Of Milk and Men

Molly and I have established a routine in problem solving and how we deal with the week. Her classes usually have to complete a quiz on Fridays, and after that quiz l use the remaining time to either give a presentation or do a word problem. This week, following a quiz that emphasized fractions, I decided to regale the students with problem #1790. The problem emphasizes the use of fractions in determining volume and introduces the concept of a factorial.

Once again, I find that the first class is much less receptive than the second class. I'm not sure if this is a result of applying my learned lessons from my first lecture to the second, or if the students in the second class are simply more involved. In both instances, I was struck by the lack of suggestions when we asked about what the students wondered. In this case, I assign some of the blame on the fact that I had copied the question onto the problem statements. However, I find that most of the students don't care enough to wonder anything about the question in question. After prompting, several of the students were willing to accede the presence of a pattern in the problem statement. Though the problem already explicitly indicates the pattern, I counted this as a win.

Solution strategies were once again lacking, the students either had no idea how to approach the problem, or just didn't care. I really would like to give the students the opportunity to work for several minutes on their own, but past experience has suggested that they just become distracted within a minute or two. Instead, I did my best to illustrate the pattern evident in the problem. Following that, I helped them construct an equation that would show how much milk was ultimately left.

At this point, several students were dismayed that we had spent nearly ten minutes in introducing the concept of factorials. While I don't regret a minute of the process, they were more upset that they were not allowed to work on their homework during that time. In fact, I'm surprised that more than one student opted to write out the final answer to the question in question.

While I can appreciate the philosophy that props up the instruction techniques from the Math Forum, I'm concerned that the level of engagement from the students is insufficient. While most of the problems are interesting from a calculation perspective, they lack any lasting impact on the students themselves. Mrs. Porter and I are in the process of discussing what the best technique is to engage the students in the problems. In particular we're trying to find some way of adding an incentive to the equation.