# First week through Guided Practice and Peer Instruction

I have completed the first week of classes. I also took a good 36 hours to sleep and play with my children, so I am feeling up to getting back to work. The retooling of my liberal arts mathematics course to handle 70 students involved a lot of work. My usual work pattern involves long stretches of thinking and indecision, followed by a short, intense burst of actual production. I had to repeat this for every class meeting this week, so I was very tired on Friday. Labor Day weekend is well-placed for me this term.

So, how did the big experiment with Guided Practice and Peer Instruction start? More after the jump.

The first big difficulty was to choose the right topic for the start of the course. I have to cover some probability and statistics at some point, but mostly I have free reign to select interesting material for this course. With so many enrolled, I wanted to be sure I had an engaging, hands-on activity for the students to do.

For each of the last three times I have taught this course, I have started with a unit on the concept of infinity. This is beautiful stuff, but the first stages are all about precise use of language. I didn’t want to start with lots of fussiness. Maybe I can charm 30 students into following me down such a path, but 70 seems like too many.

It finally dawned on me that I should use a topology unit first. I usually do one, but last. After a bit more anxiety built up, I decided to adapt my recruiting event activity on picture hanging puzzles into an opening week.

The first day I introduced the puzzle, handed out a lot of floral ribbon, and asked them to figure it out. This went pretty well. The room got hot fast, so I didn’t push them the whole 50 minutes. We ended a little early, but with a smile.

I have now designed my first three “guided practice” assignments. I got this suggestion from Bret Benesh, who pointed me at Robert Talbert’s description. Robert made it look pretty straightforward (not easy, just clear with respect to goals and structure). So far, I like the focus on a short list of explicit learning goals. It is good for the students to understand my expectations, and it forces me to design my assignments and lessons with learning goals at the forefront of my mind. This is a good thing.

Both Wednesday and Friday we spent our class time using the classic Peer Instruction model. Using the web service polleverywhere.com (for which UNI has some sort of paid plan), I designed five or six multiple choice questions for each day. I asked the students to vote for the correct answer. Usually I got some sort of split, but in favor of the correct answer. I would ask the students to convince their neighbors to the right and left that they had the correct answer and let them discuss. After a few minutes we would vote again. This is the miraculous part: on the second vote, the results were always nearly unanimous for the correct answer. Wash, rinse, repeat.

Now, there is a little lie in that last paragraph. For one question on Friday, things worked differently. On the first vote, class was split only 3/2 for the correct answer. (It was a binary choice.) On the second vote, the results were exactly the same! This meant I had to get involved a bit more. I brought out the floral ribbon again and we explored with a pair of volunteers at the front of the room. Then I explained what was going on. Fortunately, the next question I had planned was about the same idea, so I could see if my explanation had made a dent. It had! The first vote was unanimous for the correct answer. That was fun to see.

My little picture hanging puzzle mini-unit is winding down (we will finish on Wednesday), so I need to start transitioning to the next phase of the topology unit. I have been waffling over this decision all day, and soon I must choose: knots and links, or surfaces? It is time to make up my mind so I can spend tomorrow planning the next week.