.
00:25:06.480 --> 00:25:13.200
And uh, but um if if there are parents are like, huh, you know, um, I would like more information about it.
00:25:13.279 --> 00:25:25.119
Yeah, another thing that we are planning to do is is just provide resources on our on on the STEM website that they can access and find out more information about this.
00:25:25.359 --> 00:25:25.920
That's great.
00:25:26.079 --> 00:25:26.640
That's great.
00:25:26.960 --> 00:25:29.839
Arturo, thank you so much for coming on today.
00:25:30.000 --> 00:25:30.799
This is exciting.
00:25:30.880 --> 00:25:32.640
I'd love to have you back for a follow-up.
00:25:33.119 --> 00:25:33.599
My pleasure.
00:25:33.839 --> 00:25:34.720
It'd be it'd be awesome.
00:25:34.799 --> 00:25:55.680
This is exciting, uh, just because I know math, there's there's struggles with math, you know, and I think that if there's an if there's a way of of putting out that fisher and catching a bunch of fish of understanding of students that understand math better and an easier way of of of of setting of understanding how to do things, um, that's great.
00:25:55.759 --> 00:26:00.480
It uh more power to them and to uh and to us to be able to to give that to them.
00:26:00.559 --> 00:26:01.359
So awesome.
00:26:01.519 --> 00:26:02.079
This is great.
00:26:02.160 --> 00:26:02.799
Thank you for the time.
00:26:03.119 --> 00:26:03.680
My pleasure.
00:26:03.920 --> 00:26:04.559
Great time.
00:26:04.799 --> 00:26:09.519
Arturo Lujan, the STEM coordinator for Santa Fe Public Schools, uh, was our guest today.
00:26:09.680 --> 00:26:11.200
Folks, thank you for joining us.
00:26:11.359 --> 00:26:13.279
Have a safe week, have a great week.
00:26:13.519 --> 00:26:14.400
Adios.
00:00:08.640 --> 00:00:13.599
Good day, folks, and welcome to another edition of Inside Santa Fe Public Schools Podcast.
00:00:13.679 --> 00:00:19.920
I am Joe Abeta, and today with us is the STEM coordinator for Santa Fe Public Schools, Arturo Duhan.
00:00:20.079 --> 00:00:20.879
How are you doing, Arturo?
00:00:21.199 --> 00:00:21.839
Doing well, Joe.
00:00:21.920 --> 00:00:22.320
How about you?
00:00:22.480 --> 00:00:23.600
I'm doing good, good, good.
00:00:23.679 --> 00:00:25.199
Thank you for joining us today.
00:00:25.440 --> 00:00:33.200
Um, so you're here today because the school is starting a new math curriculum.
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Is that right?
00:00:34.159 --> 00:00:35.039
That is correct.
00:00:35.280 --> 00:00:42.880
Um we are we are excited to implement uh what is going to be our new math instructional material.
00:00:43.520 --> 00:00:59.840
Um and and this one promises to to kind of like shift the framework that we we usually have going on in the classrooms, okay um, to something that is more discovery approached.
00:01:00.159 --> 00:01:00.479
Okay.
00:01:00.880 --> 00:01:03.039
So that's awesome.
00:01:03.200 --> 00:01:06.079
And and so what was the I guess what was the purpose of it?
00:01:06.239 --> 00:01:16.640
Was it something that you your office kind of said, hey, we need to we need to make math a little bit more easier or more uh understanding to our students.
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How can we do that?
00:01:17.840 --> 00:01:19.040
Is that what was that the purpose?
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Was it because we weren't getting the results that we wanted with the previous one?
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Yeah, definitely.
00:01:24.319 --> 00:01:31.280
So so last year we had conversations with uh principals from all of our all of our schools in the district.
00:01:31.439 --> 00:01:31.760
Uh-huh.
00:01:32.480 --> 00:01:47.680
And one of the recurring things that would come up was um our teach our students, our students don't have that deep understanding of the mathematical concept.
00:01:47.760 --> 00:02:07.519
And so we had we had principals from uh Capital High School where they would say, uh our students are awesome, however, when they engage with geometry, when they engage with with um algebra concepts, uh we feel that there are foundational skills missing there.
00:02:08.319 --> 00:02:13.439
And so uh that was like the beginning of of a journey.
00:02:13.599 --> 00:02:21.759
Um last year we also had our math, our math adoption, um, our math instructional material adoption.
