Statistics

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“.

Related Posts

• Regents Recaps
• Regents Recap — January 2015: It’s True Because It’s True
• Regents Recap — June 2016: What Do They Want to Hear?
• Regents Recap — June 2014: Common Core Algebra, “Explain your answer”

Here is another installment in my series reviewing the NY State Regents exams in mathematics.

This is question 14 from the Common Core Algebra exam.

Setting aside the excessive, and questionable, setup (do people really think about minimizing the interquartile range of daily temperatures when choosing vacation spots?), there is a serious issue with this question:  it has no correct answer.

The student is asked to identify the data set that satisfies the following two conditions:  median temperature over 80 and smallest interquartile range.  No data set satisfies both these conditions.  According to the diagram, the data associated with “Serene Shores” has the smallest interquartile range (represented by the width of the “box” in the box-and-whisker plot), but its median temperature (the vertical line segment in the box) is below 80.

The answer key says that (4) is the correct answer, but that data does not have the smallest interquartile range shown.  Presumably, the intent was for students to evaluate a conditional statement, like, “Among those that satisfy condition A, which satisfies condition B?”  But as written, the question asks, “which satisfies both condition A and condition B?”  No set of data satisfies both.

Some may consider this nitpicking, but precision in language is an important part of doing mathematics.  I focus on it in my classroom, and it is frustrating to see my work undermined by the very tests that are now being used to evaluate my job performance.

Moreover, this is by no means the only error present in these exams, nor is it the first example of errors in stating and evaluating compound sentences.  If these exams don’t model exemplary mathematical practice, their credibility in evaluating the mathematical practice of students and teachers must be questioned.