Source
r/math•
FinitelyGenerated

"Learning styles" and math education

I was watching Veritasium's latest video The Biggest Myth In Education (great watch) and it got me thinking about the role of hands-on work, diagrams, etc. in mathematics education.

A summary of the video: in education there is the VARK theory (Visual, Auditory, Reading/Writing, and Kinesthetic) which says that individuals have different modes of learning and that they learn best when the instruction matches their preferred mode. The video explains that there is, in fact, no data to back up that theory and gives some different theories of why people say they learn better visually. Basically if you already believe yourself to be a visual learner and you see a helpful diagram, you will see this as evidence of your visual learning preference even if that diagram would be helpful to anybody. Then, if you hear a great explanation of something or carry out an insightful experiment, you will think of that explanation or that experiment being great by itself and not see that as evidence that you are not strictly a visual learner.

How does this relate to mathematics? Well, in other fields, it's quite clear what mode of instruction yields the most effectual examples. In music, auditory instruction is generally the best choice. In geography, visual. In natural science, hands-on experimentation. So what about in math? Well, in all education there is a concept of "reinforcement," you need to see the same concept multiple times or practice with the concept a few times before it sinks in.

Let's look at some example subjects. First, linear algebra. So for many students, linear algebra is going to be the first place students encounter multidimensional pictures or objects. And so a lot of teachers will show them the concepts visually, by drawing pictures, demonstrating vectors using sticks in three dimensions, then will explain the concepts algebraically, using formulas. So even thought the concepts aren't deep (we know what a line is, what a plane is), it is the translation between the visual concepts and the algebraic concepts that presents the challenge. Students will need to practice through homework or practice problems of how to translate these concepts between the visual picture to the algebra and back (not to mention translating all the new terminology). Fortunately, we now have excellent software like Geogebra that helps make experimenting with this easier.

Next, let's look at combinatorics (because that's what I'm teaching right now). So right now I'm in the process of teaching about tree algorithms: Prüfer codes, Kruskal's and Prim's algorithms. If this were a physics class, it would be clear what to do: explain the concepts in class, and have them conduct experiments in the lab section. I don't have the luxury of a lab section so I have the practice the algorithms at home or I will sometimes pause the class to let them work out an example before going over it.

For context: my students are largely CS or engineering majors with a small number of math majors. So most (but crucially, not all) of them know programming. So to explain Kruskal's and Prim's algorithm, a lot of the discussion is on how to implement it (priority queues, heaps, how to actually detect cycles). If they were pure math majors, maybe a discussion on matroids would be more beneficial instead. On the other hand, just because you're a pure math major, does not mean you only want to see theory and little implementation details. Likewise, just because you're an engineering major, doesn't mean you don't want to see any theory.

Some discussion points:

  • are there any examples, explanations, exercises, whatever, that really stand out as being exceptionally helpful to learning a concept
  • what would/should be the equivalent of a physics or chemistry lab section in mathematics? Should we have programming labs? Do you think that current tutorial/recitation sections (whatever you call it where you are) should be changed at all?
  • how do you feel about theory vs implementation? Do you feel like as a pure math major you would have liked to learn more about how to implement something in place of the theory? (Or vice versa if you saw more implementation.)
  • how do you feel about learning the theory at home and practicing it in class vs the usual method of theory in class, practice at home?
  • do you think that the VARK model (which is experimentally non-verifiable) has set back education at all?

Posted Jul 9, 2021, 4:40 PM UTC

1819
edderioferAlgebraic Topology•

I was taught during teacher training that while different learning styles are a myth, it's still helpful to teach the same topic with multiple instruction modes because it provides better reinforcement than teaching with just one mode.

Whether there's any evidence for this, I don't remember, so take this with a salt shaker.

18
FinitelyGeneratedOPCombinatorics•

Right. See 10:55 of Veritasium's video where he discusses just that.

7
LilQuasar•

this is acknowledged in the video, the explanation seems to be that different things are better taught/learnt with different modes and everyone benefits from this

1
EmmyNoetherRing•

So… I’m always very hesitant to dismiss a lot of people’s individual observations as magically psychosomatic. For instance, we know some individuals are unable to picture things in their minds (aphantasia). Presumably teaching that focuses on visual analogies of concepts isn’t as helpful for them as it is for someone who is… capable of visualizing concepts.

