Mathematics: What are the different learning styles?

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seaweed
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24 Oct 2015, 3:28 am

I've never met a teacher who could truly cater to my mathematics learning style. I can adapt to visual learning when it comes to math, which is why I was good in geometry but bad at algebra and precalculus in high school. the algebra and precalculus that involved graphing was fine but that was where it ended.

I am primarily a physical learner when it comes to many things but especially math, which I think is an overlooked learning style past the age of counting beans. I wish there was a physical math class I could take to fulfill my requirements for my sculpture degree. (makes sense, right?!). I mean when I work on structural and mechanical sculptures in the shop I run into math and physics problems all the time. I can imagine a very successful math course involving making structures, understanding limitations, and solving complex problems.



Rudin
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24 Oct 2015, 6:39 am

seaweed wrote:
I've never met a teacher who could truly cater to my mathematics learning style. I can adapt to visual learning when it comes to math, which is why I was good in geometry but bad at algebra and precalculus in high school. the algebra and precalculus that involved graphing was fine but that was where it ended.

I am primarily a physical learner when it comes to many things but especially math, which I think is an overlooked learning style past the age of counting beans. I wish there was a physical math class I could take to fulfill my requirements for my sculpture degree. (makes sense, right?!). I mean when I work on structural and mechanical sculptures in the shop I run into math and physics problems all the time. I can imagine a very successful math course involving making structures, understanding limitations, and solving complex problems.


Some mathematics objects are not physically tangible though.

Especially when we are working in higher dimensions.


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seaweed
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24 Oct 2015, 11:18 am

Rudin wrote:
Some mathematics objects are not physically tangible though.

Especially when we are working in higher dimensions.


i'm not dismissing that. just saying that for my specific degree it would make sense to allow a physical math course for the math requirement rather than the option of just taking finite or calculus. i only need to take one math class for my degree but i haven't done it yet because i'm so bad at math :(



slave
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25 Oct 2015, 12:54 am

Rudin wrote:
seaweed wrote:
I've never met a teacher who could truly cater to my mathematics learning style. I can adapt to visual learning when it comes to math, which is why I was good in geometry but bad at algebra and precalculus in high school. the algebra and precalculus that involved graphing was fine but that was where it ended.

I am primarily a physical learner when it comes to many things but especially math, which I think is an overlooked learning style past the age of counting beans. I wish there was a physical math class I could take to fulfill my requirements for my sculpture degree. (makes sense, right?!). I mean when I work on structural and mechanical sculptures in the shop I run into math and physics problems all the time. I can imagine a very successful math course involving making structures, understanding limitations, and solving complex problems.


Some mathematics objects are not physically tangible though.

Especially when we are working in higher dimensions.


Mathematics is so vast that it encompasses a continuum of problems from the concrete real world ones to the purely abstract Physically impossible ones(ie. pure maths)and likely things we have never even conceived.

We will never exhaust its range.

A course could certainly exist which would be as you wish it to be.



seaweed
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25 Oct 2015, 1:25 am

not everyone can understand theoretical math, especially in the way it is most often taught. it makes sense to not require it for people who don't understand that way, because then they are just forcing memorization and a subsequent failure of remembering because core concepts were never truly comprehended in the first place. i thought this question was about alternative learning and teaching styles in math, not alternative learning and teaching styles in advanced theoretical math. sorry for intruding :oops:



slave
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29 Oct 2015, 1:20 am

seaweed wrote:
not everyone can understand theoretical math, especially in the way it is most often taught. it makes sense to not require it for people who don't understand that way, because then they are just forcing memorization and a subsequent failure of remembering because core concepts were never truly comprehended in the first place. i thought this question was about alternative learning and teaching styles in math, not alternative learning and teaching styles in advanced theoretical math. sorry for intruding :oops:


I don't feel that you have intruded in any way.

I value your contribution to this thread. :D

I started this thread and I did not make it about 'advanced theoretical math' but about Maths in its broadest sense.

My teachers were devoid of all passion....lifers just collecting paychecks and accumulating fat pensions and no one ever taught me that Maths is about creativity and relationships not meaningless rote regurgitation.

I want to pair my learning strengths with PROPER instruction...a teaching style I can connect to.

I'm missing something and I'm trying to find out what it is.



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31 Oct 2015, 9:45 pm

[img]<a%20href="http://imgur.com/yGQ3kn9"><img%20src="http://i.imgur.com/yGQ3kn9.png"%20title="source:%20imgur.com"%20/></a>[/img]

This is gonna be my first image upload, I hope it works. I took a problem, graphed it and used an image editor to point out the parts of the graph I wanted emphasis on. Then I put it all into a text editor and explained how I determined a surface area. Its a little tedious, but if you make a mistake, someone can easily see where in the process you made it.


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MDD123
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31 Oct 2015, 10:22 pm

Fail, the link should work at least. Yea, I have reference notes from trig and most of the calc lineup. I just print them out and post them on a wall in my room, so instead of flipping through the book, I can look at my wall. Here's a link for those:
<a href="http://imgur.com/awiCi0E"><img src="http://i.imgur.com/awiCi0E.png" title="source: imgur.com" /></a>

<a href="http://imgur.com/1BdwWcp"><img src="http://i.imgur.com/1BdwWcp.png" title="source: imgur.com" /></a>

Descartes' method of finding zeros, as well algebraic division are things I usually forget as far as just algebra is concerned. I can't say I got the hang of logarithms completely either. That's the sort of algebraic stuff I'd gather for myself.

If you're learning new things, I think its a good practice to write them all down and see what kind of a list or table you can come up with. That way, you don't have to second guess yourself the moment you move on to a new section.


