A number of math teachers have complained either directly or indirectly recently that I have offered criticisms but no solutions to the problem of poorly-designed math courses, especially at the secondary level. For example:

“In my opinion the writer suggests that textbooks are merely a collection of topics with examples of exercises under each and that teachers merely race through a textbook to get to the end. In a sense I agree with this but my problem/concern is that he offers no alternative/answer to what we should be doing instead…. It seems there are so many people out there saying that this is not what we should be teaching our students and that us Math teachers are in fact wasting students time with our outdated teaching methods. My question is then what should we be teaching them? What am I missing? He offers no answer to that question.

“What…

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