Learning Styles Myth
May 20, 2018 12:05 PM Subscribe
Another nail in the coffin for learning styles. Their findings “provide strong evidence that instructors and students should not be promoting the concept of learning styles for studying and/or for teaching interventions. Thus, the adage of ‘I can’t learn subject X because I am a visual learner’ should be put to rest once and for all.”
I always felt strongly that I was not a kinesthetic learner, but that was less "not a kinesthetic learner" and more "can't we just sit down and get through this quickly?"
posted by grandiloquiet at 12:29 PM on May 20, 2018 [9 favorites]
posted by grandiloquiet at 12:29 PM on May 20, 2018 [9 favorites]
Yes. Do student-centered learning next!
posted by subdee at 12:36 PM on May 20, 2018 [7 favorites]
posted by subdee at 12:36 PM on May 20, 2018 [7 favorites]
I was always taught that "learning styles" were best used in combination; to try to hit at least two different ways of learning information. So like, if I had a bunch of vocab words to learn I should read them and their definitions out loud as well as write them down by hand. Or if I had a period of history to familiarize myself with I should read a couple books about it as well as watch some documentaries or listen to some lectures. In undergrad I took sketchbooks full of notes that were actually doodles, a visual record of lecture contents with no obvious connection to the material - but I also did revision with regular notes and annotating the course reading by hand.
I never heard the thing they're talking about in the article, where you use learning styles as a thing to stick with and not try other ways of learning things because your personal "style" is going to be what works for everything. It was always presented as a way to be more thorough or more creative in case something was particularly difficult or confusing. I feel like this must be another result of the crappy way we treat teachers - there is no shortcut and we shouldn't expect teachers to have them.
posted by Mizu at 12:42 PM on May 20, 2018 [29 favorites]
I never heard the thing they're talking about in the article, where you use learning styles as a thing to stick with and not try other ways of learning things because your personal "style" is going to be what works for everything. It was always presented as a way to be more thorough or more creative in case something was particularly difficult or confusing. I feel like this must be another result of the crappy way we treat teachers - there is no shortcut and we shouldn't expect teachers to have them.
posted by Mizu at 12:42 PM on May 20, 2018 [29 favorites]
By which i mean, it's much easier to attack the previous pet Ed theory than it is to attack the current Ed theory, studies like this notwithstanding.
posted by subdee at 12:44 PM on May 20, 2018 [2 favorites]
posted by subdee at 12:44 PM on May 20, 2018 [2 favorites]
I tweeted this and one of my friends responded that he took a learning style test at school, learned he was "auditory", and started discussing material with his friends, and his marks improved. Another friend who is a professor said "well I recommend that to all my students."
It's not hard to see that if you take a test that suggests you use certain study methods, and as a result you carefully do some kind of study you didn't do before, focussing on the material consciously, you'll do better, not because you have now nailed your learning style, but because you were induced to focus on your material more and in a new way.
posted by i_am_joe's_spleen at 12:49 PM on May 20, 2018 [26 favorites]
It's not hard to see that if you take a test that suggests you use certain study methods, and as a result you carefully do some kind of study you didn't do before, focussing on the material consciously, you'll do better, not because you have now nailed your learning style, but because you were induced to focus on your material more and in a new way.
posted by i_am_joe's_spleen at 12:49 PM on May 20, 2018 [26 favorites]
This gives me a feeling of self-justification. Though its largely misplaced, as I just couldn't be arsed to read anything about catering to different learning styles in the first place.
Classic schadenfreudic learning style.
posted by ActingTheGoat at 12:49 PM on May 20, 2018 [39 favorites]
Classic schadenfreudic learning style.
posted by ActingTheGoat at 12:49 PM on May 20, 2018 [39 favorites]
What's the learning style where you do better when you know it will give you a chance to show off and make other people feel bad about themselves? 'Cause I used all the way through high school and uni. In my own defense, I was an asshole.
posted by Mogur at 12:53 PM on May 20, 2018 [19 favorites]
posted by Mogur at 12:53 PM on May 20, 2018 [19 favorites]
Speaking as a stupid person who struggles to learn and retain nearly any information, I was always a little skeptical myself. My assumption has always been that people who lean on this as a defense; a deflective response to educational failure, are idiots like me.
posted by constantinescharity at 1:08 PM on May 20, 2018 [7 favorites]
posted by constantinescharity at 1:08 PM on May 20, 2018 [7 favorites]
I still hear educators talking about learning styles as an established thing.
posted by doctornemo at 1:12 PM on May 20, 2018 [7 favorites]
posted by doctornemo at 1:12 PM on May 20, 2018 [7 favorites]
I never heard the thing they're talking about in the article, where you use learning styles as a thing to stick with and not try other ways of learning things because your personal "style" is going to be what works for everything.Oh god, I have, including coming from places that really ought to know better, like university student success initiatives. My sense is that more people are acknowledging these days that it's not backed up by evidence, but an awful lot of students have taken quizzes to identify their learning style and really believe that they have one learning style that they should stick with.
In general, we're really incredibly crap at teaching students how to learn. Part of it, I think, is that so much of the process goes on in your head and is invisible. I'm a university academic advisor, and I've also been taking classes as a non-degree student. I took a stats class last semester that a lot of my students take and struggle with, and I tried to pay attention to how I was learning, so I could help my students come up with study strategies. And I realize that a lot of it is just thinking about the material a lot. Like, I would sit there and focus on a concept, and I would silently explain the concept to myself, and then when I realized I was fuzzy about an aspect of the concept, I would write it down and go back through my notes and try to figure it out so it was really clear. And I did do problems and draw graphs and make a study guide and all the other stuff that we tell students to do, but a lot of it was just thinking about it and asking myself a lot of questions and trying to figure out if I was satisfied with the answers or I needed to go back and clarify. And that's really hard to model for students. It's much harder than saying "if you have this kind of learning style, make this kind of study tool."
posted by ArbitraryAndCapricious at 1:20 PM on May 20, 2018 [12 favorites]
Well, as one anecdatum, I can't stand the rush to make everything a video these days, where I can't skip ahead or alter the pace, and the speaker is always posing or looking off camera in a mannered way. USE YOUR WORDS, I shout at the sky.
I suspect that is generational more than learning style driven though. I saw a poster for a Meme Party at a college campus the other night and really wanted to go just to experience this new weird type of show. Sounds like powerpoint hilarity.
posted by msalt at 1:35 PM on May 20, 2018 [24 favorites]
I suspect that is generational more than learning style driven though. I saw a poster for a Meme Party at a college campus the other night and really wanted to go just to experience this new weird type of show. Sounds like powerpoint hilarity.
posted by msalt at 1:35 PM on May 20, 2018 [24 favorites]
Being mindful of different learning styles is canon in museum exhibit design. But museums are voluntary and largely self-guided learning experiences; unlike schoolwork, there's no penalty/reward/consequences to mastering the material. There's also no instruction given on how to study, self test, etc. Consequently, it makes sense to me that museums who wish to nurture lifelong patronage (for themselves and all such institutions) would do well to accommodate all learning styles so that everyone, by virtue of having their preferences met, feels that they had an enjoyable museum experience.
posted by carmicha at 1:38 PM on May 20, 2018 [9 favorites]
posted by carmicha at 1:38 PM on May 20, 2018 [9 favorites]
grandiloquiet: I'm in the same boat. I damn near didn't graduate high school on time because of it. My Junior year Geometry course was taught in a very hands-on, exploratory manner. A lot of stuff with straght-edges, folding paper, protractors, and compasses, trying to "explore" and "understand" the various geometry rules and laws and things. I hated it. I picked up what I was supposed to understand right away, and would often end up falling asleep during class. I still passed every test, but I never got any credits for it. 1
Fortunately, in my senior year, another teacher who taught geometry let me do independent study for her, my way, and I managed to get my Geometry credits in so I could graduate. I don't need to prove the damn Pythagorean Theorem or that the sum of all the angles in a semi-circle is 180º. I trust that the rules are true. Just let me answer the damn questions and leave me alone.
1. I went to a weird high school where you didn't get grades, but earned credits. 10 credits meant you passed a class.
posted by SansPoint at 1:40 PM on May 20, 2018 [2 favorites]
Fortunately, in my senior year, another teacher who taught geometry let me do independent study for her, my way, and I managed to get my Geometry credits in so I could graduate. I don't need to prove the damn Pythagorean Theorem or that the sum of all the angles in a semi-circle is 180º. I trust that the rules are true. Just let me answer the damn questions and leave me alone.
1. I went to a weird high school where you didn't get grades, but earned credits. 10 credits meant you passed a class.
posted by SansPoint at 1:40 PM on May 20, 2018 [2 favorites]
I have literally never heard "[student] can’t learn subject X because [student is] a visual learner". The entire purpose of the whole ~learning styles~ thing, whether it was factual or not, was to enable more students to learn -- that is to say, it isn't that "[student] can't learn subject X", it's "[student] isn't able to learn subject X using method A, but this reflects a different learning style rather than some kind of immutable inability, so [student] should try methods B, C, or D instead of repeatedly trying a method that obviously has proven ineffective".
Scientific it may not be after all, but the article writer has no excuse for such nonsensical soundbitery.
posted by inconstant at 1:52 PM on May 20, 2018 [24 favorites]
Scientific it may not be after all, but the article writer has no excuse for such nonsensical soundbitery.
posted by inconstant at 1:52 PM on May 20, 2018 [24 favorites]
"Learning styles" in the sense of VARK probably arose as a way to articulate that there are alternatives to the traditional didactic classroom - that other means and modalities of education may be important as well. This is a positive development.
Where they all fall down is the assumptions they brought with it:
1. That people can be categorised into such vague taxonomies e.g. "visual learners"
2. That matching these categories of students with teaching styles would improve their learning
3. That the subject matter is less important than the student learner type. To take an extreme example:
"Class, today we're learning about the Mona Lisa. The visual learners will look at the painting; the audio learners will listen to me describe it; the kinaesthetic learners will paint their own copy..."
posted by Paragon at 1:54 PM on May 20, 2018 [26 favorites]
Where they all fall down is the assumptions they brought with it:
1. That people can be categorised into such vague taxonomies e.g. "visual learners"
2. That matching these categories of students with teaching styles would improve their learning
3. That the subject matter is less important than the student learner type. To take an extreme example:
"Class, today we're learning about the Mona Lisa. The visual learners will look at the painting; the audio learners will listen to me describe it; the kinaesthetic learners will paint their own copy..."
posted by Paragon at 1:54 PM on May 20, 2018 [26 favorites]
I have literally never heard "[student] can’t learn subject X because [student is] a visual learner".That's not how it works. How it works is "you, student X, are a visual learner, and therefore you should use visual learning methods to learn all subjects. Here is a list of visual learning methods. You should draw concept maps, rather than writing outlines." But there's no evidence that some people are visual learners who will always learn best if they make concept maps, rather than writing outlines.
Being mindful of different learning styles is canon in museum exhibit design.I actually wouldn't be surprised if that ended up leading to better exhibits, even thought the theory behind it isn't right. It's not true that everyone has a single learning style, but it probably is true that people will be more engaged by exhibits that they can interact with in lots of different ways.
posted by ArbitraryAndCapricious at 1:55 PM on May 20, 2018 [17 favorites]
Yes, I know that's not how it works. However, that's what the article says. I am criticizing the article. "There's no evidence that different learning styles work this way" (demonstrated by research evidence) is a completely different statement from "Learning styles is about telling students what subjects they can't learn" (a completely ridiculous implication and also what the article concludes with).
posted by inconstant at 1:58 PM on May 20, 2018 [7 favorites]
posted by inconstant at 1:58 PM on May 20, 2018 [7 favorites]
The real problem is there's the theory of multiple intelligences as the basis for a personality theory of learning, which is taken to derive the notion of differences in learning styles. If you reject the idea of learning styles, that forces you to revise ideas about multiple intelligences as well, because the issues are so connected. But you're not going to find that level of research discussion in the dissemination of popular science.
