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Are there Physics and Mathematics Texts for Holistic Learners

  1. Feb 10, 2016 #1
    http://www.pssc.ttu.edu/techhort/lasrvy/l_h.htm

    My learning style seams to be more holistic than linear, but it appears to me that physics and especially mathematics texts are written in a way that is best suited for linear learners. They very often give little or no context or motivation as they move along. I can work through these texts, and even do the practice problems, but very little will stick. I will forget most of it almost as fast as I process it, as if my brain has deemed it unimportant, or likely to be, and just throws it away, trying to save space for stuff worth thinking about. On the other hand, when I have the motivation to learn something, I seam to be able to learn at a much accelerated rate, and end up retaining what I learn.

    I'm looking for some mathematics texts which tell stories, give some history, motivation, a bigger picture, some intuition, and some context. They should spark my curiosity, excite me, and cause me to ponder before they expect me to dive in, learn the details, and do practice problems. I would like to read such texts to get some inspiration, intuition and vision, and then go back to fill in the blanks and learn the details as I need them. In the long run, I want to have a knowledge set and understanding that enables me to read graduate level texts or research papers from select topics in physics and mathematics.

    Anyone have any suggestions? Anyone have any insight on the issues that holistic learners face when learning mathematics, and how they can overcome them?
     
  2. jcsd
  3. Feb 10, 2016 #2
    You could try Mathematics and the Physical World by Morris Kline.
     
  4. Feb 10, 2016 #3
    You mean important stuff like shrimp tacos?! :oldsmile:

    shrimp_taco_modelo_lg.jpg

    I'd say as far as math is concerned I'm a bit of a "holistic" learner myself, whatever that means. I'm guessing you mean more "right-brained" than left-brained? Because I'm slated to enter a machine intelligence graduate program in the fall, I've been accelerating my math studies so I don't show up as a complete boob in the lab. However, I have great difficulty doing math by reading math texts. For me, it's beyond stiff and boring. As you mentioned, my brain rejects it almost immediately and I start thinking about shrimp tacos.

    The saving grace for me has been you-tube videos and video lectures from open-access universities such as Stanford and MIT. When learning math and physics, I need to have it "spoon-fed" to me with a colorful character at a white-board who is skilled in communicating difficult concepts. Then I can maintain attention and focus. Give me a dry, stiff book and I'm out the door and on my way to the local taqueria.

    Contrast this with neuroscience material which is exactly the opposite. My background is in neuroscience so I already know it forwards and backwards. Therefore, I don't have the patience to sit through any neuroscience lectures so I don't watch any of them. Instead, if I want to know something about it, I already know where to look and exactly what journals or other resource has the information I'm looking for. So when I research a neuroscience-related issue, I go straight to the written text and can scan probably on the order of a dozen or two scholarly publications per hour because I know what I'm looking for. There have been days when I've reviewed probably close to 100 papers, mostly just reading the abstracts and conclusion for clues as to whether the body of the text contains what I came to find.

    So, it does present something of a bizarre dichotomy with my learning techniques here. Maybe you can sympathize. As far as math per se is concerned, the videos I like the best are those that put up a problem on the board and then give you a chance to pause the video and try to work the problem out yourself. When you restart the video, the tutor then begins to present a fully worked out solution without skipping steps. Even though they sometimes can skip steps and I'd still be able to follow the solution, I'd rather they didn't even though it takes more time. Why? Because I like thoroughness and I like to consistently reinforce the basics. For mathematical physics, DrPhysicsA is great at this: https://www.youtube.com/user/DrPhysicsA

    For straight math, I like PatrickJMT: https://www.youtube.com/user/patrickJMT

    Those are free on you-tube. For a little bit of money, or they may have these at your local public library (where I ran into them), I'd highly suggest mathtutordvd.com

    http://www.mathtutordvd.com/

    If you're just starting your math and physics journey, especially at a later stage in life as myself did, Jason is your man.

    Also the "recitation" videos at the MIT website (also on youtube) are great for putting up problems on the board and working out solutions after giving you the opportunity to do it yourself.

