Math Study Strategies:

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

This document is evolving from original drafts by Philip Sink
...with enthusiastic encouragement from Dick Furnas

Table of Contents

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Meet Jan

Meet Jan. Jan is an incoming Freshman at Cornell. Jan is a premed and excited to get started along that career path, but distribution requirements… Calculus 1110 doesn’t frighten Jan though – Jan was good at math in high school. Thorough notes, and diligence on the homework will pull Jan through, or so Jan thinks.

Jan could be in for a rude awakening. Calculus 1110 is a different beast than high school mathematics – including AP Calculus. Note taking may have been a sufficient strategy in high school – memorize the information, solve the kinds of problems in question, and regurgitate the solution when asked. Calculus 1110 is structured, intentionally, to make such a strategy impossible. There is growing evidence that note taking can actually reduce retention of information for many people. In short, taking notes in class may inhibit how well you understand the material.

In the Math Support Center, we often see students with exceptionally detailed and organized notes. Yet they still have great difficulty understanding what is being asked of them on homework assignments and exams. Our observation is that for many students,taking notes, is an unproductive act of procrastination. Students do not retain information from their time class — it’s in their notes. This can lead to frustration with the professor for poor presentation, perhaps reduced attendance in class and continued deterioration of success in the class. Read on for a another strategy which may work for you.


Why Take Notes?

You’ve got a textbook! It’s been proofread — an editorial process neither your notes nor the details of material presented in class have been subject to (but see below about what can happen in class). Maybe NOT taking notes is a better choice!

Should I Take Notes in Calculus?

Maybe not. You can confidently study from the textbook – there is unlikely to be any secret information the professor presents that is not found in the textbook. Calculus is pretty standard. But, you ask, “How do I learn anything if I don’t take notes?!” The answer lies in considering what you are to learn.

If you copy down how a professor solves a problem, you do indeed have a record, which remember has not been proofread, of how to solve that problem. You could probably replicate a solution for that specific problem on a test. This does NOT, however, build skills and strategies. Think about breaking down learning into the following three categories:

  1. Things You Know
  2. Things You've Memorized
  3. Tools for Figuring Things Out

To learn Calculus, groom the Things You Know, minimize the Things You’ve Memorized and outfit your toolbox with Tools for Figuring Things Out. Calculus is not best learned through memorization – there are more than a zillion things to memorize. That’s too many. Strive for a deeper understanding.

Think not:

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

Think 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 with little or no memorization at all. Understanding, not memorization is the goal in Calculus.

Thanks for sticking with us so far. We’ve got concrete suggestions for you. Read on…

What Should I do Instead?

Calculus is a subject that builds on itself – each piece of the course builds on what came before. In the end, while there are zillions of different questions that can be asked on an exam, the total picture of calculus is ultimately simple, concise , and yes — beautiful!. Instead of taking notes, Pay Attention! Perch yourself on the edge of your seat with the attitude “I will pay attention and follow what is presented as closely as I can.”

Q: How do I do that? What does “Pay Attention!” even mean?

A:

  • “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.

[I’m not a fan of this link and did not refer to it in my edits above. It is clear product promotion which feeds on FoMo (Fear of Missing Out) and further contributes to procrastination — “I’ve got it all verbatim on my recording device so I can learn it later”. There is no time like the present. Learn it now. The ability to replay things faster than real time is very cool and has its uses, but should not be encouraged here. Let’s write from our observations and experience, this is not a scholarly paper. I looked for other references I would be happier with, They were not so easy to find with some suggesting that the interference from note taking was more pronounced in people “on the spectrum” — not inconsistent with the “people are different” assertion. In any case it all seemed to me to be at the same level of credibility as reportage on nutrition and diet advice. Great clickbait smile ]

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Comments

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

-- Dick Furnas - 2018-08-18

Hey Philip,

It looks like TWiki will be staying around in some form for the foreseeable future (whatever that means) with some level of access for Cornellians. With that as encouragement, I've taken what you sent me, put it in TWiki as a Topic under the MscCapsules Topic and started editing it there. You can access it, I hope, from this link:

https://twiki.math.cornell.edu/do/view/MSC/ElectricBoogaloo

Definitely a work in progress and TWiki has its quirks, but TWiki is an awesome collaboration tool which:

  • Automagically tracks changes to documents:
    • who made the changes
    • when the changes were made
  • Enables viewing things in different formats with no further editing
    • Content is maintained separately from presentation.

You are already familiar with these ideas from your use of LaTeX where you can output the same LaTeX file for different purposes.

You're also familiar with LaTeX as a markup language. TWiki has its own markup language which I often use to structure text in emails. This email pasted into TWiki will become nicely formatted with

Anyhow, take a look. I've begun a rude and ruthless edit, and included some notes along the way. Let me know what you think. If nothing else, you should be able to leave comments at the bottom of the page. It's trivial to take text from comments and incorporate it into the main portion of the document. So if you're so inclined, you can get started that way without diving in to the gory details of how to edit TWiki documents. Dip your toe in with comments or dive into the editor. Make whatever changes you like, you can't break anything.

I'm going to set this aside for a while in favor of other projects, but wanted to get this much on your radar.

See you soon.

-Dick

-- Dick Furnas - 2018-08-18

Boarding-House Geometry
DEFINITIONS AND AXIOMS

A, B, and C
THE HUMAN ELEMENT IN MATHEMATICS

-- Dick Furnas - 2018-08-21

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