I just recently marked a test I gave my class surrounding area of a rectangle. I don’t like giving tests and I avoid them when I can just for reasons like the one I’m about to show you.

I pulled a question from one of those highly regarded specialists in the industry that are so touted about by media personalities and whatnot…..Pearson. This is their test question……

Which rectangle has the greatest area?

a) Rectangle A: length 20 cm and width 5 cm

b) Rectangle B: length 13 cm and width 12 cm

c) Rectangle C: length 36 and width 9 cm

I’ll give you a second to come up with the answer yourself. Most people who look at this question would say that it assesses a student’s ability to calculate area of a rectangle, that this is a “reliable” test question. And looking at the results, 82% of my students got the question right.

Except for one little problem…….take a look at some of their answers to the follow up question of “How do you know?”

Student A: Figures out the area of each Rectangle (100, 156, and 324 respectfully). Then she said that she chose C because it produced the largest area mathematically. Smart girl.

Student B: Adds the two given sides for each rectangle ( 25, 25, 45 respectfully). He says, 45 is the largest number so that’s the biggest rectangle. Uh oh.

Student C: Figures out the perimeter of each rectangle (50, 50, 90 respectfully) and says C has the largest area by comparing the numbers. Oh boy. Got perimeter mixed up with area although I never would have known that from multiple choice alone.

Student D: Says, “Because I guessed. It looked like it would make the biggest rectangle because one side was way bigger than the others.” Crap……..

Student E takes the time to actually draw the rectangles with her ruler and then by comparison deems C to be the largest and therefore the one with the most area. She’s correct but this isn’t because she knows how to calculate area. It’s because her measurement and comparison skills are spot on. I actually admired this student the most because she clearly found a way to answer the question even though she didn’t know how to directly calculate area. Good for her! I didn’t even teach this as a strategy, it came from her head.

Yikes………..my kids aren’t as good at this as I had originally thought. Good thing I asked that follow up question.

If I hadn’t asked the question “How do you know?” I would have congratulated myself on the masterful teaching of area of a rectangle and moved on. This actually shows me I have to go back and reteach the concept. Of my 82% of the kids who got it correct, only 40% of them identified a “correct” method. Although I do admit that at least 5 of them left the follow up question blank so I have NO idea where their thought process is.

But I’d like to point out that of the students above, their “basic math” was spot on. The ability to multiply, add……none of them had any issues.

Is it really the “basics” that are getting lost in education? Or is it the ability to do something with them?

Now if you’ll excuse me, I must go plan my re-teaching lesson for tomorrow. Because truly this is the purpose of assessment. It’s to inform ME about how I’m doing as a teacher. And I’m sorry, but had I relied on the question alone, I would have thought my kids had mastered the material and skipped right along ahead.

The truth is, multiple choice doesn’t “assess” anything. It’s just an easy way to give statisticians some data they can go play with and then journalists and media and political personalities can take it and distort it to scare the heck out of the general public. They use it in a game where they convince you that these numbers actually support some kind of argument they are making.

Numbers don’t always mean what you think they mean.