<p>Some observations:</p>
<p>I went to a talk in a computer conference. The speaker has done important work and had been chief scientist in several major tech companies. He lamented that many software engineers with advanced degree are weak in high school Algebra and Geometry.</p>
<p>I had a son with LD, he spent most of his earlier years in special ed classes. So his math skill is not very strong. While he is in regular math classes in the past few years, he never takes accelerated or honor classes. His scores in the state tests are always “advanced”, so we know it is not difficult to score “advanced”. In his school, it is the norm to accelerate in math and take honor classes. Yet when we look at the state test scores of the accelerated students, only about half can score “advanced”.</p>
<p>Clearly only those think they are good at math would take the AMC tests. If we look at the AMC12 results, clearly those who can score high are really good, however if we look at the average score it is not that impressive. To get the average score, you only need to pick 7 problems out of the 25 and solve them correctly. Consider that the first 10 problems are relatively easy, in fact 5 of them are the same as the easier AMC10, we expect a higher average score. AMC problems are mostly Algebra and Geometry, maybe a few Trig but never a calculus problem. So even our better math students are not as good in Algebra and Geometry as they think.</p>
<p>The above link is about a geometry problem from Chinese university entrance exam. There are only a few posting in cc discussing it. Inverse, in his posting, points out that most engineering students in his university do not know how to draw a circle passing through three points, a really simple Geometry problem. There are a lot more discussion in other forums outside cc on the BBC article, and it is clear that most do not know how to do the Chinese test problem, at least not with a Geometry solution. BTW, the solution of the winner of the Royal Society of Chemistry contest is in <a href="http://www.rsc.org/images/Mathematicssolution_tcm18-86553.pdf%5B/url%5D">http://www.rsc.org/images/Mathematicssolution_tcm18-86553.pdf</a>.</p>
<p>So what am I trying to say? There certainly are some very good high school students who can benefited from an real AP or other university level courses. However for most of the others taking AP classes, I think they would benefit more if they can take an honor class that really goes into depth into high school subjects such as Algebra and Geometry. Unfortunately such classes are almost non-existent. If universities would refuse to consider AP classes instead of encouraging it in the admission process, maybe the high schools would be more willing to provide courses that would provide the solid foundation.</p>