Over the past several years, I've spent Tuesdays during the school year helping high school students with math, science, and other subjects. The kids often struggle with multi-level problems, where you need to stop in the middle and solve one piece of the puzzle before stepping back to solve the complete problem. Students are frequently also blocked by the language used in the problem statement; the wording may be too vague for them to know what is wanted, or the problem might use words in a specialized way that the students don't recognize.

If any obstruction of this sort appears, the students tend to wallow in confusion, often spending 15 or 20 minutes failing to understand an exercise which was intended to take 1 or 2 minutes.

Yesterday, I went to a friend's house where I had the opportunity to work with his sons. Unlike my Tuesday students, these 2 are college students with solid grades, studying chemistry, physics, and calculus. They are fun to work with because the subjects are fun and because the boys recognize when and how they are stuck, asking questions which are pertinent and even insightful.

Interestingly, these college boys would get stuck on multi-level problems, finding it hard to keep both the main problem and the lemma available to themselves clearly enough to solve both. They also found difficulties with the language of the assigned problems, such that it was hard for them to be confident about what they were asked to do. When issues like these came up last night, I found that the college boys tended to wallow in their confusion, sometimes spending 15 or 20 minutes trying to understand an exercise which was meant to be solved in less than 5.

The lesson is that the poor study behaviors I have observed among the strugglying high school freshmen are not due to immaturity or lack of experience or some sort of genetic or environmental impediment. These bahaviors are precisely mirrored by the older boys taking college courses.

In fact, I recognized in the college students behaviors which I find also in myself. What is more, I left feeling frustrated that I didn't seem to understand the subject matter well enough to be sufficiently confident in my explanations.

In **actual reality** the problems must be intrinsic to our common human
condition. If this is so, the difficulties should not be attributed to
the students but rather to the presentation of the material. Learning
is properaly a challenge, but ought not to be a looming abyss. How can
we play this game so as to maximize the understanding and minimize the
obstacles? Clearly we have yet to reach an optimum.