Math Education Newsletter

Here are links to posts on my Math Education Blog that you might find interesting.
If you are so moved, you may comment on the posts, and/or subscribe to the blog.

Whole-class Discussion

As a teacher, I had my strengths and weaknesses. One thing I did reasonably well was conduct whole-class discussions that involved students in actually doing math. That skill originated largely in my days as a graduate student, when I taught math to third graders for 40 minutes a day, and was trained in the techniques of Project SEED. Those are suitable for a wide range of grade levels: I've used them from Kindergarten to teacher professional development workshops. I share some of them in this blog post. I also obtained permission to post two important Project SEED books on my website.

Related article: Taking Notes vs. Doing Math

The California Math Framework Revision (continued!)

As I mentioned in my September newsletter, California is rethinking its K-12 math program. This has generated much commentary in the form of tweets, open letters, and (in my case) blog posts. A revised version should be coming soon, hopefully incorporating some of that feedback. Until then, I will refrain from further comments. Here are my posts so far:

• The California Math Framework Revision
• More on the California Framework
• Detracking, How To
• Yet More on the California Framework (Part 1)
• Yet More on the California Framework (Part 2)

An Integrated Path

How to develop an integrated path through high school math is actually somewhat relevant to the Framework discussions. I present the approach I developed with my colleagues when I was department chair in this blog post: Integrating the High School Math Curriculum. I believe we were reasonably effective in addressing the shortcomings of the Algebra 1 / Geometry / Algebra 2 sequence, while also making the transition manageable for the teachers.

Related articles:

• Big-Picture Planning
• The Common Core: A Closer Look (includes specific ideas on when to teach what)

New or updated on my website.

Minus

Minus, of course, is a source of many mistakes. Possibly helpful: The Three Meanings of Minus, a short discussion-provoking lesson from Algebra: Themes, Tools, Concepts.

Changing a, b, c

Where does the vertex of a parabola go when you change one of the parameters `a`, `b`, `c` in the equation `y=ax^2+bx+c`? Your students can explore this question using this applet.

Geometric Puzzles

I share a lot of geometric puzzles material on my website. Because there is so much there, I decided to map out a coherent unit that provides a possible path through some of it.

Also:

• I tweaked and reformatted SuperTangram Labs and Pentomino Labs.
• I made a PDF for the two toughest superTangram puzzles: the 14-piece convex hexagons, which are mentioned in SuperTangram Labs, and do not appear in the SuperTangram books.

Popular Pages

According to Google, these pages were the most frequently found since my last newsletter:

• Equations vs. Identities
• Geometry of the Parabola
• From Factored to Standard Form
• Pentomino Books
• Pick's Theorem
• Virtual Grid Paper
• Virtual Pentominoes
• V-shaped Graphs

And Finally...

Small updates!

• I added a Number Puzzles directory.
• I updated Infinity‘s Chaos handout to include instructions on editing the accompanying GeoGebra files.
• I added a couple of pattern block creations (by Kathy Paur and Hana Murray) to the six-fold rotation page of my Wallpaper Catalog.
• I added a brilliant compass and straightedge construction by Dan Bennett to the Soccer Angles generalization.