But what evidence do we have that suggests this mental visualization capability is strictly binary? That everyone in the world either visualizes concepts with ease, or else (more rarely) is completely unable to? Abilities that get constructed in biology usually end up in a spectrum… we all have different eyesight, different knacks for picking up languages, different levels of ease with balance or hand-eye coordination. You’d tend to expect that there’s a range of ability for mental visualization, and I’m pretty sure there’s a body of psych research on that.

It seems a hard claim to back up that people’s ability to learn from visual analogies is independent of their ability to mentally visualize concepts. So the claim that everyone learns equally well from visual analogies seems at least a bit implausible. I’d want to see some strong supporting evidence for that, with a large n and good experiment design.

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FinitelyGeneratedOPCombinatorics•

There is a list of sources in the Veritasium video. Let me bring up just one: https://anatomypubs.onlinelibrary.wiley.com/doi/abs/10.1002/ase.1777. Here they studied 426 anatomy students to see if their response to the VARK questionnaire correlated with their preferred method of study (and found no correlation). Additionally, they found that certain specific study strategies were effective regardless of the VARK questionnaire.

So maybe I didn't summarize the video as best as I can. But I think the main takeaway is that don't take what the VARK questionnaire says about you as an immutable truth and then go and try to frame your study habits around that. Focus on whether or not specific study methods work well for you rather than trying to pre-categorize them based on VARK.

Likewise, for teachers, don't worry about whether you are able to explain a concept in the 4 different modes, but do try to present concepts in multiple different ways anyway.

7
EmmyNoetherRing•

Ah… so less a question of whether there exist visual learners, auditory learners, etc… and more a question of whether that specific questionnaire is a sufficiently effective measurement tool for students’ learning approaches.

I knew about the learning types, and that meshed well with my own teaching experience (in terms of different students needing different styles/formats of explanations)… but I’d never heard before now that there was any specific questionnaire. So I’d guess in answer to your last question, it seems likely that the influence of that tool (either negative or positive) probably hasn’t been that extensive.

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FinitelyGeneratedOPCombinatorics•

It depends also on what you mean when you say "visual learner" or "auditory learner." There is a difference between ability and style. For example, a professional musician is usually going to be better, whether through natural or acquired ability, at thinking about sounds and music in their head than someone who isn't musically inclined. This is a question of ability, however, not style.

The learning styles theories try to extrapolate further than this and say that because this musician has a good ability to hear sounds in their mind, that therefore they learn best auditorily. For instance, they predict that if you take this musician and explain a concept to them—for instance, how to make a lasagna—they will remember this concept better if you explain it verbally rather than showing them a slideshow of someone making a lasagna. But when you test this theory, the experiments find no difference between "auditory learners" or "visual learners" at learning a concept auditorily or visually. If learning styles existed, we would expect to see a difference. So the conclusion is that while ability can differ, and so a musician can remember details of a song better than a non-musician, when you isolate ability, there is no "learning styles" that can predict how people learn. A musician can learn the details of a song really well, but there's no evidence that writing a song about how to make a lasagna is going to help them more than just giving them the recipe and having them practice.

6
EmmyNoetherRing•

So…. Again it feels like things are being conflated oddly.

Let’s say someone with aphantasia becomes an artistic painter. You’re making the leap that this necessarily implies they’ve become good at visualizing things mentally… which clearly isn’t true. Deaf people can become musicians without developing any auditory skills. Things don’t necessarily hook up niavely like that. People often leverage what they can conceptualize well (tactile sensitivity usually in the case of deaf musicians) in non-intuitive ways in order to accomplish what they’d like to do well.

I guess there’s a philosophical assumption underlying this that everyone has equal inherent abilities and that apparent differences in skills/preferences are a matter of training or some external influence/persuasion?

2
chillermane•

seems a hard claim to back up that people’s ability to learn from visual analogies is independent of their ability to mentally visualize concepts

It’s just as hard a claim that people who can’t mentally visualize have a harder time learning from visuals if you have no data.

Everyone learns visually. A child learns to swing a baseball bat by watching someone else do it regardless of their ability to mentally visualize.

To say that it sounds implausible is pretty meaningless in the context of science and especially math. What the data does say is that people who are good learners are good at learning all types of things, it’s never specific to certain types of learning.

