Happy New Year!
In this issue, some thoughts about the conversations we math teachers have with each other, and the discussions we lead in the classroom.
Also: registration is open for my summer workshops. (Scroll down for a link.) Last year, I had guest presenters as part of my workshops. This year, I'm going one step further: I'll prepare my No Limits precalc workshop in collaboration with Rachel Chou. As it turns out, Rachel and I have extremely compatible ideas about teaching, but over the years, we've implemented those in different ways. This combination will make for a more useful workshop, with a broader range in content, and complementary approaches in pedagogy. Also, it will add a day, making it a three-day workshop. I know I will learn a lot, and I hope some of you will join us in Silicon Valley!
My four-day Visual Algebra workshop is the one I've done the most often over the years, with the biggest enrollment, and it has always been a hit. Thus, this summer's will be largely similar to previous iterations.
On to the 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.
Department as PLC
PLC is a TLA (three-letter abbreviation) that stands for "Professional Learning Community". It's being used more and more, which frankly is a good thing: our business is student learning, and there is nothing sadder than teachers who think they have nothing more to learn. When I chaired a math department, I did my best to get my colleagues to learn from each other by setting up their schedules in a way that would yield profitable lesson-planning collaborations. Also, as a teacher developed expertise with a certain course, I would encourage them to add another to their repertoire. Over time, each of us worked with and learned from all other members of the department. This sort of collaboration turns the department into a PLC, but it can and should be complemented by a productive use of department meetings as learning opportunities. I wrote about this here.
In my teaching, I tried to balance an informal approach to group work with a formal atmosphere in class discussion. Math education research confirms that group work (in various flavors) is a powerful strategy. See in particular the books on complex instruction, and the work of Peter Liljedahl. I am not familiar with the research on class discussion, but of course that doesn't prevent me from having opinions about it.
The first thing I need to say is that class discussion is essential. A class that relies exclusively on textbooks or worksheets done in silence, or in collaboration with neighbors, is not using the teacher sufficiently. Teachers can sense what misconceptions need to be addressed, or compensate for errors in sequencing or emphasis in the written materials. They can boost the confidence of students, and stretch their reach appropriately. In short, they are the necessary leaders of the classroom. That said, even the best classroom discussion will not reach everyone. That is why it needs to be combined with group work, which helps spread understanding to those students who, for one reason or another, may not have fully benefitted from the conversation.
One key ingredient of effective class discussion is what questions you ask. I present many options from mathematicians James Propp and James Tanton, plus a few of my own, here. Another key ingredient is how you handle wrong answers. A classroom where only right answers are heard is a terribly sterile environment for learning. Mistakes need to be surfaced and discussed, and thus how you handle them is crucial. I wrote about this here.
Not much new on my Web site. As the site is now quite large, I've done some work on improving its organization, and adding internal links, in the hope it would make things easier to find. Other than that, here is what's new:
- I updated my Summer Workshops page
- I added a new PDF: three-piece pentomino puzzles, suitable for a collaborative research project at any grade level: can we find all the solutions to these puzzles? Can we solve the two puzzles simultaneously? Are there bigger rectangles and staircases that can be tiled with pentominoes?
- I gave the original Lab Gear book its own page. The current books, and the blocks, are available from Didax. The Algebra Lab: High School is not as good, but it's got a lot of good stuff, and it's a free download.
- I updated the Algebra Manipulatives page with minor tweaks. (This is the page where I compare the Lab Gear to other approaches.)
- I tweaked the sequencing in the Rep-Tiles worksheet (adapted from Geometry Labs)