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This isn't just folk wisdom either. There's an active subfield of cognitive science that focuses on working memory/cognitive load and math instruction. Broadly
by AlanYx 2y ago
This isn't just folk wisdom either. There's an active subfield of cognitive science that focuses on working memory/cognitive load and math instruction. Broadly speaking, it's hard for students to successfully transition to even basic algebra if they don't have basic calculations down.
- Ntrails 2y agoThat fits with my non expert intuition. If you don't get the basics of arithmetic it is incredibly hard to grasp the idea of "equals" as a pivot point. Division by hand helps to give us a hint that numbers can be broken up into constituents and still be the same. You internalise a whole set of behaviours, typically via repetition, and it unlocks understanding beyond itself imo
- abdullahkhalids 2y agoIt's all about building higher and higher abstractions. Arithmetic - > Algebra -> higher order algebraic algorithms. For example, when I taught differential equations, my non-scientific observation was that otherwise smart students struggled more with getting the algorithms down, if they struggled with algebra. Having to constantly jump down to a lower level of abstraction while performing the algorithmic steps is what caused confusion to mistakes.