kitchen table math, the sequel: 2/19/12 - 2/26/12

Thursday, February 23, 2012

I'm confused

What Do the NAEP Tests Really Measure?by David Klein | January 2011
The 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.

can elite students do arithmetic?

Looks like the answer is no. (pdf file)

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.

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?
For passers-by, here's a quick run-down of Wilson's original observations:
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"

Tuesday, February 21, 2012

Mooping the lady (& children with ADHD)

Two-year olds can tell the difference between "the lady mooped my brother" and "the lady and my brother mooped!" (pdf file)

I love that.

Meanwhile, people with Parkinson's can have trouble understanding sentences like:
"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.

I'm intrigued by the Parkinson's research because Parkinson's and ADHD both involve dopamine deficits and problems in "set-shifting"— and impaired set-shifting appears to be the stumbling block for Parkinson's patients reading about the king and the cook. All of a sudden, mid-sentence, they have to shift off their expectation that what they are reading is a standard Subject-Verb-Object affair. That's where they stumble.

Do kids with ADHD also have trouble reading such sentences?

I wonder.

I gave Arthur Whimbey's zoonoses test to my class two weeks ago. Around 40% of my students got the answer wrong, which is what I've seen in my other classes.

Assuming I'm reading (make that skimming) the Parkinson's article right, the answer for ADHD kids having trouble with center-embedded relative clauses would presumably be to give them lots of practice reading sentences with center-embedded relative clauses.

On the other hand, I can also imagine practice with center-embedded relative clauses making it more difficult for kids with ADHD to read any sentence....?

Is there research on this?

Lingua Links: What is a relative clause?

Monday, February 20, 2012

to do

So I was thinking of actually writing a post, or possibly reading a post (I'm behind)...when I decided I would check my course enrollment first, to see whether the two absent students are absent or no longer enrolled. The other students were bugging me about it on Wednesday, so I figured I'd get that taken care of.

But no. Turns out I can't check class enrollment because my user name and password no longer match. I don't know why.

I was semi-taking that news in stride (I say "semi" because last semester's brush with IT took two days to resolve) when I opened up my scanned copy of the sheaf of papers that came with my contract and discovered that - lo! - I have to re-take my college's online Sexual Harassment Training Unit and send a paper copy of the training certificate to Human Resources. Which I can't very well do if I can't log on, now, can I?

Moving right along....I see my college has undergone significant planning for responses to potential health or other emergencies to guarantee continuity of instruction, resulting in adoption of a new 16- or 17-step process for temporarily suspending a scheduled in-class meeting. Well, OK, the instructions don't actually say 16 or 17 steps; the instructions say 2 steps. We have a new 2-step process. But the 2 steps come with a whole lot of sub-steps, bullet points (2 kinds of bullet points: solid and hollow), add-ons, and admonitions, and the time it's going to take me to talk to the IT person, fail to fix my user name and password, talk to the IT person's supervisor plus take the Sexual Harassment Training Unit (at least an hour last year, as I recall), and master the intricacies of canceling class should the need arise is starting to make me feel a tad...pressed.

Back soon!

The achievement gap: how our schools are working hard to make it go away

If you're concerned about achievement gaps of the sort recently reported on by the Times, you could either (re)instate rigorous, structured, direct instruction in line with the latest findings in cognitive science research, teaching each child in his or her Zone of Proximal Development, i.e., at his or her instructional level, with proper scaffolding, and furnishing each classroom with teachers who've mastered both their content areas and these best practices. Or you could:

I. Eliminate the ability of academically advanced students to get ahead in the classroom by:
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.

II. Reduce the ability of students to get ahead on their own time by:
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.

III. Reduce the ability of grades to reflect achievement differences via"grade compression" and inflexible "rubrics" that:
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

IV. Reduce the ability of NCLB tests to reflect achievement differences, via:
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)

V. Lobby colleges to pay less attention to high-ceiling standardized tests like the SATs and the Achievement Tests, and more attention to grades and "leadership" activities.

But then the next question becomes how to eliminate the growing achievement gap between U.S. students and those from other developed countries.

(Cross-posted at Out In Left Field)