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35

I cannot answer the OP's question about cross-cultural/international perspectives, but here is a historical perspective that may be helpful. The issue here (whether the category "rectangles" includes or excludes the category "squares") is one aspect of a larger question having to do with whether the classification of quadrilaterals ...


17

The tutors need training. Any volunteer job has job requirements, and one of the requirements of this job [for it to be done well] is being able to tutor anything that comes along. The training can mainly involve intriguing problems that will help the tutors enjoy math themselves. Then, if they get stuck on a student's problem, they can seek help in a ...


15

Kindergartners are generally at an early stage of geometric development, in which shapes are recognized by how well they resemble prototypical images, rather than by whether or not they conform to a definition. Thus, for example, the shape on the left below is likely to be recognized as a "triangle" (despite the fact that it has four sides), the shape in ...


10

A quintessential example of a cultural clash over math education in US schools, I would say, is the entire Math Wars, an ongoing struggle over standards and pedagogy in K-12 schools. It is a struggle of curriculum reformers trying to bring research-based innovations of mathematics thinking, learning, and teaching over the last three decades into schools ...


9

There is a model of how people progress towards abstract reasoning through the subject of geometry called the Van Hiele model. The model describes five levels: visualization, analysis, abstraction, deduction, rigor. It dates to the 1950's, and continues to influence curricula. In the analysis level, children do not allow overlaps in categories, and will ...


7

Perhaps this historical example fits the bill: Khovanova, T., & Radul, A. (2012). Killer problems. American Mathematical Monthly, 119(10), 815-823. The piece was published earlier on the arXiv as Jewish Problems. Here is the abstract: This is a special collection of problems that were given to select applicants during oral entrance exams to the ...


5

I just came across this discussion https://news.ycombinator.com/item?id=16605831 which reminded me of your question. The perspective isn't exactly math and isn't exactly not-math but rather, a question in object-oriented programming. Several of the comments (search for rectangle and square to get the relevant comments) there are worth reading on their own, ...


3

Most of my job tutoring high school math is giving my students confidence -- it's rare that a student of mine will actually have trouble with math. Switch at least part of your focus to building your students' confidence: "hey, that wasn't so hard, was it?," "See, you can do this!" If you can't show their students how to do something, then you should not ...


2

I don't see that there is anything you can do other than teach the non-math volunteers math. Your normal "Joe" isn't going to be able to do pre-cal homework. The only real thing I would push is tell them to find someone who can help, but never, ever, under any circumstances say things like "Everyone has trouble with math, hey" or anything else that pushes ...


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