What Do the NAEP Tests Really Measure?by David Klein | January 2011The answer is green, right?
Or is there some aspect of this item I don't understand?
Maybe there's a right triangle hiding in there somewhere. Speaking as a veteran of SAT prep.
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
"The king that is pulled by the cook is short." (pdf file)The words "That is pulled by the cook" are a "center-embedded" relative clause.
1. implementing low level, one-size-fits-all instruction (for which there's no better model than Investigations math)
2. eliminating grade acceleration and individualized instruction
3. eliminating gifted programming or making it about time-consuming projects that supplement existing assignments rather about academic challenges that replace these assignments.
1. assigning tons of homework of the low-ratio-of-learning-to-effort variety
2. including massive summer projects and one-size-fits all reading lists.
1. employ subjective grading standards (elevating "creativity" and "engagement" over correct answers, clarity, articulateness, and solid analysis)
2. take points off for unexplained answers, however correct
3. give partial credit for "explained" incorrect answers
4. keep the purely academic demands/expectations of assessments and assignments as low as possible
4. minimize the opportunity for students to demonstrate work that exceeds those demands/expectations
5. even if students find a way to demonstrably exceed expectations or go above and beyond academically, don't give them any extra points for it
6. deploy "wild card" variables that partially randomize who gets what grade (e.g., trick questions; unclear directions; trivial requirements like including today's date on the title page of your report or using the word "I" in your science project abstract; rather than collecting homework, leaving it up to the students to turn it in and giving out zeroes for things not turned in on time)
7. assign heterogeneous-ability group projects and give everyone in the group the same grade
1. low academic ceilings
2. partial credit for explained incorrect answers; points off for unexplained correct answers (as above)
3. wild card variables (as above)