The other issue is the trend of universal psychology. By arguing there are no different learning styles, school administrators have a rationalization to not customize and personalize education. Which would be problematic; "motivated research results" intersects with funding and resource constraints as well.
posted by polymodus at 2:00 PM on May 20, 2018 [5 favorites]
The other issue is the trend of universal psychology. By arguing there are no different learning styles, school administrators have a rationalization to not customize and personalize education. Which would be problematic; "motivated research results" intersects with funding and resource constraints as well.
posted by polymodus at 2:00 PM on May 20, 2018 [5 favorites]
In general, we're really incredibly crap at teaching students how to learn.
Yes and no. Or, yes, but not necessarily due to lack of knowledge. Not data, but I attended lots of different schools growing up. They had different organizational structures, different instructional methods, etc. The more working class schools tended to focus more on compliance with immutable rules (in all aspects: student discipline, how various subjects were taught, etc.), while the more upper class schools tended to focus on developing creativity and leadership. In other words, the shadow curriculum in the different schools was quite evident on comparison, though not so obvious if each school was viewed in isolation. In some schools I was indeed taught how to learn, fairly effectively. In other schools, such skills, although encouraged by specific dedicated teachers, were more or less institutionally discouraged. I'll leave the matching problem of which schools were which as an exercise for the reader.
posted by eviemath at 2:13 PM on May 20, 2018 [32 favorites]
Yes and no. Or, yes, but not necessarily due to lack of knowledge. Not data, but I attended lots of different schools growing up. They had different organizational structures, different instructional methods, etc. The more working class schools tended to focus more on compliance with immutable rules (in all aspects: student discipline, how various subjects were taught, etc.), while the more upper class schools tended to focus on developing creativity and leadership. In other words, the shadow curriculum in the different schools was quite evident on comparison, though not so obvious if each school was viewed in isolation. In some schools I was indeed taught how to learn, fairly effectively. In other schools, such skills, although encouraged by specific dedicated teachers, were more or less institutionally discouraged. I'll leave the matching problem of which schools were which as an exercise for the reader.
posted by eviemath at 2:13 PM on May 20, 2018 [32 favorites]
It's not hard to see that if you take a test that suggests you use certain study methods, and as a result you carefully do some kind of study you didn't do before, focussing on the material consciously, you'll do better, not because you have now nailed your learning style, but because you were induced to focus on your material more and in a new way.
This sounds like my theory of diets, which is that they succeed (at least at first) not necessarily because of the exact dietary paradigm that they're based on but because you're eating mindfully rather than just stuffing your mouth with whatever comes along.
posted by Halloween Jack at 2:24 PM on May 20, 2018 [16 favorites]
This sounds like my theory of diets, which is that they succeed (at least at first) not necessarily because of the exact dietary paradigm that they're based on but because you're eating mindfully rather than just stuffing your mouth with whatever comes along.
posted by Halloween Jack at 2:24 PM on May 20, 2018 [16 favorites]
I don't need to prove the damn Pythagorean Theorem
No you don't but if you're not even a little curious about it then what is the point of all this stylism? I'm not casting blame here, just being sad about the whole thing.
posted by tirutiru at 2:38 PM on May 20, 2018 [5 favorites]
No you don't but if you're not even a little curious about it then what is the point of all this stylism? I'm not casting blame here, just being sad about the whole thing.
posted by tirutiru at 2:38 PM on May 20, 2018 [5 favorites]
tirutiru: It’s one thing to do a single exercise to “prove” the theorem, especially in a high school geometry class. It’s another to spend the entire class with straightedges and protractors “proving” it over and over and over again to make sure I get it. I got it. We all got it. How many more times must I spent proving that I got it?
I have always hated repetitious busywork. I felt the same way about the multiple weeks I had to spend diagramming sentences in 4th Grade. One week? Sure. More than that? What’s the fucking point?!
posted by SansPoint at 3:12 PM on May 20, 2018 [4 favorites]
I have always hated repetitious busywork. I felt the same way about the multiple weeks I had to spend diagramming sentences in 4th Grade. One week? Sure. More than that? What’s the fucking point?!
posted by SansPoint at 3:12 PM on May 20, 2018 [4 favorites]
Whatever my learning style it, I have no idea, because it doesn't fit into those boxes, and even the questions they ask in the inventories just feel dumb and wrong. Like, my ability to learn in an auditory fashion falls apart completely with even a slightly disorganized speaker, not to mention if they get outside of the range of voices and accents that my brain can process before getting to my auditory processing issues. I think I actually gain information reasonably well in a kinesthetic way... but my patience for that is like 1% of my patience for anything else so I'm actually pretty bad at it. I took no notes in anything, ever, until law school, and apparently now I'm pretty good at it, but I feel like note-taking for me falls less into "learning" than "memory", and the "memory" piece turns out to more involve repetition of any variety than the notes specifically.
The VAK/VARK stuff I've seen usually seems to have been presented as a way to try to make a show of being flexible but to do so with as little expense and personal attention as possible, and I can't help but feel like that's missing the point. We're all different and that the benefit of having real human beings teaching seems like it should be the ability to respond to that on a personal level. As an adult, if I can't have that kind of personal attention, I'd rather just be left to figure stuff out myself, it's so bad to get stuck in a box of how someone else decided you were supposed to work.
posted by Sequence at 3:21 PM on May 20, 2018 [5 favorites]
The VAK/VARK stuff I've seen usually seems to have been presented as a way to try to make a show of being flexible but to do so with as little expense and personal attention as possible, and I can't help but feel like that's missing the point. We're all different and that the benefit of having real human beings teaching seems like it should be the ability to respond to that on a personal level. As an adult, if I can't have that kind of personal attention, I'd rather just be left to figure stuff out myself, it's so bad to get stuck in a box of how someone else decided you were supposed to work.
posted by Sequence at 3:21 PM on May 20, 2018 [5 favorites]
I have always hated repetitious busywork. I felt the same way about the multiple weeks I had to spend diagramming sentences in 4th Grade. One week? Sure. More than that? What’s the fucking point?!
Easy to grade.
posted by Halloween Jack at 3:22 PM on May 20, 2018 [8 favorites]
Easy to grade.
posted by Halloween Jack at 3:22 PM on May 20, 2018 [8 favorites]
I think clinical and subclinical hearing problems and vision problems are common enough in kids (and uncorrelated enough), and that there is sufficient evidence for some kinds of 'critical periods' in human development, that there are probably significant populations of students who are relatively better at getting information visually than auditorially, and vice versa.
But this digest and the study it's based on seem to be mere polemics for one side of an ongoing controversy, and not terribly concerned about the truth.
posted by jamjam at 3:33 PM on May 20, 2018 [2 favorites]
But this digest and the study it's based on seem to be mere polemics for one side of an ongoing controversy, and not terribly concerned about the truth.
posted by jamjam at 3:33 PM on May 20, 2018 [2 favorites]
The problem with education fads like "learning styles" isn't just they are pedagogical diversions but also that they are adopted into popular culture and then weaponized by parents and students. Then when instructors face student and parent evaluations that will determine their career progression and salaries they are confronted with what they may now know is utter bullshit but still be required to serve it up because it is what the consumer thinks they need. Pity the poor university lecturer who fails to give his students a tactile way to learn exploratory factor analysis!
So it is not enough to put nails in the coffin, you need stakes through the heart.
posted by srboisvert at 3:52 PM on May 20, 2018 [10 favorites]
So it is not enough to put nails in the coffin, you need stakes through the heart.
posted by srboisvert at 3:52 PM on May 20, 2018 [10 favorites]
Students whose second language is English benefit a lot from also seeing the information written down on the board, and most students benefit from taking active notes (especially paraphrased notes).
But the standard lecture model already allows for all of those three modalities during instruction...
My beef with multiple intelligences is that it falls apart for anything more complicated than memorizing the preamble to the Constitution. For example, if you're teaching not just the formula for area of a triangle but also how to break apart shapes into components and problem-solve with unit conversions and so on, remembering the formula is only the first step and if you teach that step 3 ways, there is much less time available for higher-level applications.
posted by subdee at 3:55 PM on May 20, 2018 [2 favorites]
But the standard lecture model already allows for all of those three modalities during instruction...
My beef with multiple intelligences is that it falls apart for anything more complicated than memorizing the preamble to the Constitution. For example, if you're teaching not just the formula for area of a triangle but also how to break apart shapes into components and problem-solve with unit conversions and so on, remembering the formula is only the first step and if you teach that step 3 ways, there is much less time available for higher-level applications.
posted by subdee at 3:55 PM on May 20, 2018 [2 favorites]
If anyone's interested, here's the meta-review article by Hal Pashler et al that does a good job addressing the lack of evidence for learning styles. There's plenty of evidence that people have preferences about the modality of information presented to them, just not that customizing the modality has any beneficial effect on learning. The best modality is typically whatever is most suitable for the material; learning the spatial relationships between geographical locations is best done with a map, and no one's going to learn it faster with a verbal description.
posted by sloafmaster at 4:11 PM on May 20, 2018 [8 favorites]
posted by sloafmaster at 4:11 PM on May 20, 2018 [8 favorites]
So, why do I prefer written tutorials—by orders of magnitude—over YouTube videos on the same topic? E.g., I would rather spend a half hour looking for the former rather than watch a 10 minute video.
(I read the article, but not the links.)
posted by she's not there at 4:25 PM on May 20, 2018 [2 favorites]
(I read the article, but not the links.)
posted by she's not there at 4:25 PM on May 20, 2018 [2 favorites]
Warning: I actually went and read the linked article, but not the journal paper.
There is such a high stack of questionability that I can't even.
The article seemed to describe a study that was done completely without controls, and which went on to assume that correlation=causality.
The article says that students who took the trouble to use the special study methods recommended as supposedly more compatible with their supposed learning styles, didn't do any better in the course.
But in the real world, sometimes the reason that some people go the extra mile to try to use study methods they hope will be better, is because those students are having more trouble with the course. So if those people go on to do no better than other students on the course, but not much worse, that might represent a success. Or it might not! Without good control groups etc., you just can't know. But you can write up the results of your bold assumptions!
Another level of the crappiness is that although this article was headlined "Another nail in the coffin for learning styles", there was only one specific version and implementation of the vague idea 'different students do better with different learning styles' that was even pseudo-tested.
It's always possible to take a good idea that can be observed in practice by anyone who pays enough attention to what's going on around them ('different people differ in which methods of learning/study methods seem to be the most effective for them') and put together a very specific formulation that supposedly represents the idea but might miss most of the reality. Then you can go about pushing the idea that this particular formulation of the idea is *the* idea!
As for the connection to Gardner's 'multiple intelligences', that's another case where much of the reality was missed. Gardner acknowledged the reality that, for example, the ability to learn musical skills or to learn athletic skills is not the same as 'book learning'. And that's good. But what about the fact that, for example, different people seem to be showing different levels of ease in different subjects such as math vs. writing, or even in the classes teaching the use of their native language vs. a foreign language? The widely used version of 'multiple intelligences' seems to provide nothing but misdirection from those latter observed phenomena.
CONFESSION: I REEDITED FOR CLARITY with 2+ minutes left.
posted by cattypist at 4:28 PM on May 20, 2018 [13 favorites]
There is such a high stack of questionability that I can't even.
The article seemed to describe a study that was done completely without controls, and which went on to assume that correlation=causality.
The article says that students who took the trouble to use the special study methods recommended as supposedly more compatible with their supposed learning styles, didn't do any better in the course.
But in the real world, sometimes the reason that some people go the extra mile to try to use study methods they hope will be better, is because those students are having more trouble with the course. So if those people go on to do no better than other students on the course, but not much worse, that might represent a success. Or it might not! Without good control groups etc., you just can't know. But you can write up the results of your bold assumptions!
Another level of the crappiness is that although this article was headlined "Another nail in the coffin for learning styles", there was only one specific version and implementation of the vague idea 'different students do better with different learning styles' that was even pseudo-tested.
