We will be heading out soon on vacation, so I will not be blogging for awhile. The rest of this week is devoted to packing. (I hate packing!) But before I leave, here is a longish quote on teaching math from the book I am reading this week: Ian Stewart’s Letters to a Young Mathematician.
A second reason why few students ever realize that there is mathematics outside the textbook is that no one ever tells them that.
I don’t blame the teachers… If your students are having problems remembering how to solve quadratic equations, the wise teacher will stay well clear of cubic equations, which are even more difficult….
A process of self-censorship sets in. In order to avoid damaging the students’ confidence, the texts do not ask questions that the methods being taught cannot answer. So insidiously, we absorb the lesson that every mathematical question has an answer.
It’s not true.
Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren’t discussed.
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