Math notes: Not easy.

I noticed that in my Algebra II classes and my Calculus classes, students don’t take good notes. Some don’t take notes at all, some take really sporadic notes, some use scrap paper to do the “check yo’self” problems I put up after teaching a concept — to test to see if they get the concept and can do a simple and a somewhat more complicated problem. Then there are the few that take really amazing notes.

My first reaction was: what the heck are you thinkIng?

In both classes, I’m starting off the year not using the book heavily, so their notes are their primary source of material.

But then I had three subsequent thoughts, which tempered how I thought about and approached the situation:

(1) Students learn differently, and they know how they learn best better than I do.

(2) Students might not be used to having a teacher use SmartBoard exclusively, and having the ability to download the class notes each day changes things dramatically. Now the students have the ability to listen, think, and absorb instead of having to listen, think, and absorb all while frantically writing.

(3) No one has probably taught students how to take effective notes in math class, which explains why most of them just write down equations.

Instead of giving my “I’m disappointed in you” talk to students — admittedly, my first reaction — I decided to take a different course.

I decided to deal with my calculus students first. On Thursday, I went about teaching function transformations, and ten minutes into class, I stopped the class mid-sentence and told everyone to exchange their class notes with their desk partner. I asked each person to assign a grade to the notes for the day.

Unsurprisingly, some students had absolutely nothing written down, some had absolutely gorgeous notes, and most had some chicken scratch or just a series of equations written down.

I had students whisper the grade they assigned to the notebooks to the owner of the notebooks. I made some jokes, they made some jokes, and we diffused the atmosphere, which was tense. Initially a lot of people felt like they were caught with their pants down. They thought it was a pop quiz and the grade was important. I told them I wouldn’t ever hear the grade.

We used this to launch into a discussion of notetaking. I prompted three questions:

1. How do you take notes?

2. How does my using Smartboard everyday and uploading it change how you take notes?

3. Why do we take notes?

Different people had different strategies they shared when answering 1 and 2. The four things I emphasized/brought out in the discussion:

1. Different people learn differently and hence take notes differently, and until I see you start slipping, I’m not going to get on your case. But learning how to take good notes in math classes is an important skill so you might want to get on it now.

2. Keeping your notes organized (by date!) and neat can help you a lot.

3. You don’t need to take notes on everything. But when we’re first learning a concept, you want to really put a lot of attention into how you’re taking notes.

4. WORDS! WORDS! WORDS! A math notebook needs WORDS to explain each step, each tricky point, each concept. If you try to study from a series of equations without any words, you’re going to forgot why we were studying those equations or doing each step or technique. You need to understand the concepts we’re learning and words are key.

My two calculus classes meet either first or last period most days (we have a weird daily alternating schedule, but for some reason, my calculus classes always end up first period when everyone is dog tired and still waking up or last period when everyone is beat from the day and ready to go home.

I didn’t really let students answer “Why do we take notes?” even though I put it out there. They were going to come up with obvious. I wanted to say the slightly less obvious.

The number one reason: TAKING NOTES KEEPS YOU AWAKE.


I presented these with some humor, too. We talked about these ideas, and then moved back to the lesson. From start to finish, this aside took only 10 minutes. I noticed, at least for that day, students were being a lot of conscientious about what they were writing down and how they were writing it.

(I am probably going to have this “stop what you’re doing and exchange your notes with your partner” moment every so often.)

I’m going to deal with my Algebra II students’s notes next week, and slightly differently. They are younger, and me preaching to them won’t be as effective. So I asked the help of one of my students from last year, who took the most beautiful notes, wrote the most beautiful homework (with words and answered word problems with complete sentences!), and was always engaged in class. I’m having him come to my class and talk with them about his strategies for succeeding in my Algebra II class last year. How he studied from the book, how he took notes, how he did his homework, etc.

He met with the learning specialist last Friday to just hash out his ideas and get them in order, but these are his words. I didn’t tell him what to say, how to say it, anything. He has 5-10 minutes of time to say whatever he wants.

I don’t know how it’ll work. But I’m hoping that it’ll be an early wake up call to my class.

With that, I’m out.


