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An interesting new place value visualization is the "exploding dots" https://gdaymath.com/courses/exploding-dots/ https://gdaymath.com/courses/exploding-dots/
by schoen 7y ago
An interesting new place value visualization is the "exploding dots"
https://gdaymath.com/courses/exploding-dots/ https://gdaymath.com/courses/exploding-dots/
which I think I first learned about here on HN.
It teaches place value but also expands the concept into all sorts of other areas of algebraic structure, including polynomials. It's actually quite similar to a counting board plus some interesting manipulation rule variations.
- jacobolus 7y agoYes, James Tanton’s exploding dots are more or less a counting board turned into a pencil (or whiteboard marker) & eraser tool, with more focus on concepts than practical calculation. Personally I find moving counters around to be easier than drawing and erasing little dots. YMMMV. Having base ten arithmetic split into 5 × 2 (as was done historically) is convenient for practical use, but does slightly complicate the concept. Having a single number base as Tanton does makes explanations a bit simpler. It’s nice how Tanton shows that counting boards can be used with alternative rules to represent more advanced/abstract systems of calculation. We can make up counting boards for doing complex arithmetic, working in other number fields, working with formal polynomials, working with binary logic, ... Modern computer registers/memory aren’t much different than a (very large) counting board. When we combine a basic counting board with a human operator, we have a Turing-complete computing machine.