Sense-Making and Algebra 2

I gave a talk at the NCTM Institute on Reasoning and Sense-Making. The topic was "Making Sense in Algebra 2." It was an updated version of an old talk titled "Seeking Depth in Algebra 2". For the occasion, I updated the Algebra 2 page on my site. In particular, I posted the new version of the slides, which includes quite a few excellent animations. So everyone can enjoy this coolness, I posted the presentation as a QuickTime movie (no sound, though). I had been told to be ready for 70 people, but maybe 120 showed up. There was no way I could possibly have enough manipulatives for that many people, given the lack of cooperation from McGraw-Hill. Still, it went well, and many, many people came up to me to thank me over the next 24 hours. I was also pleased that a number of people were familiar with my Web site. Foolishly, I forgot to advertise my upcoming summer workshop on Hands-On Geometry.

The Institute was worth attending: it was 100% high-school focused, and the theme (reasoning and sense-making) is an attempt to undo the damage done by years of test-mania. The topic has gained some traction because reasoning and sense-making are part of the Common Core State Standards, which have been adopted by most states. Alas, this is a tough challenge, especially when many teachers feel that they are trapped between the tests on one side, and a complacent culture among students on the other. There was an attempt to address these sorts of issues by having meetings in between the presentations, but overall those did not seem very effective to me.

Still, here is one great suggestion from a participant in one of those meetings: have an explicit discussion of perseverance in class, rather than expect students to magically learn to persevere. She talked about how this helped immensely in the class of a teacher she works with. And here is one good idea from one of the tasks we worked on: have students try to model a sinusoidal situation, such as tides, before teaching them about sinusoidal functions.

Many of the presentations were terrific. I particularly enjoyed Dan Meyer, who gave a presentation that was more in-depth than his TED talk (which itself is quite interesting and thought-provoking.) Some of his suggestions for better applied math problems:

• state the Big Question first, not last (he showed a number of textbook examples where it came last.)
• have students sort out what information is needed, rather than doing that for them
• use the internet and your digital camera to get high-res images, videos, catalogs, etc. on which to base problems

His point is not that one shouldn't support students or scaffold the tasks, but that a different sort of support and scaffolding is needed. Unsurprisingly, the examples he gave were pre-algebra / algebra 1 type problems. One of the other presenters described some problems based on the realities of cell phone use. The talk was  super-interesting, but it was not material that was ready for the classroom. Creating good "real world" problems for students is actually quite challenging. (Which is why we need to collaborate, as in the Escape from the Textbook! network.)

Interesting problem from one of the other talks: "what regular polygons have 80° rotational symmetry?" 

--Henri