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SippingSpiderVenom
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05 Nov 2015, 11:06 am

Image
Image

A lesson in bbcode, wherein the image resizing is not implemented on wp.
http://www.bbcode.org/examples/?id=10


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SippingSpiderVenom
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05 Nov 2015, 11:19 am

You've applied syntax highlighting to your mathematics - novel. Which editor did you use?

And to keep things on topic.

The seven learning styles are:

visual
auditory
social
independent
kinesthetic
literary
logical


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MDD123
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05 Nov 2015, 12:02 pm

Whoa, thanks for the help with that SippingSpiderVenom, that changes things.

I used ms word for the equations and color coding, then I used concept draw pro to fit them on a page (not one of word's strong suits).

I'm pretty sure I'm a mix of kinesthetic and social learner. I've gotta do the work for myself to really learn it, but its nice to check in with people to make sure I'm doing it right.


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Kiriae
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05 Nov 2015, 4:55 pm

slave wrote:
I was a straight A student in Maths but I never felt confident in my understanding. I never felt like I really 'got it'. I believe that Maths is more a way of thinking than rote memorization of equations and rules, and somehow I never achieved mastery despite my good grades.


I was a straight A student in Math as well and I can't imagine having straight A without "getting it".

I never used rote memory at Math and I hated Geometry at first because it reguired me to remember all the formulas. For the same reason I hated multiplication in primary school - I still don't know multiplication table past x5.

I remembered only a few basic rules and everything else was just using them in creative ways. Why remember 6x7? I can get the same result by doing 5x7+7. Why remember formula for trapezoid field? I can count it by making rectangle and 2 triangles of it...

My good grades were all thanks to my understanding and creativity. I used the little information I knew to figure out what I didn't know. Often I was writing the correct formula AFTER getting the right answer. I was reinventing the wheel all the time. But I had a lot of fun doing that and I was effective.


I am logical, independant learner. Everything must make sense for me and I have to discover it by myself.



SippingSpiderVenom
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06 Nov 2015, 9:45 pm

I'm primarily logical and independent as well. My k-12 record is abysmal, mostly because I am not a social learner at all and I can't quit day dreaming. In this way I'm kinesthetic I suppose, but I don't actually understand kinesthetic really. It's usually ascribed to athletic types and those that can't sit still. I can sit still, I just don't think I should.

Later in Community College I had an instructor who preferred the Socratic method, where he asks questions and expects the answers, he might give clues if he didn't get a good response. I loved that guy, a full on propeller head who had worked for nasa and not only respected the way I felt about learning, but validated it. Now I work in computers as a technician and I'm returning to school to study math. I'm hoping once I've soaked up the math I can take at community college that I will be able to move further through moocs.

I'm happy to help MD :D I use lyx to edit my math, I don't understand why it isn't more popular, I guess because it is not Microsoft, but the code latex, is used for online mathematics as well as formal math publications and thesis papers, etc.


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MDD123
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07 Nov 2015, 5:21 pm

The screen shots in lyx looked good. I'm just used to word myself, it gets the job done but I don't like all the clicking and browsing I have to do for it. Color-coding is one thing, but I'd rather not have to click around to get the material typed up. What kinds of tasks does lyx help you with?

I use a free program called grapher (think it's a mac feature only), it allows me to plot in several coordinate-styles (cartesian, polar, square, cylindrical, spherical, etc...) It's very pain-free in the sense that pure mathematical expressions are turned into graphs with no programming required. Its a far cry from a CAD program though. Are there any CAD programs that allow you to draw shapes using mathematical expressions?

You're one tough dude if you can handle work and school. If you want any math reference material, I can put up all my notes from calc2-4, you never know what might come in handy. It's like they say in alaska, the odds are good, but the goods are odd.


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SippingSpiderVenom
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08 Nov 2015, 3:58 am

Thank you, it's one class but I'll take it.


Well to start out lyx is open source, that's how I came across it. Second it's based on the latex typesetting language developed by Donald Knuth. In this sense it is similar to an html editor, where many html editors are wysiwyg lyx is what you see is what you mean. (As an aside, you can save your math sheets in html, so it is an html editor, too.) What you see is what you mean, means the copy you are viewing is not production quality. To enter a math equation you type alt-I-enter and you get a little code interpreter that allows you to enter latex code, with code completion into your document which is interpreted on the fly for more editing. So, \frac is the code for fractions, which you can type and key tab, to bring up a fraction to work on.

I'm interested in learning latex as much as I am in learning lyx, so it is a nice arrangement. I'm using lyx for algebra right now, for graphs I use an open source app called graph (sorry, it can be difficult to find, maybe gnu graph?). I actually just piled on open source math apps on my desktop but unfortunately my monitor has crashed, so I won't list them.

Since I'm not currently on my desktop I'd have to decline documents for the time being, but thank you. I am curious to see, did you keep your color coding throughout, or just for trig? It had occurred to me that a plugin could be written for lyx that does that on the fly, maybe somewhere in my not too distant future, if it was okay with you.


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MDD123
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08 Nov 2015, 3:39 pm

I'll keep lyx and latex in mind, I might just want to branch out my note-keeping. You can use the formulas any way you want, that's what they're there for. The color coding and highlighting are reoccurring, but they aren't consistent, this sort of evolved over time. I'm trying to contrast different parts of the formulas to better illustrate the relationship. Here's a pattern i've noticed:

Variables: (x,y,z) (r,theta,z) (rho,phi,theta)
Known Constants: (a,b,c)
Functions: f,g,h
Vectors: (u,v,w)
Boundaries: Known Constants, Functions

At some point or another, I highlight these aspects of the formula. This is really geared towards calculus, calc2 is when I started taking consistent notes.


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