For anyone who comes across this thread in the future, I just want to leave feedback about what the outcome was. Son did not get any professional tutoring. He realized that the issue with the Science section was that he needed to gain more familiarity with the way in which the material was being presented (reading different graphs and charts). Taking practice tests was enough to fix that. For the Math, he said that there was material that he remembered having learned, but had not seen in years. Also, there was some Statistics that he’d never learned.
We bought the two volumes of The Best ACT Math Books Ever. He looked at the 4 practice tests he’d already done, compiled a list of the subject matter for the math questions he’d gotten wrong, and did those sections of the math books. Then he took more practice tests (officially released ones that we found online, that are legally in the public domain). He focused mostly on doing the Science sections, and the Math sections. If he got a math question wrong, he re-studied the material. Eventually, he found that the only math questions he was getting wrong weren’t even in the math books - he was having to google to find out how to do them. He also found that he was under tremendous time pressure for the math, that he had to develop techniques to get through the math section. The last ten problems were always very hard, with not enough time left.
He wound up probably having done maybe 6 complete ACT tests, and maybe 4 more just Math sections. Overall, I would say that he probably spent a total of 50 hours on test prep, usually about two hours/day, on and off through the summer, but mostly the last couple of weeks of August and first week of September. Then school started, and he didn’t have any time to do any more test prep the last week before the test.
He wound up getting a 36 overall, with 36 in everything except math, in which he got a 34. I would say that his performance on the released ACT tests that were in the public domain very closely predicted his actual test scores. I think that his original practice test was maybe a 33 or 34 overall, with some weakness in Science and Math. I think that the test prep that he did really helped with the Science, and helped some with the Math (brought it up from 32 on first practice test, to pretty consistently getting 33-35 on practice tests, and a 34 on the real thing). I think that he might have benefited from professional help with the Math, because he clearly just hadn’t figured out how to move quickly enough through it, while maintaining accuracy (I guess) or maybe there were tricks that he just never learned. But he surely had given himself a very comprehensive review of high school math by the time the test rolled around!
Looking back, I think that the advice we got was on target. He didn’t need a comprehensive prep program, but we should have gotten him some help from a tutor for the math section. I think he hit the point of diminishing returns working on his own. I was a little surprised that all the hours of math prep that he did only brought him up 2 points. But math has always been his weakest subject, so I guess I shouldn’t be surprised. And of course, overall, we are very please with his score. It should definitely help him in his applications, certainly won’t hurt him.