Notes on Notes

“When I am talking, the students are either ignoring me or listening attentively and trying to take notes, but in neither case are they actually doing mathematics, which is the one activity that I can guarantee will produce learning gains.”

Point 3 on the previous blog (above) registered something I think is important enough for its own discussion. Several years ago I went to a presentation about emerging technology, specifically the tablet P.C., and how it might influence teaching. I thought I was going to a presentation on how the tablet improved learning, but that was not the case. I am a huge fan of the tablet as a way of helping students learn, but the emphasis of this presentation was how helpful and efficient the tablet is to “give notes.” The demonstration proceeded to show how the teacher could have all of the notes for the class prepared on power point slides and how easy it was to annotate them so the students could copy them into their notebooks. Huh?

I firmly believe that we should strive to use every minute of every class for learning useful things. However, as P.J. pointed out, attentive students who are taking notes are not working on problems. So what are they learning? They are probably not thinking about much other than: did I copy this correctly? It is clear to me: the process of copying notes is not a learning experience.

Perhaps there are other reasons why it is important to take notes?

I think there is a belief that if students have good notes, they will have something to refer to when they forget or when they need to study. I propose that if their textbook does not serve that purpose, it is not a good textbook and never should have been selected in the first place. Get rid of it as soon as possible! Replace it with one that does provide an organized summary of what students are studying, with examples and sample problems.

But perhaps you are stuck with a terrible text. Or perhaps you have topics that you think are important but are not in the text. Possibly you have an alternative approach to the topic that you think is better. (I hope both of the last two situations do occur frequently in your class.) I would suggest that it might even happen that a student has an alternative approach that is not in the book and that you had not thought of, and that you have become aware of this approach by walking around and paying attention to how students are solving the problem you gave them to work. If so, doesn’t it make sense to carefully write this up and either post it on your web page for all to read, or print copies and pass them out for all to have.

This approach will provide students with the much-needed supplement, and that supplement will be carefully written, error-free, and well-organized, attributes uncharacteristic of in-class notes. This approach will also encourage students to read mathematics, an important step towards helping them become independent learners. These real or virtual documents will be legible, something my hand-written notes rarely are. I think some would call these documents, “class notes.” I prefer to call them, “supplements to the text.”

There would not be many of them, as we want students to learn to work with their text. But most importantly, it eliminates all the time that is wasted when students think they should be writing down what the teacher writes.

I take notes at every meeting I attend. They are notes, not transcripts of what the speaker has just said, or written. They are thoughts that occur to me as I am learning, thoughts I don’t want to forget. They are nuggets that someone said that I want to remember. My notes from a class I took from Dan Teague include, “There are three kinds of mathematicians, those who can count and those who can not.” I laughed and realized that I wanted to remember it, so I wrote it down. We were working on an amazing problem, and I knew my mind would immediately forget his quip as it focused attention on the problem. I put it in my notes and have used it hundreds of times since.

I think we need to distinguish between notes and transcripts. I think many do not make that distinction and as a result, their students waste a lot of class time. I understand there are even teachers who waste their own time collecting and grading their student’s notes instead of thinking up interesting problems to ask their students to work on.