Yep we need to be carefull not to teach non rigorous mathematics. Also Mathematics is a field of inquiry that deals with abstractions of quantitative aspects of reality. Most of what you described as mathematics suits better to philosophy.
Thank you very much for your comment! Certainly, mathematics and philosophy have a lot of overlap. One of the reasons that it is so difficult to define mathematics is that it has grown so big that many modern branches of mathematics are no longer only quantitative, e.g. topology.
What a way to rob students of the opportunity to apply the quadratic formula! And also the revelation that really this problem has a super secret special second solution of -sqrt(2), which represents an unstable fixed point of the continued fraction. Then it's really a question of philosophy whether you want to accept it as another solution to the equation.
Yes, probably the most elegant way to explain is by using fixed points! Ofc, it is not reasonable to prove fixed point theorems at grade 9, but some diagram illustrating the idea can be helpful. It may also spark further interest
Having a great teacher who can spot mistakes makes a huge difference. Otherwise, even with a 100% correct textbook, a teacher without an understanding of mathematics would ruin the learning process. Unfortunately, schools train their teachers using low-quality materials that aim to show some tricks. No management gives Feynman as an example because he doesn't provide shiny promises and shortcuts. P.S. Prof Feynman found most of the physics textbooks for schools to be utterly miserable.
I think the grade 9 math textbook is great. Its not extremely rigorous... but it is far from the biggest problem in math classrooms. That will *always* be teachers. Underfunded and overworked, probably in the hardest subject to teach (especially to people that sometimes dont want to learn)
I think this video is dangerous. Criticisms can be made, but 5 minutes talking about how terrible a textbook is?? Really?? Talk about how to get kids involved in math or how to teach teachers!
I agree teachers deserve better. They are not to blame. If anything, I may quote mathematician Edward Frenkel, "if anyone were to blame (for the lamentable state of basic math education), I blame myself and my colleagues, professional mathematicians, for not doing nearly enough". Often the textbook is seen as the authority (whether or not it should be can be debated). Any math education worthy of its name should foster the right intellectual habits, and textbooks play a huge role in it. This one teaches students to jump to conclusions.
Because its so incredibly useful in so many parts of life. What type of question is this, as if its wrong to see mathematics as something useful? The use of mathematics is arguably one of its greatest attributes.
