This is my third post on the in-process revision of the California Math Framework. If you haven’t yet, please read the first two: The California Math Framework Revision, and More on the California Framework. I just reread them, and find that I stand by what I wrote: the revision attempts to address an important issue: low-track… Continue reading Detracking, How To

# Blog

## More on the California Framework

The Independent Institute published an Open Letter to Governor Newsom, calling for the complete abandonment of the (currently in progress) revision of the California Math Framework. Before I share my thoughts about the letter, I will ask you to please make sure you read a previous post, in which I commented on the current draft… Continue reading More on the California Framework

## Geometric Puzzles Unit

The Geometric Puzzles home page on my website contains many links, and it is organized reasonably well. Still, someone who is not familiar with all these puzzles may need help in turning them into a curriculum unit. This is what I hope to do in this post. (I will try to not duplicate the overview of… Continue reading Geometric Puzzles Unit

## The Game of Pent

Puzzles are a big part of my work as a teacher and curriculum developer, as you can see in this article, in the Geometric Puzzles launch page on my website, and in fact throughout my books. (Not to mention my parallel career of sorts as a cryptic crosswords constructor, and how I spend much of my free time.)… Continue reading The Game of Pent

## Integrating the High School Math Curriculum

The standard middle school / high school course sequence in much of the US is Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus. This is pretty much a US-only concept: elsewhere, algebra and geometry are taught every year in middle school and high school. This American tradition leads to many endemic problems: The traditional Algebra 1 includes an enormous amount of… Continue reading Integrating the High School Math Curriculum

## The California Math Framework Revision

California is revising its Math Framework. A draft has been updated after a first round of public comments, and a second round will take place starting in December. The Framework is of course an important document that will affect math instruction in public schools throughout the state for at least several years. I have not seen… Continue reading The California Math Framework Revision

## Commitments

In a blog post seven years ago, I summarized “Embracing Contraries in the Teaching Process”, an important article by English professor Peter Elbow. In that post, and its sequel, I tried to apply Elbow’s ideas to the teaching of math. I encourage you to read both posts, and Elbow’s article (which I linked to in the first… Continue reading Commitments

## Fraction Rectangles

This is a sequel to my last post (Seeing is Believing?), addressing the same issue from a different point of view. Fractions, of course, are difficult. When teaching 4th and 5th grade in the 1970's I struggled with this, and came up with a powerful learning tool: fraction rectangles. The idea is that it is… Continue reading Fraction Rectangles

## Seeing is Believing?

“Proofs Without Words” are proofs based on a visual representation of a theorem which provides a convincing argument about its validity without the need for any accompanying text. The genre has been much enriched by the increased availability of computer animation. This is of course relevant to math education: many of the concepts we teach can be illustrated visually, including with… Continue reading Seeing is Believing?

## Transformational Geometry for Teachers

I taught geometry for decades, starting in the 1980’s, and loved it. I’m reasonably good at manipulating algebraic symbols, but I don’t especially enjoy it. In contrast, I am happy to spend plenty of time on visual puzzles, and I am enthusiastic about sharing that passion with colleagues and with students. Early in my high… Continue reading Transformational Geometry for Teachers