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 linefitting problem:
Year 
Score 
1967  516 
1968  516 
1969  517 
1970  512 
1971  513 
1972  509 
1973  506 
1974  505 
1975  498 
1976  497 
1977  496 
1978  494 
1979  493 
1980  492 
1981  492 
1982  493 
1983  494 
1984  497 
1985  500 
1986  500 
1987  501 
1988  501 
1989  502 
1990  501 
1991  500 
1992  501 
1993  503 
1994  504 
1995  506 
1996  508 
1997  511 
1998  512 
1999  511 
2000  514 
2001  514 
2002  516 
2003  519 
2004  518 
2005  520 
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........
