Themed AP Lang and Comp: Mathematics

The Advanced Placement English Language and Composition exam is focused on analysis and argument based on nonfiction texts, which means there's a lot of opportunity to theme the readings for a course that prepares students for the exam. I'll write about a few different themes; this post focuses on a mathematics theme.

The key components of a class preparing students for the AP Lang & Comp exam are:

• writing narrative, expository, analytical, and argumentative essays
• writing multiple drafts of essays
• some informal writing (journaling, etc.)
• writing assignments based on a variety of prose styles & genres
• nonfiction readings of a variety of types (essays, journalism, political writing, science or nature writing, biography, diaries, history, criticism, etc.)
• graphic/visual image analysis
• citing sources

With those components in mind, here is an example set of readings for a math themed class. I tried to assemble a set of readings that could fit together coherently while covering different types of writing and topics within mathematics.
A Mathematician's Apology is by G.H. Hardy, a 20th century English number theorist. It's a beautiful essay about pure mathematics and how one does mathematics. It's really meant to convey to laypeople what it is that Hardy loves so much about his field and his work and to convince them that pure math has value in and of itself. There's a copy here. But there's also a lot to disagree with in the Apology; this short essay touches on a few of those things, especially how Hardy talks about writing about/teaching mathematics and his attitude towards applied mathematics.

A Mathematician's Lament by Paul Lockhart (sometimes referred to as "Lockhart's Lament") takes a similar view of mathematics but looks at American mathematics education. The essay describes many of the problems Lockhart sees with math ed as well as his vision for an ideal way to introduce mathematics to students. There's a copy of the essay here. Jo Boaler's book Mathematical Mindsets discusses many of the same problems and types of solutions but in more detail.

While looking at math education, definitely look for math ed in the news. One good recent example would be the discussions between Andrew Hacker (against algebra in school math) and the many math teachers, mathematicians, and scientists who have responded to him.

There are lots of biographies of mathematicians. Some well-known ones are The Man Who Loved Only Numbers by Paul Hoffman about Paul Erdős, The Man Who Knew Infinity by Robert Kanigel about Ramanujan, Prime Obsession by John Derbyshire about Bernard Riemann, Euler: The Master of Us All by William Dunham, and Genius at Play by Siobhan Roberts about John Conway. Reading one or two of these would give students light exposure to different areas of math and different ways of approaching mathematics. These mathematicians were also all very different people, so the messages in the books about their lives and about mathematics are quite different. (Note: I know of some good collections of short biographies of women in mathematics, but not any well-known books focused on one woman. If you've read anything good, let me know!)

There are a few autobiographies of mathematicians, as well. Edward Frenkel's Love & Math is especially well-regarded; in addition to Frenkel's mathematical journey, it discusses anti-Semitism in Russia, collaboration, and the importance of mentors.

Another approach would be to read books focused on an area in mathematics instead of a particular person, such as Simon Singh's The Code Book (cryptography), Derbyshire's Unknown Quantity (algebra), Eli Maor's e: The Story of a Number (logarithms, calculus. most technical on this list), or Charles Seife's Zero: The Biography of a Dangerous Idea.

I would also recommend watching at least one of George Csicsery's mathematics documentaries. The best known is N is a Number about Paul Erdős, but I'd lean toward one of the more recent ones. I love Hard Problems (about the US team to the 2006 International Math Olympiad), and I've heard good things about Julia Robinson and Hilbert's Tenth Problem, Counting from Infinity (about Yitang Zhang and the Prime Number Conjecture), and Navajo Math Circles.

Steven Strogatz has written a couple of very accessible math or math ed books. The Joy of X focuses on explaining fundamental math concepts, and it would be easy to pick up and read individual chapters.  The Calculus of Friendship focuses on the friendship between Strogatz and his high school math teacher and how Strogatz finds mathematics in life. This is the more natural fit of the two books for a class like this; looking at chapters from The Joy of X would go better with talking about math communication (discussed more below).

Read about current mathematics by looking at sites like Science Daily and Quanta. It would also be nice to have subscriptions to some fairly accessible mathematics journals like the College Mathematics Journal. This will give students non-technical or technical but understandable exposure to mathematics being done now in a variety of fields. While he tends not to post about current developments in math, I also recommend Keith Devlin's blog for accessible mathematical content.

I think it's worth spending some time looking at how to communicate mathematics. I would especially recommend this post by Terry Tao because it could also speak well to writing multiple drafts of essays. The other piece I really like about writing and understanding proofs is this one by Richard J. Lipton. A different approach would be to study some proofs without words, which entirely rely on diagrams to show the truth of a mathematical statement. There are book collections of them, some examples online, and a gallery of animations here.

"Paradox of Proof" by Caroline Chen is an article about the proposed proof of the ABC conjecture, an important problem in number theory. The proof is based on a field of mathematics that the author developed on his own, so the proof is incredibly inaccessible. This could lead to discussions of what it means to be a mathematician, what the responsibilities of a modern mathematician are, and to what extent communication is part of mathematics.