Math is a dangerous subject to teach in today's high-stakes testing accountability environment. It's dangerous because it is the kind of subject that can be used to create right and wrong, black and white kinds of assessment tools. I'm talking specifically about multiple choice exams.
The best math teachers are those who resist the pressures to reduce mathematics to such a narrow dichotomous thinking. The art of mathematics is not found in being 'right' or 'wrong' but in the thinking and problem solving. Because of this, it can be said with confidence that these kinds of high-stakes multiple choice tests actually end up measuring what matters least.
It is important to never again brag about high scores or to become saddened by low scores, and that we must resist the temptation to allow these poor tests to encourage poor teaching.
Here's what I mean:
I still remember being taught how to divide fractions in junior high. I was told to flip the second fraction and then multiply. It was a trick that enabled me to test out correctly on the multiple choice tests. Heck, I could even get the right answer on the short answer tests.
Here's the problem.
To this day, I have absolutely no idea why I flip the second fraction and multiply. I have no idea what the mathematical reasoning is. So I can get the right answer on the test, but there is nothing mathematical about my (lack of) understanding for dividing fractions.
Another problem with testing mathematics is that questions may look elaborate or challenging, but they may be superficial.
In his book The Case Against Standardized Testing, Alfie Kohn illustrates how a seemingly difficult question can be testing rather shallow skills. He cites from Al Cuoco and Faye Ruopp's Math Exam Rationale Doesn't Add up from the Boston Globe (1998):
1 2 3 4 5 6tn 3 5The first two terms of a sequence, t1 and t2, are shown above as 3 and 5. Using the rule:tn = tn-1 + t n-2, where n is greater than or equal to 3, complete the table.
Kohn writes, "This is actually just asking the test taker to add 3 and 5 to get 8, then add 5 and 8 to get 13, then add 8 to 13 to get 21, and so on."
Cuoco and Ruopp conclude:
The problem simply requires the ability to follow a rule; there is no mathematics in it at all. And many tenth-grade students will get it wrong, not because they lack the mathematical thinking necessary to fill in the table, but simply because they haven't had experience with the notation. Next year, however, teachers will prep students on how to use formulas like tn =tn-1 + tn-2, more students will get it right, and state education officials will tell us that we are increasing mathematical literacy.
These examples go to show that too often math tests lack validity - meaning the results of these tests don't tell us what we would want them to tell us. It is far too easy to make tests that don't provide us with valid data on students' mathematical skills.
All this means that we must be very careful placing too much, if any, emphasis or importance on these tests.