Unwrapping NYSED Regression – looking at a lesson

I discussed earlier a planned neat regression lesson. (Read about it here). Tuesday I ran it, and the results are worth sharing.

I asked kids to pair up with someone they don’t normally work with. I distributed conversion charts for a mix of science and math exams from the last 2 years: Algebra, Geometry, B, Living Environment, Chemistry, and Physics.  I asked each pair to graph scaled score vs raw score.

It was interesting. The kids plotted the points ok, but they worked far more slowly than I would have expected. I suspect that they rarely create graphs by hand. No one actually needed help with appropriate scale, only one pair in either class mixed up the independent and dependent axes, but they were fairly slow.

As they finished plotting, I took away their charts. (asking them first to note (0,0), (p,65), (m,85) and (t,100)). And we discussed the shapes of their graphs. I informed them that a regression had been performed to create the charts. Linear regression was quickly eliminated. But after that, they were stuck a bit. I asked what other sort of regression would not make sense. In both classes, exponential immediately was dismissed. Kids focused on quadratic, cubic, or power regression.

I should note, the actual curves are interesting. They are cubics. (And regression would actually be silly, since they can just fit the curves exactly to the four points.) But the inflection point is quite visible on those with low cut scores – algebra, living environment – and not at all on those with higher cuts – B, physics.  I think Chemistry does not have a visible point, but Geometry does – towards the right of the scale.

Kids chose regressions to try out – their choices were quadratic, cubic, or power (which of course failed). In each class at least one pair modified the (0,0) off the origin and proceeded to test the power regression… but cubic and quadratic drew the most interest. I asked them to visually inspect the results. It was actually an interesting point – I suggested that they set the window to match their plots – only a few considered that on their own.

After each pair had a graph that looked reasonably like their original plot, I asked them to newly create a conversion table (set ∂ Table at 1, start at 0, round to the nearest whole number). And it was neat. Their numbers either exactly matched the original, or were pretty close.

Defects

• Most cubic regressions were dead on, but in several cases kids had rounded coefficients enough to throw single points off by 1 credit.
• Most quadratic regressions were close, but no cigar. However, for B and Physics, many of the points were dead on, and the others were close. It was not obvious that the choice was not the right one.

Discussion after was on the flat parts of the graph… where adding a point to a 64 leaves you with 64… or where adding 9 points to an 80 brings you to 84… And on the arbitrary nature of the conversions aside from 65 and 85 and 100. Later that day kids came by to talk more about the conversion process, and a couple wanted to know if there was a good way to object.

(if you are interested in objecting, you should know that the guy in charge is named John Svendsen and his e-mail is jsvendse@mail.nysed.gov – note the missing ‘n’)

By the way, the State refuses, so far, to review the content of the new courses until 2012. I don’t know how they handle objections to the arbitrary curve-fitting for the conversion charts.