A few weeks ago, while giving unofficial swimming lessons to an acquaintance about my age, I had an insight. It was that before you can teach something, you have to realize it’s hard.

I don’t think I noticed this before, because I thought it was obvious. Of course someone who doesn’t know how to swim isn’t going to learn perfect front crawl just by looking at yours. If I was told to watch someone else swimming a brand-new stroke that I’d never seen before, I could imitate it pretty easily, because to me it’s a trivial skill. But to someone who has nothing to refer to, it’s hard.

“You’re like the fifth person who’s tried to teach me how to swim,” my acquaintance said as I led her into the shallow end holding a foam noodle. “People just tell me to move my arms and legs, and they didn’t seem to understand why I couldn’t do it.”

There are, needless to say, a lot of different ways to move your arms and legs. Some of them resemble swimming. A subset of those actually work to keep someone’s head at the surface, and an even smaller subset of those are effective enough that they have names, like front crawl. To me, this is obvious, because I’ve watched hundreds of children in my classes flail and struggle in their front crawl, or lift their head to breathe, or turn their toes inwards in whip kick, and make the same mistakes persistently even when I corrected them, both verbally and by literally grabbing their arms/legs and moving them. I know it’s hard.

I went through this flailing/struggling phase too and have no memory of it whatsoever, having been three at the time.  This is probably true of most good swimmers; the procedural memory is so embedded that it makes sense to say “move your arms and legs” because that's all you think about consciously; you forget how many other things you’re doing just to stay afloat. (Poor swimmers might have a different perspective, but they aren’t likely to use that perspective to try to teach other people how to swim.)

In order to bring a non-swimmer to the point of doing perfect front crawl, you have to teach them, one at a time, a long list of motor skills that have to be learned well enough to come naturally before you can move on. With adults, you can compress this process into a much shorter period than with restless, distractible, and lacking-fully-developed-motor-skills children, but you can’t omit it. You have to teach them how to float, and you can’t just tell them to float; you have to hold them up in the water and tell them, one at a time, which muscles to relax and which parts of their body position to change, and then you can let go. You have to teach them how to blow bubbles out their nose to avoid getting water in it. (I wonder how many people are eternally wary of jumping into the water or doing somersaults because no one told them this). You have to slowly shape their flutter-kick from a flailing mess into something that will actually move them somewhere. And then you can teach them front crawl, which comes with its own miles-long list of small details to fix and ways to fix them.

I watch my coworkers teach their class, and it amazes me how often they tell their kids to swim, watch them, and say “that was bad. Do it again.” As if that comment is useful in any way. As if doing the same thing over and over again will ever produce different results.*

I wonder how much this applies to other areas (teaching math in elementary school, for example?) How many teachers teach the same skills the same way, over and over, answering confused questions with exactly the same explanation they gave originally? Different minds work differently, just like different bodies work differently. You have to find the right metaphors, the right words to describe things that aren’t really conveyed by words. (“Kick your legs like a ballet dancer would” is a swimming metaphor I found recently that works quite well with some people and not at all with others.)

I would be interested to hear from other people who’ve either taught in other areas and found useful tricks or metaphors, or who’ve been taught in either good or ineffective ways.

*Note: Although I criticize it here, this is basically how I teach treading water. I hold children in water above their head, tell them to make scooping motions with their arms and legs, let go of them while maintaining eye contact, and immediately pick them up again the moment they start to go under. Two seconds becomes five seconds, becomes ten seconds, becomes a minute, and then I teach them fancy skills like eggbeater. But this is because treading water is a very basic, simple skill that I find really, really hard to explain verbally to four-year-olds.

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I used to teach English as a second language. It was a mind trip.

I remember one of my students saying something like "I saw a brown big spider". I responded "No, it should be 'big brown spider'". He asked why. Not only did I not know the rule involved, I had never even imagined that anyone would ever say it the other way until that moment.

Such experiences were pretty much daily occurrences.

Yes, I only recently found out that English has rules for adjectival order, and was shocked to realize it. I always did it without thinking. Apparently as a general rule of thumb, the more subjective something is the earlier it should go. But that's not all, since apparently age always goes after subjective opinion but always before colors. And there are lots of other priority rules. I'm waiting for someone to construct an example where one has adjectives in pairs that exhibit non-transitive order.

I'm waiting for someone to construct an example where one has adjectives in pairs that exhibit non-transitive order.

To me, a "solitary blue Smurf" is the color blue, but a "blue, solitary Smurf" is sad.

From The Night Before Christmas

"He was chubby and plump, a right jolly old elf,"


"He was chubby and plump, a right old jolly elf,"

The original doesn't make me think that Saint Nick is literally old. It's more like the "old" in "good old boys" (which is another example; compare to "old good boys"). The transposition seems to change the literal meaning. If you permute some more, you can wind up with nonsense - "an old jolly right elf", "an old right jolly elf", etc.

As another example, I would have a different idea of what's being said if someone pointed out to me a "sweaty hot runner" versus a "hot sweaty runner". The first makes me think the runner is sexually attractive, but the second doesn't.

The nonsense permutations, where "right" doesn't come first, are probably because "right" is acting as an adverb here, modifying the adjectives and not the noun.

As another example, I would have a different idea of what's being said if someone pointed out to me a "sweaty hot runner" versus a "hot sweaty runner". The first makes me think the runner is sexually attractive, but the second doesn't.

