They have a couple interesting results. One is that "changes in scores depend strongly, reproducibly, and with high statistical significance, upon poverty level even after controlling for previous achievements of students." So, even kids who are good at math at an early age tend to have their scores drop if they belong to poor families.
The other result I found interesting was this visualization showing that the "flow" is consistent from year to year, but that the biggest dropoff occurs in the sixth and seventh grades:
The size of the arrow is the number of students with that score, the direction indicates the average next score of students starting with a particular score. The yellow region is passing. The authors suggest that if it were possible to increase scores in sixth and seventh grades, then it could have a nonlinear effect on final scores, given that there is little change from year to year thereafter.
Unfortunately, they do not really speculate on what might cause this drop--- a change in curriculum? The shift from elementary to middle school? A difference in how the test is written?