## Blog Posts

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)

## MathEducation.page

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.