It's always possible to take a good idea that can be observed in practice by anyone who pays enough attention to what's going on around them ('different people differ in which methods of learning/study methods seem to be the most effective for them') and put together a very specific formulation that supposedly represents the idea but might miss most of the reality. Then you can go about pushing the idea that this particular formulation of the idea is *the* idea!
As for the connection to Gardner's 'multiple intelligences', that's another case where much of the reality was missed. Gardner acknowledged the reality that, for example, the ability to learn musical skills or to learn athletic skills is not the same as 'book learning'. And that's good. But what about the fact that, for example, different people seem to be showing different levels of ease in different subjects such as math vs. writing, or even in the classes teaching the use of their native language vs. a foreign language? The widely used version of 'multiple intelligences' seems to provide nothing but misdirection from those latter observed phenomena.
CONFESSION: I REEDITED FOR CLARITY with 2+ minutes left.
posted by cattypist at 4:28 PM on May 20, 2018 [13 favorites]
I have always hated repetitious busywork. I felt the same way about the multiple weeks I had to spend diagramming sentences in 4th Grade. One week? Sure. More than that? What’s the fucking point?!
Anecdotal, but my very smart 13 year old still can't spit out 6 x 7 without a good long think. In math now they study "units" of, say, multiplication for a week or two at most and then go off to a totally different topic. They also show them about 20 different ways to do it and make them practice all the different ways. But no multiplication sheets with 30 problems per page. Rinse and repeat every 2 weeks all year. I was good at math and at the time I hated the repetitive worksheets but for the basics I'd have to say that's probably how that stuff got ingrained in me.
Also, I'm diverging, but it's also now a ton of handouts which my kid can't keep organized. Me: "Don't you have a math BOOK?" Her: "I'd LOVE that!"
posted by freecellwizard at 5:29 PM on May 20, 2018 [3 favorites]
Anecdotal, but my very smart 13 year old still can't spit out 6 x 7 without a good long think. In math now they study "units" of, say, multiplication for a week or two at most and then go off to a totally different topic. They also show them about 20 different ways to do it and make them practice all the different ways. But no multiplication sheets with 30 problems per page. Rinse and repeat every 2 weeks all year. I was good at math and at the time I hated the repetitive worksheets but for the basics I'd have to say that's probably how that stuff got ingrained in me.
Also, I'm diverging, but it's also now a ton of handouts which my kid can't keep organized. Me: "Don't you have a math BOOK?" Her: "I'd LOVE that!"
posted by freecellwizard at 5:29 PM on May 20, 2018 [3 favorites]
tirutiru: It’s one thing to do a single exercise to “prove” the theorem, especially in a high school geometry class. It’s another to spend the entire class with straightedges and protractors “proving” it over and over and over again to make sure I get it. I got it. We all got it. How many more times must I spent proving that I got it?
Oh that's not proof, that's verification. And yes, I agree that sounds really annoying.
posted by peacheater at 5:35 PM on May 20, 2018 [3 favorites]
Oh that's not proof, that's verification. And yes, I agree that sounds really annoying.
posted by peacheater at 5:35 PM on May 20, 2018 [3 favorites]
Gardner acknowledged the reality that, for example, the ability to learn musical skills or to learn athletic skills is not the same as 'book learning'. And that's good. But what about the fact that, for example, different people seem to be showing different levels of ease in different subjects such as math vs. writing, or even in the classes teaching the use of their native language vs. a foreign language? The widely used version of 'multiple intelligences' seems to provide nothing but misdirection from those latter observed phenomena.
As a list of different domains of human performance that might be called "intelligence" it's hard to say anything is inherently wrong with it - though you could just as easily add more. The issue I think is that the way it is usually taught implies that there is minimal correlation of performance across any of the different domains. That independence is not really established and in some cases there's research that suggests that there are correlations. As a model of what are the fundamental dimensions of human cognition, then, it's not very empirically supported.
posted by atoxyl at 6:38 PM on May 20, 2018
As a list of different domains of human performance that might be called "intelligence" it's hard to say anything is inherently wrong with it - though you could just as easily add more. The issue I think is that the way it is usually taught implies that there is minimal correlation of performance across any of the different domains. That independence is not really established and in some cases there's research that suggests that there are correlations. As a model of what are the fundamental dimensions of human cognition, then, it's not very empirically supported.
posted by atoxyl at 6:38 PM on May 20, 2018
I’ll preface this by saying that I’m perfectly willing to accept that the notion of learning modalities has no real predictive power, but: one thing I wonder, as someone who’s long been pretty unable to absorb information from lecture-format materials, is whether there’s research into the different affordances that the various learning-style categories offer. That is, I wouldn’t say I’m “not an auditory learner,” but that in light of attentional difficulties, the fact is that spacing out for a few minutes during a talk can often lead to my missing some important point that later points depend on. So, compared to a book, where I can revisit previous items at will to re-orient myself, the inability to “rewind” in a lecture makes it a deeply challenging environment for absorbing information. That seems much coarser-grained than the notion of being an auditory vs. a visual vs. a kinesthetic learner, though.
posted by invitapriore at 6:41 PM on May 20, 2018 [6 favorites]
posted by invitapriore at 6:41 PM on May 20, 2018 [6 favorites]
But what about unlearning styles? Particularly of things that are eldritch and cyclopean, and with impossible angles?
posted by turbid dahlia at 7:03 PM on May 20, 2018 [10 favorites]
posted by turbid dahlia at 7:03 PM on May 20, 2018 [10 favorites]
Also, I'm diverging, but it's also now a ton of handouts which my kid can't keep organized. Me: "Don't you have a math BOOK?" Her: "I'd LOVE that!"
Sorry to further this derail, but I've noticed that too and I'm not even a parent. At least in elementary school, textbooks are thin on the ground. Everything is now haphazardly-modified photocopies of poorly-designed handouts printed from some half-baked website run by an educational consulting firm that the school presumably contracted with because it was the cheapest one they could find that was Common Core Certified. It's all garbage.
posted by Anticipation Of A New Lover's Arrival, The at 7:08 PM on May 20, 2018 [2 favorites]
Sorry to further this derail, but I've noticed that too and I'm not even a parent. At least in elementary school, textbooks are thin on the ground. Everything is now haphazardly-modified photocopies of poorly-designed handouts printed from some half-baked website run by an educational consulting firm that the school presumably contracted with because it was the cheapest one they could find that was Common Core Certified. It's all garbage.
posted by Anticipation Of A New Lover's Arrival, The at 7:08 PM on May 20, 2018 [2 favorites]
I don't know about that study-- students took a quiz in which they basically said which way they liked to learn (instead of researchers actually testing them to see if they comprehended information better one way or another). And then the majority of students didn't even try studying their recommended way? How did they conclude anything from that?
And if I don't have a learning style, then I suppose I have a learning disability or processing disorder. Not sure what the difference is, but my ability to comprehend and remember what I've heard is dreadful. Like, I watch movies and TV with subtitles on since I've realized I can understand twice as much of it that way.
posted by Margalo Epps at 7:50 PM on May 20, 2018 [5 favorites]
And if I don't have a learning style, then I suppose I have a learning disability or processing disorder. Not sure what the difference is, but my ability to comprehend and remember what I've heard is dreadful. Like, I watch movies and TV with subtitles on since I've realized I can understand twice as much of it that way.
posted by Margalo Epps at 7:50 PM on May 20, 2018 [5 favorites]
Learning Styles became a way of neurodivergent students to finesse accommodaitons without claiming disability, tho...
posted by PinkMoose at 7:55 PM on May 20, 2018 [4 favorites]
posted by PinkMoose at 7:55 PM on May 20, 2018 [4 favorites]
In general, we're really incredibly crap at teaching students how to learn.
It depends on many factors. How the teacher relates to students is a small factor, but how much they know is more important -- there has to be understanding of a subject rather than just memorizing from a script.
Students need to think about tomorrow, and not think they are entitled to pass -- the point is to learn, not get an A. Some students have no self-confidence, and some don't want to learn, and remaining ignorant is a form of willful protest for having to be a captive audience. Some make excuses and like to drag teachers into some sort of dysfunctional dynamics where the student is Lucy Van Pelt with the football and the desperate teacher is Charlie Brown. Others want to learn, but have other obstacles that are not easy to overcome.
Then there are parents who meddle, making bizarre demands to preserve some sort of narrative that their children are fragile and delicate -- or are geniuses, and they cannot grasp the fact that sometimes it is the kid and the parent who is in the wrong.
Then there is how much money a school gets to be able to pay for the bells and whistles to encourage a higher degree of learning.
Try to navigate through all of it -- and it is not easy, especially when a lot of students and parents have some sort of magic wand theory of learning and forget it takes hours of studying, practice, and hard work to achieve a solid level of mastery. There is no app for deep learning, and, if I had my way, students would begin without lights or furniture and have to get in touch with their primal selves before working their way up their personal evolutionary ladder.
People want to play it safe and sterile, when progress comes only from learning without a safety net. It is not "leaning styles" that help students because they should develop all of their senses and not just rely on the ones that come easy to them.
But until you have a system that rocks the boat and encourages unpredictability in a classroom, students will continue to memorize scripts, but not actually learn -- or more importantly, learn to apply and test their knowledge in new and innovative ways.
posted by Alexandra Kitty at 8:42 PM on May 20, 2018 [2 favorites]
It depends on many factors. How the teacher relates to students is a small factor, but how much they know is more important -- there has to be understanding of a subject rather than just memorizing from a script.
Students need to think about tomorrow, and not think they are entitled to pass -- the point is to learn, not get an A. Some students have no self-confidence, and some don't want to learn, and remaining ignorant is a form of willful protest for having to be a captive audience. Some make excuses and like to drag teachers into some sort of dysfunctional dynamics where the student is Lucy Van Pelt with the football and the desperate teacher is Charlie Brown. Others want to learn, but have other obstacles that are not easy to overcome.
Then there are parents who meddle, making bizarre demands to preserve some sort of narrative that their children are fragile and delicate -- or are geniuses, and they cannot grasp the fact that sometimes it is the kid and the parent who is in the wrong.
Then there is how much money a school gets to be able to pay for the bells and whistles to encourage a higher degree of learning.
Try to navigate through all of it -- and it is not easy, especially when a lot of students and parents have some sort of magic wand theory of learning and forget it takes hours of studying, practice, and hard work to achieve a solid level of mastery. There is no app for deep learning, and, if I had my way, students would begin without lights or furniture and have to get in touch with their primal selves before working their way up their personal evolutionary ladder.
People want to play it safe and sterile, when progress comes only from learning without a safety net. It is not "leaning styles" that help students because they should develop all of their senses and not just rely on the ones that come easy to them.
But until you have a system that rocks the boat and encourages unpredictability in a classroom, students will continue to memorize scripts, but not actually learn -- or more importantly, learn to apply and test their knowledge in new and innovative ways.
posted by Alexandra Kitty at 8:42 PM on May 20, 2018 [2 favorites]
Learning styles seem similar to anti-vax where years of attempts to roll back previous poor science just reinforces their existence because people keep on hearing about learning styles.
I hear you, but I think learning styles are more like the creationism of the education world. Belief in learning styles persists even though we've had overwhelming evidence against them for years (not that proponents ever came up with a stable taxonomy of styles in the first place or even a passingly plausible explanation of absurdities like kinesthetic learning). But advocates either dig in their heels and dismiss the research as ivory tower irrelevancies or they claim (incorrectly) that it only applies to crude versions of learning styles theory, not the more intelligently designed ones that turn out to only differ in superficial ways. It speaks extremely poorly of ed schools that this stuff persists even as folk theory.
Maybe most frustrating of all, imagine how much more fruitful it would have been to focus on universal design and accessibility than on this pseudoscience!
posted by This time is different. at 9:42 PM on May 20, 2018 [2 favorites]
I hear you, but I think learning styles are more like the creationism of the education world. Belief in learning styles persists even though we've had overwhelming evidence against them for years (not that proponents ever came up with a stable taxonomy of styles in the first place or even a passingly plausible explanation of absurdities like kinesthetic learning). But advocates either dig in their heels and dismiss the research as ivory tower irrelevancies or they claim (incorrectly) that it only applies to crude versions of learning styles theory, not the more intelligently designed ones that turn out to only differ in superficial ways. It speaks extremely poorly of ed schools that this stuff persists even as folk theory.