00:02:21.840 --> 00:02:22.240
Uh-huh.
00:02:22.879 --> 00:02:45.199
And and the committee that came together was which was comprised of uh um uh general education teachers, um uh district staff, coaches, um, principals, they they um they kind of came together to share what their vision of how of what would be considered high quality math instruction.
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Okay.
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What what would that look like?
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What what is it that we've seen that works in in the classroom?
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And so um uh Santa Fe Public School's um math vision was developed.
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Okay.
00:02:56.800 --> 00:03:01.599
That vision was basically what drove the adoption committee.
00:03:01.840 --> 00:03:07.280
Um, they used that lens when they would look at the different instructional material that was offered.
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And and there there were there were like three or four instructional materials that that kind of like align with that vision.
00:03:15.919 --> 00:03:16.240
Okay.
00:03:16.719 --> 00:03:31.599
Um, but really at the end of the day, it was this this one instructional material that that really um gathered all those aspects of that vision in in a well-rounded uh uh material.
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That seems like a a huge task, man, and a huge responsibility on on the committee, right?
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That did that, right?
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To get together the task force that got in together.
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So I I would assume then that like because you want to be careful about what you're bringing in, and there was just like a lot of, I'm sure, sessions of like, why why can't we use this one?
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Why should we use this one?
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Um how did I mean how long did it take for you guys to it took you guys over a year to figure this out to get the to get the right one?
00:04:02.319 --> 00:04:04.319
Or how what was the process like?
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Well, the the process was um there um the public education department has like a list of approved material.
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So so uh many vendors go through through the through the PED, and then the PED kind of like does the the the first part of that work, right?
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And so they they say, okay, these this list of uh high quality instructional materials are actually considered high quality instructional materials.
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Okay.
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And so we go from that list and and teachers look at different aspects of the of the material.
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Uh um how uh what what resources does it offer?
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Um what uh supports the that do teachers get with the instructional material?
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Does it have a digital component?
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Uh does it have activities uh in or or material that families can get so that they can support students?
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And after they look at the ones that that kind of check off all these boxes, yeah, then they they got a chance of test driving it.
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So some teachers uh uh got to teach an actual lesson from from the one from the materials that they were considering.
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And and that was a game changer because they they thought that at first, oh, this material is is great, but when they would actually teach the lesson, they found that there were some things missing.
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Yeah, that's other instructional material that they were ready to discard once they taught the lesson.
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It was like, oh, wait a minute.
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Um, this really felt differently in a good sense.
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Um, so they went through all of that.
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Um, we they they made the recommendation, and that was sent to uh Dr.
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Griffin, our our superintendent, and and ult and she made the ultimately the decision.
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What was the one thing that stuck out from the teachers with this new program that they really liked?
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So one of the things that stuck out was um was the how the instructional material prioritizes developing conceptual understanding.
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And one might ask, well, what is that?
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Yeah.
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So to give a a very um uh practical example, um, if I were to ask you, hey Joe, um at which grade level do you think that a student learns the standard algorithm for adding and subtracting?
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And by that I mean, you know, when when you have like a uh two-digit um um uh um you you have two digits and two digits, and you add the ones first, the ones in the in the digits and the ones column, and then if you if you go over 10, you carry over to the tens column and you add which grade level do you think that should be taught?
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Well, if I'm thinking of my old man self of when I I learned, I would have to think I would think that my deepest memory would be probably first grade.
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We dabbled in it, I would think, but that was back in 76.
00:07:09.279 --> 00:07:10.240
Okay, okay.
00:07:10.560 --> 00:07:18.560
So I'm thinking first grade, but now kids are a little more complex and they're there there's more accessibility to technology and information.
00:07:18.800 --> 00:07:21.199
So maybe kindergarten, maybe kindergarten.
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Okay, so according to Common Core, that is a fourth grade standard.
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Oh wow, yeah, okay, okay.
00:07:26.879 --> 00:07:36.319
So um common core establishes that students should not be exposed to the standard algorithm for adding and subtracting until they reach fourth grade.
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Wow.
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And okay, and and it's it's um it's not uncommon that answer that you just provided, because even um teachers across the nation, when they are asked uh that same question, they say first grade, second grade, and then when they are given the answer, they're like, whoa, whoa, whoa, no, wait a minute.
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I have a son in second grade, and that's exactly what my son is is getting.