This “types of learning” theory has existed forever and there has never been any real evidence to support it. If you want to ignore the fact that experiments have tried and failed then go ahead, just don’t act like you simultaneously care about scientific data

5
armedt•

I didnt even know that when people imagined things they actually like could picture and see them until i was 20 😂😂

2
CrazySD93•

I only learnt about these learning styles when googling mid way through college a few years ago my struggle with some courses.

I describe my struggle with lectures that were spoken only

My buffer is only 100 bytes long, and when that fills up I need to process and store it, while new information is being heard and ignored. (couldn't take notes and hear at the same time)

Has affected hearing instructions at work where I just don't recall them saying something that was said.

Lectures where I can read the text, beautiful, my compensation strategy was to record lectures myself, and type of the notes sections at a time, and then read over it, otherwise I would just no be able to internalise it.

If I'm wrong and it's psychosomatic, give me the cure.

2
EmmyNoetherRing•

I don’t think you’re wrong. Whenever we’ve got decades of diverse, widespread lived experience backing up the claim that X is true, and then someone comes along and says “there’s no evidence that X is true!”… I find it’s often informative to go look at their experiment design. They tend to run a bit silly… small n (and/or no meaningful effort to sample individuals from different groups), heavily warped or oversimplified interpretations of what ‘X’ is, etc. Everyone’s gotta publish.

1
GustapheOfficial•

My driving school had illustrated posters of the vark system on the walls, except someone had gone absolute ham and created like ten different learning styles, some of which made no sense at all. Things like "you learn best by working with numbers" like that's going to help you when learning anything except numbers. I would have probably been suspicious of the system anyway, but those posters really tipped me off.

3
sillymath22•

Feynman had a great approach to teaching. I take his approach as a teacher myself. The key to learning which is what the vdieo was getting at was engagement. You can get a kid to learn if they are engaged or 'hooked' as Feynman puts it.

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https://www.youtube.com/watch?v=BY6VntTmtIo

2
CodeTinkerer•

I used to teach programming at two different universities. One had a computer lab, the other did not. The reason there wasn't a computer lab was a lack of resources (at the time) to have computers for all students.

Initially, the big problem with a computer lab for beginning programmers is getting everyone set up. That can just be a lab by itself. You can demo the steps, think it will take 10 minutes, and everyone's ready to go, and after 50 minutes, people still can't get logged in or install software or what-have-you because you assumed students knew how to install stuff and could follow directions.

For a chemistry lab, you're not exactly problem solving. You are typically running a controlled experiment, making measurements, recording observations. It's basically like being taught to cook a recipe. The same might be said of a biology lab. Follow these steps, look for these things.

With math? I mean if you ask them to solve math problems, that can take far longer than the lab. Some students might get it in 10 minutes, some might need hours, some might need to see a TA and break the content over several nights. To sit for 3 hours in a lab doesn't seem all that fruitful. A standard math section is likely to go over homework problems, take a quiz, and go through some more examples. Students are expected to digest this material when they are back at the dorm.

When I taught a computer lab, I'd do 3 easy questions (to me), and still, no one could think algorithmically and even solve a single problem. Here's an example. I tell you that you have a calendar, not in a leap year, and say this is the 201st day of the year. What month and day is that? People found this really difficult to solve. It's arguable that they could solve it without a program, but I doubt many could (and then they blame their lack of programming skills when they generally lack general problem solving skills).

So, to me, computer labs were kind of a waste of time. You'd basically have to run in like a chemistry lab. Here's some code. Change some values. Run it, run it with new values, etc. So you tell them minor things to modify and they aren't exactly learning to program.

I suppose it could be useful to make the lab about finding bugs as that's something that's rarely taught. At least you'd be going through the code trying to understand it, but most people think of programming not debugging, and it's a bit hard to come up with good debugging exercises.

2
PartyBaboon•

I think are 2 ways in which one could be a visual learner in math (where one seems kind of weird) and the other perfectly reasonable.

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The first way is to just to try making everything visual. You learn the definition of a ring, but you have to make it visual in some way.(why?) The second is to try to have pictures of different things in your mind when possible, as a sort of visual aid when learning new concepts and trying to make some things visual. If you have a stronger habit of doing this ,than other people you might call yourself a visual learner. I feel like this kind of distinction can be usefull.

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