Here is a fantastic presentation by a maths teacher, Dan Meyer, explaining what is wrong with virtually every maths textbook out there:
What I like about his idea is that it focuses on first understanding the concept, and only then applying the maths. It harnesses your intuition about a problem you would normally encounter in the real world to get you on the hook, so you have no choice but to learn the maths to get your answer.
He speaks as if this is a problem unique to the US, but it is not. As he says, teachers from all around the world have approached him about his ideas, because they resonate on a global basis. Nobel Prize-winning physicist Richard Feynman has a famous essay on the irrelevance of mathematics textbooks in a similar vein.
Notice that Meyer identifies five symptoms of bad maths teaching. I think all of us in our school system have suffered from these symptoms at some point; the aversion to word problems and the over-eagerness to harness a simple formula must ring a bell for anyone who's ever stepped into a classroom here. Now the question is, how can we bring this new philosophy of teaching into our classrooms and textbooks?
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