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That my son is getting uh um um homework or worksheets where they are uh you know practicing adding using the standard algorithm.
00:08:14.079 --> 00:08:19.920
And when you look at the instructional material, well, no wonder why why teachers are doing that.
00:08:20.079 --> 00:08:29.120
The instructional material is is is leading the students and teachers to using the standard algorithm for adding and subtracting.
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Common core, well, common core, but uh common core is founded on research.
00:08:33.600 --> 00:08:33.919
Yeah.
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Um all the research says that from kindergarten all the way up to fourth grade, students need to um, what I said, they need to develop conceptual understanding.
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And what does that mean?
00:08:46.000 --> 00:08:51.919
So um some examples will be um if students students need to structure number, right?
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Uh they need to know how much is um uh three and five.
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And and getting the right answer is not the the ultimate uh uh objective.
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Students can go uh one, two, three.
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You know, we I've seen first grade students that that that do precisely that.
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Yeah, they they first let's say if they're going to add uh I don't know five and and three.
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They go one, two, three, four, five, and then they count again.
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One, two, three, four, five, six, seven, eight.
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And then they do a third count.
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One, two, three, four, five, six, seven, eight, eight.
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Yeah.
00:09:32.320 --> 00:09:46.960
They got to the correct answer, but uh the where they are in in their learning is completely different from a student that goes five, six, seven, eight, eight, which is what we call counting on.
00:09:47.120 --> 00:09:58.960
The student built the five, knows that here are five, but there they the student doesn't have to reassure that there are five elements here and just goes and goes one, two, three, that's eight.
00:09:59.679 --> 00:10:02.000
So those are two widely different approaches.
00:10:02.320 --> 00:10:03.600
Well, it's interesting too.
00:10:03.759 --> 00:10:09.200
I mean, uh, you know, comparing to like memorization, right?
00:10:09.279 --> 00:10:21.519
That we would go home and do uh uh five plus three is eight and write it twenty times and just memorize it without any concept of what five plus three is that equals eight, correct?
00:10:22.000 --> 00:10:28.879
Right, not understanding why it is that, why is it that, other than I memorize that, and when that comes up, I know that it's eight.
00:10:29.120 --> 00:10:36.000
Not because I of quantity or right or thinking of it in my mind that it's now a quantity of eight.
00:10:36.240 --> 00:10:43.840
I just know that five plus three is eight because that's what I wrote down 20, you know, 20 or 50 times in a row, and I I know that, correct?
00:10:44.000 --> 00:10:48.240
Yeah, and funny that you mentioned that because you know what have we always heard, right?
00:10:48.399 --> 00:10:53.919
Like, like, you know, when we talk about multiplication, if you memorize your multiplication fact, that was a great example of that.
00:10:54.080 --> 00:10:55.279
Yeah, you should be good, right?
00:10:55.440 --> 00:10:55.919
Yeah.
00:10:56.159 --> 00:11:08.240
Um uh I've actually screened seventh graders uh here in our district, and and I ask them uh a simple uh multiplication task, like uh what does it say there?
00:11:08.320 --> 00:11:09.759
And then they read it six times four.
00:11:09.840 --> 00:11:11.039
And how much is six times four?
00:11:11.120 --> 00:11:12.399
And they go, well, 24.
00:11:12.559 --> 00:11:14.320
But then I ask them, how do you know that?
00:11:14.559 --> 00:11:17.279
And they go, Well, uh, because I memorized it.
00:11:17.360 --> 00:11:19.600
Uh also it kind of rhymes.
00:11:20.480 --> 00:11:21.279
I'm like, okay.
00:11:21.440 --> 00:11:28.559
And then I I put in front of them a six by four array and another image that has six dots and four dots.
00:11:28.960 --> 00:11:33.200
And then I ask them, uh, which of these two represents six times four?
00:11:33.759 --> 00:11:39.679
And I have students that point to the six dots and four dots instead of pointing to the six by four array.
00:11:39.840 --> 00:11:42.240
So that's what we mean by conceptual understanding.
00:11:42.559 --> 00:11:43.440
Gotcha, gotcha.
00:11:43.759 --> 00:11:59.200
So, so going back, teachers like this curriculum because it teaches the algorithm or it leads up to it as far as like it it teaches in a different way where kids now can really understand the mechanics of what it is.
00:11:59.440 --> 00:11:59.840
Right.
00:12:00.000 --> 00:12:00.240
Right.