Maybe most frustrating of all, imagine how much more fruitful it would have been to focus on universal design and accessibility than on this pseudoscience!
posted by This time is different. at 9:42 PM on May 20, 2018 [2 favorites]
cattypist, just wanted to say thanks so much for reading the study, I wish I could give you cookies through some kind of blue tube (bleumatic?)
(I kind of feel like it's immoral to discuss a press release about an article without somebody reading the article. How about as each person joins the discussion, they have a certain probability of being tasked with doing this? This naturally generalizes also to commenting on a posting of a news article having read only the quoted headline.)
posted by away for regrooving at 12:49 AM on May 21, 2018 [1 favorite]
(I kind of feel like it's immoral to discuss a press release about an article without somebody reading the article. How about as each person joins the discussion, they have a certain probability of being tasked with doing this? This naturally generalizes also to commenting on a posting of a news article having read only the quoted headline.)
posted by away for regrooving at 12:49 AM on May 21, 2018 [1 favorite]
It is tough as an educator. For years the VAKT was an element of my pre-service TESOL training, and it always struck me as a little bit too "woo"...
But it is all in the execution. Until we have completely mapped the brain and understand how the mind emerges from that, learning is going to be a little bit fuccy, OK? And the thing is, REFLECTING on your learning is a good thing, and the vehicle does not necessarily matter... process, not product. So "what does your spirit animal say about your study techniques?" or "what learning strategy works best for your star sign?" are valid inroads, even if totally non-scientific. They are FUN, and they will generate discussion and thought...
And there is also the dynamic tension between most effective learning and most interesting, fun, engaging way to learn. What if the behaviorists are right, and the most effective way to learn is to get plugged into a Skinner box? It is not fun, it is not interesting, it denies us our human connection to a world that we make meaning in. So let's do it the human way anyways, OK?
posted by Meatbomb at 1:32 AM on May 21, 2018 [2 favorites]
But it is all in the execution. Until we have completely mapped the brain and understand how the mind emerges from that, learning is going to be a little bit fuccy, OK? And the thing is, REFLECTING on your learning is a good thing, and the vehicle does not necessarily matter... process, not product. So "what does your spirit animal say about your study techniques?" or "what learning strategy works best for your star sign?" are valid inroads, even if totally non-scientific. They are FUN, and they will generate discussion and thought...
And there is also the dynamic tension between most effective learning and most interesting, fun, engaging way to learn. What if the behaviorists are right, and the most effective way to learn is to get plugged into a Skinner box? It is not fun, it is not interesting, it denies us our human connection to a world that we make meaning in. So let's do it the human way anyways, OK?
posted by Meatbomb at 1:32 AM on May 21, 2018 [2 favorites]
Terry Pratchett in The Science of Discworld talks about the concept of lies-to-children to teach them important things even if the method might not be entirely truthful; I've always thought of learning styles as lies-to-teachers.
Yes, learning styles don't exist - but if teachers behave as they do then they find three different approaches to teach the same work (visual, auditory, kinaesthetic) - and if they've done the work to teach it three ways then there's a lot more in there for the students to get hold of than there would be with a simple case of chalk and talk. So the lessons are richer and the teachers teach better if they pretend that the three learning styles exist than they would if they didn't and just taught things one way.
So of course people believe in them; when they test assuming that their kids have them they do better than when they don't even if the actual reason is false. (And if they stop believing it they have less reason to go for the other learning styles because it's no longer considered necessary so they can afford to be lazy).
The problem is when the students rather than the teachers start treating them as true.
posted by Francis at 2:17 AM on May 21, 2018 [4 favorites]
Yes, learning styles don't exist - but if teachers behave as they do then they find three different approaches to teach the same work (visual, auditory, kinaesthetic) - and if they've done the work to teach it three ways then there's a lot more in there for the students to get hold of than there would be with a simple case of chalk and talk. So the lessons are richer and the teachers teach better if they pretend that the three learning styles exist than they would if they didn't and just taught things one way.
So of course people believe in them; when they test assuming that their kids have them they do better than when they don't even if the actual reason is false. (And if they stop believing it they have less reason to go for the other learning styles because it's no longer considered necessary so they can afford to be lazy).
The problem is when the students rather than the teachers start treating them as true.
posted by Francis at 2:17 AM on May 21, 2018 [4 favorites]
I'm not at work, so can't access the article. But this paragraph from the press release made me favorite the FPP for future reading:
Instead, there were specific study strategies, such as practising microscope work and using lecture notes, that were associated with better grade performance, regardless of students’ learning style. Other activities, such as using flash cards, were associated with poorer performance, perhaps because they were a sign of learning by rote rather than deeper learning.
I teach engineers, and they want evidence-based teaching, so I collect all there is.
In my experience, practice and analogue note-taking are essential learning tools. I know there is evidence for it too, but again, I'm not at work and can't find it from here. But as a result, I force my students to take notes in a designated sketchbook (by making the sketchbook count for 20% of their grade). I also make them repeat stuff. They hate both things when they start and at the mid-term evaluation, but we always get top marks at the final evaluation when the students realize that they have actually learnt something.
I don't care about the learning styles, like it's been mentioned above it is folk-theory that students and parents use against professors when they are failing. I just heard it at the exam a few weeks ago, and responded that laziness is not a learning style, and if 97% of a class can pass without problems, learning style is not the issue.
posted by mumimor at 2:42 AM on May 21, 2018 [5 favorites]
Instead, there were specific study strategies, such as practising microscope work and using lecture notes, that were associated with better grade performance, regardless of students’ learning style. Other activities, such as using flash cards, were associated with poorer performance, perhaps because they were a sign of learning by rote rather than deeper learning.
I teach engineers, and they want evidence-based teaching, so I collect all there is.
In my experience, practice and analogue note-taking are essential learning tools. I know there is evidence for it too, but again, I'm not at work and can't find it from here. But as a result, I force my students to take notes in a designated sketchbook (by making the sketchbook count for 20% of their grade). I also make them repeat stuff. They hate both things when they start and at the mid-term evaluation, but we always get top marks at the final evaluation when the students realize that they have actually learnt something.
I don't care about the learning styles, like it's been mentioned above it is folk-theory that students and parents use against professors when they are failing. I just heard it at the exam a few weeks ago, and responded that laziness is not a learning style, and if 97% of a class can pass without problems, learning style is not the issue.
posted by mumimor at 2:42 AM on May 21, 2018 [5 favorites]
Learning styles have always seemed like a good high-level way to think about learning conceptually but their direct application often appears to work out as a McNamara Fallacy type of endeavor. I was immediately suspicious as a kid because the process of having everyone take learning style tests and then interpreting the results was very similar to getting your horoscope read.
posted by XMLicious at 2:46 AM on May 21, 2018 [1 favorite]
posted by XMLicious at 2:46 AM on May 21, 2018 [1 favorite]
So it turns out some men don’t have to pee on the electric fence for themselves.
I think one reason for the persistence of the idea of learning styles is that the concept is in line with the personal experience of so many people. As some have mentioned up thread, I am someone who would much rather read about something than watch a video about it. But there have been plenty of things I have learned by watching videos (or even 16 mm film!) And there is so much that is inherently subjective about this topic. Despite my stated preference for reading I would still rather watch a well-done video than read a poorly written book. Furthermore, the subject matters as well. The study was done with med school anatomy, which is a highly visual course and is tested as such. Would they have gotten the same results with pharmacology or biochemistry?
posted by TedW at 3:33 AM on May 21, 2018 [1 favorite]
I think one reason for the persistence of the idea of learning styles is that the concept is in line with the personal experience of so many people. As some have mentioned up thread, I am someone who would much rather read about something than watch a video about it. But there have been plenty of things I have learned by watching videos (or even 16 mm film!) And there is so much that is inherently subjective about this topic. Despite my stated preference for reading I would still rather watch a well-done video than read a poorly written book. Furthermore, the subject matters as well. The study was done with med school anatomy, which is a highly visual course and is tested as such. Would they have gotten the same results with pharmacology or biochemistry?
posted by TedW at 3:33 AM on May 21, 2018 [1 favorite]
I'm not at work, so can't access the article. But this paragraph from the press release made me favorite the FPP for future reading:
Instead, there were specific study strategies, such as practising microscope work and using lecture notes, that were associated with better grade performance, regardless of students’ learning style. Other activities, such as using flash cards, were associated with poorer performance, perhaps because they were a sign of learning by rote rather than deeper learning.
On the topic of flashcards: so they definitely have traditionally been used for rote memorization, but flash cards can also be used for learning concepts! Modulo re-training students how to use them, at least; which might be non-trivial at, say, the university level. Your engineering students might particularly like College Info Geek's study tips.
(Based on your comment, muminor, I assume you're also familiar and/or involved with the work of the physics education community on stuff like the force concept inventory, peer instruction, or other stuff around teaching concepts?)
posted by eviemath at 5:19 AM on May 21, 2018 [3 favorites]
Instead, there were specific study strategies, such as practising microscope work and using lecture notes, that were associated with better grade performance, regardless of students’ learning style. Other activities, such as using flash cards, were associated with poorer performance, perhaps because they were a sign of learning by rote rather than deeper learning.
On the topic of flashcards: so they definitely have traditionally been used for rote memorization, but flash cards can also be used for learning concepts! Modulo re-training students how to use them, at least; which might be non-trivial at, say, the university level. Your engineering students might particularly like College Info Geek's study tips.
(Based on your comment, muminor, I assume you're also familiar and/or involved with the work of the physics education community on stuff like the force concept inventory, peer instruction, or other stuff around teaching concepts?)
posted by eviemath at 5:19 AM on May 21, 2018 [3 favorites]
I teach programming, and I definitely hear people use learning style as a reason for poor performance. The problem is that our training program already uses a more diverse set of inputs than you'll get on the actual job. If reading and typing is not your jam, expanding your programming skills will be very difficult. There are high-quality video tutorials out there, but they tend to be more expensive than text sources, so you are unlikely to use them for every new task. I worry sometimes that by accomodating different learning preferences, we are setting people up for future disappointment in their career down the road.
On the other hand, some of these folks end up totally rocking it because of the theory some of y'all espoused above. When those students go out and create their own method of learning the material, whatever that method is, they are investing themselves mentally in their learning and probably exposing themselves to the material more times than if they didn't create their own methodology.
posted by tofu_crouton at 6:22 AM on May 21, 2018 [2 favorites]
On the other hand, some of these folks end up totally rocking it because of the theory some of y'all espoused above. When those students go out and create their own method of learning the material, whatever that method is, they are investing themselves mentally in their learning and probably exposing themselves to the material more times than if they didn't create their own methodology.
posted by tofu_crouton at 6:22 AM on May 21, 2018 [2 favorites]
As an example, I personally think drilling flashcards is an ineffective way to learn programming concepts. Making flashcards, on the other hand, requires thinking about how to break the concepts down into meaningful chunks and then typing them out.
posted by tofu_crouton at 6:24 AM on May 21, 2018 [2 favorites]
posted by tofu_crouton at 6:24 AM on May 21, 2018 [2 favorites]
I have always hated repetitious busywork. I felt the same way about the multiple weeks I had to spend diagramming sentences in 4th Grade. One week? Sure. More than that? What’s the fucking point?!
I felt exactly that way as well. First thing I was given to do in Year 7 maths class, after moving from primary school to high school, was a pile of worksheets featuring trivial one- and two-digit arithmetic problems of the kind I'd mastered in Year 2. I hated it. Did about four of the problems, then felt so bored and insulted that I spent the rest of the session just doodling on the answer sheet. That kind of thing kept on happening, and that first semester I was given my first ever failing grade in maths, accompanied by the first of many comments that all said essentially that I could clearly do far better if only I applied myself.
