I’m fairly sure such a response would receive no credit. I invite you to take a look at the scoring guidelines to judge for yourself: http://www.nysedregents.org/algebraone/.

]]>Thanks for duplicating your response here, and for letting me know that your principal shared the piece. It’s great hearing that my work inspires conversations elsewhere!

Yes, the question clearly presents the student with an “either .. or” decision. However, as noted above, the argument provided in the sample response applies equally to *both* options, thus, it can not possibly be a valid argument in support of either. We should be not supporting, not encouraging, such unsound reasoning.

A deeper issue here is that students in this course actually have no mathematical tools available to make an informed judgment about which model is better. Correlation coefficients between different kinds of regressions are incomparable, so the one legitimate procedure students are taught to apply in this situation is of no help.

]]>I agree that NYS did not choose a convincing sample of a full-credit response. On one hand, it is easy to look at this sample response and critique that it rejects the linear model because of the non-constant rate of change rather than showing a student argue for the exponential model (or how the student doesn’t doesn’t elaborate on what he/she means by non-constant rate of change.) However, I think we should also look at the question. By narrowing it down to two choices for the student (linear or exponential), instead of asking a question that elicits student thinking about how they see the growth of this function, it petty much puts the student in a position where they can argue for one choice by dismissing the other.

]]>Of course the exponential model is better, but as you point out, the linear model is pretty good.

]]>The linear fit for all the data is R = .96

Knock off the first two, R=.977

This data also fits a quadratic model fairly closely. y=16.515x^2-26.758x+259.33, R=.999

It does give R=1 for an exponential though, 179.37*e^(x/4.4718). There’s a measure of rounding error in the value of R, of course, but “the data isn’t perfectly fit by an exponential model, either” isn’t accurate.

Having said that, I agree with your statement about the approximation usage of models but asking for “the better model” is an okay question since a cursory look sees that the data are increasing at an increasing rate. Their sample response is problematic, but not the question itself.

]]>