Taking Notes vs. Doing Math

Some time ago, during a professional development workshop, a participant asked how I teach students to take notes in math class. I explained that I didn’t think students can simultaneously do math, and take notes. It’s really one or the other. The teacher gave me a contemptuous look that made clear she disapproved of my answer. Later in the day, the very same teacher asked if I was going to share my slides, because she was having trouble both listening and taking notes.

I have led workshops for teachers hundreds of times. “Will you share your slides?” is definitely a Frequently Asked Question. You, dear reader, may have asked it. You certainly have heard someone ask it. It makes sense! The more worthwhile a presentation is, the more you want to give it your undivided attention, and the more you want to have access to all the slides later. 

What should we make of this? Teachers are well educated, with many years of experience as students behind them. They know that taking notes interferes with their own ability to focus. And yet, many of these adults believe that their teenage students should be able to multitask: take down information, and simultaneously engage in challenging intellectual work. That is unrealistic: in that situation it is the clerical task that wins, and the intellectual engagement that suffers. Anyone who believes most students will then go home and engage intellectually with the notes they have taken is deluded.

This fixation on teaching note-taking is a largely unquestioned part of the landscape of secondary school math education. It may reflect a certain view of how math is learned. 

As I see it, you learn math by doing math, not primarily by listening carefully and taking notes. The main part of any math class should consist of students solving problems. And yes, of course, at a certain point it is important to put what is learned from this work into words. That itself is an intellectual challenge for students, which can be taken up during a teacher-led discussion. And yes, after many students have spoken, it is essential for the teacher to summarize, using standard terminology and notation. That phase is what French math educators call “institutionalization”: bring the students into the international institution of mathematics.

It is at that point that students should write things down as a reference they can return to. But really, they should write down exactly what the teacher asks them to write, in a place where they will be able to find that summary later. Such teacher-controlled notes are vastly more useful than what students might put down on the fly when the teacher is talking. Knowing that the punch line will be spelled out clearly later allows students to keep their focus on problem solving during the main part of the class. It is in that problem-solving part of the lesson that the mental infrastructure is built that makes it possible to understand the final summary when it comes.

If, in addition to this, the teacher shares slides, or interactive whiteboard files, or reference sheets, or interactive notebook pages, that’s all good. But the key is that students should spend most of the time doing math. If note-taking during a lecture  is really an important skill, students should learn it in a lecture-based class, not in a math class.

— Henri

Read more of my thoughts About Teaching on my website.