This doesn't' seem to be a transitivity issue. Rather, this seems to rest on the fact that the same adjectives have different meanings, and the different meanings fall into different parts of the hierarchy. But I'm not sure.

First, I guess I should clear up that we're talking about commutativity, not transitivity.

I think it is an example of non-commutativity. It's exactly the same words with the order switched, and the meaning changes. However, you're also right to point out that the meaning of the word "hot" is changing even though the word itself is not.

Here's an example of non-commutativity in which the words' individual meanings stay the same, but the overall meaning changes.

"I remember my good first attempt."

"I remember my first good attempt."

Yes, I meant transitivity, as in the correct seeming order for adjectives A,B,C seems in pairs to be AB, BC,CA.

Oh, I see. Sorry I missed the point. I don't have any examples of examples of that.

The idea of non-transitivity sounds really interesting -- can you point to an explanation of the supposed rules?

This has a rough summary of the rules. If the rules are as hierarchical as they suggest then there aren't any non-transitive issues. But there are some adjectives that don't fall into those categories.

That's not really a grammatical error though. If you were giving off a description as you got it, you wouldn't be expected to restart -- you could say, "I saw a brown ... big ... spider" rather than "I saw a brown ... no, big brown spider."

It's not the same level of error as if he said "I seed a big brown spider" or "I saw a big brown spiders." True, you may not know why we have a preference for placing certain adjectives first, but then, it's not as important to learn, either.

Now, if you had to explain why French only conjugates verbs in written rather than spoken form ...

Now, if you had to explain why French only conjugates verbs in written rather than spoken form ...

For the same reason English spells write, right, Wright, and rite differently. They used to be pronounced differently, but aren't any more, and the spelling hasn't been updated to reflect that.

this has always driven me nuts and English is my first language... I would start using phonetic spelling right now, but it seems like more effort than it is worth to convince everyone I know to accept it.

I wouldn't call it an error per se, but it's definitely unidiomatic. Native speakers will consistently produce big brown spider far more often than ?brown big spider. Some languages enforce this more strictly than others, and in some the words can be deliberately moved out of the usual order for emphasis. (E.g. in such a language, a phrase equivalent to "brown big spider" would roughly mean "big brown spider".)

Now, if you had to explain why French only conjugates verbs in written rather than spoken form ...

We do?

Like Yvain, I once taught French as a second language, and don't remember that. I did have a lot of cases of "there's probably a rule but I don't know how to spell it out".

We do?

In a way -- I'm referring to how a lot of the forms sound the same but have to be written differently -- e.g. parle vs. parles.

Oh, that, yes - I ascribe that more to the fact that written French just has a lot of letters you don't pronounce, or only pronounce in certain contexts, especially at the end of words (or h at the beginning).

But those letters still exist, even in spoken french: the verbs in "tu vois" and "il voit" sound the same ("vwa") in isolation, but with "arriver" behind them, they can sound like "tu vwazarriver" and "il vwatarriver".

Not to mention the fact that only some of the forms are homophones anyway: parle/parles/parlent sound the same, but they're different from parlons and parlez.

Is there some context where you can distinguish ait from aient in the spoken language?

Probably not, even the vois/voit example is far-fetched, most people would pronounce both "vwa'arriver", except maybe in a context where they want to put extra emphasis.

Verb forms' frequently being homophones is really not the same thing as their not being conjugated when spoken.

If all verb forms were homophones then it would be exactly the same thing. French still hasn't gone so far.

Do you know the rule now why you say 'big brown' and not 'brown big'? I don't...I'm very curious though!

The rule I learned in French when I studied it was "BAGS" (beauty, age, goodness, size) adjectives come first. I think I tracked the application of this heuristic in English for a while and didn't notice any obvious contradictions, but I could easily have missed something.

Good heuristic.

Can still play with it a bit within BAGS...

Size and beauty sometimes seem to come before age: "a small, old lady" and "a pretty young thing" and size seems to come before prettiness: "a big ugly brute"

Yeah, more complicated than I'd ever considered before. great find!

French is special in that adjectives can go either before or after the noun; I don't know what the rule is but the one you give sounds right (though you'd say "une fille mignone" for "a cute girl", so I'm not sure it's the whole rule - there may be a finite set of adjectives (mostly short ones?) that are allowed to go in front).

In english though, adjectives are always in front, and I don't think the same rule works for their order: "Sad little boy" and "interesting old man" sound like a counter-examples, though your rule would work for the French translation. For most cases in English of "A1 A2 N" I can think of, the French translation is either "B A2 A1", "A2 B A1" or (more rarely) "A1 A2 N", which suggests that the "most important" adjective (A2) always stays closest to the noun, in French even going in front of it if it's very close.

So the rule in English would be the opposite of the rule in French :D (except for when both adjectives go in front of the noun in French, in which case their order is the same as in English).

ETA: this was probably wrong, I could think of plenty of counter-examples to those rules.

It's worth mentioning that the position of the same adjective in French (and other Romance languages) can vary, affecting the meaning to any degree from connotational nuance to literal denotation. A general rule taught to foreigners is that placing the adjective before the noun tends to suggest that the quality characterizes all members of the class denoted by the noun, while placing it after characterizes the individual specifically. (An example from the delightful old version of Teach Yourself French that sticks in my mind is savant professeur vs. professeur savant.)

Sometimes the adjective is placed before the noun as a kind of rhetorical flourish, as in assoluta innocenza, an Italian phrase I've had occasion to use.

