If you are one who sees the value of having your students collaborate during class time and delve into solving mathematical problems, you may have experienced “blow back” from some students from time-to-time who just want to sit back and be told what “to do”. Not long ago, a student emailed me and asked if we could reduce the amount of time he spent on group work. The student complained that it was difficult to “fumble over words to explain something and discussing the problems with others students interfered with the instructor’s more accurate presentation of the information.”

What this (and other) students do not realize about “real” mathematics and that is that it isn’t pretty and linear to “do mathematics”. It takes persistence, creativity, communication, and downright hard work to do actual problem solving. Mathematics is not solely about calculating and following clear-cut procedures directly to a single solution. My email response to this student follows. I may have become a little “preachy” but I wanted him to see that I had researched this and thought long and hard about my teaching philosophy.

*“I cannot reduce the time for group work. While I understand your point, you must understand how learning (at least learning the way I envision it) does not happen when students passively watch an instructor lecture. The purpose of the group work is to allow students to begin to think and make sense of ideas. In my opinion, the traditional role of a student and the traditional role of assessing learning is to see to what extent a student is able to mimic what the professor wrote on the board. What I am aiming for is to help students learn how to make sense, work to create understanding, and ultimately learn much more than just following a procedure. In doing so, a student will take a “stab in the dark” and there certainly will be some “fumbling over words.” This is how mathematics truly is done by professional mathematicians! *

*It is clear in every research study that the U.S. falls sadly behind the rest of the world in mathematical understanding. This is largely due to the fact that students in the U.S. see mathematics as something to remember how to do and not something to make sense of and understand. I refuse to perpetuate that belief. Rather, I hope to attempt to guide the learners through a process of doing mathematics…making sense of ideas…building understanding. This is not a clean, efficient, simple process. In my opinion, you should not be concerned with deleting mistakes. You should use the whole process as a way to learn deeply. Over the years that I have been teaching, it has become clear that many students choose to take my classes because they have the opportunity, with some amount of controlled guidance, to truly learn the how’s and why’s and go well beyond only memorizing or mimicking procedures.*

*I think you can see that I cannot change how I teach. I believe strongly in it and I have seen how it can change students. I respectfully ask that you hang in there and continue to work to make sense, comparing your thinking to mine and your classmates, and using this as a way to learn.”*