The thing that nobody ever explained, and the thing that I'm completely convinced would have made a difference to my attitude and caused me to spend my high school years much more productively, is why the fuck am I being given this bullshit to do that I've already known how to do for half my fucking lifetime?
It took me until I was an adult to work it out, because kids don't really see the difference between knowing how to do a thing and the kind of being able to do the thing that can only ever come from practice at actually doing the thing. For me, as a kid, the entire purpose of school had always seemed to be learning about things, the more and newer the better. Learning about new things was cool and exciting and deeply satisfying. It never even occurred to me that being able to do things was actually the point and that this was actually different from knowing how.
The intent of those endless worksheets was not, as I had conceived of it, some kind of insulting test of my ability to get correct answers to one- and two-digit arithmetic problems. It was assumed that I could do that shit. The point of the worksheets was to give me an opportunity to practice doing it faster while maintaining accuracy. And because I simply didn't know that, I completely failed to take that opportunity.
Such facility as I've always had and still have with small arithmetic problems rests squarely on my completely solid grasp of the times tables. Having grown up as the designated Fattest Kid, and therefore the natural target of every boy with any bullying instinct whatsoever which is basically all of them, I'd always taken that times-tables ability as evidence of my clear intellectual superiority over my peers. But of course it was nothing of the kind; it was completely down to the endless, endless times-tables drills and class chants that the legendarily fearsome Mrs Maguire* had subjected my entire third grade class to. I doubt that there was a single member of that class who came away from it with a less solid grasp of times tables than mine. There are certain kinds of knowledge that brute force rote learning is absolutely the best way to acquire and Mrs Maguire, being the personification of Old School, knew that.
It took me a long time - way too long - to join the dots between an effortless ability to summon a times table result and the hours of practice that had been put in before being able to do that. I'd certainly never joined them before I left school.
If I had understood what practice was actually for before having left school, I would undoubtedly have achieved better maths results in years 11 and 12 than I did, because I would have had stuff like trig identities and integration formulae as ready to hand as my times tables, instead of having had to work every problem from first principles every time and running out of time. And I might have been less inclined to experience the daily half-hour of piano practice that Mum required of me as a pure embuggerance worth applying all my considerable ingenuity to weaselling out of.
*four foot six tall, seventy years old, and apparently constructed entirely from steel wire, fierceness and a burning sense of justice; still easily my favourite teacher of all time
posted by flabdablet at 6:45 AM on May 21, 2018 [7 favorites]
I felt exactly that way as well. First thing I was given to do in Year 7 maths class, after moving from primary school to high school, was a pile of worksheets featuring trivial one- and two-digit arithmetic problems of the kind I'd mastered in Year 2. I hated it. Did about four of the problems, then felt so bored and insulted that I spent the rest of the session just doodling on the answer sheet. That kind of thing kept on happening, and that first semester I was given my first ever failing grade in maths, accompanied by the first of many comments that all said essentially that I could clearly do far better if only I applied myself.
The thing that nobody ever explained, and the thing that I'm completely convinced would have made a difference to my attitude and caused me to spend my high school years much more productively, is why the fuck am I being given this bullshit to do that I've already known how to do for half my fucking lifetime?
It took me until I was an adult to work it out, because kids don't really see the difference between knowing how to do a thing and the kind of being able to do the thing that can only ever come from practice at actually doing the thing. For me, as a kid, the entire purpose of school had always seemed to be learning about things, the more and newer the better. Learning about new things was cool and exciting and deeply satisfying. It never even occurred to me that being able to do things was actually the point and that this was actually different from knowing how.
The intent of those endless worksheets was not, as I had conceived of it, some kind of insulting test of my ability to get correct answers to one- and two-digit arithmetic problems. It was assumed that I could do that shit. The point of the worksheets was to give me an opportunity to practice doing it faster while maintaining accuracy. And because I simply didn't know that, I completely failed to take that opportunity.
Such facility as I've always had and still have with small arithmetic problems rests squarely on my completely solid grasp of the times tables. Having grown up as the designated Fattest Kid, and therefore the natural target of every boy with any bullying instinct whatsoever which is basically all of them, I'd always taken that times-tables ability as evidence of my clear intellectual superiority over my peers. But of course it was nothing of the kind; it was completely down to the endless, endless times-tables drills and class chants that the legendarily fearsome Mrs Maguire* had subjected my entire third grade class to. I doubt that there was a single member of that class who came away from it with a less solid grasp of times tables than mine. There are certain kinds of knowledge that brute force rote learning is absolutely the best way to acquire and Mrs Maguire, being the personification of Old School, knew that.
It took me a long time - way too long - to join the dots between an effortless ability to summon a times table result and the hours of practice that had been put in before being able to do that. I'd certainly never joined them before I left school.
If I had understood what practice was actually for before having left school, I would undoubtedly have achieved better maths results in years 11 and 12 than I did, because I would have had stuff like trig identities and integration formulae as ready to hand as my times tables, instead of having had to work every problem from first principles every time and running out of time. And I might have been less inclined to experience the daily half-hour of piano practice that Mum required of me as a pure embuggerance worth applying all my considerable ingenuity to weaselling out of.
*four foot six tall, seventy years old, and apparently constructed entirely from steel wire, fierceness and a burning sense of justice; still easily my favourite teacher of all time
posted by flabdablet at 6:45 AM on May 21, 2018 [7 favorites]
For a long time, I thought I "wasn't an auditory learner" because I just could not with lectures. I couldn't follow them, I couldn't absorb them, whatever. I was generally able to compensate and still passed challenging classes, provided that the lecture information was also available in a book or notes or elsewhere, so the teachers and diagnosticians I sought did not believe me when I told them how much I was struggling. But for the classes where the content in the book was really different than the content in the lecture, I was fucked.
By college, I learned what subjects I "could" and "couldn't" take, based primarily on lecture/content style (math was easy enough because it tracked with the book and I could learn while working through the problem sets; something like history was a total no-go.)
Turns out my lecture struggles were driven by ADHD and I was discounting all the non-lecture times that I could learn from auditory stimulus just fine. I'm so sad I missed out on all those subjects available primarily in auditory form.
On one hand, attributing those really intractable challenges to my "learning style" helped me feel (less) dumb and lazy while I fought to "just listen better" and failed, again and again. On the other hand, I totally believe it's junk science. I don't know what to make of that.
posted by mosst at 6:50 AM on May 21, 2018 [6 favorites]
By college, I learned what subjects I "could" and "couldn't" take, based primarily on lecture/content style (math was easy enough because it tracked with the book and I could learn while working through the problem sets; something like history was a total no-go.)
Turns out my lecture struggles were driven by ADHD and I was discounting all the non-lecture times that I could learn from auditory stimulus just fine. I'm so sad I missed out on all those subjects available primarily in auditory form.
On one hand, attributing those really intractable challenges to my "learning style" helped me feel (less) dumb and lazy while I fought to "just listen better" and failed, again and again. On the other hand, I totally believe it's junk science. I don't know what to make of that.
posted by mosst at 6:50 AM on May 21, 2018 [6 favorites]
Anecdotal, but my very smart 13 year old still can't spit out 6 x 7 without a good long think. In math now they study "units" of, say, multiplication for a week or two at most and then go off to a totally different topic.Eh, I did the multiplication-table drills as a kid and even had a times table poster at some point I think, but I had to think about that just now (turned it into 6*6+6). I don't think drilling this stuff as a kid necessarily guarantees that you will keep that skill for the rest of your life.
I grant you I am not in the most arithmetic-heavy profession but I do frequently stop to puzzle out per-unit prices in the grocery store and I 100% rely on those much-maligned New Math type tricks that I was never personally taught in schools, but which I have always used in my own head nevertheless.
posted by inconstant at 7:09 AM on May 21, 2018 [4 favorites]
flabdablet: The difference for me is that I got the principles pretty quick. At least for basic math. (Once I got into trig and pre-calc, I was in trouble, which is a big part of why I have a degree in English.) Another issue is that I have ADHD, and so giving me week after week of the same shit to do is a recipe for having my brain spit the dummy. The classes I always did best in were the ones where teachers kept the material and approach fresh, or at least interesting. These were often my English classes, but also high school American History, and high school Physics.
There's value in doing something over and over again until you get it right. I just usually picked it up faster than my classmates, at which point I wanted to move on to something, anything else (again ADHD). I'd probably do swimmingly with the Common Core stuff, and, indeed, a lot of the Common Core worksheets I've seen floating around seem to make sense to me. I'm just old enough to have been taught, essentially, New Math, though I was never taught arithmetic in Base 8. I still don't see the point, though, of doing a million constructions with folding paper, compass, protractor, and straightedge to prove that the sum of the angles in a semi-circle is 180. That shit's apparent. It's basic arithmetic. Let's do the goofy papercrafts to show it, fine. But doing the goofy papercrafts for a whole class? For a whole week of classes? That's a waste of my time.
I mean, hell, while I was failing high school Geometry because I refused to do papercrafts for an hour, I was invited to go take a college level math or English course at the local community college. I chose English. (This didn't end well, for reasons unrelated to the discussion, though.) It's not that I wasn't learning the material. I just wasn't learning it in the way my high school Geometry teacher wanted me to learn it.
Side note: My favorite High School teacher, Dr. Lee, would start every American History class and every Social Science class by writing out a long, detailed, outline of notes on the board that he expected students to copy down. I never did, but Dr. Lee picked up very quickly that I didn't need to. Reading the notes was enough for me to pick it up, and I always did good work and contributed well in class. That he caught that and let me slide on the busywork is something I'll appreciate. Too many teachers were insistent that I do the busywork, despite demonstrating that I knew the material.
posted by SansPoint at 7:11 AM on May 21, 2018
There's value in doing something over and over again until you get it right. I just usually picked it up faster than my classmates, at which point I wanted to move on to something, anything else (again ADHD). I'd probably do swimmingly with the Common Core stuff, and, indeed, a lot of the Common Core worksheets I've seen floating around seem to make sense to me. I'm just old enough to have been taught, essentially, New Math, though I was never taught arithmetic in Base 8. I still don't see the point, though, of doing a million constructions with folding paper, compass, protractor, and straightedge to prove that the sum of the angles in a semi-circle is 180. That shit's apparent. It's basic arithmetic. Let's do the goofy papercrafts to show it, fine. But doing the goofy papercrafts for a whole class? For a whole week of classes? That's a waste of my time.
I mean, hell, while I was failing high school Geometry because I refused to do papercrafts for an hour, I was invited to go take a college level math or English course at the local community college. I chose English. (This didn't end well, for reasons unrelated to the discussion, though.) It's not that I wasn't learning the material. I just wasn't learning it in the way my high school Geometry teacher wanted me to learn it.
Side note: My favorite High School teacher, Dr. Lee, would start every American History class and every Social Science class by writing out a long, detailed, outline of notes on the board that he expected students to copy down. I never did, but Dr. Lee picked up very quickly that I didn't need to. Reading the notes was enough for me to pick it up, and I always did good work and contributed well in class. That he caught that and let me slide on the busywork is something I'll appreciate. Too many teachers were insistent that I do the busywork, despite demonstrating that I knew the material.
posted by SansPoint at 7:11 AM on May 21, 2018
The difference for me is that I got the principles pretty quick.
Same same. And I really enjoyed getting the principles, all of which have a certain beauty. And having grokked the principles was why I had no trouble looking at whatever trig identity we were being shown on the day and saying, yeah, that's neat and it makes sense, and then completely ignoring it because I knew I'd be able to re-derive it any time I needed it.
There's value in doing something over and over again until you get it right. I just usually picked it up faster than my classmates, at which point I wanted to move on to something, anything else
Same same again. What I failed to perceive at the time, and what took me far far far too long to notice as a thing, is that there's also value in keeping on doing something over and over again after having learned to get it right. And I think the main reason that this failed to occur to me, apart from having had a mindset that school is for learning about rather than learning to, is that acquiring effortlessness via repetition has always required me to perform much more repetition than acquiring mere competence. As a kid, I was never really wired to notice the improvement that practice confers, the hit from basic competence acquisition being so much faster and more fun.
