There is actually a whole field of research on mathematics education. I'm sure this 28 year old essay is nice, but probably the most up to date and comprehensive guide to evidence-based teaching of college math is this free Instructional Practices Guide from the MAA: <a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" rel="nofollow">https://www.maa.org/programs-and-communities/curriculum%20re...</a><p>For K-12 math education, I haven't been keeping as close an eye, but there are several books and resources, such as work by Jo Boaler: <a href="https://www.youcubed.org/resource/books/" rel="nofollow">https://www.youcubed.org/resource/books/</a>
This is a nice article. I teach mathematics at a community college and the last section of article resonated with me. What can we do about education of mathematics to improve it?<p>Years ago it dawned on me that most of the students taking a class of mine needed the class so that they could take physics. It’s been a long time since I took physics and I don’t really know what math problems students in physics classes have. I went to the physics department and asked for a list of types of mathematical mistakes that are common. Give me the list and I’ll make sure I emphasize this in my classes. No response.<p>I’ve since learned that what my students really need to know to be successful in physics really isn’t covered in course that is a prerequisite. I’m not really sure why I teach the topics I’m required to cover. They mostly are to give my students enough knowledge to take calculus and almost none of them end up taking calculus. I think things are done the way they are because it’s always been done this way.<p>Change is slow and hard.
That's <i>the</i> Bill Thurston! He's the guy that practically invented low-dimensional topology. He sewed up the entire field of foliation theory, and showed that most knots are hyperbolic. He won the Field's Medal ... he's someone to listen to!
In this context I highly recommend Lockhart’s Lament: <a href="https://www.maa.org/external_archive/devlin/LockhartsLament.pdf" rel="nofollow">https://www.maa.org/external_archive/devlin/LockhartsLament....</a>
The following quote from the paper in my opinion applies to coding interview tests:<p>"The competitions reinforce the notion
that either you ‘have good math genes’, or you do not. They put an emphasis on being quick, at the expense of being deep and thoughtful. They emphasize questions
which are puzzles with some hidden trick, rather than more realistic problems where a systematic and persistent approach is important"