My son, a sophomore in high school, had several tests yesterday and today. Yesterday morning was the CAlifornia High School Exit Examination (CAHSEE) English test, yesterday afternoon was the AMC-10 math contest, and this morning was the CAHSEE math test. The CAHSEE tests were predictably easy (though we had not realized that there was an essay component on the English test—that must be expensive to grade).
The contrast between the AMC-10 and the CAHSEE math tests is pointed. Both supposedly cover math through algebra 1 and geometry, and both are multiple-choice, but the level of difficulty of the questions is quite different. The CAHSEE test is at the level of entrance to high school, not exit—everything on it should have been covered in middle school (still, about 18% of California sophomores fail the CAHSEE math). The AMC-10 test is tough, though some of the toughness is just time pressure. Neither my son nor I were able to finish the AMC-10 test in 75 minutes. I took it just for fun—I’d paid for the school to get the tests, and no other kids from the school were taking it, so I figured that doing it at the same time as my son was my privilege. I did not, of course, submit my answers to the contest, as I am not eligible, either by grade level or age.
In our defense, both my son and I had bad colds, but even if we’d been in perfect health we probably would have only gotten one more question finished. To do well at the AMC-10 requires practice, and neither of us have been practicing contest math. I probably could have done better 40 years ago, when I spent a lot of my time doing math for fun, but I’ve done only sporadic bits of math since then, and mostly not contest math. Even 2 years ago, when I was coaching a middle-school math team I did better —I got about 120 points then out of 150, and only 102 yesterday—my son beat me with 108 points. I knew that one day he’d be beating me on math, but I thought I had another couple of years. [Correction: I forgot to add the points for unanswered questions: his score was 118.5 and mine was 114.]
One question comes up now: do we want to spend some time doing contest math prep next year for the AMC-12 or are there better things to spend our time and energy on? I have mixed feelings—it might be fun, but it might not be all that valuable. Contest math prep is mainly recreational math with fun little problems of no particular utility. It would be fun to do such puzzles as mental exercises, but there would be more benefit in the long run to spending the time doing physics and calculus or computer science and combinatorics or machine-learning and Bayesian statistics. I’m afraid that over the past 45 years I’ve switched my mindset from that of a pure mathematician to that of an engineer. I still like math, but I like it more when it is useful. Doing very well on the AMC tests (better than we did this year) could get him invitations to study math with other mathy high-schoolers and take the AIME, but it is not clear that is such a big win for him. He likes math, but is not driven to do it all the time, which is what it would take to reach the top levels of math competition.
If we could get a group of kids to do contest prep together, it might be a fun social event, but I have a feeling that having just my son and I doing it would get boring for him after just a couple of sessions. I won’t have sabbatical next year—in fact, I’ll have a higher than usual teaching load—so scheduling such a group will be a bit more difficult than it would have been this year.