Ah, that makes sense, though I can't think of that many constructions where that rule works: "Un curieux animal" and "un animal curieux" mean different things ("a curious-looking animal" and "an animal that seems to feel curious"), and I think that's a one-off rule more than an instance of a general rule.

I suspect some adjectives "naturally" go in front of the noun (those Alicorn listed), but you can put them behind it for extra emphasis; the rest always go behind. With a lot of idiomatic exceptions like "curieux" which means something different depending on whether it's before or after the noun.

Don't forget that event-related idioms can skew meaning as well...

I don't think there's any justification more interesting than "do it this way because that's how it's done", but if it helps, at least it's annoyingly complicated.

I think it would be because it's a "brown spider" more than a "big spider", i.e. "brown" would be more important/more permanent/more "fundamental" in describing it than "big".

That would explain why you would say a "sad little boy" and "short sad song" ("little boy" and "sad song" being "closer" descriptions of the object in question than if the order was reversed).

I'm not sure that's the full story though (the explanations on grammar we come up with are often wrong ), and don't know the "proper" linguistic explanation.

Surely the size of the spider is often the most fundamental aspect? "Don't look now, but there's a huge brown spider behind you." If "big spider" were a species then it's inseparable (as benelliott points out) because it's a species name, but that's a different story. I wouldn't talk about a green enormous chameleon even if I knew that the chameleon was about to change colors without changing its size.

I think this work. To test it, imagine if there was a specific species of spider called "big spiders" and one of them was brown. I would then consider "brown big spider" to be more appropriate.

Marius makes a good point with the chameleon - Although when describing something as skinny/fat the color comes first (Red Faced Fat Man vs. Large/Huge Red-faced man)

Almost seems to me that we place words that categorize the object closest to the object - Brown Spider/Green Chameleon/Fat Man are all categories of those objects whereas a Big spider isn't as much of a category as it describes the size of the spider relative to other spiders in the same category.

Yes! I've had this experience repeatedly in the course of helping international math graduate students with English.

Learning to walk again after my stroke was both frustrating and hysterically funny that way.

I mean: it's walking! How can I not know how to walk? But of course it's something I hadn't given any thought to in over three decades... my body knew how to walk, I didn't have to. And then it forgot... sort of... and I had to learn it again.

Physical and occupational therapists are really good at this -- or, well, good ones are. I figured out how to walk level on my own (with some very funny-in-retrospect failures, including once when I missed the floor altogether), but someone had to tell me how to climb a flight of stairs... I just couldn't quite figure out what to do with my knee. Most people were, like, "just step up!" My PT actually talked me through the process of bending and raising my knee, planting my foot on the stair, and then straightening it out to lift my other foot off the ground.

Of course, most people don't remember the frustrating months or years they spent learning to climb stairs (compounded by the fact that children are physically too small for adult size staircases). Whereas most people remember learning, say, computer programming, and remember it being hard, and would probably be better at teaching it than teaching someone to walk even though their "level of expertise" in walking is higher. (Also, programming is based on language, and thus easier to explain using language, than a purely procedural skill like walking or climbing stairs.)

Heh, I learned to program when I was six, I don't happen to remember it being hard -- and I think I therefore pretty much suck at teaching programming.

I rock at explaining specific concepts to programmers -- libraries, techniques, tools -- but I cannot teach a non-programmer to program. "What do you mean? You just write functions! They accept arguments, and do stuff...ummm...it's like subroutines?"

My eldest daughter is eight, and I haven't taught her to code yet. I'm such a bad parent :-)

We'll do "Hello World!" tonight after school!


Language choice is important, though. If you're proficient in JavaScript, I would suggest that, since later on, you can have a for loop updating an absolute position of an IMG dom element ("animation") for relatively little effort -- and this, hopefully, will make her realize that programming is cool. When she starts doing collision-detection for a kitten-based game, you'll know you've succeeded :)

Upvoted for describing exactly my experience.

Six? I am insanely jealous. I only started learning two years ago.

Six! That's crazy, and I'm so going to teach my kids to program at that age! Yeah, I can see why you wouldn't find teaching others easy. Still, if you discovered you liked teaching (like I discovered I liked swimming) and spent a lot of time explaining concepts to beginners, I expect you could be a good teacher.

And in spite of this, you'd probably find it even harder to explain how to walk.

Learned to program at five. If someone has the programming gear, five is a perfectly good time to teach them to program. Just show them some Python code (I was reading BASIC, bleah) and see if they can deduce the rules and try writing their own. If someone is meant to be a programmer then a programmer they shall be.

I would think the only hard prerequisites for programming would be knowing how to read and how to do arithmetic. Most people don't have arithmetic down by five.

I started with Java at eleven; unfortunately I had internalized from my environment that programming was a hard, miserable duty, and so I didn't get particularly far at that age. I wish there was a way to communicate to children "No, really, this is fun, not scary."

Programming in Java is a hard, miserable duty.

I completely agree. Unfortunately, a lot of educational languages take an overly structured approach to programming and therefore end up delivering exactly the wrong impression.

One thing I miss about the computers of my childhood was the BASIC interpreter bundled with pretty much every classroom and personal computer; it's an appalling language, but it does provide a simple and friendly environment for bare-bones programming, and that's invaluable from a learning perspective. As late as my high school years, similar development environments existed on things like graphing calculators (I once stumbled into teaching my stoner lab partners the basics of programming, as a side effect of competing to discover creative ways of displaying crude messages), but it's a feature that seems to have fallen by the wayside now.