It was really only when I joined the chess club and saw my own rating start to climb without any specific study or effort on my part that I first noticed that just doing a thing attentively again and again and again could make me better and quicker at it, and that this had in fact been happening my entire life and was probably the sole reason why I was a faster and more fluent reader than any of my TV-addled peers* and a better singer than kids who had not been going to choir practice twice a week for six years because it was fun.
*Mum and Dad, both of whom were working teachers, chose not to own a television until the youngest of us had finished primary school, for which decision they have my undying gratitude.
posted by flabdablet at 7:36 AM on May 21, 2018
Same same. And I really enjoyed getting the principles, all of which have a certain beauty. And having grokked the principles was why I had no trouble looking at whatever trig identity we were being shown on the day and saying, yeah, that's neat and it makes sense, and then completely ignoring it because I knew I'd be able to re-derive it any time I needed it.
There's value in doing something over and over again until you get it right. I just usually picked it up faster than my classmates, at which point I wanted to move on to something, anything else
Same same again. What I failed to perceive at the time, and what took me far far far too long to notice as a thing, is that there's also value in keeping on doing something over and over again after having learned to get it right. And I think the main reason that this failed to occur to me, apart from having had a mindset that school is for learning about rather than learning to, is that acquiring effortlessness via repetition has always required me to perform much more repetition than acquiring mere competence. As a kid, I was never really wired to notice the improvement that practice confers, the hit from basic competence acquisition being so much faster and more fun.
It was really only when I joined the chess club and saw my own rating start to climb without any specific study or effort on my part that I first noticed that just doing a thing attentively again and again and again could make me better and quicker at it, and that this had in fact been happening my entire life and was probably the sole reason why I was a faster and more fluent reader than any of my TV-addled peers* and a better singer than kids who had not been going to choir practice twice a week for six years because it was fun.
*Mum and Dad, both of whom were working teachers, chose not to own a television until the youngest of us had finished primary school, for which decision they have my undying gratitude.
posted by flabdablet at 7:36 AM on May 21, 2018
flabdablet: You also, I assume, don’t have ADHD, so you might not have perceived the value, but you did have the ability to grind through it. I did not, and even as a medicated adult, I still chafe at professional busywork. (Thank goodness for automation tools!)
Practice is great, and when I enjoy the thing I’m doing and practicing, I’m more than happy to do it. But I derived no enjoyment in diagramming sentences or doing papercrafts to prove the rules of Euclidean Geometry. Or, for that matter, factoring equations, or doing polynomials, or anything like that. Just as well, because I found what I enjoyed and was happy to practice at later.
I can do basic multiplication and division in my head. I know the Pythagorean Theorem. I could maybe factor an equation if I needed to, but don’t expect it to be done fast. I learned the material, and it stuck. Isn’t that enough?
posted by SansPoint at 7:48 AM on May 21, 2018 [1 favorite]
Practice is great, and when I enjoy the thing I’m doing and practicing, I’m more than happy to do it. But I derived no enjoyment in diagramming sentences or doing papercrafts to prove the rules of Euclidean Geometry. Or, for that matter, factoring equations, or doing polynomials, or anything like that. Just as well, because I found what I enjoyed and was happy to practice at later.
I can do basic multiplication and division in my head. I know the Pythagorean Theorem. I could maybe factor an equation if I needed to, but don’t expect it to be done fast. I learned the material, and it stuck. Isn’t that enough?
posted by SansPoint at 7:48 AM on May 21, 2018 [1 favorite]
Isn’t that enough?
If you don't need it maybe two or three layers deep in a stack of foundational skills in order to do or learn something built on top of it, it's plenty.
You also, I assume, don’t have ADHD
ADHD was not a diagnostic category when I went through school, as far as I'm aware. Having recognized quite a lot of myself in accounts from people who have been diagnosed with it I suspect that I might well have some quite strong ADHD traits, but I've never sought diagnosis or treatment for it.
you might not have perceived the value, but you did have the ability to grind through it.
I really, really didn't. In my entire school career, I never ground through anything I didn't find engaging and enjoyable if I could possibly get away with skipping it. Still don't.
But when I've looked at some of the stuff I do find myself doing over and over and enjoying - like crosswords, or Sudoku, or Vipassana meditation, or playing Solitaire, or driving a car with a manual gearbox in traffic - it's occurred to me that quite a lot of it is not inherently more interesting than diagramming sentences or factoring equations or dividing polynomials, and that most of what makes the difference comes back to attitude going in. If I'm convinced ahead of time that what I'm about to do will be tedious and annoying, it surely will be - especially if I've been practising telling myself that about it since Year 7 :-)
posted by flabdablet at 8:21 AM on May 21, 2018 [1 favorite]
If you don't need it maybe two or three layers deep in a stack of foundational skills in order to do or learn something built on top of it, it's plenty.
You also, I assume, don’t have ADHD
ADHD was not a diagnostic category when I went through school, as far as I'm aware. Having recognized quite a lot of myself in accounts from people who have been diagnosed with it I suspect that I might well have some quite strong ADHD traits, but I've never sought diagnosis or treatment for it.
you might not have perceived the value, but you did have the ability to grind through it.
I really, really didn't. In my entire school career, I never ground through anything I didn't find engaging and enjoyable if I could possibly get away with skipping it. Still don't.
But when I've looked at some of the stuff I do find myself doing over and over and enjoying - like crosswords, or Sudoku, or Vipassana meditation, or playing Solitaire, or driving a car with a manual gearbox in traffic - it's occurred to me that quite a lot of it is not inherently more interesting than diagramming sentences or factoring equations or dividing polynomials, and that most of what makes the difference comes back to attitude going in. If I'm convinced ahead of time that what I'm about to do will be tedious and annoying, it surely will be - especially if I've been practising telling myself that about it since Year 7 :-)
posted by flabdablet at 8:21 AM on May 21, 2018 [1 favorite]
Something I've figured out over the years is that I have a great visual memory. So for me, taking notes in class, then rewriting those notes, and rereading them, was a great system for putting it all into my head in a format I could recall for a test. I could almost recall and read the note pages in my brain if I had looked at them enough.
I don't think a studying style based on me wearing a blindfold and listening to a taped lecture a few times would have been anywhere as successful because my mind wanders when I listen to stuff and my auditory recall isn't nearly as good as my visual recall.
I wonder what kinds of studies have been done on memory/recall, rather than just "learning."
posted by Squeak Attack at 11:31 AM on May 21, 2018 [3 favorites]
I don't think a studying style based on me wearing a blindfold and listening to a taped lecture a few times would have been anywhere as successful because my mind wanders when I listen to stuff and my auditory recall isn't nearly as good as my visual recall.
I wonder what kinds of studies have been done on memory/recall, rather than just "learning."
posted by Squeak Attack at 11:31 AM on May 21, 2018 [3 favorites]
Eviemath, one of my former students, whom I hired as an assistant professor at my old job, took concept learning to a whole new level. I really miss her and wish I could have brought her along to my new job. So yes, I believe it can have value (and I taught it to the class she attended in the first place before she took it away), and specifically I learnt that it has potential. But it can also banalize studies and make classes boring for everyone because the level of discussion is lowered to the level of "concepts" that aren't really concepts.
Generally, students in my classes are sorted into study groups and the bulk of their work is handed in at group exams, with the sketchbook as the only individual assignment. Since university students normally have zero tolerance for lazy group members it works like a dream. They even prefer that my lectures are relatively short, so they have more time for group discussions :-) I am in teaching heaven.
SansPoint and flabdablet, I can so much relate to what you are discussing from a personal point of view, but since I have become interested in didactics, I have realized that teaching children is a whole different thing from teaching adults, and one of the big issues is the enormous variations there may be between the children's learning abilities in each class and the lack of support teachers get to deal with those differences. The teacher cannot always adapt their teaching to each individual and they have to use methods that work for a majority, whilst teaching to the tests to avoid losing their jobs. In other words: the difference lies not in the age of the students, but in the pressure from outside the classroom.
I disagree with the statement that students with ADHD can't deal with the busywork, in my 26 or 27 years of experience, I have had lots of students with ADHD (I don't know why, but engineering, architecture and design all attract them), and they have found great pleasure and growth in the inane repetition that is needed to do well, even as they have had struggles with school before engineering or design school exactly because they couldn't deal with endless math problems that were "too easy" and repetitive. I recently talked with an older designer, who still struggles with the fact that they were thrown out of school in 8th grade and had to train as an apprentice in the 1950's, many years before ADHD was known. Now they are strongly dedicated to their craft, one that requires endless repetition.
I think that the thing we are sometimes able to do at higher educations*, or in a working studio, in spite of having more students and less time for them, is to personalize the study. We don't have to teach to the test like school teachers do, we can discuss the student's learning issues with themselves, and we don't have too many worrying parents and politicians messing stuff up. I can tell a student who struggles with focus and attention how they can pass — well — by stepping a bit away from the curriculum for a while. I can make a special assignment for midterm that gets them back on track. To do that with 5th graders, you need to be a very strong personality who can face the school management and parents without a blink. I went to a school from 4th to 9th grade where the teachers believed they could work with children in the same way, it was amazing, and I think that was what got me interested in didactics in the first place. Hey, maybe I had/have ADHD. I was thrown out of half my classes in the 5th and 6th grades, but if I wasn't sent to the school psychologist, I was nearly always sent to wherever my math teacher was. So if she was teaching 8th grade math, I'd have 8th grade math while the rest of my class had English. If she was teaching some of the smaller kids, I'd be a little TA. I'd happily do five pages of near identical problems for her, because I felt I was doing it for her, helping her to get good marks just like she helped me. She taught religion too, so sometimes I got some weird philosophy in 9th grade instead of math, it was all good.
TLDR: we should respect and pay schoolteachers much more than we do.
* sometimes, because sometimes even university managements get scared and can't handle individual teaching either. That is one of the reasons I have found a new job.
posted by mumimor at 1:30 PM on May 21, 2018 [3 favorites]
Generally, students in my classes are sorted into study groups and the bulk of their work is handed in at group exams, with the sketchbook as the only individual assignment. Since university students normally have zero tolerance for lazy group members it works like a dream. They even prefer that my lectures are relatively short, so they have more time for group discussions :-) I am in teaching heaven.
SansPoint and flabdablet, I can so much relate to what you are discussing from a personal point of view, but since I have become interested in didactics, I have realized that teaching children is a whole different thing from teaching adults, and one of the big issues is the enormous variations there may be between the children's learning abilities in each class and the lack of support teachers get to deal with those differences. The teacher cannot always adapt their teaching to each individual and they have to use methods that work for a majority, whilst teaching to the tests to avoid losing their jobs. In other words: the difference lies not in the age of the students, but in the pressure from outside the classroom.
I disagree with the statement that students with ADHD can't deal with the busywork, in my 26 or 27 years of experience, I have had lots of students with ADHD (I don't know why, but engineering, architecture and design all attract them), and they have found great pleasure and growth in the inane repetition that is needed to do well, even as they have had struggles with school before engineering or design school exactly because they couldn't deal with endless math problems that were "too easy" and repetitive. I recently talked with an older designer, who still struggles with the fact that they were thrown out of school in 8th grade and had to train as an apprentice in the 1950's, many years before ADHD was known. Now they are strongly dedicated to their craft, one that requires endless repetition.
