In a Compare and Contrast Activity, each small group solves a slightly different example of the same calculation. The focus of the activity, then, is often on the full-class discussion that happens after the activity.

Because each group is effectively doing the same calculation, it is possible, at any time during the activity, to pull the class back together briefly to give clarifying comments or to discuss problems that seem to be common to many groups. This strategy becomes particularly important as class size increases. It is not possible for an individual instructor to effectively and consistently talk to more than about four groups during a half hour activity. With a faculty member and a TA in the room, then, it is possible to manage 8 groups of 3, or about 24 students. The paradigms now typically have closer to 30 students. It doesn't work as well, but these strategies help.

In the wrap-up, there are a number of things that need to happen: (Add a link to videotape from Day 2 preface 06 where students are asked to come up with hypotheses for a rule about the geometric interpretation for determinants by looking at different cases, each calculated by a different group, as the groups present. The video shows clearly how the students ideas change as they have more and more examples to consider.)

1) Make sure that all the groups, even those that may not have reached the end, understand all the main parts of the calculation.

2) Make sure that students have a chance to reflect on what their calculation shows, what it means for physics, how it might be generalized, what the limitations are, etc.

3) Compare and contrast the results of different groups. What can you guess about possible patterns from what the different examples show. Now is the time for the instructor to confirm or deny the pattern. Or immediately after this experience to give the general proof, if necessary. Now the students are prepared to believe it. This is backwards from the traditional lecture style of give the general proof and then have students work out examples for homework.

4) This is a great time to let students get some experience with mini-presentations. Every group has to present. There's not a lot of time to stress out about it beforehand or to worry if you do something silly because the pace moves on. Since the class has many opportunities for such presentations within just a few weeks most students are comfortable. Also, this is a great chance for the faculty member to point out presentations style stuff. We call that ..., det without a det of something isn't right, speak loud enough for people to hear, break the chalk to keep it from squeaking, write big enough, etc. (put this in the making small group activities work section.)

Last updated 4/7/06