00:12:00.639 --> 00:12:12.240
So, so the standard algorithm and and you know how to follow um uh you know like a step-by-step, uh, that is what we call uh procedural fluency.
00:12:12.399 --> 00:12:12.720
Okay.
00:12:12.879 --> 00:12:20.639
So this instructional material builds that procedural fluency, all right, but on a foundation of conceptual understanding.
00:12:20.879 --> 00:12:21.200
Gotcha.
00:12:21.360 --> 00:12:37.279
So we are going to get to that, we're going to get to the algorithm, but um working those foundational skills is essential so that when they get to the algorithm, they are like, oh yeah, I know exactly how why that works.
00:12:37.440 --> 00:12:40.720
It's because they have soaked up all of that.
00:12:41.120 --> 00:12:48.159
And what that does is hopefully is what we're hoping is that so they they they find that, they understand it.
00:12:48.240 --> 00:12:53.759
So then when they get to more complicated, complex mathematics, it's easier for them to understand.
00:12:54.000 --> 00:12:54.399
Right.
00:12:54.639 --> 00:13:04.000
To give you a very practical example, um, I've seen uh students where they have they they go into fractions, right?
00:13:04.320 --> 00:13:09.759
And so they have uh seven eighths plus a half.
00:13:10.159 --> 00:13:22.639
Now, um if if if I were to give you that, or if I were to do that myself, you know, with our mathematical background, how we were taught back then, those are two fractions that have different denominators.
00:13:22.799 --> 00:13:23.120
Yes.
00:13:23.279 --> 00:13:32.960
So I I mean, if I go back to to my teaching, I know that when I have two fractions that have different denominators, I have to find first a common denominator, a common denominator.
00:13:33.279 --> 00:13:37.440
And so I'm I'm there thinking, okay, so which are the multiples of eight?
00:13:37.519 --> 00:13:41.519
And then where am I going to match multiples of two and eight?
00:13:42.000 --> 00:13:49.759
And and I've seen students that immediately tell me, uh, well, that's a hole and and three eighths.
00:13:50.000 --> 00:13:51.440
And I'm like, how do you know that?
00:13:51.679 --> 00:13:56.720
Well, because seven eights, within seven eighths, there's a half, which is four eighths.
00:13:56.879 --> 00:13:57.759
So that's a half.
00:13:57.840 --> 00:13:59.440
A half and a half make a hole.
00:13:59.600 --> 00:14:01.840
And what I have left from that seven eighths is three.
00:14:01.919 --> 00:14:03.360
So that's a hole in three eighths.
00:14:03.840 --> 00:14:07.360
And I'm like, well, yeah, that is exactly correct.
00:14:07.519 --> 00:14:07.759
Yeah.
00:14:08.000 --> 00:14:26.080
They then they didn't use an algorithm, they just use their understanding of multiple of um of factors, of of uh, uh, partitions of of these different numbers, and they are actually more efficient than going to the algorithm.
00:14:26.399 --> 00:14:26.879
Wow.
00:14:27.120 --> 00:14:29.120
Yeah, that that's incredible.
00:14:29.360 --> 00:14:36.000
That's something that it's interesting that you know, we think math has changed, right?
00:14:36.080 --> 00:14:52.080
I mean, I've had kids and uh my kids they're they're both really good at math, but the thing is is there's only a certain point that I could help them out, is because you know, you only you're taught a different way and they're taught a different way, and you're thinking, wow, this is pretty insane.
00:14:52.159 --> 00:14:54.240
The way the they called it the new math, right?
00:14:54.480 --> 00:14:54.799
Yeah.
00:14:55.039 --> 00:14:57.279
So now which is not new, by the way.
00:14:57.440 --> 00:14:59.759
It's not this is research from the 60s.
00:14:59.919 --> 00:15:00.240
Correct.
00:15:00.320 --> 00:15:01.519
So no, no, no.
00:15:01.679 --> 00:15:02.240
I gotcha.
00:15:02.399 --> 00:15:08.879
So so now we have this new math curriculum that's gonna be when is this gonna be implemented?
00:15:09.200 --> 00:15:12.559
So that was implemented on day one of the school year.
00:15:12.799 --> 00:15:13.039
Okay.
00:15:13.279 --> 00:15:17.679
Um, we teachers have already started using it.
00:15:17.919 --> 00:15:26.480
Um, I have had we had an email that came from one of our teachers here at Aspen.
