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My SO teaches elementary math, and we've had a few discussions about this. When teaching a new concept, say the area of a parallelogram, she will present the c

My SO teaches elementary math, and we've had a few discussions about this. When teaching a new concept, say the area of a parallelogram, she will present the concept in multiple different ways: - Give printouts of parallelograms on graph paper, so the students can count the number of squares in a parallelogram. Also give them scissors and see what happens. - Give students two triangles and a square (which they know how to get the areas of already), as well as some tape. - Simply give students the length of the base, height, and the area of multiple parallelograms. The interesting thing is that there will be a somewhat equal split among which way makes the concept click for the students. Some will instantly start counting squares on graph paper and figure it out. Some will tape the different shapes together and go from there. Others will play with the base and height numbers and arrive at a formula. So while "learning styles" may be a misnomer, I do believe that presenting one topic in a variety of ways is beneficial.

deleted 8y ago
[deleted]
reificator 8y ago
You might like Lockhart's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....
- turingcompeteme 8y ago
  I love it, and I think most people here will as well. And it highlights how important it is to not force one method of learning on children. So even if one thinks that we shouldn't teach multiple learning styles, it's important to keep the lessons in Lockhart's Lament in mind: Discovery is important. Variety is important. Rote memorization is not.
mattferderer 8y ago
I strongly agree in presenting a topic in a variety of ways since being able to relate new information to information already known is a major key to learning new concepts. The more ways a topic is presented, the better chance a person's brain can relate it to something already known. I have a strong assumption that when many people hear "learning styles", they assume it to this instead of auditory vs visual.
- dmix 8y ago
  > I have a strong assumption that when many people hear "learning styles", they assume it to this instead of auditory vs visual. Or the assume each individual only benefits from one in all situations (being half awake, interested in the subject, etc, etc). Which is a ridiculous assumption once you really think about it.
  - jldugger 8y ago
    And yet I've have teachers growing up who gave classes workshops to help them identify their learning style, as if it was as inherent as a pokemon type.
- mygo 8y ago
  > The more ways a topic is presented, the better chance a person's brain can relate it to something already known. Well there’s that, but it also goes further. The more ways a topic is presented, the more context there is for the learner to see how those things relate to each other. Give me both a formula and a graph and I will be able to use them together to better understand the concept. They reinforce each other.
r00fus 8y ago
> So while "learning styles" may be a misnomer, I do believe that presenting one topic in a variety of ways is beneficial. Absolutely. I think "learning styles" is a reductionist view of Universal Design for Learning [1], which is essentially what you described how your SO teaches. It's quite possible that at a given time, someone may be inclined to visual learning, but may be more kinesthetically inclined in another setting/moment. [1] https://en.wikipedia.org/wiki/Universal_Design_for_Learning https://en.wikipedia.org/wiki/Universal_Design_for_Learning
Nition 8y ago
The best part of this is the simple fact that they're helping the students understand why the formula is what it is, and not just learning it by rote.
conistonwater 8y ago
What you're describing is usually called teaching methods, rather than learning styles. Teaching methods are real, figuring out which ones work best is a field of its own, like mathematics education research. But the article is specifically about learning styles, which is a specific term in psychology and a different idea. I think it's unnecessarily confusing to mix up the two, learning styles aren't real and definitely not a "misnomer".
- kaycebasques 8y ago
  Teaching methods are something I’m very interested in as a technical writer, and I’d love book / article recommendations.
  - conistonwater 8y ago
    Something like this, it has further reading references at the end? http://www.md.utoronto.ca/sites/default/files/What_works%2C_What_doesn%27t.pdf http://www.md.utoronto.ca/sites/default/files/What_works%2C_...
jacobolus 8y ago
The way we define area is in terms of little squares. (We could use little equilateral triangles or little right-angled isosceles triangles or some other unit instead, but we don't, conventionally preferring squares.) So the way to learn about areas in general is to start with the area of a unit square = 1, and then clarify the properties of area in general, notably that we can cut and paste shapes without changing the total area, as long as we don't overlap them, which means we can count up the number of unit squares and that tells us the area of a figure. Most of the rest can be figured out by students if guided by a well organized set of problems which build on each-other. We can proceed to first finding areas of shapes made using axis-aligned sides of natural number lengths on a square grid. For these the area can be found by directly counting squares, and e.g. by natural number multiplication in the case of rectangles. Then we can look at the areas of other shapes with vertices on a square grid. Then we can look at the areas of rectangles with rational side lengths (no longer nicely on the original unit grid; instead we need to make a finer grid to count, resulting in rational-number areas, since we must relate the grid units). Then we can next proceed to parallelograms – in a square-area-unit conventional world these are arguably more fundamental than triangles, but we could deal with right-angled triangles at about the same time. Triangles where we can find base and height can come next; these can be split into a pair of right-angled triangles or duplicated and glued into a parallelogram. After that finding areas of other shapes (e.g. with irrational side lengths) takes more machinery from Euclidean geometry (starting from the Pythagorean theorem), and can be delayed a while. While talking about parallelograms it would be nice to take some squares and other rectangles outside and look at the shadows they cast on the ground. This is a nice chance to introduce the concept of affine transformations, which preserve parallel lines and area ratios, as we can see by observing the shadow cast by a square grid (e.g. made of wire or drawn on a transparency sheet), especially if we have some translucent shapes lying on the grid. Basic transformation geometry (especially discussions of reflection/rotation/translation [isometries] and snowflakes, wallpaper tilings, etc., and affine transformations) is accessible at quite a young age and some hugely valuable topics to introduce early so that kids will be prepared to extend them later. More general projective transformations can wait a while.

