Regents Recap — August 2015: Modeling Data
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
Data and statistics play a much bigger role in algebra courses now, due in part to their increased emphasis in the Common Core standards. I am generally supportive of this, but I do worry about how statistical concepts are presented and assessed in these courses and on their exams.
For example, here is question 27 from the August, 2015 Common Core Algebra exam.
Evaluating mathematical models is an extremely important skill in many aspects of life. But properly evaluating mathematical models is subtle and complex.
The following sample response, provided by New York state as an example of an answer deserving of full credit, does not respect that complexity. And it makes me worry about what we are teaching our students about this important topic.
It’s true that the given data does not grow at a constant rate. But that isn’t a good reason to reject a linear model for this set of data. Models are used to approximate data, not represent them perfectly. It would be unusual if a linear model fit a real set of data perfectly.
The weakness of this argument becomes even more apparent when we notice that the data isn’t perfectly fit by an exponential model, either. Therefore, how could it be wrong for a student to say “We should use a linear model, because the data doesn’t grow at a linear rate and thus isn’t exponential”?
This is another example of the problems we are seeing with how statistics concepts are being handled on these high stakes exams, which is a consequence of both the rushed implementation of new standards and an ever-increasing emphasis on high-stakes testing in education. It is also an example of how high-stakes tests often encourage terrible mathematical habits in students, something I address in my talk “g = 4, and Other Lies the Test Told Me“.