Asking for a letter of recommendation

Here is my advice to students who need to ask their professor for a letter of recommendation. Ask your professor nicely and politely. You do not have to ask the professor in person, but do not ask the professor in a quickly jotted, informal email in all lower case! Early, early, early. It takes time…

How to curve an exam and assign grades

We have all given exams where the grades end up lower than we hoped. A curve is in order. How do we do it? In this post I share my thoughts on when you should (or should not) curve an exam. I give ten sample curving techniques, including pros and cons of each, I explain…

A solution for tight budgets?

All educators face challenges during these troubling economic times. The USA Today has an article about one teacher’s solution: Ads on tests add up for teacher.

Thoughts on how to teach induction

In their article “Some observations on teaching induction,” (MAA Focus, May/June 2008, pp. 9–10) Mary Flahive and John Lee give tips on how to teach induction. For a variety of reasons, they encourage professors to downplay proofs of theorems such as the “baby Gauss” formula for all . Indeed, I have noticed that students can…

Do you give partial credit? How to grade Venn diagrams

Suppose that on an exam you asked your class to shade the region corresponding to  in the figure below. The problem is worth 5 points. The correct answer is: When you received their solutions, some students had regions shaded that shouldn’t be shaded and left regions unshaded when they should be shaded. My question is:…

Advice for the budding mathematician of any age

Fields Medal winner Terry Tao put together a page on his blog titled Career Advice. He writes: Here is my collection of various pieces of advice on academic career issues in mathematics, roughly arranged by the stage of career at which the advice is most pertinent (though of course some of the advice pertains to…

Flash cards are a good idea

I recently came across an article by the mathematician Ethan Akin, whose work in topology and dynamical systems I admire greatly, called “In Defense of ‘Mindless Rote’“.  In the article he defends the traditional education model of having students memorize mathematical facts and techniques. He begins with the following quote from Alfred North Whitehead’s Introduction to Mathematics….

The nuts and bolts of writing mathematics

This was a handout that I made for my Discrete Mathematics class.  At our college this course is the gateway to the mathematics major and is the students’ introduction to writing mathematical arguments. Here is a pdf of the handout. The nuts and bolts of writing mathematics You know that I write slowly. This is chiefly…

Student podcasts in a history of mathematics course

I would like to take this opportunity to showcase some of my students’ work from last year.  I taught a class called “Great Theorems and Ideas in Mathematics.”  It was an upper-level history of mathematics course with a focus on some of mathematics’ greatest theorems.  I used William Dunham‘s Journey Through Genius for a good…

Wobbly tables and the intermediate value theorem

Tomorrow I’ll be introducing the intermediate value theorem (IVT) to my calculus class.  Recall the statement of the IVT: if is a continuous function on the interval and is between and , then there exists a value such that .  In other words, achieves all of the intermediate values between  and . This is a very underappreciated theorem…

Line Rider Calculus

The first time I saw Line Rider in action, I knew I should use it for a calculus class, but I didn’t know how.  Recently 360 wrote about using Line Rider in a calculus course, and so did  Teaching College Math, who suggested creating a video of the action using the screen capture software Jing. This week’s topic in…