Being a teacher

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.

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.

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.

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.

This article should probably reference Inferential Distance

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.

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:

http://lesswrong.com/lw/pc/quantum_explanations/.

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!

http://ilab.usc.edu/surprise/

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

Seriously?

Seriously?

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

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 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.

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.

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 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 is the first Less Wrong post which I have read and really deeply agreed with. I haven't done much teaching, but I am used to teaching those who I am on equal footing with, my fellow students. Teaching people who don't have background knowledge, who might not feel comfortable saying 'I don't understand' is really hard.

From my inept experience learning to dance I can say it makes it much easier when the teacher recognises that it is hard for you, although easy for them. That little piece of recognition, even without the ability to modify your teaching style, makes learning easier.

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.

This is one of the reasons why I think AI algorithm development is going to appear to go nowhere until it is nearly done, and then change more in a matter of months than it has in decades before. Nobody really has a clue how to teach the English language, or how to walk, or how to create goals. Once we can get the problems humans are naturally good at solving with very little help out of the way, programming an AI to understand the scientific method, existential risks, and how to overcome its own biases is most likely going to seem easy in comparison.

The way I learned to swim was pretty interesting, I remember the moment pretty clearly because of the absolute shock of fear at the time -- but it was a rather interesting method. I don't remember if the teacher tried to teach me in the same failed way you're talking about here to being with -- but whether she did, or didn't, I couldn't swim. I was pretty young at the time, so the surrounding memories are a little hazy -- though the moment itself is quite clear.

So since I couldn't swim, and couldn't figure out how from explanations, the teacher had me pushing off from the wall and grabbing onto this floating barbell thingy -- no swimming involved, except for bringing it back to the wall, which I could do because I had something keeping me from going under. I'd then push it away from the wall, push off the wall and grab it, and do it again. The teacher had to fetch it a few times, because it got too far away for me to get to in one push.

Then one day (I don't remember how long I did the push-off-the-wall thing) I was proceeding as normal, and the teacher came along to watch. And I pushed off the wall again, as hard as I could, to grab the floating thing -- and she grabbed it and pulled it back. And with what I realize now was probably a shock of adrenaline, I swam towards it. And she swam backwards with it, and I kept swimming towards it. It was a horrid doggy paddle, of course, but I was swimming.

I don't think this is an effective method for most things, and it might not work for some people, but it certainly worked for me, in that situation. Problem is, I can't think of many other situations where it would be effective -- bike riding is the only other skill I can think of where this method might work. Can anyone think of anything else?

This looks to me very like Moravec's paradox.

I agree completely that naturals have a hard time being teachers. At least to anyone who isn't a natural.

I started practicing karate at 24, I also have cerebral palsy that effects my right side, and I never seriously perused any sports in my education. So as a white belt even moving around for an hour of class was hard. making my hands do what was asked of them was very hard.

One of my teachers was a natural, had spent so many years training that anything looked effortless. He would show you how to do something once, and fast. then would move onto variations on that because he was bored with teaching "the basics"

Then there was another instructor, overweight and just about to be 40. He had to think about where he was, what he was doing. And had also spent much of his young life as an officer on a frigate. He could teach you a Kata in an hour and make it stick.. He was methodical, he knew to describe all the problems you would have if you weren't a natural.

I'm sure naturals thought he was slow.

I appreciate what the first instructor can offer six years later. When the basics come easy to me. But he still inspires more than teaches.

So it has definitely been my experience that people who have had to work through something hard find it easier to teach people who find it hard. That they are naturals at teaching people who aren't naturals.

I also have experiences with this kind of thing. In my spare time, I'm training kids at my local chess club. Showing them how a knight moves, what a fork is or why pinning a piece to the king is so strong, I realize to mainly use explanations that also helped me learing this when I was younger. Indeed, I notice how only few immediately understand it, so I try giving other explanations and that does indeed work.

It's surely some sort of projection bias as we assume the students' minds are similar to ours, but what makes this special is that you are in a position of power, and the student is not. So this might indeed lead into students repeating the teacher's buzzword without knowing the meaning behind it, even in something with as few buzzwords as chess.

Total Immersion was invented by a man who was an average swimmer until he became a swimming teacher, and had a better chance to study the aesthetic difference between excellent and average swimmers. This eventually led to exploring the physics of how to swim efficiently, which is important because minimizing drag is so crucial.

People call me an excellent teacher, and I've probably spent more time figuring out why people think I'm an excellent teacher than I have getting better at teaching. Some techniques I find universally applicable:

1. Teach yourself. Imagine yourself knowing everything you now know minus the thing that needs to be taught and everything that requires that knowledge as a prerequisite. Now picture trying to teach yourself. Humans are terrible at remembering when they learned something, how long it took them, what it felt like and where they had problems, etc. By starting with the idea of how you would teach yourself, you're focusing on what you would absolutely NEED to tell ANYONE regardless of their prior knowledge or understanding; these are good things to focus on. Just as importantly, you also prime your brain to think about the subject on a less automatic level.

2. Metaphors are absolutely critical. Everyday human experience seems to very far more within people's minds than it does on the outside. Give concrete examples from the physical world as metaphors: the internet is not a big truck, it's a series of tubes! It might be funny, but it made at least as much sense as anything else in the speech.

3. Talk a LOT. Throw out a lot of information and your student will tend to latch onto the one thing that they were missing and ask about it, leading to a breakthrough. When you make an important point, repeat it a second or third time in different ways, then explicitly point it out later during examples. When the student is actually attempting something that requires a great deal on concentration, be absolutely silent unless they need a nudge; otherwise, avoid ever letting the room be silent for more than five seconds. This doesn't mean rush through your explanations, it means belabor the point and add more metaphors if possible. It also means build a habit in your student of talking about his thought process so you can gauge what to say next and when it's appropriate to move on.

4. Prime the mind to recognize. Try to employ a fixed set of terms, even if you have to make it up on the spot, so that you can immediately point it out later and the student will know what you're trying to point out. If you sum up a conceptual explanation by calling it "ordered complexity", you can then point it out later, "see, that's what I meant by ordered complexity!" This will pull the entire explanation into their thought process the moment that it's needed.

5. If all else fails, give up and go back to basics. If it seems like you're not making progress for a while - if they simply don't "get it" - you've usually incorrectly assumed that the student has a prerequisite level of skill or knowledge. Stop immediately and trace back to prerequisites that are most likely to not be met, do some trouble-shooting to find the biggest culprit, and start a new lesson in the trouble spot. Resist the urge to do a quick-fix bare-bones lesson to get them up to speed so you can return to the original lesson; you must endeavor to genuinely teach them the more basic knowledge/skill, or you will just waste your time later.

This post is very reminiscent of the book Mastery by George Leonard. He writes about the need to practice seemingly simple skills until they become natural. I got a lot out of the book; there were many sections on dealing with plateaus.

I love his breakdown of learning and teaching styles.

What I got out of the book was a realization that a good teacher will focus on the fundamentals, and will set realistic expectations.

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.*

Actually, this "technique" is rather useful for training muscle memory. For example, it's how I learn to play songs on the piano: I keep doing it wrong until I can do it right.