I suppose we've got things like Lua scripting, and of course there's a copy of gcc squirreled away on every Mac that ships, but I really don't know how well it compares.

I believe there's a copy of Python squirreled away on every Mac and most Linux computers, so I'll call this progress, if we ignore Windows.

I read all my highschool math textbooks within the first couple months of the school year, so I usually spent the rest of the class period writing reversi or minesweeper or snake on my TI-85.

I learned to love both math and programming by attempting to write a Scorched Earth game on my TI-83. I had a really tough time figuring out how to do ballistic calculations, but I thought it was the coolest thing ever when I figured it out.

Learned to program at five.

Out of curiosity, how far down that road did you go? As far as I know you've never given any public indication of how well you can program (which is emphatically nonbinary), but some people seem to think it's important. (I realize that programming skill is notoriously difficult to measure, but a crude approximation, such as log-lines-written, would be sufficient.)

100000 lines? Woah. Where are they all? You didn't program for money or contribute to open source projects, right?

100k lines sounds like a lot, but it isn't, especially considering the reduced concept-density of both older languages and novice programmers. My first 100k lines were unpublishable.

100000 lines is probably an underestimate. Doing a line count on all the files in my development directory, I find that I've got about 35000 lines of code in there, and I still consider myself somewhat of an amateur (I've been coding for about a year now). I code probably five hours a week or so, so a full-time programmer with similar productivity who had been programming for a decade would have written 2.8 million lines of code.

100000 lines sounds like a lot, but it's really not.

I considered that possibility and disregarded it because exp(5) ~ 148), which is way too low.

I was slow...and I didn't have a computer to program on until 8.
On the other hand, I've been teaching for ~20 years, and I've been teaching programming for half that. Learning to iterate through a collection of data structures is the killer feature in programming. Some folks get it....and immediately. Most folks who are not naturals take a lot longer to understand the concept...and most classes jump over it like it's easy. Usually 3-10 different explanations, and 5-20 examples will get folks over the hump.

You mention reading BASIC -- did you by any chance have those math textbooks with BASIC programs printed in the appendices?

Was it your parents' decision that you were going to learn to program at five, or yours? The latter would be even awesomer.

Somehow I doubt it would have worked for me though. I started trying to teach myself programming a few years ago (I was maybe 15) and I was looking at Python, but it was really opaque to me and even with my dad's "help" (he had no idea what he was doing either and we proceeded by trial and error) I got pretty much nowhere...I succeeded in writing a program that got stuck in an infinite loop, which I thought was hilarious, and that was it. I did take an introductory university course in Java later on though, and it was the easiest A+ of my life, so maybe I'm not completely hopeless.

Was it your parents' decision that you were going to learn to program at five, or yours?

I had a similar experience, and my two sibling did not also learn to program at age 5, so it wasn't entirely determined by my parents.

I often had a similar experience in grade school; teachers would present a concept for the first time as if they were reviewing it.

So far as I could tell, the teachers were saying the words that allowed them to refresh their memory of how a technique worked, rather than words that would allow someone with no prior experience of the technique to give it a try. E.g., frequent flyers here on LW can say things to each other like "don't forget to test your ideas," or "update your probability estimates" and the words have meaning, because they are handles that we have all built and designed to pull on a whole cluster of related memories and skills. But if you said that to someone with little or no exposure to the modern Enlightenment, they wouldn't be able to follow along unless they could infer all of the intermediate steps from the skeletal verbal outline you're providing.

I've done some occasional tutoring and so on, and my pupils are usually impressed, but all I'm doing is listening to people to find out what they already know, and then explaining the next few steps, one step at a time. It helps me to have an outline or a diagram showing all of the steps that I want the student to be comfortable with, and then we can look at it together and decide what the student will learn next.

Even when I am unable to acknowledge that a subject is hard, I can at least acknowledge that it is made up of many parts, each of which is necessary for mastery, and then make an effort to teach each of those parts.

Have you had any success teaching the ability break topics down into small steps? This is not something that seems trivial to me.

Hm! Nobody has ever asked me to teach them how to teach. It's very difficult to formalize the knowledge without a context, but here are some questions to ask yourself that may help you think of subtopics:

(1) What data or inputs do I typically need to solve a problem in this subject? E.g., if you want to send a robot to the moon, you need to know the mass of the robot, the location of the moon, the cost of fuel, the gravitational co-efficient, and so on. Each of these inputs can be a subtopic of "rocketry" -- you might want to teach your students how to weigh a robot, how to trace the moon's orbit, how to comparison shop for fuel, and how to look up a universal constant. Only after learning all four of these skills would a beginning rocketry student be in a position to independently (i.e, don't hire somebody else to do it) and directly (i.e., don't just judge based on past accomplishments / perceived difficulty) assess the likelihood that an arbitrary moon-launch project would succeed.

(2) What are the prerequisites for attacking a problem in this field? Any ordinary group of Americans will have a median student who is woefully deficient at one or more prerequisites. No matter how much it might "make sense" to assume that people in your class know what they are "supposed" to know, if your goal is to actually teach them the next step, then you can best achieve your goal by discarding this assumption, testing for competency at the prerequisites, and then making subtopics out of any prerequisites where people seem weak. E.g., if you are trying to teach people how to compost their domestic food waste, you might think that the most important information to convey relates to the size, shape, and composition of a compost pile -- what to put in each layer, how big to make each layer, etc. But the task "add a layer of dead foliage that's two feet thick and six feet around" is not a primitive task. It assumes that people know how to, e.g., operate a shovel, identify which foliage is dead, and measure distances with rough accuracy. Chances are, at least some of your audience can't do these things well, or at all. Think about what concrete actions your students will need to take in order to follow each of your instructions, and then make each of those concrete actions a subtopic.

