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Math Study Strategies:

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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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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 — They were too busy paying attention to 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.
>
>
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 in class — They were too busy paying attention to 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.
 

Revision 122018-08-28 - pls239

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META TOPICPARENT name="MscCapsules"

Math Study Strategies:

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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.
Changed:
<
<
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.
>
>
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 — They were too busy paying attention to 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.
 

Revision 112018-08-27 - DickFurnas

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Math Study Strategies:

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 This document is evolving from original drafts by Philip Sink
...with enthusiastic encouragement from Dick Furnas
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This is the working document. See the release document DoNotTakeNotesPayAttention which includes from this page.
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This is the working document. See the release document DoNotTakeNotesPayAttention which %INCLUDES% from this page.
 
Table of Contents
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  A: Here are some examples of what it means to Pay Attention!
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  • You are learning in the present, during the lecture.
    • If something isn't clear, ask the question!
    • If something seems incorrect, ask the question!
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  • Learn in the present, during the lecture.
    • If something isn't clear, ask a question!
    • If something seems incorrect, ask a question!
 
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  • "levels" to follow during a lecture:
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The whole class will benefit if you ask a question. You will get your question answered, help insure more clarity during the presentation, and catch the inevitable errors that can occur in any presentation.

  • Follow at as many of these "levels" as you can:
 
    • What are the gory details of the algebra being performed as the problem is being solved?
    • How do those details fit into the arc of the solution?
    • How does this problem involve the topic of the day's lecture?
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      • things I already know?
      • things in other courses I'm taking?
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The whole class will benefit if you ask a question. You will help insure more clarity in the presentation, and catch the inevitable errors that can occur during any presentation.
 For whatever remains difficult, we at the MSC are here to help you figure it out. Best of luck!

When Should I Take Notes, and What Should They Look Like?

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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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When is it useful to take notes?
  • If there is no textbook, notes can be useful
  • Notes may be a primary way to have access to the material after lecture -- remember office hours and the MSC can also help.
  • People are different. For some, notes may be a good start to help learn information.
  • Remember, though, taking notes:
    • can seriously hinder the opportunity to learn and understand in the moment
    • can make it impossible to pose questions in a timely fashion in class

What should your notes look like?

  • Highlights of what is presented:
    • Key definitions
    • Enough to reconstruct the details
  • Unexpected results
  • Enough to jog your memory to look up in the textbook; on-line; or ask about in the MSC
  • Anything that doesn't make sense deserves an in-class question before it goes in your notes.
 
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Comments

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 This document is evolving from original drafts by Philip Sink
...with enthusiastic encouragement from Dick Furnas
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This is the working document. See the release document DoNotTakeNotesPayAttention which includes from this page.
 
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Meet Jan

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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.

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  Thanks for sticking with us so far. We’ve got concrete suggestions for you. Read on…
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What Should I do Instead?

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What Should I do Instead of taking notes?

 
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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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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'm going to learn this now!" How? Pay attention and follow what is presented on as many levels as possible.
 
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Q: How do I do that? What does “Pay Attention!” even mean?
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Q: How do I do that? What does it mean to "Follow on as many different levels as possible"?
 
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A: Here are some examples of what it means to Pay Attention!
 
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  • “What key ideas is the professor seeming to emphasize?”
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  • You are learning in the present, during the lecture.
    • If something isn't clear, ask the question!
    • If something seems incorrect, ask the question!
 
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  • “What key ideas do I see myself?”
>
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  • "levels" to follow during a lecture:
    • What are the gory details of the algebra being performed as the problem is being solved?
    • How do those details fit into the arc of the solution?
    • How does this problem involve the topic of the day's lecture?
    • How is today's lecture important to the material
      • for the week?
      • since the last exam?
      • since the start of the semester?
    • How does any of this relate to
      • the homework? (you have looked at the homework, haven't you?)
      • things I already know?
      • things in other courses I'm taking?
 
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  • “How does this relate to the other material from today?”
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The whole class will benefit if you ask a question. You will help insure more clarity in the presentation, and catch the inevitable errors that can occur during any presentation.
 
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  • “How does this relate to the other material from this week?”
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For whatever remains difficult, we at the MSC are here to help you figure it out. Best of luck!
 
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  • “How does this relate to the other material from this unit?”
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When Should I Take Notes, and What Should They Look Like?

 
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  • And most importantly
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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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  • “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
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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 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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    • Set TINYMCEPLUGIN_DISABLE = 1

 

Comments

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Math Study Strategies:

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Table of Contents
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%BEGININCLUDE%
 

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.

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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 at the same time making 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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  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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  Think instead:
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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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N.B. Red and Green may be indistinguishable to the colorblind...
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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”.
  Q: If I take notes, won’t I memorize this “understanding”?
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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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Comments

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 A, B, and C
THE HUMAN ELEMENT IN MATHEMATICS

-- Dick Furnas - 2018-08-21

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Math Study Strategies:

 

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

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

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What Should I do Instead?

