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Addition is one of the first mathematical operations children meet, but that doesn’t mean it’s simple.
In this episode of AfterMaths, Jon and Becky take a closer look at what it really means to understand addition. They explore why knowing lots of different strategies matters, why column addition should be a tool rather than the destination, and why Jon has, somewhat inexplicably, developed a favourite addition calculation.
There’s also some Wordle mathematics, new research into the importance of spatial reasoning and partitioning, and a trip through the surprisingly long history of the humble + symbol.
In this episode01:16 – Can mathematics help you beat Wordle?
Researchers at Binghamton University have used Shannon entropy and information theory to develop a Wordle strategy that solved more than 99% of puzzles in simulations.
05:50 – What’s your favourite addition?
Jon nominates 8 + 7, and uses it to explore number bonds, partitioning, near doubles, compensation and the different ways children might see the same calculation.
10:58 – The structures of addition
What is the difference between aggregation and augmentation, and do children actually need to know those words?
15:00 – Column addition: servant or master?
Written algorithms are incredibly useful, but they aren’t automatically the most efficient or sophisticated strategy. Jon and Becky discuss why children need a repertoire of approaches and the freedom to choose between them.
20:54 – Research: partitioning is spatial as well as numerical
New research from Chelsea Cutting explores how spatial visualisation, spatial structuring and proportional reasoning can support young children’s understanding of partitioning and fractions.
26:33 – Where did the + symbol come from?
Becky heads down a mathematical-history rabbit hole, from ancient Egyptian walking legs to medieval shorthand and the emergence of the modern plus sign.
34:30 – Free primary maths CPD
Jon and Becky look ahead to Twinkl’s programme of free live primary maths sessions, including subtraction, problem solving, cognitive load and mathematical talk.
And next week: subtraction.
Links and further reading Wordle and information theoryBinghamton University: researchers use maths to crack Wordle
Research paper: Solving Wordle Using Information Theory
Partitioning and spatial reasoningFurther reading:
Wilson, Myers, Edgington & Confrey: Fair Shares, Matey, or Walk the Plank
The history of mathematical symbolsMacTutor: Earliest Uses of Symbols of Operation
Free primary maths CPDExplore Twinkl’s upcoming TeachMeet events
Twinkl Primary Maths CPD collection
Quote from the episodeJohn Dewey, Logic: The Theory of Inquiry (1938):
“It is a familiar and significant saying that a problem well put is half-solved.”
The Primary Maths Podcast: AfterMaths
With Jon Cripwell and Becky Brown.
New episodes exploring the ideas, research and slightly unexpected tangents behind primary mathematics.
