Math and Education Links

Here's some of what I've been reading over the past few months!

DeanDad on active learning.
I took an inquiry-based (pretty strictly Moore Method) course the semester that I was in Budapest, and I remember the professor telling us that any course that was very inquiry-based needed to be opt-in. He'd taught IBL Calculus at UChicago, where it was one of several options; it wouldn't have worked if it had been the only choice (even with the right class sizes). Some of that is because of what DeanDad talks about here. Active learning can be really empowering (as Francis Su talked about at the IBL conference in August), but it can also feel like abandonment, and I've seen it go both ways.

Modeling as creative science.
This is an article from earlier this year that Rhett Allain reposted this fall. After reading him for a few years, getting more experience doing mathematical modeling, and going to a conference that focused on using and teaching modeling in the classroom, I pretty much agree with Allain's focus on models. This particular post is about having students do the modeling work, which is really important; I also agree with him that there's great value in presenting information as models.

Using Student-Generated Examples.
This reminded me a lot of some of the problems that were assigned in my real analysis class, except there so often there was one type of intended example, and here that changes a lot by question (and variety is part of the point). What kinds of math classes does this fit into well? It seems natural for thinking about patterns and functions.

Ben Orlin does interesting things to the high school math curriculum.
I have an immediate adverse reaction to the Utility Belt Curriculum, and I'm not quite sure why. I love the Go Forth and Prosper Curriculum and would love teaching any of the 11th/12th grade courses, but as Orlin mentions, it's not feasible in most schools. I don't find Four Square Meals particularly appealing, partially because I don't really understand doing AP Calc AB and BC in two years, so I don't like the rationale. (Though yes please to it being normal for everyone to get decent stats ed.) I like the Verb-Powered Curriculum, though not doing some calc in the modeling class or circling back to modeling in the class that involves calc seems unfortunate. There's a ton of modeling that you can do without calculus, obviously, but so many modeling possibilities open with calculus.

Math with primary sources.
Could be good for integrating into math courses, for math history courses, or for history projects related to math topics.

Some More Math Links

Jeremy Kun's Habits of Highly Mathematical People.
He doesn't actually spend a ton of time on how the math we do in the classroom teaches the habits/skills he mentions; he's mostly defining and discussing examples of these skills in mathematical people. It's still pretty fascinating and useful.

Mark Chubb on Closing a Lesson
This post includes links to interesting things about orchestrating math discussion, and in general it talks about some things I've been thinking about (and struggling with) recently

Francis Su's Freedom Through Inquiry
I was fortunate enough to be at the IBL conference where Francis Su gave this speech, and it's so good. I love the humor of parts of it ("This set's closed, this set's open, this one's neither, this one's clopen!"), but Su also says so many important things about freedom in learning and how inquiry allows this freedom.

Dylan Kane on Lecturing
I'd never heard the bit about lecturing in MS/HS because in HS/college there would be lectures, but I agree with the reasons Kane lists to not use this excuse. My favorite part of the post, though, is the bit about not being sure how to respond when asked if he lectures, with these two quotes:
"Based on that knowledge I may choose to deliver some explicit instruction. Maybe for two minutes at a time, maybe for twenty."
"There’s no magic bullet, no one right answer. That intellectual work of figuring out what is going to work tomorrow for my students is probably my favorite part of the job."


Joshua Bowman on Expectations of an Upper-Level Math Class
This is mostly an excerpt from Bowman's analysis syllabus, setting up expectations from which specifications for grading will be taken. I really like the idea of explicitly basing an upper-level course around the ideas of definition, theorem, proof, and community. (I love that he includes community because it's so important.)

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.

Links and Thoughts on Math and Math Ed

Here are a few things I've read recently related to math and math ed!

Sam J. Shah wrote about having a book club in a math class. I like the readings and the thoughts on organizing the discussion, and it would be interesting to think more about how to scale it. I've been putting together a set of mathematics related readings, more focused on thinking about writing and analysis with math as the subject than the other way around, and that list will definitely be influenced by this set of readings.

Steven Strogatz on math, modeling, and his math course for liberal-arts students. I really enjoyed reading what he had to say about that course, both the approach and what it's important to learn in such a class. The part of this that hit me the most, though, was the part about mathematical beauty. I'm definitely prone to describing math, or at least good math, as beautiful and elegant, and while I've had success explaining to people where I see that beauty, Strogatz is right that it can also be alienating. I'd like to keep that in mind.

Francis Su (MAA president and Harvey Mudd professor) on focus on process vs grades, growth mindset, and academic dishonesty.

SIAM and COMAP (which runs the Mathematics Contest in Modeling) put out this guide to teaching math modeling in K-16. It's cool.

Mark Chubb wrote about an estimation-focused task near the end of a unit on multiplication and about what it means in terms of focus on concept vs focus on procedure. All the questions at the end of the post are really important, and I would ask another question. I don't wonder only what students think being successful at mathematics looks like but what they think mathematics is. Also, I love the task itself.

Literature as Ballet

A number of ballets are based on literary works, so a class around literature, ballet, and the translation between them could be really interesting! This is an outline for the content of such a class; note that this will be far better with students who have reasonable familiarity with ballet and preferably know basic ballet history.

The ballets in the recommended list are all available on DVD. There are some ballets that would be good fits for a class like this (ex. John Cranko's Onegin) but have not been released on film. And of course, if there are ballets based on literary works being performed by nearby companies, go see them!

Themed AP Lang and Comp: Sports

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 sports 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 sports themed class. I tried to assemble a set of readings that could fit together coherently while covering different types of writing and sports.

Themed AP Lang and Comp: Biology

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 biology 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 biology themed class. I tried to assemble a set of readings that could fit together coherently while covering different types of writing and fields within biology.