Teaching

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

This is question 25 from the Common Core Algebra exam.

I’ve already complained about the contrived, artificial contexts for these questions (why not just ask “Is the sum of these two numbers rational or irrational?”), so I’ll ignore that for now.  What’s worth discussing here is the following sample student response provided by the state.

So, why is the sum of a rational number and an irrational number irrational?  Because the sum of a rational number and an irrational number is always irrational.  This circular argument is offered as an example of a complete and correct response.

I’m not sure there’s a way to rewrite this question so that it admits a sensible answer.  That’s probably a good indication that it shouldn’t be on a high-stakes test.

As I’ve argued time and again, questions on these exams should stand as examples of proper mathematics.  But questions like this actually encourage bad habits in students, and teachers too, who are being told that this constitutes an appropriate response to this question.  This is yet another example of the danger of simply tacking on “Justify your reasoning” to a high-stakes exam question.

Related Posts

• Regents Recaps
• Regents Recap — June 2016: What Do They Want to Hear?
• Regents Recap — August 2015: Modeling Data
• 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 8 from the Integrated Algebra exam.

“Four students are playing a math game at home.  One of the math game questions asked them to write an algebraic equation.“

The context of this question is utterly absurd  The question might as well have been

“Four students are taking a math test.  One of the questions asked them to write an algebraic equation.  Which student answered the test question correctly?”

Why not just ask “Which of the following is an example of an algebraic equation?”.  Maybe there are people who believe that framing questions as games, or humanizing them, will engage test-takers more, but it’s hard to believe that contrivances like this do anything but further separate students from the concepts they purport to assess.  This is another example of the negative impact these poorly-designed tests can have on students, which I discuss at length in my talk “g=4, and Other Lies the Test Told Me“.

Math teachers are familiar with the notion of pseudo-context, but I’m not sure what I would call this.  Meta-pseudo-context?  Pseudo-meta-context?  Pseudo-pseudo-context?  Ridiculous, at the very least.

Related Posts

• Regents Recaps
• g = 4, and Other Lies the Test Told Me
• Regents Recap — January 2016: No It Wasn’t