    I hope this helps. If you or anyone else know of a resource where I can find more videos as the ones I've listed above, please do post them.
     
  5. Feb 10, 2016 #4
    I am a holistic learner too.

    I had the same problem with high level math. While I could learn procedural things like integration and differentiation easily, when it came to proofs I found that they were presented with no context, and no motivation. That made it hard for me to learn. I remember going through various proofs and thinking to myself "Why the hell would anyone think to do that in first place." I would get tripped up trying to figure out why I should be thinking a certain way rather than following the procedure they provided. It doesn't help that a lot of mathematics texts (and many mathematicians I know) are kind of snotty in that they like to present their material in the most unapproachable way possible or sometimes overly terse without any context or insight into the problem they are solving. I found I could understand problems by coming up with my own way to visualize the problems they are trying to solve.

    What I found worked for me but took some extra time was to research and acquire background information on problems I was solving. Maybe your homework will take longer to solve, but you will be much more knowledgeable.
     
  6. Feb 10, 2016 #5
    I do share this same sentiment with you and the OP's post:

    "when holistic learners do finally understand the material given, more extensively"

    It takes me a long, long time to understand a mathematical-physics concept. However, when I finally "get it," I feel I have a much deeper understanding of it than most people do. Again, I think that this is a left brain-right brain thing. The "shut up and calculate" crowd (IMHO) are really just blindly executing formal operations in their left hemisphere without any (much) extrapolation as to what these calculations "mean" in a greater context.

    I think the distinction may be that the "holistic" crowd may not take the calculations on blind faith but require some kind of conceptual visualization of what is going on that the left-brain thinkers don't require. This requires much more work/effort and is not always successful. But if you can connect with this, i.e., connect the right and left hemisphere understanding of these concepts, you do have a much deeper and richer understanding of the mathematical physics.
     
  7. Feb 10, 2016 #6

    bcrowell

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  8. Feb 10, 2016 #7
    Last edited by a moderator: May 7, 2017
  9. Feb 10, 2016 #8

    For me, it is knowing the context of the problem. Specifically, I need to know WHY I should be thinking a certain way. How does solving the problem in this manner lead me to getting the answer vs just applying the formula and getting a number. I have found as well that my line of thinking has lead me to being particularly good at extrapolating knowledge. Maybe I didn't get the highest marks in the class, but I could usually figure out some higher level concepts that weren't touched on until a later semester or in graduate work. Ironically, one of the reason I left graduate school was because I felt like all my classes were "shut-up and calculate". At the expense of actually understanding the material I felt one had to just do what they had to do to get the answer given the lack of time that was available. It was quite disheartening. I might go back though.

    EDIT:
    In some sense the holistic approach eliminates the "why not". There are many ways to solve a problem, without knowing the context why cant it just be solve in another, maybe faster or more simple way. What are the problem solving methods limitations? Again, it comes back to context.
     
  10. Feb 10, 2016 #9
    I see this has been moved to Math and Science Text Books. It's understandable, but unfortunately I think that means I'm most likely not going to get much help finding the books I'm looking for. For one reason, I'm not really looking for text books; I'm not sure the books I am looking for exist as text books. Another is that I don't think there is much traffic here. I guess I should be asking this on a Q&A site like Quora or something.

    If you took a normal text book in mathematics and added 5 to 20 extra pages to give context before each section, that might be sort of what I'm looking for. But I'm not sure this exists. I would settle for a book that just gives the context, and I can pair it with a text book if I need to. Is there a name for these types of math books, that are not written for use in a classroom, but rather for enlightenment, that don't actually teach you how to do math, but covers topics like topology, differential geometry, algebra, dynamical systems, complex analysis, real analysis, etc.
     
    Last edited: Feb 10, 2016
  11. Feb 11, 2016 #10
  12. Feb 11, 2016 #11

    bcrowell

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    I've been teaching full time for 20 years. Scientific evidence trumps anecdotal evidence.
     
