Tuesday, April 12, 2011

Do you want the true answer or the right answer?

Iris found another mistake in her most recent math "benchmark" test.

Her school gives multiple choice assessment tests at the beginning of each trimester to determine the appropriate class assignment and then to determine if students mastered the material. This is in addition to the state-mandated tests that they will take at the end of April. The textbook publisher writes the tests. But, as Iris has already pointed out in Error! Error! Error!, the publisher is fallible.

On her last pre-Algebra benchmark test, there was a picture of an equilateral triangle and the kids are supposed to select which choice describes the figure. Both equilateral and isosceles triangles were possible choices, but saying both was not an option.

Iris had a dilemma. The true answer is both as all equilateral triangles (all 3 sides and angles the same) are also isosceles (at least 2 equal sides and angles). But the test implied that there was only one right answer.

Which should she choose?

She had to guess. In the end, she decided that the test-writer didn't realize that all equilateral triangles are also isosceles so she had better select equilateral.

Then she came home and told me about it.

Then I emailed her math teacher, who was very annoyed with the publisher for making such a bone-headed mistake. (Do the publishers employ copy-editors?)

The teacher said that all the tests would be hand-checked so that kids were not penalized, and that they would flag that question when they used the test in subsequent years. She didn't mention alerting the publisher about the mistake.

That's too bad. So I am alerting Holt, Rinehart and Winston right now that there is a problem with their California state Mathematics Course 2: Pre-Algebra materials.

Perhaps you would like to hire my ten-year-old to copy-edit for you? She's been a proven beta-tester since she was five.

Don't miss Stanley Fish's classic gem, The True Answer and the Right Answer. I do like cranky and opinionated done well. ;-)

I agree that kids need to learn the distinction between the true answer and the right answer to get along and get along in our society. But, as Hopeless but not serious pointed out in I never really liked marshmallows, we lose something as well, when we bring up kids to perform the 'right' way.


  1. She is just like my son, who found three errors on his SAT (on which
    he got a perfect score!!!)
    He told his teachers and the SAT people, but they didn't act surprised.
    I think the kids take too many tests.

  2. I think that question has been around far longer than that particular test as I remember the same question from my own childhood, and I remember pointing it out to my teacher and my parents at the time, along with other errors. Of course that was decades ago in a different state.

    I am not convinced that testing always tests one's abilities to learn or accumulate knowledge but rather one's ability to interpret expectations and provide the "right" answer. This in turn is deemed predictive of how well one might adapt.

    But then, perhaps I am growing increasingly cynical with the passage of time.

  3. Ha! I just had an argument with my partner over whether squares were also rectangles (of course they are- but it occurs to me that if we teach 'basic shapes' in e.g. toddler puzzles so differently from 'geometrically defined shapes' in class, we are asking for trouble).
    Anyway, I also remember a time when I was learning to take standardized tests and I went through similar issues. I don't think it's 'cynical' at all to tell kids to find the 'right' answer rather than the true answer... it's an important distinction.

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  5. The mistake Iris caught is one that comes up a lot. Elementary scool and middle school teachers and textbooks often have problem with the seemingly simple concept of every element of one set being an element of a larger set: the idea that every square is also a rhombus, or that every rectangle is also a trapezoid, and so on. If you can't insist on formal definitions for geometric shapes, where can you? One doesn't always need to use language formally and carefully, but sometimes you do have to, and basic shapes are a good place to practice. You might object (ok, readers of this blog won't object, but some people do object) that defintions of shapes are mere pedantry, but later, when the fallacy is "he's not a person, he's a defendant!" the stakes are higher!

  6. Anonymous18:08

    I love the last comment. Such a good point. As far as bringing kids up to know right vs. true answer, I think kids primarily learn from watching you the parent, and if you navigate society successfully, while still maintaining your integrity, most probably they will too. Keep talking to them, though. Sometimes, as you've discovered, it does need to be spelled out.