I’m not saying we shouldn't have high hopes and standards for our children. But by focusing our attention on the kids who get the top SAT scores, we reinforce the fixation on genius to the detriment of everyone else
No amount of idealism will change the fact that mathematicians , with virtual certainty, tend to score very high on such tests. To find the next generation of mathematician, look to kids who are getting ceiling scores on the math part of the SAT at the age of 13. Sometimes 'late boomers' exist, but still they exhibit preciosity at youth and then later decide to turn to mathematics and learn the material very quickly due to having a high iq. If genius is defined by having a high IQ (which according to the Stanford Binet Intelligence scale it is) and standardized test scores, virtually all mathematicians are geniuses, regardless of how much recognition they later get in their careers.