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

4 thoughts on “Taking Notes vs. Doing Math”

  1. I’ve always had the impression that Interactive notebooks are fairly time intensive as well as meaning to be used/created through the whole class period. (They seem fairly procedural in focus as well) This is a leading question but am I off on my impressions and/or how would they really integrate into a class where doing math is the focus for most of the time?

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  2. I incorporate interactive notebooks into my math class by providing students with a notes sheet (already completed by me) with all the pertinent information to put into their notebooks as well as any foldables, reference pages, or graphs, etc. that I can’t fit on the 1/2 sheet of notes for each content area. For the most part, this takes about 5 minutes for them to cut the sheet in half (the other half has a listing of all the associated assignments. Then, the remainder of the class is spent doing guided practice where I have different students demonstrate work on the board in front of the class while the others work on the problems in their notebooks, and then correct anything after we discuss the problems. Some students, but not many, also add other things on their own into their notebooks or take notes as well in addition to the note sheets that I provide.

    The vast majority of students are able to put together very neat notebooks that are useful when doing their homework. Even the kids with the worst handwriting are able to have a reference, although their examples may not be the best. Parent feedback has been good because they also have examples to look at. I’ve even had a few students that have told me they save their books from year to year and have used them in for other math classes. Well worth the 5 – 10 minutes on average per new content instruction.

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  3. Henri, I really like what you say here. Do you know if there’s any research to back it up? (I had forgotten the details, and told my colleagues I had read something saying taking notes in math wasn’t all it’s cracked up to be.)

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    1. I don’t know of any research on this. The post is an opinion piece based on decades in the classroom. But really, how would you design a study to research note-taking? I’m pretty sure this is one of the zillion aspects of teaching that is beyond the reach of math ed research.

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