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## 2005 SAT Scores

In case you have not heard the news, the 2005 SAT scores are the highest ever, increasing to 520 from 518 in 2004 and 14 points higher than ten years ago.

Other good news: Since 1995, there has been an 11% increase in precalculus enrollments (from 37% to 48%) and a 5% increase in calculus enrollments (from 22% to 27%).

The above facts are taken from a report of the news in NCTM's News Bulletin (November 2005). But, this report raises some questions on my part relative to how the news was reported...and then I get lost in exploring these questions...

First, what happened in 1995 to lead to such a dip in scores? On investigating this, I become more puzzled and find some interesting data that should be shared with students as a good line-fitting problem:
Year Score
1967516
1968516
1969517
1970512
1971513
1972509
1973506
1974505
1975498
1976497
1977496
1978494
1979493
1980492
1981492
1982493
1983494
1984497
1985500
1986500
1987501
1988501
1989502
1990501
1991500
1992501
1993503
1994504
1995506
1996508
1997511
1998512
1999511
2000514
2001514
2002516
2003519
2004518
2005520
Reflecting on this data set, one begins to wonder what happened in the early 1980's. Given the progression of scores, one concludes (?) that the NCTM Professional Standards and reform curricula are having a positive effect.

My other quandry is what the phrase "11% increase in precalculus enrollments (from 37% to 48%)" means. For example, if X is the # elegible students in 1995, then 0.37X is the # students in precalculus, and to my mathematical leanings, a 11% increase implies that now there should be 1.11(0.37X) or 0.4107X students in precalculus courses. But then, suppose Y is the number of elgible students in 2005. So, we need 0.4107X = 0.48Y, which implies that Y = 0.855625X or that the total population of elgible students is decreasing. This cannot be...yet it also cannot be that you associate a "11% increase" with the addition of two percentages: 37% + 11%, since their bases are not the same. Ugh! whose fault is this........