One of the hallmarks of the class was the “15-minute” problem. This was a problem that students were told to work on the night before class for a good 15 minutes, and to write down all of their thoughts on the problem. There are two major reasons for giving these assignments. The first is that many students believe that if they cannot solve a problem in 5 minutes, they will never solve it. Thus, by asking for just 15 minutes, and not demanding an answer, we hope to get students to spend longer on a problem. Indeed, CL said about the problem solving assignments, “At first some that were like no way I can do this. All I need is 5 seconds to know I can’t do it. But have to try taking a leap of faith with techniques that might get you to the end, but ‘you don’t know.’” Thus she actually learned the lesson that even though she “knew” she couldn’t do it, by focusing on just working for 15 minutes, she discovered that often she could do them.
A second reason for the assignments is to include a meta-cognitive writing assignment inside of the problem solving assignment. Another common problem for students is to focus on the answer, but not on how you solve the problem. This metacognitive assignment then pushes students to think about solving problems, not simply having solutions. As one student in the student responses (which were anonymous) stated, “It took the pressure off of solving the problem and allowed me to think.” This focus on how to solve the problem encouraged students to share multiple solutions in class, thus opening the door for more peer sharing. AF (one of the honor students) said, “for any one problem there might be three different people presenting different solutions. Just the differences that lead to the same conclusion is interesting and really helpful as far as further mathematics is concerned.” Thus, even if he had an answer the focus on the how of the solving, made him open to listening to other students, and in particular that opened his eyes to how he could learn from other students.
An unexpected outcome of the assignments, however, was that they also provided students with an acceptable excuse for not having solved the problem (i.e., “took the pressure off”). This in turn made some students more willing to present, although others felt this was not the case. In particular, CL mentioned, the “15 minute role did make more comfortable because “like, I only had 15 minutes, I did my best.” Other students were not as convinced, but AD also felt the 15 minute helped make her more comfortable, and while ES felt it did not help, he used the excuse of only having 15 minutes one day in class. Four of the 15 students explicitly mentioned the 15 minute time frame in their responses to the questions about the class.
Another aspect to the 15 minute problems is that the time frame is often intentionally too short to be able to finish the problem. Thus the “honor” students often came to class without a full solution. Thus they would need to collaborate to solve problems. Thus, the problems promoted collaboration by providing a safe space for students to converse and admit to not knowing. Six of the fifteen students commented on the collaborative aspect in the anonymous questionnaires, and all five of the interviewed students mentioned collaboration on the problems. Several of them refer to how they saw an importance of building off of other students’ ideas in problem solving. For example, one day in class, CL gave an incorrect answer to a problem involving eight equations in eight unknowns. ES then used her solution to solve the problem. Both students referred to this in their discussion. AD also referred to the notion of wrong answers still having important information, and she said, “I know a couple of times I've said things where I've gone, “Oh god, that was so wrong” but then you'll go in and say, “yeah, but it shows us this”, and it sort of has shown me that while it might not be the right answer it might show us something else or it might show us another way to approach the problem.” This idea also showed up in the focus group when two of CL’s four responses to the question of naming at least three ways in which the workshop course influenced you mentioned that work that appears useless or incorrect may lead to a correct answer.
Return to student thoughts on workshop course.