『Addition: structures, strategies and why 8 + 7 matters』のカバーアート

Addition: structures, strategies and why 8 + 7 matters

Addition: structures, strategies and why 8 + 7 matters

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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 additionWhat 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 numericalNew 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 CPDJon 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 readingWordle and information theoryBinghamton University: researchers use maths to crack WordleResearch paper: Solving Wordle Using Information TheoryPlay WordlePlay NerdlePartitioning and spatial reasoningChelsea Cutting: Exploring the critical role spatial reasoning plays in young children’s early partitioning developmentFurther reading:Wilson, Myers, Edgington & Confrey: Fair Shares, Matey, or Walk the PlankThe history of mathematical symbolsMacTutor: Earliest Uses of Symbols of OperationFree primary maths CPDExplore Twinkl’s upcoming TeachMeet eventsTwinkl Primary Maths CPD collectionQuote 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: AfterMathsWith Jon Cripwell and Becky Brown.New episodes exploring the ideas, research and slightly unexpected tangents behind primary mathematics.
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