So my former Algebra II student said this is what worked for him:

1. Read the section BEFORE going to class, so it at least looks familiar
2. Take notes on the bolded terms in the book (e.g. “leading term”) — the math terminology
3. Try every problem to the furthest, even if it seems like it’s going nowhere. Because it might go someplace good, and if not, it’s fun to see how far you can get.
4. Write the entire solution to problems done in class, even if you know the process. Writing things down helps.
5. Ask questions, but wait until the teacher (me!) finishes his thought; the question may be answered if you give the teacher a chance.
6. Make a formula page, with all the formula we learn.
7. Study 2 days before the quiz, not the night before.



  1. Indeed, a great idea. I’m tempted to consider trying it in my calc classes as well (largely first year college students).

    Of course, I’d feel a bit hypocritical. I don’t remember taking notes in any math classes until I got to grad school. I guess I just got by with the textbook. This puts me in somewhat uncharted territory for giving advice on note-taking. I suppose I’d be more tempted to teach them how to read the textbook.

  2. @Jackie: I don’t know if my student would be comfortable with that, but if I remember, I’ll (ahem) take notes, and post them up here.

    @Nick: Ah, yes, the *other* problem: reading the textbook. If you have any good ideas about that, holla.

  3. @samjshah I really wish I knew. I do know that in the calculus class I took freshman year of college we were expected to sort things out for our selves as much as possible. This was done by making homework due on a section every day, and not talking about that section in class until after the homework was due. Looking back, I’m surprised that we all went along with this. I can’t imagine trying to work that in the classes I teach these days. I feel like there’d be an uprising. And plenty more office hours than I’m ready to offer. Perhaps in a few years…

  4. @Nick: Oh, that’s awful! I’d revolt too! There isn’t anything wrong with having students read the book, but not to ask questions until after the homework is due?!

    I think that something to try is to not assign homework problems one class and tell students their homework is to: read the next section in the book and be ready for a very mini-quiz the following day on that material.

    Then the next day I wouldn’t give the quiz, and diffuse the tension in the class with something unrelated (e.g. a short 3 minute fun youtube video)… but then use their homework to launch into of a discussion of the book. I’d have the pages scanned in and easy to pull up on the projector…

    and we would talk about difficulties they had trying to learn the material on their own, what they didn’t understand, how they approached the text, etc.

    It might take 20 or 30 minutes, but that discussion might help students get a lay of the book, that there’s an art to reading math, that the text and pictures in a book are just as important as the equations, etc.

    I don’t know if it would work. It’s an idea…

    In fact, maybe it’s something I should try. Once we start using the book. (Right now all we’re doing in reviewing.)

  5. I think this is a really good idea, Sam. The last time I taught introductory English linguistics the other TA and I spent a long time trying to model different studying and note-taking techniques to our students. It actually did help their performance in the end, and I think they were grateful. (Much more grateful than students are when we explained thesis statements for the umpteenth time, for instance.) I like your technique a lot, although in my case I had to take a much more top-down approach with my truculent co-eds.

    And incidentally back in the medieval day, all most beginning students did was learn how to take notes and internalize them. You’re totally old school, smartboard or not.

  6. starting from 10th grade, I stop taking notes.
    Reason 1: to keep myself asleep.
    Reason 2: to not engage in the lesson.
    until I slip of course. but that never happens.

  7. @Nick: I agree with samjshah, reading maths is *a lot* of trouble for beginners. I TA’d an “Introduction to mathematics” course for 1-year undergrads 3 times, and I have to say, they had *no idea* of how maths were written or what was going on. I prepared a special set of texts, much like in books on foreign languages, with a set of questions for each text (like: “This proof is divided into three parts. Explain where do they begin/end and what is their purpose”, or: “Try to explain what train of thought might have led the author of the proof to this idea”, or: “The proof says ‘without loss of generality, we can assume that and that’ in line 8; explain why it is so” etc.), but had no chance to actually try it out – I was assigned different courses then. But I guess I’ll come back to this idea someday. If I find time, maybe I’ll post some examples of these texts & questions on my web site (I’d have to translate them into English first;)).

  8. @mbork: That’s an amazing idea. I’m not doing too many proofs in my calc class, but I think it might be a neat thing to try in my multivariable calc class.

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