Retirement is turning out to be super-busy. After last summer's workshops, I had a variety of consulting gigs, then I took quite a bit of time writing about the Common Core, and now I'm in the middle of a six-month commitment doing workshops and curriculum development for the Fresno school district.
This is not a surprise, as the main reason I retired from teaching high school was to do this sort of work. One benefit for readers of this newsletter is that the middle school lessons I am developing are available for free download here. Hopefully those will find users far and wide.
I expect things will slow down after this summer's workshops. I should be available for more projects come the fall. If you have ideas for me, let me know!
On to this month's newsletter.
Middle School Page
If you teach middle school, you may appreciate a new page on my site, where I have been posting units on a wide range of topics.
Some of them are adapted from Algebra: Themes, Tools, Concepts, the textbook I co-authored with Anita Wah. Here I break them into more realistic, lesson-sized chunks, clarify some of the wording, add some material, and generally adapt it to grades 7 and 8. (By the way, I received a rave review of the book from an instructor in Utah who has used it in middle school, high school, and with pre-service teachers. Read her comments here.)
The Middle School page also includes brand new units I wrote to respond to the Common Core middle school demands, particularly on transformational geometry.
- I've been making GeoGebra applets to illustrate a range of topics:
- Sum of the angles in a triangle
- Reflection, rotation, and translation
- Area of a parallelogram defined by two vectors
- The best use of these sorts of animations is as a spark for class discussion, followed perhaps by a writing assignment, asking students to explain what is being illustrated.
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.
Julia Robinson Math Festival
I attended a wonderful event where I got to do some excellent math with students, mostly but not exclusively middle school girls. It was remarkable. What must have been hundreds of kids were engaging with high quality, challenging problems with curiosity and tenacity. I hope these festivals spread far beyond the Bay Area, as they hold the key to reaching a much wider range of kids than the ultra-competitive channels offered by math competitions. Read more about it here.
A New Kinesthetic Activity
In a recent issue of The Mathematics Teacher, I read an article by Maureen Macinnis, a teacher in Nova Scotia. She described a great kinesthetic activity to introduce the unit circle and the graphing of the basic sine and cosine functions. It seems like a terrific activity, with a lasting impact. I summarized it here and added it to the kinesthetics page on my Web site.
In this post, I discuss a few examples of my curriculum ideas reaching a wider audience through inspiring others. I also suggest that when a curriculum developer picks up an idea somewhere, they really should credit the source! Without going so far as detailed footnotes, I have always acknowledged my inspirations in the front of my books.
Learning to Ride a Bike
Here is most of a blog post from July 2009:
From The Mathematics Teacher, October 2008, the start of an opinion piece by Gregory Freeman and Lisa Lucius:
"I learned to ride a bike at age six. The experiences leading to my first solo bike ride are still vivid memories. First, my father gave a wonderful explanation of bike riding. The mechanics of leg motion required to pedal were explained. Hand placement on the handlebars, and the nuances of steering were described with clarity. Braking, maintaining balance, and every other conceivable aspect of bike riding were laid before me. Next, my brother modeled bike riding. Down the block he rode: pedaling, steering, maintaining balance. He managed a 180-degree turn, returned, braked, and came to a perfect stop. Having gained a conceptual understanding of bike riding and having observed successful bike riding, I was able to ride the bike by myself at first attempt. I attribute my riding independence to my father's excellent explanation and my brother's superb modeling."
Of course, this is pure fiction, and few people would believe this story. And yet so many are ready to believe similar nonsense about learning math. One learns to ride a bike best by riding a bike, with guidance from an adult. Likewise, one learns to do math best by doing math, with guidance from an adult.