<p>Does your son not want to do the contests? Does he want to enter the contest, but peer pressure that is keeping him from doing them? Or does he kind of, sort of want to do them, but not put in any effort? </p>
<p>If the first, let him find activities that he enjoys. Students can be good at math, but not enjoy doing contests. If he doesn’t enjoy the contests, he won’t do well, anyway.</p>
<p>If the second, he may want to try USAMTS, which he can do at home without peer involvement. If USAMTS interests him, he may join other contests.</p>
<p>If the third, perhaps you could set aside one evening a week to have a mini-math competition with him at home. If he becomes more interested, he’ll work harder. If he doesn’t, you can assume he would prefer to do something other than math contests.</p>
<p>BTW, I don’t think that doing math contests will have a significant impact on SAT/ACT scores. For SATs/ACTs, a student needs to understand <em>basic</em> math (the math is not difficult) and to read with understanding. Half of SAT math is reading. For SATs, a student has to ask, “What is the question asking?” Often, all a question is asking is if the student knows the square of a negative is positive, that the angles in a triangle add to 180, or something equally fundamental. Math contest problems, on the other hand, require much more mathematical thinking. In math contests a student has to ask, “How can I find an elegant approach to solve this problem?” (Brute force won’t get students very far.)</p>