00:15:27.039 --> 00:15:47.039
And and and I just love the quote because when we were when we were looking at the instructional material and all the components that come with it, we're like, okay, um we want to we're going to we we're going to purchase this part of the other structural material, but not not this one.
00:15:47.200 --> 00:15:52.159
And we would see the the vendor like, hmm, like what?
00:15:52.559 --> 00:15:56.799
Well, it's it's kind of like if you're going to if you're going to buy the mozzarella, right?
00:15:56.879 --> 00:15:57.120
Okay.
00:15:57.279 --> 00:16:04.000
And then you tell me, but uh I don't want the the the hood on the mozzarati, or I don't want the but the bumper in the mozzarati.
00:16:04.240 --> 00:16:07.440
If you're going to buy the mozzarati, you need to buy the whole thing, right?
00:16:07.519 --> 00:16:07.840
Yeah, yeah.
00:16:08.000 --> 00:16:12.799
Because that that is how you're going to uh be driving that vehicle.
00:16:12.960 --> 00:16:16.399
And and it's and and it's that that just stuck stuck to me.
00:16:16.559 --> 00:16:21.519
And it's funny that the the teacher over at Aspen said, this is like driving a Ferrari.
00:16:21.600 --> 00:16:23.360
So I don't know what we have with vehicles.
00:16:23.759 --> 00:16:28.240
Uh this is like driving a Ferrari because last year it was like driving a Volkswagen.
00:16:28.320 --> 00:16:33.200
Yeah, I've never driven a Volkswagen, but uh, but I guess I I get the idea, right?
00:16:33.279 --> 00:16:38.480
Is that this really feels like we are cruising along nicely.
00:16:38.799 --> 00:16:40.399
When is this gonna be introduced?
00:16:40.559 --> 00:16:45.120
Is it introduced right away in kindergarten and then works up its way?
00:16:45.200 --> 00:16:48.480
Is it right away that these that uh our students are gonna be getting this?
00:16:48.799 --> 00:16:49.200
Yes.
00:16:49.440 --> 00:16:56.960
So right now, all K through eight um uh grade levels have IM as their instructional material.
00:16:57.679 --> 00:17:07.119
Um there is um there the the first unit in every single grade level is uh building a math community.
00:17:07.279 --> 00:17:16.559
So one of the one of the that's another thing that teachers like very much about it, which is um, you know, when you hear people saying, Well, I'm not a math person.
00:17:17.279 --> 00:17:23.200
And uh and and I remember uh my colleague Peter McGwain saying, Well, I tell him, Well, I'm not a reading person.
00:17:23.279 --> 00:17:26.400
Then everybody looks at me, we are like, Well, what do you mean you're not a reading person?
00:17:26.480 --> 00:17:30.559
Well, that's how we should feel about people when they say, Oh, I'm not a math person.
00:17:31.119 --> 00:17:34.160
No, we are all math, but because that is a thing.
00:17:34.319 --> 00:17:41.200
Um uh Imagine Learning's uh illustrative mathematics starts off with that component, how to develop a math identity.
00:17:41.440 --> 00:17:51.200
And that is the first unit in every uh single grade level because uh we know the need to create that that environment in our classrooms, right?
00:17:51.359 --> 00:18:00.400
We are all mathematicians, we are all math people, and we have something valuable to to contribute and and and to bring on on and put on the table.
00:18:00.799 --> 00:18:01.839
So it's interesting.
00:18:02.000 --> 00:18:13.039
I I think it's great because you what you're doing is you're creating, if you want to think of your brain as a as a computer with a bunch of connections, you're creating a strong foundation of connections, right?
00:18:13.119 --> 00:18:27.599
Yeah that lay that are able to uh handle eventually more and more data and to be able to process it, but you've already established the foundation, the connection uh foundation of the way the brain works, right?
00:18:27.680 --> 00:18:37.039
And so then when you get to a certain point and you start having to figure out the more complicated problems, you go, oh yeah, well, I already I already have the network inside my brain right now to be able to do that.
00:18:37.759 --> 00:18:39.039
Yeah, that is completely correct.
00:18:39.200 --> 00:18:54.720
And thank you for saying that because that that is one of the most one that is one of the quotes that I most like about John Pi J, which is like, you know, like a very important uh uh individual in the education world.
00:18:55.359 --> 00:18:57.680
Uh and and there is a quote that he has.