(3) Is this really a single problem, or is a related cluster of problems? There's nothing wrong with teaching related problems in close (geographical or temporal) proximity to each other so that people will find it easier to cross-apply skills, but that's different from trying to teach a group of related problems all at the same time. "Being rational," e.g., turns out to subdivide into "seeing things as they really are" and "doing what actually achieves my goals." Although these two skills have similar prerequisites and are deeply complementary, they're still distinct: you can imagine being good at one but not the other. Try to identify the smallest subset of your topic that would still be a useful skill to have if you had it independently -- if I'm training a soccer player, and the big game starts in two minutes, and I have an empty bench, it'd be at least somewhat handy if my protege had figured out how to boot the ball down the field, even if she was still hopeless at all other soccer-related tasks. That means "booting" is a sub-topic. Don't teach "soccer" except in some meditative/spiritual sense; at the algorithmic level, teach booting, running, passing, teamwork, etc.

(4) Mix and match the questions to get narrower sub-topics. E.g., suppose booting is a subtopic of soccer. Well, what are the inputs that a student will use in deciding how to boot? At a minimum, you need to know where your own goal is and where the ball is so that you can move the ball away from your goal. So, I will probably give an instruction like "find the ball." What are the prerequisites of "finding the ball?" It helps a whole lot if you are consciously following the ball as it moves from one person to the next; this skill is generally easy, but some absent-minded people don't realize that they should be doing it, and some unusually absent-minded people might not know how to do it. It turns out that it helps to see which direction people are running in; they tend to run toward the ball. So we have soccer > booting > finding ball > visually following ball > visually following people. When you dig four levels down, it's easy enough to get to twenty or eighty sub-sub-subtopics within "soccer," and if you spend a few minutes teaching each of those, you'll usually have exhausted your audience's attention span.

Hope some of this helps; feedback is welcome.

I think it's not just realizing that it's hard. It's realizing that it is potentially hard in a lot of different ways.

I recently learned how to swim after many failed attempts. I'm not any good, but I can do it, and the primary problem was that I was (am) afraid of the water rather than a lack of technique, and it was very frustrating because the wonderful woman teaching me could wrap her head around what it was that I found to be hard; she assumed at first I didn't know how, then when it was clear that I did know how she did work on my fears with me but she still basically tried repeatedly to get me to shut up and swim already.

I like teaching adult lessons because adults can, and often do, ignore their fears and "shut up and swim already". At which point they realize they aren't going to die, and the fears tend to diminish with time and practice. Do you find that's happening with you? If it isn't yet, it will. I've never had a student who didn't get used to the water eventually.

Not to imply that adults' fears are worth less consideration than childrens' fears. Adults learning to swim for the first time can be a lot MORE afraid, especially if they've had bad experiences with water, but they can be incredibly self-motivated to overcome these fears, whereas three year olds...just aren't.

I had problems from worrying to much constantly when I tried to get decent at swimming recently. I think I might have taken lessons for a year over a decade ago, but I forgot almost everything I learned so I was eventually only able to swim by just flailing around inefficiently in a way that does not resemble any stroke. A few months ago, I decided that I actually wanted to be able to swim quickly, dive, and tread water as long as necessary without exhausting myself. So I went to a pool every week after studying a guide, and spent a few hours drilling the movements until I no longer felt on the verge of drowning constantly. I learned more slowly when someone was teaching me because it made every failure feel worse, but when I was motivated to improve and willing to look like an idiot in the process it went quite quickly. The more I assume that I should already be good at something, the worse I am as a student, which is something I really need to fix.

The more I assume that I should already be good at something, the worse I am as a student, which is something I really need to fix.

I can understand that. Don't know how much it's true of me. It is interesting that you learned more slowly with a teacher because you felt your failures more strongly. I've never experienced that but I can see why someone might.

It does seem like there's an age effect. None of my little cousins have ever showed fear of water, and I suspect this is because they've been in the water before they knew that it could be scary- they knew how to swim before they were physically strong enough to keep their head out of the water.

Dogs show the same effect- dogs that grow up never having swam seem to always dislike water, and dogs that were thrown in the water as puppies seem to love it and not start out scared.

Exactly...which is why I hate it when parents wait until their kids are school-age and then sign them up for group swimming lessons when they've never set foot in a pool. It's a nightmare waiting to happen, and by the time I get them, they've usually been through enough classes with lazy or just plain incompetent instructors that they're really scared, and set in their beliefs that they can't swim. We offer parent-and-tot swimming lessons starting at age 3 months; I just wish more parents took advantage of it. Or you could do this program: http://www.youtube.com/watch?v=mL7XOo_LyWU

I was forced to do school-age swimming lessons, which pissed me off, since I could totally swim already.

Anyway, do you have any tricks to getting them over the fear (other than the obvious and marginally effective 'encourage them to get in the water and remind them that they arent going to die')?