I think that the thing we are sometimes able to do at higher educations*, or in a working studio, in spite of having more students and less time for them, is to personalize the study. We don't have to teach to the test like school teachers do, we can discuss the student's learning issues with themselves, and we don't have too many worrying parents and politicians messing stuff up. I can tell a student who struggles with focus and attention how they can pass — well — by stepping a bit away from the curriculum for a while. I can make a special assignment for midterm that gets them back on track. To do that with 5th graders, you need to be a very strong personality who can face the school management and parents without a blink. I went to a school from 4th to 9th grade where the teachers believed they could work with children in the same way, it was amazing, and I think that was what got me interested in didactics in the first place. Hey, maybe I had/have ADHD. I was thrown out of half my classes in the 5th and 6th grades, but if I wasn't sent to the school psychologist, I was nearly always sent to wherever my math teacher was. So if she was teaching 8th grade math, I'd have 8th grade math while the rest of my class had English. If she was teaching some of the smaller kids, I'd be a little TA. I'd happily do five pages of near identical problems for her, because I felt I was doing it for her, helping her to get good marks just like she helped me. She taught religion too, so sometimes I got some weird philosophy in 9th grade instead of math, it was all good.
TLDR: we should respect and pay schoolteachers much more than we do.
* sometimes, because sometimes even university managements get scared and can't handle individual teaching either. That is one of the reasons I have found a new job.
posted by mumimor at 1:30 PM on May 21, 2018 [3 favorites]
flabdablet and SansPoint: You have both really captured a lot of my thoughts on this as a secondary math teacher in the US.
First, to address the issue of fluency versus more challenging problems: I believe both are important. There are some math skills, even at a secondary level, that are extremely important to gain an incredible degree of both speed and accuracy, such as algebraic manipulation (distribution, factoring, etc.) Without those there's no way to focus on the actual meat of higher mathematics, since you're lost in the details. It does need to be, as flabdablet said, "effortless". So some degree of continuous practice of those skills is really important.
On the other hand, we know that teaching in the zone of proximal development is the fastest and strongest way to build better understanding and connections between different subjects, and, in any case, solving equations is mostly not a useful real-world skill; applying mathematical thinking to novel problems is.
All I can really say from this is: I should probably be more explicit with my students whether we're working on fluency or conceptual understanding, so they know what to expect.
As for learning styles and "teaching to" different learning styles, I'm not aware of any teacher I work with who uses these concepts in their planning. However, giving students "multiple opportunities for learning" has become a bit of a buzzword (buzzphrase?) in my school, and is generally popular with teachers. The concept is not that different students learn consistently in different styles, but that some students are better able to access a particular lesson visually and others kinesthetically, etc. For another lesson, it might be the other way around. This bit of universal design is probably beneficial to students, but I'm not aware of any sound research on the subject.
Circling back around to SansPoint's frustrations with doing boring or seemingly unnecessary work: I think the strategy that we're seeing more teachers use in secondary education is just a focus on giving students choice. Students, shockingly, will sometimes choose more challenging problems, if it means getting out of repetitive work they find boring, while students struggling, will, of course, choose the appropriately easy work.
It can be difficult to manage having students working on three different sets of classwork, and it can certainly mean more prep work. And, of course, there's no hard research I know of which proves it's beneficial to students. But from a student engagement perspective and frankly just being less awful then boring math problems or else ones students can't figure out, it seems like a strategy to try.
posted by thegears at 3:52 PM on May 21, 2018 [2 favorites]
First, to address the issue of fluency versus more challenging problems: I believe both are important. There are some math skills, even at a secondary level, that are extremely important to gain an incredible degree of both speed and accuracy, such as algebraic manipulation (distribution, factoring, etc.) Without those there's no way to focus on the actual meat of higher mathematics, since you're lost in the details. It does need to be, as flabdablet said, "effortless". So some degree of continuous practice of those skills is really important.
On the other hand, we know that teaching in the zone of proximal development is the fastest and strongest way to build better understanding and connections between different subjects, and, in any case, solving equations is mostly not a useful real-world skill; applying mathematical thinking to novel problems is.
All I can really say from this is: I should probably be more explicit with my students whether we're working on fluency or conceptual understanding, so they know what to expect.
As for learning styles and "teaching to" different learning styles, I'm not aware of any teacher I work with who uses these concepts in their planning. However, giving students "multiple opportunities for learning" has become a bit of a buzzword (buzzphrase?) in my school, and is generally popular with teachers. The concept is not that different students learn consistently in different styles, but that some students are better able to access a particular lesson visually and others kinesthetically, etc. For another lesson, it might be the other way around. This bit of universal design is probably beneficial to students, but I'm not aware of any sound research on the subject.
Circling back around to SansPoint's frustrations with doing boring or seemingly unnecessary work: I think the strategy that we're seeing more teachers use in secondary education is just a focus on giving students choice. Students, shockingly, will sometimes choose more challenging problems, if it means getting out of repetitive work they find boring, while students struggling, will, of course, choose the appropriately easy work.
It can be difficult to manage having students working on three different sets of classwork, and it can certainly mean more prep work. And, of course, there's no hard research I know of which proves it's beneficial to students. But from a student engagement perspective and frankly just being less awful then boring math problems or else ones students can't figure out, it seems like a strategy to try.
posted by thegears at 3:52 PM on May 21, 2018 [2 favorites]
I should probably be more explicit with my students whether we're working on fluency or conceptual understanding, so they know what to expect.
I remain completely convinced that if any teacher at any time during my high school years had even mentioned that fluency was a thing and that this was what the scut work was for, I would have experienced a great deal less internal resistance to doing it.
If it had been made into a competitive challenge by offering some kind of reward for fastest 100% accurate completion, I might even have enjoyed it.
posted by flabdablet at 4:10 PM on May 21, 2018 [1 favorite]
I remain completely convinced that if any teacher at any time during my high school years had even mentioned that fluency was a thing and that this was what the scut work was for, I would have experienced a great deal less internal resistance to doing it.
If it had been made into a competitive challenge by offering some kind of reward for fastest 100% accurate completion, I might even have enjoyed it.
posted by flabdablet at 4:10 PM on May 21, 2018 [1 favorite]
On the other hand, we know that teaching in the zone of proximal development is the fastest and strongest way to build better understanding and connections between different subjects, and, in any case, solving equations is mostly not a useful real-world skill; applying mathematical thinking to novel problems is.
I have a lot to say about this, but I am very tired, and probably won't get back before this tread has died. So I'll just post anecdotal stuff: my 19-year old is a very bad reader. Countless tests have placed her just above or just below the level of dyslexia required for special education. She is excellent at math. But "problem math", which requires reading skills is really hard for her, and almost impossible during exams when she can't have someone reading the problems out for her because she isn't dyslexic enough for reading aid. She can't break down a realistic math problem, because she can't read the problem. That doesn't make her stupid, it makes her worried and lonely.
This is one of those problems we can easily solve at the higher education level, because many of us have similar problems. Where is the "real world"? A big part of the real world loves people who can dig into math problems even though they can't read a novel. And I say this as someone who loves reading novels and who has occasionally persuaded book-haters to try out specific novels.
posted by mumimor at 4:21 PM on May 21, 2018
I have a lot to say about this, but I am very tired, and probably won't get back before this tread has died. So I'll just post anecdotal stuff: my 19-year old is a very bad reader. Countless tests have placed her just above or just below the level of dyslexia required for special education. She is excellent at math. But "problem math", which requires reading skills is really hard for her, and almost impossible during exams when she can't have someone reading the problems out for her because she isn't dyslexic enough for reading aid. She can't break down a realistic math problem, because she can't read the problem. That doesn't make her stupid, it makes her worried and lonely.
This is one of those problems we can easily solve at the higher education level, because many of us have similar problems. Where is the "real world"? A big part of the real world loves people who can dig into math problems even though they can't read a novel. And I say this as someone who loves reading novels and who has occasionally persuaded book-haters to try out specific novels.
posted by mumimor at 4:21 PM on May 21, 2018
thegears: I should make a clarification that, though I sucked at it, I did get the point of the drill aspect in trig and pre-calc stuff. I blame my ADHD for me half-assing the work there. But it feels like there's a difference between worksheets of polynomials to factor and equations to simplify—something that is at the core of doing higher mathematics—and spending a week proving the angle bisector theorem with ruler, compass, protractor, and straightedge, over and over again. A handful of examples and problem solving should be enough for that.
In my head, at least, factoring polynomials is learning how to execute an algorithm, while being able to figure out the lengths of the sides of a triangle is just plugging values into a formula. Once you know the formula, you're good on the latter, but the only way to nail the former is to just bang away at it until it's permanently embedded in the brain.
Though I still haven't found a use for diagramming sentences. Maybe if I'd gone into linguistics, it would have application alongside parse trees.
posted by SansPoint at 6:39 PM on May 21, 2018
In my head, at least, factoring polynomials is learning how to execute an algorithm, while being able to figure out the lengths of the sides of a triangle is just plugging values into a formula. Once you know the formula, you're good on the latter, but the only way to nail the former is to just bang away at it until it's permanently embedded in the brain.
Though I still haven't found a use for diagramming sentences. Maybe if I'd gone into linguistics, it would have application alongside parse trees.
posted by SansPoint at 6:39 PM on May 21, 2018
and spending a week proving the angle bisector theorem with ruler, compass, protractor, and straightedge, over and over again. A handful of examples and problem solving should be enough for that.
Side note: what you describe, as another commenter said above, is verification, not mathematical proof. A proof is a convincing* argument as to why something is always true. Always, as in, every one of infinitely many cases. Checking even a large number of cases is insufficient to mathematically prove a statement. (Although even one single counterexample suffices to prove that a statement is false - that is, not always true.)
So yeah, if you understood the actual proof - that is, the argument - for the geometric principle, and you didn't need to develop greater speed and facility with measuring angles or whatever, then that was absolutely unnecessary busy work. Specifically of the sort that we mathematicians tend to dislike. Please do not let that incorrectly labeled experience sour you on more advanced math or on mathematical proof, however!
* For suitable values of "convincing" - part of advanced training in math is learning to become very skeptical and rigorous about one's logical arguments. High school students, students just learning calculus, etc. do not necessarily need to worry about the same level of rigor as research mathematicians, of course.
posted by eviemath at 5:44 AM on May 22, 2018 [2 favorites]
Side note: what you describe, as another commenter said above, is verification, not mathematical proof. A proof is a convincing* argument as to why something is always true. Always, as in, every one of infinitely many cases. Checking even a large number of cases is insufficient to mathematically prove a statement. (Although even one single counterexample suffices to prove that a statement is false - that is, not always true.)
So yeah, if you understood the actual proof - that is, the argument - for the geometric principle, and you didn't need to develop greater speed and facility with measuring angles or whatever, then that was absolutely unnecessary busy work. Specifically of the sort that we mathematicians tend to dislike. Please do not let that incorrectly labeled experience sour you on more advanced math or on mathematical proof, however!
* For suitable values of "convincing" - part of advanced training in math is learning to become very skeptical and rigorous about one's logical arguments. High school students, students just learning calculus, etc. do not necessarily need to worry about the same level of rigor as research mathematicians, of course.
posted by eviemath at 5:44 AM on May 22, 2018 [2 favorites]
eviemath: It's me mislabeling it, I think, not my former teacher. Either way, I'm glad you're with me on this one. I'm not going to study more advanced math, though. I'm almost 35 with an English degree, and I'm more interested in literature and art than higher math. Higher Math is fascinating, but not for me.
posted by SansPoint at 6:48 AM on May 22, 2018
posted by SansPoint at 6:48 AM on May 22, 2018
As an aside—as far as I could tell after spelunking through old geometry textbooks on Google Books in the course of attempting to answer an AskMe years ago, the use of the word "proof" for its modern meaning in mathematics is relatively recent. (So... maybe SansPoint was just demonstrating a versatility with and timeless understanding of the English language!)
posted by XMLicious at 7:57 AM on May 22, 2018 [1 favorite]
posted by XMLicious at 7:57 AM on May 22, 2018 [1 favorite]
I have no idea how this works in a school setting, but one of the interesting things for me as I get older is to realize how I absorb and process information, and that I'm pretty thoroughly convinced at this point that it's entirely different for different people. But the thing is it's taken me 50+ years to get there and I still don't really understand it in myself. I have no idea how you'd make an accurate and useful assessment of someone who's mind is still forming and doesn't know themselves that well.
