MrHonner

Regents Recap — January 2013: Recycled Problems

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

I reuse problems on tests all the time.  I’m sure every teacher does.  Sometimes I’ll change a number or two, sometimes I’ll change what the question asks for, or sometimes I’ll use the problem just as it is.

But I’m not writing tests for thousands of students state-wide, and my tests don’t determine whether or not students graduate, teachers keep their jobs, or schools remain open.

So it seems reasonable to ask if reusing problems on high-stakes exams, like the Regents, is an appropriate practice.

Compare number 38 from the January 2013 Algebra 2 / Trig exam

Regents 2013 January AT 38

with number 27 from the 2005 Math B exam.

Regents 2013 January Math B 27And one more important difference between my tests and these standardized tests:  I don’t pay millions of dollars to educational specialists to develop my exams.

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By MrHonner, ago

Math Quiz — NYT Learning Network

cooper unionThrough Math for America, I am part of an ongoing collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

Test Yourself Math — March 6, 2013

This question is about how the Cooper Union is contemplating an end top its longstanding no-tuition policy, due in part to a current $12 million operating loss.  How much would Cooper Union have to charge in tuition to cover that loss?

By MrHonner, ago

Regents Recap — January 2013: Question Design

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

One consequence of scrutinizing standardized tests is a heightened sense of the role question design plays in constructing assessments.

Consider number 14 from the Integrated Algebra exam.

Regents 2013 January IA 14

In order to correctly answer this question, the student has to do two things:  they need to locate the vertex of a parabola; and they need to correctly name a quadrant.

Suppose a student gets this question wrong.  Is it because they couldn’t find the vertex of a parabola, or because they couldn’t correctly name the quadrant?  We don’t know.

Similarly, consider number 21  from the Geometry exam.

Regents 2013 January G 21

This is a textbook geometry problem, and there’s nothing inherently wrong with it.  But if a student gets it wrong, we don’t know if they got it wrong because they didn’t understand the geometry of the situation, or because they couldn’t execute the necessary algebra.

Using student data to inform instruction is a big deal nowadays, and collecting student data is one of the justifications for the increasing emphasis on standardized exams.  But is the data we’re collecting meaningful?

If a student gets the wrong answer, all we know is that they got the wrong answer.  We don’t know why; we don’t know what misconceptions need to be corrected.  In order to find out, we need to look at student work and intervene based on what we see.

And what if a student gets the right answer?  Well, there is a non-zero chance they got it by guessing.  In fact, on average, one out of four students who has no idea what the answer is will correctly guess the right answer.  So a right answer doesn’t reliably mean that the student knows how to solve this problem, anyway.

So what then, exactly, is the purpose of these multiple choice questions?

By MrHonner, ago

Regents Recap — January 2013: Where Does This Topic Belong?

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

There seems to be some confusion among the Regents exam writers about when students are supposed to learn about lines and parabolas.  Consider number 39 from the January 2013 Integrated Algebra exam:

regents january 2013 ia 39

Compare the above problem with number 39 from the June 2012 Geometry exam:

regents june 2012 g 38These questions are essentially equivalent.  They both require solving a system of equations involving a linear function and a quadratic function by graphing.  Yet, they appear in the terminal exams of two different courses, that are supposed to assess two different years of learning.

When, exactly, is the student expected to learn how to do this?  If the answer is “In the Geometry course”,  the Algebra teacher can hardly be held accountable if the student doesn’t know how to solve this problem.  And if the answer is “In the Integrated Algebra course”, what does it mean if the student gets the problem wrong on the Geometry exam?  Is that the fault of the Geometry teacher or the Algebra teacher?  The duplication of this topic raises questions about the validity of using these tests to evaluate teachers.

And if that isn’t confusing enough, check out this problem from the 2011 Algebra 2 / Trig exam.

regents june 2011 at 39Here, we see the same essential question, except now the student is required to solve this system algebraically.  These three exams–Integrated Algebra, Geometry, Algebra 2/Trig–span at least three years of high school mathematics.  In the integrated Algebra course, a student is expected to solve this problem by graphing.  Then, 2 to 3 years later, a student is expected to be able to solve the same kind of problem algebraically.

What does that say about these tests as measures of student growth?

By MrHonner, ago
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