My basic attitude towards memorization in mathematics education is to memorize the absolute minimum, but memorize that minimum perfectly. Part of a mathematics teacher’s job, in my view, is to guide students to understand what this “minimum” is, and then encourage them to memorize it, helping them to find effective means for memorization. Effective means, … Read more
I’m teaching first-year electricity and magnetism this semester, and we are using the textbook College Physics by Knight, Jones, and Field. Students find it very clear, and it’s worked out well (we used the same textbook last year). The workbooks are very effective, as they walk students through concept development very nicely. As teacher resources, … Read more
Thomas Wolf, who is a professor in the Brock University Mathematics Department, has created a wonderful series of mathematics contests for elementary-school students: the Caribou Mathematics Competition. Contests are available at each of three Grade levels: Grades 3/4, Grades 5/6, and Grades 7/8. The next contest date is 16 February 2011, so if you are … Read more
My mother was on her deathbed in 1954 (before I was born), and received the last rites. That she is still alive, and still living independently, is an inspiration to me, and a testament to the power of persistence. A great man once told me that his biggest successes came about because of his “sheer … Read more
The more you understand, the less you have to memorize. A good example is trigonometric identities, of which there are quite a number. Should a student memorize trigonometric identities? Well, at first, it is probably wise to memorize a few of them. Part of a teacher’s job is to help students identify what is essential … Read more
Seth Godin has a fantastic blog, and today’s post makes pointed comments about education, although it is more generally intended to discuss how to help people get things done. Check it out here. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)
One of the traditional purposes of culture is to educate. Before books were common, the spoken word was the essential tool for teaching. Stories are memorable, and so telling stories was an effective way to pass on life lessons, particularly moral lessons. But in recent times, “information media” have been used overwhelmingly often only for … Read more
One of my beloved professors told me a story about 30 years ago that has stuck with me, and has informed (not enough, alas) my own teaching practice. He was taking a full-year graduate course in C*-algebras with (I believe) Israel Halperin. By the end of the course they had covered 16 pages (!) of … Read more
For four consecutive years I taught a fourth-semester course called “Introduction to Analysis,” in which we looked at differential calculus for a second time, stressing the foundations, the logical structure, and proving all the key theorems. We used Stephen Abbott’s excellent book, Understanding Analysis. The course was intended primarily for math majors, although we had … Read more
One day a graduate student submitted some writing to me, in which she was explaining rates of change at the high school level. She made an interesting statement: The slope of a secant line joining two points $(a, f(a))$ and $(b, f(b))$ on the graph of a differentiable function $f$ is the average of the … Read more