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

# Tag: Teaching

## 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?

## Tiling and Transformations

In my last post, I argued that tiling is a good topic to include in a geometry program. Students find it engaging: on the one hand, it connects with art and culture; on the other hand, it provides a context for student creativity. At the same time, it presents many connections with the geometry curriculum in middle school and high… Continue reading Tiling and Transformations

## Tiling

Covering the plane with an unlimited supply of identical tiles is called tiling the plane, or tessellation. Over the years, I’ve developed a number of classroom activities about tiling. You can find links to those on the Tiling home page on my website. In a conversation with a teacher a few months ago, I realized… Continue reading Tiling

## Virtual Manipulatives: Part 2

In the previous post, I discussed virtual manipulatives in general, and a particular implementation for algebra, using a Google Drawings representation of the Lab Gear. In this post, I will explore GeoGebra as a platform for virtual manipulatives. Pattern Blocks Virtual pattern blocks are not hard to find on the Web. One good implementation is on the Math… Continue reading Virtual Manipulatives: Part 2

## Virtual Manipulatives: Part 1

Learning Tools In 1981, after ten years in K-5, I switched to teaching high school math. In some ways, this felt like starting a whole new career: the math was more involved, the relationship with students less like parenting, and tradition weighed a lot more heavily on the profession. Still, in other ways, teaching is… Continue reading Virtual Manipulatives: Part 1