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

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?

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