The linked PDF is a Workbook for a semester-long course using Tannenbaum’s Excursions in Modern Mathematics. I used them as lecture notes at Austin Community College.
The general approach is that of “discovery learning”. I’m a recovering fan of the Moore method (see rant below).
- Voting theory/Arrow’s Theorem (1 chapter)
- Fair division (1 chapter)
- Graph theory (3 chapters, includes a little set theory)
- Transformation geometry (1 chapter)
- Fractals (1 chapter, includes complex arithmetic)
- Intro to probability (1 chapter)
If I had it do over again (these notes are from 2008), I’d definitely pick different topics. These notes are too much about abstract math (5 of 8 chapters) and not enough about the real social issues to which I would like to see students apply the reasoning skills we’re teaching them.
Rant: Noted class chauvinist and racist educator R. L. Moore
When I wrote these notes, I was fresh out of Texas State’s Math Department, where the Moore method was heavily promoted.
Nowadays, I view the Moore method as flat-out inequitable.
However, my experiences teaching at a diverse urban community college with these notes suggest that they avoid many of the issues that make the Moore method problematic—by which I mean, profoundly socially retrogressive.
The Moore method throws students to the wolves. My notes don’t. I think they do what the Moore method does at its best in that they facilitate engagement, confidence, and retention. I think they deviate from the Moore method in that they provide guidance and facilitate teacher-student empathy.
Story about R. L. Moore when he taught at UTexas: Moore saw one of his grad students doing grounds maintenance on campus. Moore asked why the student wasn’t working on math instead. The student said they needed the money. Moore judged that they weren’t serious about math and worked to have them removed from the program.
I heard that story in Austin. But how come no one in Texas ever told me how racist Moore was?
What a gem of a man.
And as future math teachers, we were taught to emulate him.
I remember one such Moore-head prof laughing out loud when I used the word “problematic”.
“That word is for English majors,” he told me. “It doesn’t mean anything.”
It’s for anti-racists, too, dude. It just didn’t mean anything to *you*.