00:18:57.839 --> 00:19:26.160
Um I I'm obviously going to kind of like uh quote uh John Piaget all wrong, but but basically the idea is that he says when you prematurely expose a student to something that they could have uh invented on their own, then you uh deprive that student from understanding the concept completely.
00:19:26.400 --> 00:19:26.960
Yeah.
00:19:27.200 --> 00:19:38.160
And and his the the whole approach in education is that um uh going back to John Piaget, that we have different uh types of knowledge, and then one is the logical mathematical and the other one is the social.
00:19:38.400 --> 00:19:47.920
Uh, he says that the logical mathematical, you should never show the student uh your thinking because all of us develop our own schemas.
00:19:48.079 --> 00:19:48.480
Yeah.
00:19:48.799 --> 00:19:56.319
How you understand the concept is going to be completely different from how I understand the concept, and that is okay.
00:19:56.559 --> 00:20:02.319
We have we have different strategies and different approaches to resolving a particular problem.
00:20:02.640 --> 00:20:12.960
When will you guys know that there's uh as far as like when are you expecting like your first um results where you can establish a benchmark of like, hey, this is really taking on.
00:20:13.039 --> 00:20:15.519
How how long are you are you thinking it will take?
00:20:15.759 --> 00:20:16.400
Three years.
00:20:16.640 --> 00:20:16.960
Okay.
00:20:17.200 --> 00:20:17.839
Three years.
00:20:18.079 --> 00:20:25.039
Um I am has been implemented in other states, um, places like New York, California.
00:20:25.200 --> 00:20:25.519
Okay.
00:20:25.839 --> 00:20:58.640
Uh, and and and it's and it's always a struggle because going from a a gradual release approach where I teach you the concepts, we do it together, and then you do it on your own, the famous I do, you do, we do, uh I inflips that that that approach to to how math should be taught, whereas the student engages with the mathematical concept, the I do the the you do, and then works together with their with their peers uh through the standards of mathematical practice is kind of like okay, how did you solve it?
00:20:58.720 --> 00:20:59.759
Well, I solved it this well.
00:20:59.839 --> 00:21:03.279
I I had no idea that there was another strategy to that.
00:21:03.440 --> 00:21:24.160
And and and then I am concludes with with the synthesis, where okay, now that all of you had a chance to engage with a mathematical concept, some of you um uh came to some some conjectures, others uh were awesome enough to to generalize the the the pattern or the the uh or the mathematical concept.
00:21:24.319 --> 00:21:34.079
Um and that that approach of the teacher being more of a facilitator rather than this the sage on the stage is a huge shift.
00:21:34.240 --> 00:21:39.839
Um many many educators, including myself, we were used to the other model.
00:21:40.319 --> 00:21:42.880
Um, so it takes some time.
00:21:43.039 --> 00:21:50.240
And what we've seen in and uh where I am has been implemented in other parts of the United States, it's precisely that.
00:21:50.400 --> 00:21:59.680
It takes three years for teachers to make the shift, know the resource, and and and find ways of making the the lesson.
00:22:00.400 --> 00:22:01.759
Theirs, their own style.
00:22:02.000 --> 00:22:10.079
And obviously, because uh PET has approved it, and then we took it on that these other states have been successful in their endeavors, right?
00:22:10.160 --> 00:22:11.359
With this with IM?
00:22:11.839 --> 00:22:12.799
Definitely.
00:22:13.039 --> 00:22:17.039
Um, it is it is many things have to come together.
00:22:17.200 --> 00:22:19.759
Um and and and the pet knows it.
00:22:19.839 --> 00:22:30.720
Um, we've seen we've the public education department has looked at states that have made significant growth in their mathematics um um learning.
00:22:30.960 --> 00:22:33.119
And we look at states like Alabama.
00:22:33.440 --> 00:22:37.920
Alabama was pretty much where where New Mexico is right now, yeah.
00:22:38.240 --> 00:22:44.480
Uh, and we saw basically what their their their blueprint to proficiency is, right?
00:22:44.640 --> 00:22:46.400
Or their pathway to proficiency.
00:22:46.559 --> 00:22:46.880
Yeah.
00:22:47.119 --> 00:23:04.720
And and it was a combination of passing legislation that um would kind of dig uh show what is has been what has been effective as far as as far as math teaching, uh, what does the research say?
00:23:04.960 --> 00:23:07.119
What has been proven to work?