The best trick I've found is to get kids to try things that, to them, seem scary and impossible, but which I know that no one can actually fail at. Example: stand on the side of the deep end with them, jump in holding their hand, and push them to the surface as soon as my feet hit the bottom. They're not underwater long enough to panic, and then I'm holding them up in the deep end, and I can praise them warmly for jumping into the deep end...and even if they didn't jump entirely voluntarily, they can't exactly say 'no I didn't jump'.

Just as a lot of people don't know that swimming is hard, they don't know that teaching is hard-- possibly harder in a sense, since at least you get immediate feedback if you're swimming badly.

There is feedback to be gleaned when teaching badly if one knows what to look for. And I think being able to interpret the passive feedback and respond appropriately is a large part of what makes a good teacher.

Many teachers, in my experience, don't notice when students are confused or bored -- or maybe they notice but don't care -- and their teaching method and pace is completely unresponsive to the immediate feedback of how well it is working.

Many teachers, in my experience, don't notice when students are confused or bored -- or maybe they notice but don't care

Or they notice, and care to some extent, but have other things to worry about. Like a pressure to cover a certain amount of material, or a fear of boring one group of students while they slow down for another, or a (maybe partly justified) belief that the students who are confused and bored just aren't trying.

And I think being able to interpret the passive feedback and respond appropriately is a large part of what makes a good teacher.

I think this is a lot of Nancy's point: it takes a good teacher to notice feedback. This suggests a sort of vicious circle: good teachers get better, but bad teachers stay bad.

Fair enough-- I should have said something to the effect that when you're swimming badly enough, the feedback is impossible to ignore.

Click help at the bottom of the input area and it shows a guide. [name of page] (url) <- without the space in the middle

That is how to make a link in a comment. To make a link in an article, highlight the text you want to be a link, and click on the link button whose icon is a three link chain. This will bring up a dialog box with an input for the url.

without the space in the middle

You can show the literal text "[name of page](url)" by escaping the control characters with "\", you would enter "\[name of page\]\(url\)".

That is how to make a link in a comment. To make a link in an article, highlight the text you want to be a link, and click on the link button whose icon is a three link chain. This will bring up a dialog box with an input for the url.

Interesting--- I'd just been going in and out of the html box.

Thanks, I did not expect that it would be different.

I agree with this notion somewhat tangentially. I think that learning feels hard, but that too much is played up about it actually being hard. I think this is comparable to some of the historical remarks found in this post:


More often than not, in the circle of topics that I have experience with teaching and learning, syntax represents the first hurdle. I believe this is true in many domains of learning, even swimming. Learning the grammar rules associated with balance in a body of water and how to generate motive force to make yourself go are, at the most basic level, instances of syntax, although the (perhaps context-free) language of human activities doesn't necessarily feel very much like the type of algorithmic rule-following we learn in lectures.

Speaking of that post on quantum explanations, there is a nice quote buried in there or in one of the posts nearby, "There are no surprising facts, only models that are surprised by facts; and if a model is surprised by the facts, it is no credit to that model."

I feel that, when properly understood, this expresses the reason why learning feels hard. There was a recent publication in PAMI, a machine-learning journal, on a quantity called Bayesian surprise (reference at end of post). The Bayesian surprise of some observed data, given a class of models to be used for describing the observation, was loosely defined as the distance between the posterior distribution and the prior distribution -- that is, after updating one's beliefs in the face of the evidence, how much have those beliefs changed from the moment before the evidence was observed? If they have changed a great deal, the surprise (defined in terms of the KL-divergence and other information-theoretic quantities) will be large, hence that observation is surprising.

To a young person (or someone with little practical experience around water), the models of human motion and balance trained in bipedal movement would be incredibly surprised by the feelings and feedback in the water. It is similar in a probability lecture I am giving to some engineering students. Various Bayesian decision questions, dressed up in rudimentary coin-flipping examples, feel hard and appear to be counter-intuitive when a student's prior model (usually based upon limited experience and intuition) is challenged.

I wholeheartedly agree that we ought to take this Bayesian surprise into account when thinking of the best way to teach new material. In some sense, there may be a "geodesic path" connecting a pupil's current (prior) belief to the desired posterior belief, which may provide a quantitative basis for optimal teaching strategies... but that seems far off.

Interesting post!


I think one of the things that makes learning things hard, given this interpretation, would be difficulty in actually updating the model. It may be that large amounts of surprise, being related to large differences in model produced by updating, make it hard to update, and this is certainly one level of hardness felt when learning. But additionally, there is also likely to be some variance in general ability to update certain models: some people have limited kinesthetic senses would not only be operating with less data to update on, but may also have a more rigid model.

Model rigidity seems to me like a good candidate for the variance between students' subjective experience of the hardness of learning certain things. It also seems like it would be strongly correlated to the appropriate types of intelligence- kinesthetic intelligence relates to a more easily changed model of physical syntax, procedural intelligence relates to a more easily changed model of procedural syntax, &c.

This also seems to correspond well to my own personal experiences with what is hard and easy to learn- my understanding of how the different elements of the problem can interact changes with speed proportional to how easy the subject seems, eg I can change my understanding of how abstract quantities/qualities interact fairly quickly making math easy to learn, my understanding of systems of social interaction changes very slowly (due in part to difficulty collecting evidence) and thus I was socially awkward for a long time, and it took a lot of effort to overcome.

Thank you, that's a very interesting comment.

When I read this, I remembered also being told to "move your arms and legs".



