Celebrating a return to Lab Math

After a number of years teaching other interesting things, I’m coming back to a course I taught (and in some ways, helped design) in my first few years of teaching (can that really be 11 years ago?) :  An AP Calculus course (for advanced high school Juniors) taught as a lab.

If you’ve never conceived of Math as a laboratory subject, you might be wondering what makes lab math different from a traditional course.  Here is part of an explanation I wrote for this year’s class:

The classwork is different

• You work through material at (more or less) your own pace: Read the lab and check the related references; answer the prompt questions, follow the examples, do the exercises and - most importantly - try out your own ideas. You share responsibility for your own learning; you're expected to engage with the material.  Try things out.  Play.
• A considerable portion of lab math includes physical examples; proofs of key ideas are outlined or described along the way. It is assumed that you want to know why things work, not just 'the formula to use to get the right answer.'
• You self-assess (check your understanding) as you go, doing more practice in selected topics as needed. There is little distinction between 'classwork' and 'homework;' the course content is a body of work that contributes to your understanding.
• You are encouraged, nay, expected to work together. Your computer is a tool to help you try out ideas, doing the hard work of plotting and visualizing the results. But that means you must know how to speak its language - an important part of the lab course is learning to use Mathematica. Some will come to proficiency faster than others; help each other develop the necessary skills.
• There are still concepts to be understood and problems to be worked by hand (we haven't left the deeply-rooted traditions of mathematics education completely behind). And that brings up the dreaded m-word: while we stress conceptual understanding, there are still some things that you just gotta memorize.

The role of the teacher is different

• There is very little 'lecture;' the teacher does not work problems on the board while you pretend to pay attention -- while actually hurrying to get homework out of the way. You see, we know your game!
• The teacher understands that there are often multiple ways to reach a solution to a given problem - math is not a game of follow the leader. Just remember that not everything we (and that includes both students and teachers) try works the first time - and we learn from that experience.
• Students and teachers both take time to reflect on what worked and what didn't. Learning takes work and it is worthwhile thinking about how you learn best - understanding that process will make it easier for you to learn in every subject.

The outcome is different

If you've chosen to take lab math, it is likely that you already enjoy doing math. Time spent exploring math is the best way to take your interest to a higher level. The best thing you can say at the end of a lab math course is this: "I want more."

Needless to say, I’m excited about coming back!  And after 3 days of classes, I can already report that it is working:  kids gather in small groups to discuss problems, share techniques and gain confidence in their abilities.  I’m confident that students in these classes will soon be ready to tackle some really challenging problems and they might even enjoy the experience.