Lessons from CPM (and other thoughts on promoting deeper understanding)

Just in case you're thinking that I'm stuck in the middle of a text message, let me tell you that CPM stands for College Prep Math. OK, stop laughing. You may think I made that up, but CPM is a math program developed through UC Davis in which a bunch of math teachers and 2 UCD professors got together and wrote several courses that require students do problems and participate in activities in order to develop their knowledge of mathematics.

I've taught Algebra, Geometry, and Algebra 2 using these materials. In fact, I'm one of the original authors of Course 3. I am a fan. However, years ago I had to concede to the fact that only one other member of my department would use the text. This created a problem for any student that the counselors moved into or out of our classes so we both agreed to teach the mundane textbook version of our courses. I have since tried to integrate the CPM problems into my curriculum, but that proved too daunting a task. This year I decided to take advantage of some of the CPM strategies instead. Here are some of my ideas for the upcoming year.

Algebra Review Lessons That Students Can Do On Their Own
The CPM text has Algebra review problems scattered throughout the course. There are also focused lessons on some of the more important concepts that usually appear at the end of traditional Algebra books. I thought I might give my students a quick assessment at the start of each chapter so they would know what they needed to work on. Then I could either put problem sets up on our school website or refer them to another site. (Suggestions anyone?)

Spiral Homework Problems
CPM homework assignments contain a fair range of problem types. New ideas are covered as well as concepts studied from previous chapters. I will have to create all of my homework assignments for each chapter in advance so that I can be sure to include problems that vary in both topic and level of difficulty.

Use Big Problems to Focus Each Chapter
Each CPM chapter begins with the introduction of a problem. The students solve this "big problem" at the end of the chapter. I would like to do the same, but I would use more open-ended problems.

Concept Exams Revisited
I used to give my students this long list of concepts at the beginning of each semester. Each concept was tested on 3 exams in a row. Students had a chance to improve their scores by doing better each time. I went away from this because it was so time consuming. After reading dy/dan and f(t), I decided to return to this strategy with the following changes.

1. I'll use a much shorter list of concepts.
2. Each concept will appear only twice. This should make the exams much shorter and easier to grade.
3. Students will have opportunities outside of class to remediate.
4. I will give a midterm exam to reinforce the idea of true test taking. This should balance my inner conflict between do-overs and getting the students ready for college.

Here are some other ideas that are not generated from the CPM materials.

Pre-reading Activities at the End of Class
I'm currently attending the Reading Institute for Academic Preparation through Sacramento State University. As a result, I've come to realize the importance of emphasizing reading strategies as they apply to math textbooks. Since I will require my students to prepare for each class session by reading their textbook, I want to end each class with a short activity designed to build each student's prior knowledge.

Teach Students to Annotate Text
My students are not allowed to write in their textbooks so I will teach them to annotate their texts using sticky notes. I'm contemplating letting them use these notes on their exams. They would then be required to turn the notes in with their exam so I can hold them accountable for the process. (Let me know what you think about this one.)

In Conclusion
I want two things to occur. I want to see greater student success in terms of exam scores (That's admin for mastery). I also want my students to have a deeper understanding of Geometric concepts as a result of my training them to self-assess, self-remediate, and utilize college level study techniques. The next few weeks may be long and exhausting, but the end results should be well worth it.