Here is another installment in my series reviewing the NY State Regents exams in mathematics.
One significant and negative consequence that standardized exams have on mathematics instruction is an over-emphasis on secondary, tertiary, or in some cases, irrelevant knowledge. Here are some examples from the January 2013 Regents exams.
First, these two problems, number 10 from the Algebra 2 / Trig exam, and number 4 from the Geometry exam, emphasize notation and nomenclature over actual mathematical content knowledge
Rather than ask the student to solve a problem, the questions here ask the student to correctly name a tool that might be used in solving the problem. It’s good to know the names of things, but that’s considerably less important than knowing how to use those things to solve problems.
The discriminant is a popular topic on the Algebra 2 / Trig exam: here’s number 23 from January 2013:
It’s good for students to understand the discriminant, but the discriminant per se is not really that important. What’s important is determining the nature of the roots of quadratic functions.
If you give the student an actual quadratic function, there are at least three different ways they could determine the nature of the roots. But if you give them only the discriminant, they must remember exactly what the discriminant is and exactly what the rule says. This forces students and teachers to think narrowly about mathematical problem solving.
In number 3 on the Algebra 2 / Trig exam, we see a common practice of testing superficial knowledge instead of real mathematical knowledge.
Ostensibly, this is a question about statistics and regression. But a student here doesn’t have to know anything about what a regression line is, or what a correlation coefficient means; all the student has to know is “sign of the correlation coefficient is the sign of the coefficient of x”. These kinds of questions don’t promote real mathematical learning; in fact, they reinforce a test-prep mentality in mathematics.
And lastly, it never ceases to amaze me how often we test students on their ability to convert angle measures to the archaic system of minutes and seconds. Here’s number 35 from the Algebra 2 / Trig exam.
A student could correctly convert radians to degrees, express in appropriate decimal form, and only get one out of two points for this problem. Is minute-second notation really worth testing, or knowing?