Final exam week just wrapped up at our school. Let’s consider an honors-level Geometry multiple choice question:
Find the area of an equilateral triangle with a side length of 14 inches. Leave in simplest radical form if necessary. (The whole test is with a calculator. Choices below with her answer circled.)
Here’s the student’s work:
What the student does correctly: draws the triangle, splits it in half, uses the Pythagorean Theorem to find the height, and calculates the area of the triangle to the nearest hundredth
What the student does incorrectly: claims that 196 – 49 = 47 instead of 147 (maybe she wrote over the 1 with her square root symbol?)
To be fair, this question can be done using special right triangles (or this formula). If she did do the subtraction right, she would have just checked her answer against the radical answers. Hey – she makes an error – but does she deserve 0% of the credit on that question? It’s not like you get any extra credit for getting a multiple choice question right, so why do you lose all credit for missing a small part? Giving a grade based on multiple choice questions disproportionately penalizes students who might understand all of the concepts, but make a handful of small mistakes.
It’s a basic, but frustrating example. At my high school, our math midterm and final exams are often split pretty evenly between multiple choice and open-ended questions. On multiple choice questions, there’s no partial credit (urgh) and on the open-ended we use a key with points assigned pretty specifically (not the best system either).
There are many reasons multiple choice questions are unfair to students and don’t do a great job of measuring how much they know, despite the College Board’s defense of them. The history of multiple choice is worth looking into and while the format does have some merits, it is overused and often doesn’t reflect a student’s true ability.
Regardless of any debate on multiple choice as a question format, I guess I am raising this question: Is scoring multiple choice as or all nothing fair?