Math by the Mountain

During my first year of teaching, every topic that we covered was very chunked.  We learned about exponential functions, then we tested on exponential functions.  Then we learned about conic sections, and we tested on conic sections.  Then we moved on to trig, and we tested on trig.  As connections to prior material arose, we definitely talked about them, but students didn’t see much of the old material in class again until the final, which made preparing for it a huge task since much of the material had to be relearned.  Long-term retention did not happen, despite students doing very well on unit tests.

In an attempt to try to build stronger retention with my students, last year (my first year) I tried including a bit of spiraled review with each homework assignment to keep old material fresh in students’ minds, but as I discussed in this post, students just skipped over these problems since they didn’t make up a large portion of the assignment.  Since out of class review wasn’t happening, and also wasn’t leading to a stronger long-term understanding like I was hoping, I decided that I would try something new during class this year, and changing my warm-up routine seemed like the perfect spot to do it.

Normally, I start class off with a 2-4 problem recap warm-up that covers the material from the previous day.  Students take about 5 minutes to work independently, then 2-3 minutes to confer with a neighbor, and then students present the warm-up solutions.  I enjoyed this routine as it worked very well for my classes last year, but I think I can improve it in the sense that it shouldn’t need to be so focused on only one topic.

Instead of doing a daily warm-up that reviews only the most current topic, I decided I would, instead, review 5 topics in each warm-up: (1) the topic covered the day before, (2) the topic covered the week before, (3) the topic covered 3 weeks before, (4) the topic covered 6 weeks before, and (5) the topic covered 10 weeks ago.  (There’s a specific pattern to these lengths being chosen–do you spot it?).  At the beginning of the year, I will use review topics and more recently covered topics until the various lengths of time (3 weeks, 6 weeks, 10 weeks) have been met.  After that, I will continue to use this pattern (even after the semester break) to continually review older material and keep it fresher in students’ minds.

I’ve included a blank template for an example of what this will look like.  Each week I’ll print out all of the problems on the front and back, which students will get on Monday.  We will do our weekly Glance Back problems, as I’m calling it, every day and on Friday students will be assigned the reflection portion of this assignment to complete over the weekend, due the following Monday (along with their work for these problems). Normally I don’t assign much homework over the weekend, but I think 3 short reflection problems is manageable.

This is something that I’m really excited about for the upcoming year, and I can’t wait to do it everyday (It could be a disaster, though.  Hopefully not, but who knows?).  I hope that it will lead to much richer discussions during our warm-up period of class and will help students to build their own connections as we learn new material.