Developing Understanding in Algebra and Geometry

Last week, my district brought in a Pre-AP math consultant to work with us on Pre-AP Strategies. Initally, most of us were not pleased with having to miss a day of school to attend a PD day, mainly because we had missed 2 weeks of school in February due to a blizzard and we have end of course exams coming in mid April, so a lost instructional day was not high on our to-do list. However, we were also very grateful that the district was trying to bring in PD that would be applicable and ready to implement. In a nutshell, we had a great day :) Here are some tidbits of knowledge that I took from it...

General comments
"You (the student) will feel uncomfortable in this room! Your brain will hurt daily!"

The "Rule of 4" should be on every assessment and potentially every problem.

Make the kids communicate in complete mathematical sentences. Communication helps ALL kids - the answer alone does not. With just the answer, the struggling kid still doesn't know what to do or where to start.

Students should be asked to read, interpret, communicate, draw, label, compute, and explain/justify on a regular basis.

We as teachers should not have to put "Show all work" on every test - this should be an implied directive that they do no matter what.

More Specific Ideas
One of the key components of the workshop was the focus on how to communicate mathematically both your process and your product. One of the activities she used came from the Math Connections book by Dale Seymour. She used the "What are you likely to be asked" activity, but in the Amazon link, you can see an example of the "How do you know" activity. I can really see both of these as great warmup/journal prompts or even as exit slips.

Another idea she had was based on the game "Would you rather?" I think it would be neat to sit down and brainstorm a bunch of these for various courses. This again could be a neat journal activity.

She also refered us to the Algebra Lab website and we looked at the All Tied Up in Knots problem, which explores a system of equations using two ropes, tying knots in each of them and measuring their length. This could be a great pre-ap Algebra problem as you could go into what the y-intercept and slope really mean, which is a vital skill in AP Statistics. I'm eager to go through the other activities on that site to see what else I could use in my classes.

We also explored some neat geometry problems such as constructing a tangram using compass/straightedge, a fun manipulative proof the Pythagorean Theorem, 3D solid constructions using pipecleaner pieces and coffee straws, and peeling an orange to discover that the surface area of a sphere is 4(pi)r^2.

All in all, it was a fun and productive day that really allowed us to get some creative juices flowing.