  13. Feb 11, 2016 #12
    Ok, that's a matter of opinion. I think that each teacher has to find what worked for him and his class. If the teacher "anecdotally" finds out that certain methods work for certain students, he has to use that method, even if some science paper says it doesn't work.
    And finding my learning style helped me in my studies.
    For me, it's reality.
    Sometimes I trust real experiences of real people more than research. Especially in social sciences. But that's a matter of world view.
     
  14. Feb 11, 2016 #13
    FYI, your reference doesn't support your argument.
     
  15. Feb 11, 2016 #14
    I don't think this is always true honestly. This is outside the topic of the thread, but the whole "publish or perish" culture in academia gives people incentives to publish useless research. And ignoring everyday/anecdotal/life experience just makes a person naïve and not functional in society.
     
  16. Feb 13, 2016 #15

    Student100

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    Huh, I've tried reading that twice now and still can't make out what the point was or how it was supported by what you said.


    Here's a suggestion OP, why don't you get a textbook at the level of where you need to be, read each section and then Google the rest of the ancillary information that you find useful. It's all there on the internet, and nothing is stopping you from expanding on texts by Googling more information.
     
  17. Feb 14, 2016 #16

    jasonRF

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    Jarvis323,

    I'm not sure exactly what you are looking for, but for complex analysis perhaps a book like "an imaginary tale", followed by "Dr Euler's fabulous formula" , both by Nahin, may be along the lines of what you are looking for. They give lots of history and some interesting applications of complex analysis, cover some of the important topics like Cauchy's theorem, but do not really teach complex analysis with all of the gory details that you would get from a real math book.

    jason
     
  18. Feb 14, 2016 #17

    mathwonk

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    i don't have time to write a complete answer, but I agree this is somewhat of a myth. It is on you to modify how you learn rather than the book to accomodate you. Try what professionals do: read the statement of a theorem and then try to prove it yourelf before reading the proof in the book. Try to think up examples and applications of the material. I.e. work at it. mind you i agree there are very dry books that do not speak to me and others that seem user friendly, but to really learn takes a struggle and neither type of book will make this unnecessary. the best books are the ones written by the masters of the subject. so for algebra, try euler, and for geometry try euclid, maybe with hartshorne as a guide. and try reading your books non linearly. you can really open to any page you choose. its allowed. the book "what is mathematics" by courant and robbins is recommended. Russian books are also very good at pedagogy. the book Geometries and groups by Nikulin and Shafarevich is excellent. Also read the introduction to the books where the author gioves his overview. E.g. in Matsumura's intro to his Commutative Ring Theory, he says the most important theorem in commutative algebra is krull's princip[al ideal theorem. This is very valuable knowledge.
     
    Last edited: Feb 14, 2016
  19. Feb 15, 2016 #18
    I don't believe in learning style, but the way a teacher goes about explaining and the presentation of information can really affect students knowledge and motivation (not the same thing as learning style IMO) but maybe the "for dummies" series might help (no really, I use it and its a great series for everything) or schaums outlines
     
  20. Feb 15, 2016 #19
    If you do find the time, please write it, even if it's in piece-wise bits.

    Really? So you should just pick up the first book on a subject you're interested in, and if it doesn't speak to you, then engage in a laborious process of modifying how you learn rather than looking for other books in the category that are talking more your language?

    You mean the left-brained biased professionals right? Not the right-brained, more creative and visually minded biased "holistic" professionals?

    It's easy to call differences in learning strategies a myth when your bonded to a particular way of looking at things. It's like a shark telling a human that the reason he can't swim is because he's deficient in is caudal-fin propulsion strategy rather than encouraging him to work on his "free-style" technique. The shark has no conception of any other method of swimming than the caudal-fin propulsion mechanism so he tells the human that "learning styles" are a myth and the reason you can't swim is that you're not getting your "caudal fin" technique on and you better study it. That's a naive and one-dimensional way of looking at the learning process.
     
  21. Feb 15, 2016 #20

    mathwonk

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    diracpool, i am also a holistic/creative learner, but practically that means i need to learn how to provide myself with the sort of "aha" moments that illuminate me. i have tried to give you some techniques. my key point is that holistic learners can make it in the linear world if they work at it.
     
    Last edited: Feb 15, 2016
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