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/