# Are These Tests Any Good? Part 3

This is the third entry in a series examining the 2011 NY State Math Regents exams. The basic premise of the series is this: if the tests that students take are ill-conceived, poorly constructed, and erroneous, how can they be used to evaluate teacher and student performance?

In Part 1, I looked at several questions that demonstrated a significant lack of mathematical understanding on the part of the exam writers. In Part 2, I looked at several poorly constructed questions that were vague, incoherent, or tested irrelevant material. Here, in Part 3, I’ll look at a single question that highlights problems with the scope of the exams.

This is number 10 from the 2011 Algebra 2 / Trigonometry Regents exam: given the three sides of a triangle, find the measure of one of the angles.

There is nothing wrong with this question. It’s clear and unambiguous. It connects to a fundamental idea in trigonometry, that knowing three pieces of information is often enough to determine everything about that triangle. And the question is designed to test the student’s knowledge of a fundamental skill in trigonometry: applying the Law of Cosines.

The problem here is that this is only question on this exam related to these topics. This two-point, multiple choice question is the only place on this Trigonometry exam that requires the use of either the Law of Cosines or the Law of Sines.

Perhaps there is a useful discussion to be had about just how important the Laws of Sines and Cosines are. To me, mastery of these theorems is one of the clear end-goals of a trigonometry course. Trigonometry literally means “measure of triangles”, and these two theorems represent the culmination of our knowledge about measuring triangles. Therefore, they should be featured more prominently in a final assessment.

It’s reasonable to debate *just how* *prominently* they should be featured, but it’s hard to imagine any trigonometry teacher agreeing that, based on their relative importance, two points out of 88 is a reasonable representation.

Furthermore, a debate about the relative importance of these particular theorems becomes less meaningful when you realize what, instead, appears on this exam. A rough estimate suggests that 12-14 points on this test deal with quadratic functions, a topic from Algebra 1. That’s 15% of the exam. In fact, a review of the entire test suggests that 34-36 of the points relate to topics that should be taught in an introductory Algebra course; that’s nearly 40% of the exam. Why are we testing 9th grade material on an 11/12th grade Regents Exam? That’s probably a topic for another day.

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