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I would be really interested in seeing a concrete example of a maths question at this level that has more than one correct answer. I can conceive one at a sligh

I would be really interested in seeing a concrete example of a maths question at this level that has more than one correct answer. I can conceive one at a slightly more advanced level, say a curve with several equal "minimas" and finding any one of them is a valid answer. Or finding one of several equal shortest paths through a graph. Both of those have real-world applications. But either way there is still a finite set of "correct" answers. I would not want to drive over a bridge designed by, or in a car designed by, ethnomathematics.

singron 6y ago
A lot of math is based on word problems and has ambiguities from language. E.g. "Alice gives Bob half her apples and Bob gives Alice half his apples". The number of apples each of them has depends on whether the actions were simultaneous or sequential and whether "his apples" refers to the apples Bob just received from Alice. It's just good teaching to highlight these ambiguous cases because they do happen in the real world when talking about mathematics. Some ambiguities are general, but some are also aligned with racial/cultural/linguistic backgrounds. E.g. double negatives. There exists a mathematical language to unambiguously specify these differences, but we don't make kids read the principia mathematica for a reason.
- goatinaboat 6y ago
  A lot of math is based on word problems and has ambiguities from language. E.g. "Alice gives Bob half her apples and Bob gives Alice half his apples". The number of apples each of them has depends on whether the actions were simultaneous or sequential and whether "his apples" refers to the apples Bob just received from Alice. That's a great example and teaches about race conditions too! But there's still a finite set of correct answers, and without showing working there's no way to teach them. And for all I know, this question might not work in languages other than English and isn't that one of the points of this whole exercise...

singron 6y ago

A lot of math is based on word problems and has ambiguities from language. E.g. "Alice gives Bob half her apples and Bob gives Alice half his apples". The number of apples each of them has depends on whether the actions were simultaneous or sequential and whether "his apples" refers to the apples Bob just received from Alice. It's just good teaching to highlight these ambiguous cases because they do happen in the real world when talking about mathematics. Some ambiguities are general, but some are also aligned with racial/cultural/linguistic backgrounds. E.g. double negatives. There exists a mathematical language to unambiguously specify these differences, but we don't make kids read the principia mathematica for a reason.

goatinaboat 6y ago
A lot of math is based on word problems and has ambiguities from language. E.g. "Alice gives Bob half her apples and Bob gives Alice half his apples". The number of apples each of them has depends on whether the actions were simultaneous or sequential and whether "his apples" refers to the apples Bob just received from Alice. That's a great example and teaches about race conditions too! But there's still a finite set of correct answers, and without showing working there's no way to teach them. And for all I know, this question might not work in languages other than English and isn't that one of the points of this whole exercise...