## 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.

### Commitments

A central challenge for all of us is the tension between our commitment to mathematics, on the one hand, and our commitment to our students on the other. I wrote about it in 2013, and more generally about the concept of embracing opposites in 2015. But there is a third commitment which interferes with both of these: a disproportionate emphasis on enforcing student compliance. Read about it here.

### The California Math Framework Revision

California is rethinking its K-12 math program. The goal of the revision is to reduce learning gaps, including by de-tracking secondary school classes. I support this, but I worry that implementation is not going to be easy, and I fear that a possible backlash may drastically set us back, as happened after the 1992 Framework was adopted. Read about this here.

### Big-Picture Planning

In my role as math department chair I could not limit myself to planning individual lessons. I learned early on that effective lesson plans depend largely on well-thought-out plans for units, courses, and in fact the whole high school math program. In the past few years, I wrote a number of blog posts about the need to zoom out and see the big picture. I recently concatenated and edited some of those posts into an article on my website: Big-Picture Plannning.

## MathEducation.page

New and newish on my website.

### Sequences and Series, Formulas

A recurrent question in teaching secondary school math is about the pedagogical use and misuse of formulas. One approach is to teach a formula, and have the students practice using it. Another is to minimize memorization without understanding by encouraging students to rethink each problem from first principles. In a new 10-minute video about Sequences and Series, I articulate a middle course: *formulas should encapsulate understanding, not substitute for it.*

### Games

Three math games, implemented as GeoGebra applets:

- Signed Numbers: In this new game, students practice signed number arithmetic, their understanding of decimals, and their estimation skills.
- Complex Numbers: This is the same game for complex arithmetic. It's been on my site a long time, but I recently fixed a bug and slightly improved the interface.
- Pent: This two-person strategy game was invented by George Mills. It is inspired by Hex, but it is played on a flattened and stretched-out soccer ball.

### Functions

Functions, of course, are a major topic in middle school and high school. I recently added some material aimed at Algebra 2 and Precalculus.

- Window Shades: Lessons about rate of change by Rachel Chou. They are inspired by the Doctor Dimension concept, but they are somewhat more "real world".
- Tri, Tri Again, an interesting application of iterating linear functions to geometry. (Suggested by Rachel Chou.)
- Two linked function diagram applets to visualize the composition and iteration of functions. You can use them to make images for copy-pasting into a word processor or presentation software.

### Geometry of the Parabola

In my already substantial Geometry of the Parabola page, I added:

- An eight-minute video guide to a construction of the parabola in GeoGebra (or in some other interactive geometry application)
- Yet more evidence that all parabolas are similar. This time an applet showing that given two parabolas with parallel axes of symmetry, one is a dilation of the other.
- A new GeoGebra applet to show the parabola as the envelope of a family of lines

### Symmetry

Two small changes to my Symmetry materials:

- I improved my Spirograph Simulation: it is faster, and it is now possible to hide the moving parts so as to better see the final image.
- I added pattern block creations by Hana Murray and Simon Gregg to the Dodecagons and Wallpapers Catalog pages.

### Popular Pages

According to Google, these are the "top growing" and "top performing" pages and queries for my website in the past five months.

From *Algebra: Themes, Tools, Concepts*

- Equations vs. Identities — some basic pre-algebra
- The Cover-Up Method — an alternative approach to equation-solving.
- Algebra Magic — analyzing and inventing "magic" tricks
- Working Backwards — a whole chapter
- Constant Sums, Constant Products, Constant Differences, Constant Ratios — an untraditional approach to traditional topics
- Skidding Distance, a "real world" application of the square root function — a perennial hit, inexplicably

Transformational Proof:

- Transformational Proof in High School Geometry — a rigorous development, co-authored with the late Lew Douglas.
- Transformational Proof Basics — a subset and predecessor of the above. I don't know how people found it, as I don't think I link to it anywhere.
- Triangle Congruence and Similarity (v1, v2),another predecessor of Transformational Proof — both versions are interesting for different reasons.

Algebra 2 / Precalculus

- From Factored to Standard Form, a parabolas worksheet — another perennial hit, according to Google
- Geometry of the Parabola — construction, reflection property, and more

Puzzles

- Virtual Pentominoes — great puzzles online!
- Pentomino Puzzle Books — great puzzles in free downloadable books!
- Number Pyramids — addition-based puzzles for upper elementary and middle school students

Other:

- Using the Geoboard — a versatile manipulative learning tool
- Virtual Grid Paper — for non-graphing uses
- Symmetry — K-12 activities!
- Math Education — the front page