“When an Adult Took Standardized Tests Forced on Kids,” by Marion Brady

Marion Brady wrote a wonderful piece for a Washington Post blog a couple of days ago, which I found out about thanks to Susan Ohanian’s very informative site. A very successful member of American society, with two master’s degrees, who is also a member of a school board, decided to take his state’s standardized tests … Read more

Using Failure As A Friendly Tool For Learning

Current grading policies at most schools are intended to measure learning, but they are counterproductive in that they actually inhibit learning. Taking a typical university mathematics course as an example, students might have a handful of assignments, a mid-term test, and a final exam. The number of graded items is small because universities are strapped … Read more

On teaching how to prove mathematics theorems

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

On the fundamental theorem of calculus

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

On procrastination, and our broken undergraduate education system

I believe that the main reason that we procrastinate is that we don’t feel competent. We fear that our results will not be up to some expectation, and the fear paralyzes us. Or rather, in this era with abundant opportunities for diversion, we distract ourselves in wasteful activities so that we don’t have to face … Read more