Teaching a “profound understanding of fundamental mathematics” is very different from teaching traditional collegiate mathematics, but for the next few decades, some mathematically knowledgeable people must do it if all university mathematicians are to be able to teach university-level mathematics some day.
I don’t think this is literally true—the subculture of the mathematically savvy people seems quite self-sustaining, especially because, as the author has previously correctly noted, they often ignore the school system and teach their kids mathematics at home (at least until the kids get sufficiently solid fundamentals so they can continue learning from books and videos).
There are also some great educational tools such as Khan Academy etc., where the problem is on a meta level: you need to be told about the tool, and you need the motivation to use it. (There is probably also a lot of educational snake oil out there.) The problem with these tools, from the perspective of the article, is that they teach math, but they don’t teach teaching math. They are great for the students, but the teachers need something different to do their jobs well.
Continual remedial programs for math teachers, definitely a good idea! (I assume they would be voluntary, which means the participants would be motivated.) Just maybe change the name to something like “math teachers giving each other advice”; anyone can join, anyone is free to give or not give a lecture, always invite one or two experts. Because you also want feedback from the teachers, what works for them and what does not, and also encourage them to try their own things.
(Congratulations for surprising me, by the way. I didn’t expect to read an article that has “racial equity” in title that I would agree with so much.)
I’m glad you liked the article! As for your one disagreement with the quoted passage, I think the all in the phrase “all university mathematicians” is key to her point. Mathematicians at prestigious private universities and well-known state flagship universities are indeed able to teach university-level mathematics due to the adequate supply of mathematically-prepared students that remains despite bad k-12 math education. But a large percentage of university mathematicians are at less prestigious institutions where very few students major in math and most of the demand for math courses comes from students who didn’t have a good math experience in k-12 schooling (and weren’t taught math at home by mathematically savvy parents) but need to satisfy a gen ed requirement.
A related article from 2005 arguing that it’s important to teach elementary school teachers more mathematics in order for their teaching to improve: https://www.ams.org/notices/200502/fea-kenschaft.pdf.
This is perfect. Thank you!
I don’t think this is literally true—the subculture of the mathematically savvy people seems quite self-sustaining, especially because, as the author has previously correctly noted, they often ignore the school system and teach their kids mathematics at home (at least until the kids get sufficiently solid fundamentals so they can continue learning from books and videos).
There are also some great educational tools such as Khan Academy etc., where the problem is on a meta level: you need to be told about the tool, and you need the motivation to use it. (There is probably also a lot of educational snake oil out there.) The problem with these tools, from the perspective of the article, is that they teach math, but they don’t teach teaching math. They are great for the students, but the teachers need something different to do their jobs well.
Continual remedial programs for math teachers, definitely a good idea! (I assume they would be voluntary, which means the participants would be motivated.) Just maybe change the name to something like “math teachers giving each other advice”; anyone can join, anyone is free to give or not give a lecture, always invite one or two experts. Because you also want feedback from the teachers, what works for them and what does not, and also encourage them to try their own things.
(Congratulations for surprising me, by the way. I didn’t expect to read an article that has “racial equity” in title that I would agree with so much.)
I’m glad you liked the article! As for your one disagreement with the quoted passage, I think the all in the phrase “all university mathematicians” is key to her point. Mathematicians at prestigious private universities and well-known state flagship universities are indeed able to teach university-level mathematics due to the adequate supply of mathematically-prepared students that remains despite bad k-12 math education. But a large percentage of university mathematicians are at less prestigious institutions where very few students major in math and most of the demand for math courses comes from students who didn’t have a good math experience in k-12 schooling (and weren’t taught math at home by mathematically savvy parents) but need to satisfy a gen ed requirement.