deleted 8y ago

[deleted]

reificator 8y ago

You might like Lockhart's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

turingcompeteme 8y ago
I love it, and I think most people here will as well. And it highlights how important it is to not force one method of learning on children. So even if one thinks that we shouldn't teach multiple learning styles, it's important to keep the lessons in Lockhart's Lament in mind: Discovery is important. Variety is important. Rote memorization is not.

mattferderer 8y ago

I strongly agree in presenting a topic in a variety of ways since being able to relate new information to information already known is a major key to learning new concepts. The more ways a topic is presented, the better chance a person's brain can relate it to something already known. I have a strong assumption that when many people hear "learning styles", they assume it to this instead of auditory vs visual.

dmix 8y ago
> I have a strong assumption that when many people hear "learning styles", they assume it to this instead of auditory vs visual. Or the assume each individual only benefits from one in all situations (being half awake, interested in the subject, etc, etc). Which is a ridiculous assumption once you really think about it.
- jldugger 8y ago
  And yet I've have teachers growing up who gave classes workshops to help them identify their learning style, as if it was as inherent as a pokemon type.
mygo 8y ago
> The more ways a topic is presented, the better chance a person's brain can relate it to something already known. Well there’s that, but it also goes further. The more ways a topic is presented, the more context there is for the learner to see how those things relate to each other. Give me both a formula and a graph and I will be able to use them together to better understand the concept. They reinforce each other.

r00fus 8y ago

> So while "learning styles" may be a misnomer, I do believe that presenting one topic in a variety of ways is beneficial. Absolutely. I think "learning styles" is a reductionist view of Universal Design for Learning [1], which is essentially what you described how your SO teaches. It's quite possible that at a given time, someone may be inclined to visual learning, but may be more kinesthetically inclined in another setting/moment. [1] https://en.wikipedia.org/wiki/Universal_Design_for_Learning https://en.wikipedia.org/wiki/Universal_Design_for_Learning

Nition 8y ago

The best part of this is the simple fact that they're helping the students understand why the formula is what it is, and not just learning it by rote.

conistonwater 8y ago

What you're describing is usually called teaching methods, rather than learning styles. Teaching methods are real, figuring out which ones work best is a field of its own, like mathematics education research. But the article is specifically about learning styles, which is a specific term in psychology and a different idea. I think it's unnecessarily confusing to mix up the two, learning styles aren't real and definitely not a "misnomer".

kaycebasques 8y ago
Teaching methods are something I’m very interested in as a technical writer, and I’d love book / article recommendations.
- conistonwater 8y ago
  Something like this, it has further reading references at the end? http://www.md.utoronto.ca/sites/default/files/What_works%2C_What_doesn%27t.pdf http://www.md.utoronto.ca/sites/default/files/What_works%2C_...

jacobolus 8y ago

The way we define area is in terms of little squares. (We could use little equilateral triangles or little right-angled isosceles triangles or some other unit instead, but we don't, conventionally preferring squares.) So the way to learn about areas in general is to start with the area of a unit square = 1, and then clarify the properties of area in general, notably that we can cut and paste shapes without changing the total area, as long as we don't overlap them, which means we can count up the number of unit squares and that tells us the area of a figure. Most of the rest can be figured out by students if guided by a well organized set of problems which build on each-other. We can proceed to first finding areas of shapes made using axis-aligned sides of natural number lengths on a square grid. For these the area can be found by directly counting squares, and e.g. by natural number multiplication in the case of rectangles. Then we can look at the areas of other shapes with vertices on a square grid. Then we can look at the areas of rectangles with rational side lengths (no longer nicely on the original unit grid; instead we need to make a finer grid to count, resulting in rational-number areas, since we must relate the grid units). Then we can next proceed to parallelograms – in a square-area-unit conventional world these are arguably more fundamental than triangles, but we could deal with right-angled triangles at about the same time. Triangles where we can find base and height can come next; these can be split into a pair of right-angled triangles or duplicated and glued into a parallelogram. After that finding areas of other shapes (e.g. with irrational side lengths) takes more machinery from Euclidean geometry (starting from the Pythagorean theorem), and can be delayed a while. While talking about parallelograms it would be nice to take some squares and other rectangles outside and look at the shadows they cast on the ground. This is a nice chance to introduce the concept of affine transformations, which preserve parallel lines and area ratios, as we can see by observing the shadow cast by a square grid (e.g. made of wire or drawn on a transparency sheet), especially if we have some translucent shapes lying on the grid. Basic transformation geometry (especially discussions of reflection/rotation/translation [isometries] and snowflakes, wallpaper tilings, etc., and affine transformations) is accessible at quite a young age and some hugely valuable topics to introduce early so that kids will be prepared to extend them later. More general projective transformations can wait a while.