After a conversation with a "well respected mathematician who was heavily involved with K-12 mathematics education," W. Stephen Wilson re-analyzed the results of the arithmetic test he gave his Calculus III students at Johns Hopkins in 2007. The unnamed mathematician had told Wilson that fewer than 1% of college students would be unable to work a multiplication problem by hand, so Wilson took a look:
He was a little off on his estimate.For passers-by, here's a quick run-down of Wilson's original observations:
In the fall of 2007 I gave a 10 question arithmetic test to my 229 Calculus III (multi-variable calculus) students on the first day of class. Among other things, this means they already had credit for a full year of Calculus. The vast majority of these students were freshmen and ... and the average math SAT score was about 740.
Seven of [the problems involving multiplication] were each missed by 8% or more of my students and 69 students, or 30%, missed more than 1 problem.
These are high achieving, highly motivated students (remember the 740 average SAT math score). These are disturbing numbers for them, but I suspect the numbers are much much worse among college freshmen with an average math SAT of 582, and, from Table 145 of Digest of Education Statistics 2009 we see that the average SAT score for the intended college major of engineering is 582 in 2008-2009.
Anyway, there is no real purpose to this paper except as a resource for me. It does suggest, very strongly, to me, that we have lost the pro-arithmetic war. This is a revelation to me and it calls into question what I will do next year with my big service course. I now feel compelled to assume that [my students] are chronically accident prone or they really are arithmetically handicapped. It isn’t clear that there is a difference. The question remains, how can I teach serious college level mathematics to students who are ill-prepared?
As another experiment, Wilson gave a short test of basic math skills at the start of his Calculus III class in 2007. The results predicted how students later fared on the final exam. Those who could use pencil and paper to do basic multiplication and long division at the beginning of the semester scored better on the final Calc III material. His most startling finding was that 33 out of 236 advanced students didn’t even know how to begin a long division problem.
Back to Basics for the "Division Clueless"
DECEMBER 6, 2010 | BY LISA WATTS