I hope you're enjoying a nice winter break, and that you'll find time to peruse this, my last newsletter of 2015.
After the usual links to blog posts and Web pages, I announce the dates and locations for the workshops I'll be offering this summer. I'll be presenting algebra topics ranging from 6th grade to precalculus. Click here if you're in a hurry to get those into your calendar!
I'll see you again in the new year.
In the wonderful mockumentary Teacher of the Year, the protagonist says "there is no one way to do this job." Amen! Teaching is complex, and you should not trust anyone who claims to have found the way to do it. In reality, we must constantly navigate between opposites, sometimes in ways that go against our natural tendencies. Read more about this in a recent post, and in an older post. You can use this worksheet to think about embracing opposites in your own teaching.
The dominant culture of math education in the US is largely built around a huge misconception: it is widely believed by parents, students, teachers, and administrators that learning math consists of remembering a gigantic list of how-to's — how to carry out calculations, how to solve certain equations, how to find a derivative, and so on. In that frame of mind, good teaching consists of presenting these techniques with clever mnemonics, and successful learning consists of memorizing them in preparation for the test. Alas, this approach, when divorced from understanding, does not yield long-term retention. I wrote a blog post in which I analyzed the particular case of equation solving. Read it here.
As I see it, a school subject counts as a literacy if it is broadly applicable to other subjects. For example, it is very difficult to learn anything if one cannot read, and thus reading is a literacy. Writing is a powerful way to engage with ideas in any discipline, and thus writing is a literacy. Math is a distant third, as it is "only" applicable to the sciences. To this fairly short list, I have long believed we should add computer programming, which is a tool that can enhance learning in several fields, especially mathematics. I wrote about this here, and here.
(You might also want to take a look at my 1997 article: Why I Still Teach Programming, though it dates from another era.)
New Lab Gear Books
Back in the 1990's I developed the Lab Gear, a manipulative environment for algebra. I incorporated the best design features from previous algebra manipulatives such as multibase blocks and algebra tiles, but also broke some new ground. (You can see a comparison of various algebra manipulatives here, but if you're new to the whole thing, you're better off starting on the Lab Gear home page.)
The Lab Gear was a big success, back in the day, and was quickly imitated. It remains unequaled in pedagogical savvy and mathematical depth, but alas, its original publisher was gobbled up by McGraw-Hill, who had zero interest in selling manipulatives, preferring the very lucrative textbook market. They stopped promoting the Lab Gear, and in spite of the unambiguous language in my contract, it took me twelve years to get them to revert the rights to me. As soon as they did, I was able to find another publisher.