Math Study Strategies:

Or, How I Learned to Stop Taking Notes and Love Calculus


Consider Jan. Jan is a premed, ready for her freshman year at Cornell. Jan is excited to start on the path that will lead her toward her career, however, distributions stand in her way. Calculus 1110 doesn’t frighten her though – she was good at math in high school. Thorough notes, and diligence on the homework will pull her through, she thinks.

Jan could potentially be in for a rude awakening. Calculus 1110 is a different beast than high school mathematics – including AP Calculus. Note taking is a sufficient strategy in high school – memorize the information, solve the kinds of problems in question, and regurgitate it when asked. Calculus 1110 is structured, perhaps intentionally, to make this very difficult. Moreover, studies show (there is a URL at the end to an article giving the general theory) that note taking can actually reduce retention of information. Quite literally, taking notes in class will inhibit how well you understand the material.

Frequently, we have seen students with exceptionally detailed and organized notes still have difficulty understanding what is being asked of them on homework assignments and prelims. Our theory is that, in taking notes, the students do not retain information from the class. This can lead to accusing the professor of poor presentation, which from their perspective makes a good deal of sense. We think for many the theory outlined here can help alleviate these stresses and anxieties. __________________________________________________________________________

Why Take Notes?

When is it useful to take notes? If there is no textbook, notes can be useful – the only way you have access to the material after lecture is through your notes. Furthermore, for some, notes may be a good start to help memorize information. Though, as the studies cited in the link below can attest, notes can also seriously hinder memorization and especially understanding.


Should I Take Notes in Calculus?

Let’s break down the above two situations in detail. Calculus 1110 has a textbook, so the first situation does not apply. You can confidently study from the textbook – there shouldn’t be any secret information the professor presents that is not from the textbook. Calculus is pretty standard. But, you ask, how do I learn anything if I don’t take notes?! Answering this is where it becomes important to understand what sort of information we think is being learned if you copy down what a professor in a math course says verbatim.

If you copy down how a professor solves a problem, you do indeed have a good sense for how to solve that problem. You could probably replicate a solution for that specific problem on a test. This does NOT, however, give you skills and strategies. You can think about breaking down information retention in the following three ways:

Things You Know

Things You've Memorized

Things You Know How to Figure Out

To learn Calculus, groom the things you know, minimize the things you memorize and build your toolkit for figuring things out. Calculus is not best learned through memorization – there’s simply too many kinds of problems and too much information for this to be viable. Instead, a deeper understanding of what is going on is required. Hence, you should not be thinking:

“I know how to solve this problem because I’ve seen similar ones before and solved those”

but instead:

“I know how to solve this problem because I understand what is being asked and what we’ve learned in the past”.

Q: If I take notes, won’t I memorize this “understanding”?

A: Maybe, but there’s a lot of information, and Calculus problems can be done more easily and effectively without any memorization at all. Since memorization is not the goal for most of Calculus, we suggest a new strategy.


What Should I do Instead?

Calculus is a subject that builds on itself – each piece of the course builds on what came before, and in the end, while there are hundreds of different kinds of questions that can be asked on a prelim, the total picture of calculus is ultimately simple and concise (even beautiful!). So instead of taking notes, we propose what we will call “Critical Attentiveness”. Instead of memorization, we propose simply listening to what the professor is saying, and constantly asking yourselves these questions:

“What key ideas is the professor seeming to emphasize?”

“What key ideas do I see myself?”

“How does this relate to the other material from today?”

“How does this relate to the other material from this week?”

“How does this relate to the other material from this unit?”

And most importantly

“What don’t I understand/what questions do I have?”

Too often, notes can serve as a crutch – you think to yourself “I’ll figure this out later when I study” rather than ask the question in class. The whole class will benefit if you address something that is unclear to you – chances are, someone else is unclear on that point as well. The textbook is essential as well – all the information is there. If you forget what something is later, when working on homework, you can look it up there. And, because you assessed the information with the above strategies, it will be far less inscrutable to read. For whatever remains difficult, we at the MSC are here to help you figure it out. Best of luck!

There was a young premed in Calc

Whose notes copied the board full of chalk

They didn’t understand

Thought the professor was bland

And complained when their grade took a dock.

-- Dick Furnas - 2018-08-18


Original Document received by Dick Furnas from Philip Sink. Pasted here for further work.

-- Dick Furnas - 2018-08-18

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Topic revision: r1 - 2018-08-18 - DickFurnas
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