WTF WAS WRONG WITH THOSE PEOPLE oh never mind OP said it better.

It does work eventually. If you tell kids enough times to move their arms, and prevent them from actually drowning, they figure it out by trial and error in the end. But that's not teaching.

It's a tragic fact that most people not only can't teach, they lack the introspective abilities necessary to understand that they can't teach. They just can't comprehend that something they find easy is actually hard, or that something they perceive as atomic has steps. Thus they blame the students for their poor teaching skills.

Were you moving both your arms and your legs? At the same time? If not, perhaps it was a reasonable starting instruction. From there perhaps they were planning to proceed to "No, move your legs up and down... yes, like that, but don't forget to keep moving your arms!"

I don't know... that seems like a pretty good explanation to me. Caps lock makes anything better.

I taught my daughter to swim after well over a year's worth of "professional" swim training had seemingly achieved very little.

The approach I used worked well. I tried to teach her one skill at a time - like the Montessori method.

Learning to swim is hard because you have to do several things at once or you start to drown.

So, contrary to dogma, I got her some flippers and a floating vest. Her first task was to work out how to move around. Because of the floating vest she did not have to worry about keeping afloat. Because of the flippers she found learning to get around by kicking quite easy.

I progressively let down the vest over a period of a few visits. She progressively learned to leverage her "getting around" skills into "staying afloat" skills.

I then showed her how to swim in various styles ie dog paddling, breast stroke, then freestyle with head out of the water, then freestyle with proper breathing.

Eventually we took off the flippers and after a short adjustment, she could swim! All in less than a month. It was amazing to see after all those swimming lessons.

I would love to find a similar way to teach riding a bicycle. You can easily take learning to pedal offline. Steering plus balancing seem to be tightly coupled though, and the way you have to turn is very unintuitive thus hard to learn.

Teaching requires that you take all your implicit procedural knowledge and turn it into explicit declarative knowledge. In effect you have to reverse-engineer your skill.

When I was teaching my daughter French, she said "French is so dumb - why do they have all those irregular verbs?". So I took her through a few irregular English verbs. She had learned them all without explicitly realizing the fact that many common English verbs are irregular.

Unfortunately a lot of swim instructors do not teach very well...maybe because we're all teenagers getting paid $0.50 an hour more than minimum wage to be wet and freezing for 3 to 4 hours at a time. I'm fairly passionate about teaching swimming, but I'm a bit if an anomaly at work and people think I'm odd. If your daughter listens to you, she's probably better off learning at least preliminary swimming skills from you. If you want her to get really good, the quality of swim team teaching is usually better than your standard public swimming lessons. Or I could send you a list of suggestions...it would actually make me really happy. How old is your daughter?

I would love to find a similar way to teach riding a bicycle. You can easily take learning to pedal offline. Steering plus balancing seem to be tightly coupled though, and the way you have to turn is very unintuitive thus hard to learn.

Take a set of training wheels that are adjustable in height, and gradually raise them farther and farther off the ground. That's how I learned.

For teaching bicycle riding the same way, you need one of these: http://www.thegyrobike.com/

You can slowly reduce the power on it in the same way as letting air out of the floaties.

Learning to swim is hard because you have to do several things at once or you start to drown. So, contrary to dogma, I got her some flippers and a floating vest.

I don't know what the swimming programs in your area are like, but where I live (under the jurisdiction of the Canadian Lifesaving Society), the kids start out with skills in the shallow end (floats, front and back, first assisted and then unassisted, kicking on noodles, dunking their heads, etc) and as soon as Preschool C, the third level, one of the items on the checklist is having them swim around in a lifejacket in the deep end. I don't rigidly follow the checklists because I find it limiting, but most instructors do, meaning that in most of Canada at least, they should be taking 4-year-olds in the deep end with aids.

As far as biking, there are roller setups that bicyclists ride their bikes on sometimes (for warmups maybe?). If you had something like that, you could stand next to her and hold her up giving less and less support until she can stay up there.

I'm studying to be a (biology) teacher and learning to use the didactic method is big part of our training. In fact this entire partim (December until now) has dealt with giving clear instructions, asking the right questions, etc. We'd give classes to each other and then let the other students point out anything that isn't crystal clear. Whenever I study something I try to write it down as if I was explaining it to a six year old child. If I can't then there is still something I don't quite understand.

I find myself in the opposite position, because math always came very easily to me, and yet I've had a lot of success tutoring it. I think, though, that that largely comes out of my interest in why it worked rather than how, and my ability to make connections that weren't explained to me.

I wanted to make almost the same comment. I'm convinced that my interest in logic and foundations makes me better at teaching algebra and calculus, because I'm often thinking anyway about why those "obvious" things work the way that they do. (In particular, why don't algebra textbooks discuss the general logical principle of substitution of equals for equals? I tell beginning students that it's the most important lesson of algebra, but it's not in their book!) It's also important to listen to how the students think about things (both prerequisites, and the errors that they're making now) and adapt my explanations to fit them.

Very good point. Which is why I think that it sometime's harder for someone to teach something if they're very naturally good at things. Some of the best teachers I've had or seen where people who found it tough to learn themselves.

Having said that, this is partially psychological, as it's more encouraging if the teacher can say that they had to work at this too: it means the ability/understanding seems achievable. Plenty of teachers pretend that they don't think something is easy or obvious to them for that precise reason.

