Some Links to my Math Education Page and Blog
The Common Core
I finally completed the analysis of the Common Core State Standards for high school math that I promised in the previous issue of this newsletter. The short version:
＊ I like the direction the CCSSM takes in high school in its stated goals, in the shifts in algebra and geometry content, and in the acknowledgment of a central role for technology.
＊ I don't like the unrealistic implementation timetables, the shrinkage of geometry, the fact that there are way, way too many standards, and the fact that many come too soon.
＊ I hate the tie-in with high-stakes tests.
But please, don't agree or disagree based on this summary. If this topic matters to you, please take the time to read the paper. Alas, it's long (21 pages.)
Initial response has been gratifying: I received supportive messages from three national leaders in math education — three people I highly respect.
Read it for yourself online, or better, download the PDF. If you want to respond, you can post a public comment here, or just e-mail me. Of course, you should feel free to forward these links to whoever you think might be interested.
A Curriculum Model
I made an annotated visual representation of how I see the various ingredients that go into effective math curriculum development. The resulting blog post turned out to be surprisingly popular. The diagram is largely based on an image I created in the early 90's in conjunction with the textbook I co-authored with Anita Wah.
Geometry of the Parabola
Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the proofs of those properties.
On my Web site, I present the basics: the geometric definition in terms of focus and directrix, the construction, the reflection property, and "all parabolas are similar". I just updated that page with the addition of new GeoGebra applets. Check it out!
From there, you can click to more geometry of the conic sections, including proofs that they are indeed conic sections.
"Showing Work"
This is a post about a teacher who gave zero credit for homework if the student did not "show work", a response to an e-mail from an anonymous source. It dates back to the early days of my blog. I still agree with what I wrote. I have given a lot more thought to assessment and grading since then, and hope to write about these broader issues in the coming months. Stay tuned!
