You may find the book "Developing Math Talent" useful. The authors (Assouline & Lupkowski-Shoplik) describe an approach called Diagnostic Testing-Prescriptive Instruction. The first step is to determine aptitude with an above level test. If the child scores >50th percentile you analyze the missed items and the student studies the topics not yet learned. This is followed by post-testing and if the student scores >85 percentile you go to the next level.
I think this approach makes sense for topics outside of math as well. You may be able to get an idea of aptitude using the Stanford Workbook with practice tests if the school won't help.
