My Discovery-Based Math Elective: Introductions (Part 1)

In my short teaching career so far, I have been privileged in my exposure to teaching high school math electives. Given significant curricular and pedagogical liberty, I decided this year to make a pretty radical pedagogical shift in how I teach the class. It went pretty well, and my goal is to share the curriculum I developed, and reflect on structure and experience.

I'll reflect on the different components of the course over the course of a few blog posts, and will link them below. Providing this kind of Table of Contents will help me remember what all the components of the course are. I will link the posts below as I write them and might add things as they come up.

Table of Contents

1. Introductions (this post)
2. The Purpose of the Elective
3. A Typical Week
4. Practice Standards
5. Grading and Feedback
6. Circulation Notes Tracker
7. Compiling PSets
8. End-of-PSet Discussions
9. Exhibitions
10. Modifying for Distance Learning
11. Different Things Become Difficult
12. Pedagogy of the PSet
13. Architecture of a PSet
14. Content Threads
15. Impact on My Teaching

Before writing, let me share some relevant context:

• How is the curriculum packaged?
• The curriculum is packaged in a series of 26 problem sets (PSets). Here they are. They are a living document, and I'm always tweaking them. Check them out! Feel free to leave a comment on anything you have questions about, or if you notice an error.
• Full disclosure, however, they are imperfect, and I can't promise they are error free.
• There is also a set of unit plans to go with the PSets. Here they are.
• Same as above!
• If you have a question about any of the materials contained in this curriculum, leave a comment, or hit me up on Twitter @BearStMichael
• Where did you get the curriculum?
• James Tanton's Exploding Dots and Without Words, PROMYS for Teachers, PCMI, PlayWithYourMath.com, Joey Kelly, the #MTBoS, and a million other places. I haven't done a great job of citing sources, and it is an objective of mine to do so in a way that is helpful, honest, and honorable. If you see any problem that should have a source, feel free to leave a comment direction on the material, and I work on adding that citation.
• How did this course come to exist in your school?
• For a few years, my school required all juniors to take an SAT Math prep. They had scheduled me to teach a couple of sections. I asked if I could instead teach a pure math elective. Based on the meh experience that our school had with widespread mandated SAT prep (shocking), and the already virtually non-existent options for student choice in the classes they took, my school took a chance on letting me teach a portion of this course, as an optional alternative to SAT prep. I initially modeled the course pretty directly off of the course I'd seen Joey Kelly teach when I was his student teacher.
• The year after, we had built some momentum in favor of math electives and student choice, and my department was able to expand this course into a year-long course, broken into two independent semesters.
• What is your school's demographics and background?
• I teach in Boston Public Schools. You can see my school's data here, and it's pretty accurate, though an obviously incomplete picture of the school. But the major points are: