QTC #5

            I remind my students all the time that learning math is not about memorizing facts and procedures. I tell them that math is the greatest subject to learn, because you need to memorize almost nothing. Learning math is about understanding concepts and ideas. Understand why we are doing what we are doing, and you can figure out many problems, even ones you have not encountered before.

            I encourage students to try to construct a meaning for the new information we encounter, to integrate it into their prior knowledge. For example, for most calculus students, it is nearly common sense that to find velocity, one divides the change in position by the change in time. I push them to see that this is just another way of saying the “slope” of the position function. And finally, they realize that when we are talking about derivatives, this idea is all that we really mean. There is no reason to memorize the definition of derivative. You already know it from your common experience with velocity.

            Also, we continue to use the same ideas over and over in novel contexts. Rarely do we learn something and then never use it again. With all the new connections and uses we have for a concept, I can hope the students are able to commit the idea to long-term memory.

            As for the CSEL case study, if the students’ behavior is related to them not being engaged with the material, then I think some cognitive learning ideas could be helpful. Ideally, I would want to be able to present the mathematics in a way that is meaningful to them and builds upon their prior knowledge. Maybe this helps spark some interest, they are more engaged, and thereby less disruptive.