In this issue:
Summer is Coming!
Summer, for me, can be a very intense work time, as that is when I present my workshops to teachers. My style for those is to pack as much as I can into a limited time frame. As a result, planning is a very time-consuming proposition, as one day of workshop time can correspond to weeks of classroom time. Moreover, I also build a temporary summer Web site where I share relevant links and materials in a way that indexes and complements my Math Education Page. I've already started to prepare!
This year I'm bringing back two workshops that have been very successful in the past: Hands-On Geometry, geared to grades 7-10, and No Limits!, a selection of topics for Algebra 2 and Precalculus. Much of the math content I present in these workshops is standard stuff, but my approaches are usually unorthodox, relying on kinesthetic, manipulative, and electronic activities in order to reach the broadest possible range of students, and to aim for depth of understanding.
In between these tried-and-true workshops I will offer two new ones: an in-depth introduction to Transformational Geometry; and a one-day teacher-level course on using GeoGebra to create curriculum materials. (The latter absolutely requires some prior experience with GeoGebra, which can be acquired by taking either or both of the geometry workshops first.)
On to this month's newsletter.
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.
The Function Dance!
If you like to get students out of their seats, and don't mind doing a little performing yourself, check out this blog post, where I share a fun kinesthetic activity to review functions in Algebra 2 or Precalculus.
Is your school or department under pressure from parents who believe their student needs to be taught math as early as possible, whether it makes sense or not? In many communities, the push for hyper-acceleration results in shallow and rote learning. I wrote four posts on this:
You may be familiar with some of my ideas about how to handle heterogeneous classes, which I've discussed in past issues of this newsletter. Whether you are, or not, check out this blog post, which briefly reviews one key strategy: lagging homework. The post links to previous writings on this question, and to a new document in which I offer practical advice on how to actually implement the strategy.
New feature on the blog: you can find a list of my most popular posts at the bottom of the right-hand pane. I don't know what all goes into making a post popular, but here are three of the winners so far:
- "A New Algebra", in which I summarize the philosophy behind all of my curriculum development efforts over the last 20+ years.
- Interactive White Boards, in which I respond to a one-sided and simplistic attack on that technology. I later expanded the post into a Mathematics Teacher op-ed.
- The Common Core, in which I explain why I strongly support the goals of the Common Core State Standards for high school math, while I question some of their content, and out-and-out oppose some aspects of their implementation.
Check out these new items on my Math Education Page.
I animated a classic dissection proof of the Pythagorean theorem. As always with so-called "proofs with no words", it will work best if students are asked to put it into words. You might first go through the whole thing on a projector, then go back through it slowly, having the students discuss the meaning of each step. Finally ask them to write up a step-by-step explanation. Click here to see the animation.
I have added new links and materials on two pages: Middle School (which ranges over a wide spectrum of topics), and Slices (where I use pie charts to help teach about angles, time, money, and more.) The latter actually has uses in elementary school as well.
About 50 years ago, as a teenager, I had this idea that I would grow up to be an astrophysicist, and in that capacity I was going to prove the non-existence of God. It didn't work out, because every time I took a class in the physical sciences, I managed to burn, break, or otherwise damage the lab equipment. (Divine intervention?) So I turned to math.
When teaching elementary school some time later, my interest in astronomy was rekindled, and I developed a six-week naked-eye astronomy unit, which worked well with my fourth and fifth graders, and I imagine can also work in middle school or even high school. You can download the whole thing here.
Last week, there was a lunar eclipse, and my daughter asked me if I could explain why the size of the penumbra was roughly equal to the diameter of the Moon. I created a figure in GeoGebra to help me think about this. (Great application of the construction techniques I include in my Hands-On Geometry summer workshop!) See what I came up with here.