Through 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?
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.
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.
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?
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:
Compare the above problem with number 39 from the June 2012 Geometry exam:
These 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.
Here, 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?
Through 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 — February 27, 2013
This question pertains to the gambling addiction of the former mayor of San Diego, who reportedly wagered over a billion dollars in casinos over the past ten years. On average, how much did she lose a day?