I think this also depends on the natural ability of the student, a teacher who is naturally very good at something is ideal for teaching students who are also naturally good at that thing. Of course, those students aren't generally the ones who need teaching the most desperately.

Yes: assuming they're naturally good in the same way. It's perfectly possible for one person to be a natural linguist through an intuitive 'hearing the language spoken' approach, and another picking it up very easily through an 'explicitly understanding the underlying grammar' approach. Either teaching the other would be disaster if they didn't constantly bear in mind that people learn in different ways.

Whereas a slow learner CAN still apply their own bad, slow way of learning to all and sundry (I've definitely seen it done), but I think is more likely to at least teach in a way that slowly but surely makes sense, and might have tried a wider range of tricks due to not picking it up so quickly.

I had had the exact same experience teaching, the faster I learned something, the harder it is to explain it to someone else. Maybe I should be teaching English instead of computer science...

As before...Teacher for 20+ years...dozens of different topics taught (~40K hours): Math (K-16), English (to Natives and Foreigners), Sports (Springboard Diving, Soccer, Basketball), Programming(C-->Java mostly).

The most interesting part of explanations is that the same explanation doesn't work for everyone. If you're going to be an effective teacher, you need 2+ backup explanations for when the first one doesn't work. Examples are frequently even better than explanations, and enough examples will get most folks a long ways.

My personal obsession in education is the feedback system, which is all but ignored in most education discussions. Difficulty with swimming is that folks with low kinesthetic awareness have very little ability to check what they're doing. Underwater video-cam would give quite a bit of advantage here.

3 takeaways:

  1. Teaching != Learning. Practice = learning.
  2. There is no Universal best method -- people have massively different relevant prior experience.
  3. Feedback systems allowing folks to correct their practice in a reasonable action-fix loop is the killer feature missing from most practice.

I can easily see posts about your experience teaching being very informative. Specifically: digging into the details about how to deal with inferential distance.

I've long been frustrated about how much easier it is for me to explain concepts to others, compared to how hard it is to get a good explanation out of others. I was planning writing an article, and have an early pre-draft, in which I tell my "secret", but I've delayed it for ... way too long.

There are several tricks, but it's basically this: trace back to the nearest point of common understanding ("nepocu"), and then follow the inferential path back to the concept you want to explain, making sure to go over the motivation for each step, and to connect related topics. And of course, actually understand the topic yourself. (Anyone can PM me if they want the current draft.)

You would think that this is obvious, but in my experience, people generally don't follow it, or lack the requisite understanding.

I've done that before, but I'm not sure if I do it consistently. You've had long discussions with me, have you noticed whether do I do this more or less than others?

My advice mainly applies to high bandwidth exchanges (i.e. real-time conversation). Other than that, I don't know how to explain our failure to overcome the impasse.

I don't know how I learned to swim. One day I couldn't stay afloat without a life jacket or other flotation device, and the next day I could.

This reminds me of how I learned to whistle. I tried to whistle once every morning right after I woke up. One day I woke up and I could whistle.

I had a similar experience; one day I couldn't snap my fingers, the next I could. While I was in the former state, I noticed an interesting thing: every single time I had a conversation about my inability to snap with someone who could, it went like this:

Me: You know, I actually have never been able to snap my fingers.

Other person: Really? (snaps fingers)

Me: Why did you do that? I already know what it looks like when someone snaps their fingers.

Other person: ... You know, I'm not sure why I did it.

I still have no idea why everyone's first reaction was to snap their own fingers. Was it pride at having a skill someone else didn't? Was it an impulse to demonstrate it based on some low-level expectation that I might go "Ooooh, that's how to snap your fingers!" Were they just double-checking that they still knew how?

I still have no idea why everyone's first reaction was to snap their own fingers.

Important data:

1) Everyone did it. 2) Everyone claimed not to know why they did it (I am taking you at your word - that your dialog is representative)

Both of these point to something close to an involuntary reflex.

Recall the game, "Simon Says". That game is fun because it is hard (under the right conditions) to avoid doing what someone commands you to do. It takes concentration to hear the command and then not perform the action. One might have thought (and one would have been wrong) that someone playing "Simon Says" would hear the command, then decide whether it was in the right form, then follow it. Everyone wants to play it this way and thus win. But the nervous system has a strong tendency to short-circuit the path from hearing the command to performing the action. You try to consider the command carefully before performing the action, but you fail!

This suggests that the mental path from thought to action is only imperfectly under voluntary control. What it takes to suppress, or amplify, this path is presumably not simple.

Stop reading this.

Did you stop? So I don't think the difficulty is avoiding compliance with commands in general. Rather, it's switching between the mental modes of "complying" and "not complying" under time pressure.

The very fact that there is a "compliance mode" rather than individual acts of hearing each command and deciding whether or not to obey each command one at a time I think demonstrates that all is not in accordance with our folk model of voluntary action, according to which each action is willed. Rather, the mental path from thought to action is only imperfectly under voluntary control.

By the way the book The Illusion of Conscious Will deeply explores the limitations of voluntary control, which as Wegner demonstrates is in some sense a fiction.

Weirdly I did it while reading the post... I think in part because I had had to consciously learn it myself so I was checking the movement (aside: what no-one told me was the sound comes from the impact on the the pad of the thumb, not the two fingers rubbing against each other as I had thought, when I realised that it became easier).

Though [deleted]'s theory makes a lot of sense. In general people reflexively perform actions when prompted. BLINK

I still can't clap with one hand. my life is not complete.