00:23:07.440 --> 00:23:13.519
And it's a matter of adopting that and and then that trickling down to to districts.
00:23:13.920 --> 00:23:28.720
But ultimately, as you and I know and many teachers know, um we need to have teacher buy because what the teacher decides to to do in the classroom with the student is ultimately what's what's really going to happen.
00:23:29.039 --> 00:23:33.119
And and this year we we have been telling educators, hey, you know what?
00:23:33.279 --> 00:23:37.920
This year, uh don't expect to have everything mastered, right?
00:23:38.160 --> 00:23:39.680
There are going to be many questions.
00:23:39.839 --> 00:23:46.960
There are going to be many instances where you're like, I don't know if if I'm doing things uh correctly, and that is okay.
00:23:47.119 --> 00:23:47.759
That is fine.
00:23:47.920 --> 00:23:49.519
Uh it's going to take some time.
00:23:49.680 --> 00:23:50.000
Yeah.
00:23:50.160 --> 00:23:55.599
And and and we know that it's going to take some time, and we we are confident that we are going to get there.
00:23:55.839 --> 00:23:56.480
That's awesome.
00:23:56.640 --> 00:23:57.759
That's great.
00:23:58.240 --> 00:24:14.160
So, Arturo, uh, if folks want to do a little bit more research on it, where can they, is there some place they can go where they can find more, you know, the the parents or guardians that are out there right now listening, watching our podcast right now, is there a place where they can go and look more in on uh on Imagine I Am?
00:24:14.559 --> 00:24:14.799
Right.
00:24:14.960 --> 00:24:16.640
They can go to Imagine I Am.
00:24:16.960 --> 00:24:20.640
Uh, they can uh they can just Google illustrative mathematics.
00:24:20.720 --> 00:24:23.200
What is what is uh the the research behind it?
00:24:23.359 --> 00:24:28.160
There is there is a lot of information out there that is accessible to the public.
00:24:28.480 --> 00:24:50.400
But specifically for Santa Fe Public Schools, um, we are we are currently developing um um communications that are going to help uh staff and parents kind of like not only get a sense of what I am is, but how can I support my student at home, right?
00:24:50.480 --> 00:24:55.599
Um I don't want to do something that's going to kind of short circuit the the whole thing.
00:24:55.839 --> 00:25:03.200
How how can I best support my student in in with this new instructional material with this new quote unquote approach to mathematics?
00:25:03.359 --> 00:25:06.000
And and yeah, that is that is that is coming out.
00:25:06.480 --> 00:25:13.200
And uh, but um if if there are parents are like, huh, you know, um, I would like more information about it.
00:25:13.279 --> 00:25:25.119
Yeah, another thing that we are planning to do is is just provide resources on our on on the STEM website that they can access and find out more information about this.
00:25:25.359 --> 00:25:25.920
That's great.
00:25:26.079 --> 00:25:26.640
That's great.
00:25:26.960 --> 00:25:29.839
Arturo, thank you so much for coming on today.
00:25:30.000 --> 00:25:30.799
This is exciting.
00:25:30.880 --> 00:25:32.640
I'd love to have you back for a follow-up.
00:25:33.119 --> 00:25:33.599
My pleasure.
00:25:33.839 --> 00:25:34.720
It'd be it'd be awesome.
00:25:34.799 --> 00:25:55.680
This is exciting, uh, just because I know math, there's there's struggles with math, you know, and I think that if there's an if there's a way of of putting out that fisher and catching a bunch of fish of understanding of students that understand math better and an easier way of of of of setting of understanding how to do things, um, that's great.
00:25:55.759 --> 00:26:00.480
It uh more power to them and to uh and to us to be able to to give that to them.
00:26:00.559 --> 00:26:01.359
So awesome.
00:26:01.519 --> 00:26:02.079
This is great.
00:26:02.160 --> 00:26:02.799
Thank you for the time.
00:26:03.119 --> 00:26:03.680
My pleasure.
00:26:03.920 --> 00:26:04.559
Great time.
00:26:04.799 --> 00:26:09.519
Arturo Lujan, the STEM coordinator for Santa Fe Public Schools, uh, was our guest today.
00:26:09.680 --> 00:26:11.200
Folks, thank you for joining us.
00:26:11.359 --> 00:26:13.279
Have a safe week, have a great week.
00:26:13.519 --> 00:26:14.400
Adios.
