An illustration from Oliver Byrne's 1847 edition of Euclid's Elements. Image: Public domain, via Wikimedia Commons.

I’ll be teaching a math history class for the first time this semester. I’m excited to be teaching it, but I’ve noticed that preparing for this class has been very different from preparing for other classes I’ve taught, which have all been math content courses.

I know how to teach a math content course. I don’t mean that I don’t have a lot to learn about teaching, but that I basically know what I want students to be able to do at the end of a math class, and that knowledge guides my teaching from day one. But when I first started preparing for my math history class, I wasn’t really sure how to start because I didn’t know where I wanted my students to finish.

At the end of a math content course, there are certain skills my students need to have. In calculus, they need to know what a derivative is, understand the chain rule, find the integral of a function. They’ll probably need to be able to use some of these skills in their next math classes.

Of course, it’s not just about content. I want my students to learn what qualifies as a convincing argument, persevere at problems, and communicate clearly about their thinking. Whether they continue taking math classes or not, those skills will help them in the future.

But it wasn’t quite as obvious to me what my students should get out of a math history class. It’s definitely not a list of when and where different mathematicians lived, or what theorems they proved. It's not the life stories of famous mathematicians. Of course, I want it to help them develop their critical thinking and research skills, but that is too vague to be useful. Pretty much every college class should develop critical thinking skills.

A few facts about my class helped me think about what my goals should be. At my school, math history is a class in the math department, so it is probably more focused on mathematics than the same class would be if it were in the history department. It has a prerequisite of at least calculus I, and most of the students who enroll are majoring in math, engineering, or computer science. The course fulfills an upper-level writing and communication credit for the university, which means I have to make sure it satisfies certain requirements about how much writing students do.

I decided to let mathematics topics guide the course. Instead of presenting an overview of all of mathematics happening at one time in one place, my class will be somewhat modular. In each section, we’ll start early in history and follow the subject’s development over time. Mathematically, I’ll be focusing on number systems and number theory, the development of non-Euclidean geometry, and calculus. But I think more than in content courses, the exact topics I’m choosing to focus on are secondary. My students could get what I want them to get out of the class with a lot of different choices of topics.

If my students only get one thing out of this class, I want them to see that mathematics did not spring from the head of mathematicians fully-formed in little definition-theorem-proof packages. It was (and is) invented and discovered in bits and pieces by many people through creative processes, and people are still creatively inventing and discovering math.

I will be focusing on original sources as much as possible. I want my students to get practice reading unfamiliar mathematics and putting themselves in the shoes of the people who first wrote about it. By the end of the class, I my students should have experience reading original sources carefully and finding trusted secondary sources to illuminate the original sources if necessary. They should be able to do computations using some historical techniques and understand how those techniques relate to the modern ones they're more familiar with.

As far as the writing component of the course is concerned, my main goal is for students to write clearly, correctly, and creatively to the audience that they intend to read a paper they write or listen to a presentation they deliver.

If you’ve taught a math history class, I’d be happy to hear what your goals for the course were and what you think about mine.