I prefer to read information, except when I don't. There are things that I read that I can't wrap my head around that I have to look for a video of, and then it's simple. Other things I simply cannot follow in a video, it's too slow and meandering most of the time, and I will rarely choose a video if I have a choice.
Spacial things are very odd to me. I can not read or listen to a description of a building or room and have any sort of idea of it. At all. But I'm really good at packing things, filling a truck, arranging things in a room. I can imagine exactly where everything should go.
I have a lot of trouble following people in movies, I don't even recognize them. So much so that I've taken online face blindness test, and was surprised that I score far above average.
This shit is complicated. Trying to make it fit in neat boxes probably isn't going to work.
posted by bongo_x at 9:24 PM on May 22, 2018 [3 favorites]
I prefer to read information, except when I don't. There are things that I read that I can't wrap my head around that I have to look for a video of, and then it's simple. Other things I simply cannot follow in a video, it's too slow and meandering most of the time, and I will rarely choose a video if I have a choice.
Spacial things are very odd to me. I can not read or listen to a description of a building or room and have any sort of idea of it. At all. But I'm really good at packing things, filling a truck, arranging things in a room. I can imagine exactly where everything should go.
I have a lot of trouble following people in movies, I don't even recognize them. So much so that I've taken online face blindness test, and was surprised that I score far above average.
This shit is complicated. Trying to make it fit in neat boxes probably isn't going to work.
posted by bongo_x at 9:24 PM on May 22, 2018 [3 favorites]
As an aside—as far as I could tell after spelunking through old geometry textbooks on Google Books in the course of attempting to answer an AskMe years ago, the use of the word "proof" for its modern meaning in mathematics is relatively recent.
Standards of proof became more rigorous in the mid to late 1800s through early 1900s, with Emmy Noether pioneering modern abstract algebra, the development of mathematical logic, Russell and Whitehead attempting to place all math in an axiomatic framework (and realizing that the task was impossible), etc. - what's considered modern math. Mathematicians were still using the term in a similar way beforehand, but "proof" was more on the level of the reasonable explanations from grade school textbooks than what one would find in research articles nowadays.
The proofs that I learned to do in high school Euclidean geometry, which involved writing down a sequence of equivalence theorems ("angle-side-angle" and such) without any connecting words, are proofs in the same way... but highly stylized. I know in my high school geometry course they kind of missed the point that they were supposed to teach careful logical deduction (which is the basis of the "convincing argument" for what we currently consider mathematical proofs, though proofs in a modern research paper will have, you know, connecting words, since we realize that we're trying to communicate ideas to an audience of other humans). So they may look quite different, though in the background they are also proofs in the same sense.
posted by eviemath at 7:34 AM on May 23, 2018
Standards of proof became more rigorous in the mid to late 1800s through early 1900s, with Emmy Noether pioneering modern abstract algebra, the development of mathematical logic, Russell and Whitehead attempting to place all math in an axiomatic framework (and realizing that the task was impossible), etc. - what's considered modern math. Mathematicians were still using the term in a similar way beforehand, but "proof" was more on the level of the reasonable explanations from grade school textbooks than what one would find in research articles nowadays.
The proofs that I learned to do in high school Euclidean geometry, which involved writing down a sequence of equivalence theorems ("angle-side-angle" and such) without any connecting words, are proofs in the same way... but highly stylized. I know in my high school geometry course they kind of missed the point that they were supposed to teach careful logical deduction (which is the basis of the "convincing argument" for what we currently consider mathematical proofs, though proofs in a modern research paper will have, you know, connecting words, since we realize that we're trying to communicate ideas to an audience of other humans). So they may look quite different, though in the background they are also proofs in the same sense.
posted by eviemath at 7:34 AM on May 23, 2018
But "problem math", which requires reading skills is really hard for her, and almost impossible during exams when she can't have someone reading the problems out for her because she isn't dyslexic enough for reading aid. She can't break down a realistic math problem, because she can't read the problem. That doesn't make her stupid, it makes her worried and lonely.
So I have many thoughts and feeling about your students' struggles. The first of which is, if they can't interpret problems on exams, she does, as a simple matter of fact, need a readaloud accommodation. /rant
I also think it is possible to state a "realistic" (at least pseudo-contextualized) problem in relatively few words. I think modern assessments like question 3 here do a decent job (though not question 4). In addition, increasing moving towards electronic testing of math seems to offer easier accommodations; I know our statewide test will offer a recording of any test item being read out loud to any student on its computer-based testing.
I also think that much of the benefit of contexualized problems is in the teaching, not in the assessing. There's a lot to be said for giving fairly simple (though not necessarily easy) test items compared to much richer tasks in class. I don't think that has really been consistently embraced, though.
I'm also just going to point out that, at this point in time, most secondary math teachers don't really make those decisions--those are largely made at the district level, or even by the authors of curricula that the districts buy. Certainly districts vary in how much this is true and how much independence teachers have, but I think teachers often have plenty of healthy skepticism of their instructional materials.
I also think we in the US need to re-evaluate the way our grading system is set up; if we expect that a "good" student will answer at least 85% of the questions correctly on a test, we can't write terribly interesting or novel test questions. If we were okay with students only getting 60% of questions right, we could give them much more challenging problems that would actually test their ability to solve novel problems. I'm not sure I'm actually committed to that idea, but it's fun to think about...
I know in my high school geometry course they kind of missed the point that they were supposed to teach careful logical deduction
Yeah, I'm honestly not convinced that 15-16-year-olds are, for the most part, developmentally equipped to handle the kind of two-column proofs we tend to ask them to produce, and not just turn it into a guessing game of "I think I saw Mr. thegears write down 'alternate interior angles' once" rather than understanding the flow of the proof. I personally think that having students find errors in proofs is honestly more valuable, but that's hard to write test items for, so it doesn't get assessed, so....teachers don't have a lot of impetus to teach it, faced with many other demands for them to cover material in their curricula.
posted by thegears at 3:39 PM on May 23, 2018 [2 favorites]
So I have many thoughts and feeling about your students' struggles. The first of which is, if they can't interpret problems on exams, she does, as a simple matter of fact, need a readaloud accommodation. /rant
I also think it is possible to state a "realistic" (at least pseudo-contextualized) problem in relatively few words. I think modern assessments like question 3 here do a decent job (though not question 4). In addition, increasing moving towards electronic testing of math seems to offer easier accommodations; I know our statewide test will offer a recording of any test item being read out loud to any student on its computer-based testing.
I also think that much of the benefit of contexualized problems is in the teaching, not in the assessing. There's a lot to be said for giving fairly simple (though not necessarily easy) test items compared to much richer tasks in class. I don't think that has really been consistently embraced, though.
I'm also just going to point out that, at this point in time, most secondary math teachers don't really make those decisions--those are largely made at the district level, or even by the authors of curricula that the districts buy. Certainly districts vary in how much this is true and how much independence teachers have, but I think teachers often have plenty of healthy skepticism of their instructional materials.
I also think we in the US need to re-evaluate the way our grading system is set up; if we expect that a "good" student will answer at least 85% of the questions correctly on a test, we can't write terribly interesting or novel test questions. If we were okay with students only getting 60% of questions right, we could give them much more challenging problems that would actually test their ability to solve novel problems. I'm not sure I'm actually committed to that idea, but it's fun to think about...
I know in my high school geometry course they kind of missed the point that they were supposed to teach careful logical deduction
Yeah, I'm honestly not convinced that 15-16-year-olds are, for the most part, developmentally equipped to handle the kind of two-column proofs we tend to ask them to produce, and not just turn it into a guessing game of "I think I saw Mr. thegears write down 'alternate interior angles' once" rather than understanding the flow of the proof. I personally think that having students find errors in proofs is honestly more valuable, but that's hard to write test items for, so it doesn't get assessed, so....teachers don't have a lot of impetus to teach it, faced with many other demands for them to cover material in their curricula.
posted by thegears at 3:39 PM on May 23, 2018 [2 favorites]
I personally think that having students find errors in proofs is honestly more valuable, but that's hard to write test items for, so it doesn't get assessed,
The mathematical concepts book that I teach future elementary school teachers out if has some quite nice problems in this style, actually! We've been working on creating some for university calculus too. I do quite like questions or activities that require students to think about another (real or fictional) student's reasoning process - they're good for developing important metacognitive skills as well as conceptual understanding.
The problem with the high school geometry two column proofs I think is not that 15-16 year olds can't do the logical reasoning, but that there's no narrative, so they don't see that they are constructing an argument. At least, that was the issue for me when I was taking high school geometry and found them quite boring, as opposed to the logical reasoning I had been doing to solve other sorts of logic puzzles from a very young age. I was not an average student, so my experience isn't fully generalizable of course, but my classmates at the time also seemed to think they were doing some sort of symbol manipulation exercise rather than a logical reasoning exercise. I'd say at least the simple majority of them were able to understand the logical reasoning component of two column geometry proofs though; possibly more (that's hard to evaluate as a fellow student, of course).
There are a variety of comouter games from computer scientists aimed at teaching kids as young as five or so basic logical reasoning. Rocky's Boots, from MIT, was one of my favorite games as a young kid, for example, and it involved using logic gates (AND, OR, NOT, XOR) to build "machines" to turn on lights, or power a boot that kicked a little ball on the screen, or similar challenges. Features that made it work well included:
* simple, visually engaging interface;
* cute story framing;
* clearly stated tasks or puzzles to solve;
* increasing difficulty level of the puzzles, with later puzzles re-using earlier puzzles as components to their solutions;
* built-in self-check methods - either the goal is accomplished, so you know right away that your solution worked, or you could see, based on the design on the puzzles and the game components, where things went wrong.
One can find versions of Rocky's Boots online to run on emulators, but it's pretty slow and sometimes hard to get running in the first place. It would be super awesome if someone could make an updated version, maybe as a flash game on the internet or something!
But anyway, even little kids can learn logical reasoning. But the instructional activities do have to be carefully designed.
posted by eviemath at 7:23 AM on May 24, 2018
The mathematical concepts book that I teach future elementary school teachers out if has some quite nice problems in this style, actually! We've been working on creating some for university calculus too. I do quite like questions or activities that require students to think about another (real or fictional) student's reasoning process - they're good for developing important metacognitive skills as well as conceptual understanding.
The problem with the high school geometry two column proofs I think is not that 15-16 year olds can't do the logical reasoning, but that there's no narrative, so they don't see that they are constructing an argument. At least, that was the issue for me when I was taking high school geometry and found them quite boring, as opposed to the logical reasoning I had been doing to solve other sorts of logic puzzles from a very young age. I was not an average student, so my experience isn't fully generalizable of course, but my classmates at the time also seemed to think they were doing some sort of symbol manipulation exercise rather than a logical reasoning exercise. I'd say at least the simple majority of them were able to understand the logical reasoning component of two column geometry proofs though; possibly more (that's hard to evaluate as a fellow student, of course).
There are a variety of comouter games from computer scientists aimed at teaching kids as young as five or so basic logical reasoning. Rocky's Boots, from MIT, was one of my favorite games as a young kid, for example, and it involved using logic gates (AND, OR, NOT, XOR) to build "machines" to turn on lights, or power a boot that kicked a little ball on the screen, or similar challenges. Features that made it work well included:
* simple, visually engaging interface;
* cute story framing;
* clearly stated tasks or puzzles to solve;
* increasing difficulty level of the puzzles, with later puzzles re-using earlier puzzles as components to their solutions;
* built-in self-check methods - either the goal is accomplished, so you know right away that your solution worked, or you could see, based on the design on the puzzles and the game components, where things went wrong.
One can find versions of Rocky's Boots online to run on emulators, but it's pretty slow and sometimes hard to get running in the first place. It would be super awesome if someone could make an updated version, maybe as a flash game on the internet or something!
But anyway, even little kids can learn logical reasoning. But the instructional activities do have to be carefully designed.
posted by eviemath at 7:23 AM on May 24, 2018
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posted by biffa at 12:17 PM on May 20, 2018 [10 favorites]