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Math Study Strategies:
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Math Study Strategies:

  Or, How I Learned to Stop Taking Notes and Love Calculus
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________________________________________________
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This document is evolving from original drafts by Philip Sink
...with enthusiastic support from Dick Furnas
 
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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.
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Table of Contents
 
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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.
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Meet Jan

 
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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. __________________________________________________________________________
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Meet Jan. Jan in 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.
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[Jan is a monosyllabic, gender-neutral name. I’ve reworked the text to avoid third person pronouns altogether. When I am tutoring, this is a strategy I encourage students to use in the interest of clarity when talking and thinking to themselves about problems. Often students’ difficulties evaporate when pronouns are carefully replaced with their antecedents. But I digress... Jan is inclusive of people with transitioning or non-binary gender identity while being at the same time makes for easier reading. The text can be taken personally by anyone while avoiding some of the in-your-face distractions of other approaches to inclusiveness.]
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Why Take Notes?
 
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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.
 
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__________________________________________________________________________
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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.
 
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Should I Take Notes in Calculus?
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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.
 
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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.
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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:
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Why Take Notes?

 
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Things You Know
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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!
 
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Things You've Memorized
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Should I Take Notes in Calculus?

 
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Things You Know How to Figure Out
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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.
 
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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:
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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:
 
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“I know how to solve this problem because I’ve seen similar ones before and solved those”
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  1. Things You Know
  2. Things You've Memorized
  3. Tools for Figuring Things Out
 
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but instead:
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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.
 
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“I know how to solve this problem because I understand what is being asked and what we’ve learned in the past”.
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Think not:
 
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Q: If I take notes, won’t I memorize this “understanding”?
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“I know how to solve this problem because I’ve seen similar ones before and solved those”
 
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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.
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Think instead:
 
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__________________________________________________________________________
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“I know how to solve this problem because I understand what is being asked and what we’ve learned in the past”.
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What Should I do Instead?
 
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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:
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Q: If I take notes, won’t I memorize this “understanding”?
 
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“What key ideas is the professor seeming to emphasize?”
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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.
 
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“What key ideas do I see myself?”
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Thanks for sticking with us so far. We’ve got concrete suggestions for you. Read on…
 
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“How does this relate to the other material from today?”
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What Should I do Instead?

 
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“How does this relate to the other material from this week?”
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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.”
 
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“How does this relate to the other material from this unit?”
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Q: How do I do that? What does “Pay Attention!” even mean?
 
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And most importantly
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A:
 
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“What don’t I understand/what questions do I have?”
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  • “What key ideas is the professor seeming to emphasize?”
 
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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!
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  • “What key ideas do I see myself?”
 
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There was a young premed in Calc
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  • “How does this relate to the other material from today?”
 
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Whose notes copied the board full of chalk
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  • “How does this relate to the other material from this week?”
 
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They didn’t understand
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  • “How does this relate to the other material from this unit?”
 
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Thought the professor was bland
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  • And most importantly
 
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And complained when their grade took a dock.

https://www.panopto.com/blog/put-down-that-notebook-new-studies-find-taking-notes-is-bad-for-your-memory/

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  • “What don’t I understand/what questions do I have?”
 
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-- Dick Furnas - 2018-08-18

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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!
 
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Comments

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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.
 
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Original Document received by Dick Furnas from Philip Sink. Pasted here for further work.
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https://www.panopto.com/blog/put-down-that-notebook-new-studies-find-taking-notes-is-bad-for-your-memory/
 
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-- Dick Furnas - 2018-08-18
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[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 Urbandictionary: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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Revision 12018-08-18 - DickFurnas

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META TOPICPARENT name="MscCapsules"
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.

https://www.panopto.com/blog/put-down-that-notebook-new-studies-find-taking-notes-is-bad-for-your-memory/


-- Dick Furnas - 2018-08-18

Comments

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

-- Dick Furnas - 2018-08-18

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