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!
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 mor...
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.