Changed:
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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.” 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.”
>
>
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?
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A:
 
  • “What key ideas is the professor seeming to emphasize?”

  • “What key ideas do I see myself?”
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There was a young premed in Calc
Whose notes copied the board full of chalk
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They didn’t understand They didn?t understand Thought the professor was bland And complained when their grade took a dock. And complained when their grade took a dock.
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They didn’t understand Thought the professor was bland And complained when their grade took a dock.
 
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  Hey Philip,
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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: 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:
>
>
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:

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  You are already familiar with these ideas from your use of LaTeX where you can output the same LaTeX file for different purposes.
Changed:
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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 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. 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. I'm going to set this aside for a while in favor of other projects, but wanted to get this much on your radar.
>
>
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

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  Boarding-House Geometry
DEFINITIONS AND AXIOMS

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Math Study Strategies:

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

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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.
Line: 42 to 44
  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:
Changed:
<
<
  1. Things You Know
  2. Things You've Memorized
  3. Tools for Figuring Things Out
>
>
1. Things You Know 1 Things You Know 1. Things You've Memorized 1 Things You've Memorized 1. Tools for Figuring Things Out 1 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:

Line: 75 to 81
 

What Should I do Instead?

Changed:
<
<
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.”
>
>
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.” 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?
Changed:
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A:
>
>
*A:* *A:*
 
  • “What key ideas is the professor seeming to emphasize?”

  • “What key ideas do I see myself?”
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There was a young premed in Calc
Whose notes copied the board full of chalk
Changed:
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They didn’t understand Thought the professor was bland And complained when their grade took a dock.
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They didn’t understand They didn?t understand Thought the professor was bland And complained when their grade took a dock. And complained when their grade took a dock.
 
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  Hey Philip,
Changed:
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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:
>
>
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: 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:

Line: 145 to 157
  You are already familiar with these ideas from your use of LaTeX where you can output the same LaTeX file for different purposes.
Changed:
<
<
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.

>
>
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 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. 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. 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

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  Boarding-House Geometry
DEFINITIONS AND AXIOMS

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Math Study Strategies:

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-- Dick Furnas - 2018-08-18

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Boarding-House Geometry
DEFINITIONS AND AXIOMS

A, B, and C
THE HUMAN ELEMENT IN MATHEMATICS

-- Dick Furnas - 2018-08-21

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

This document is evolving from original drafts by Philip Sink

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...with enthusiastic support from Dick Furnas
>
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...with enthusiastic encouragement from Dick Furnas
 
Table of Contents

Meet Jan

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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.
>
>
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.
 %TWISTY{ mode="div" showlink="Note from Dick..."

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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.]
>
>
[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 at the same time making 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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[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 ]
>
>
[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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Math Study Strategies:

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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 ]
</>
<--/twistyPlugin-->
Added:
>
>

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

<--/commentPlugin-->

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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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________________________________________________
>
>
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.
>
>
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.
>
>

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. __________________________________________________________________________
>
>
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.
<--/twistyPlugin twikiMakeVisibleInline-->
[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.]
<--/twistyPlugin-->
 
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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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__________________________________________________________________________
>
>
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?
>
>
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:
>
>

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.
 
Changed:
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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:
>
>
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.
>
>
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”.
<--/twistyPlugin twikiMakeVisibleInline-->
N.B. Red and Green may be indistinguishable to the colorblind...
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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:
>
>
Q: If I take notes, won’t I memorize this “understanding”?
 
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“What key ideas is the professor seeming to emphasize?”
>
>
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?”
>
>
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?”
>
>

What Should I do Instead?

 
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“How does this relate to the other material from this week?”
>
>
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!
>
>
  • “What key ideas do I see myself?”
 
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There was a young premed in Calc
>
>
  • “How does this relate to the other material from today?”
 
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Whose notes copied the board full of chalk
>
>
  • “How does this relate to the other material from this week?”
 
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They didn’t understand
>
>
  • “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
 
Changed:
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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/

>
>
  • “What don’t I understand/what questions do I have?”
 
Changed:
<
<

-- Dick Furnas - 2018-08-18

>
>
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!
 
Changed:
<
<

Comments

>
>
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.
 
Changed:
<
<
Original Document received by Dick Furnas from Philip Sink. Pasted here for further work.
>
>
https://www.panopto.com/blog/put-down-that-notebook-new-studies-find-taking-notes-is-bad-for-your-memory/
 
Changed:
<
<
-- Dick Furnas - 2018-08-18
<--/commentPlugin-->
>
>
<--/twistyPlugin twikiMakeVisibleInline-->
[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 ]
<--/twistyPlugin-->

Revision 12018-08-18 - DickFurnas

Line: 1 to 1
Added:
>
>
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

<--/commentPlugin-->
 
This site is powered by the TWiki collaboration platform Powered by Perl This site is powered by the TWiki collaboration platformCopyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.