Uncritical Thinking

A friend sent me the challenge at right that his daughter was given in school.

What would you answer?

(Please decide how you would answer before reading further.)

The reason he sent me this, and the reason I’m blogging about it, is because this is a very good example of how there can be math instruction that ends up being counterproductive.

The teacher sought the specific answer of 10, which can be realized as follows:


where the front of the line is to the left and O’s represented unnamed people. All other answers were marked wrong.

But there are many configurations that satisfy all the constraints with different numbers of people in line, such as the following:

O J R K O O,


J O R K O,


O O O K O O O O O O O R O O O O O O O J O O O O.

Math classes are normally a great way to learn how to be thorough. Countless math problems demand meticulous attention to finding all possibilities. Such problems often press students to eliminate false assumptions, which is a valuable skill applicable in many situations outside of mathematics. This could have been such a problem, but the way it was handled, it became the opposite.


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We're a math club for girls.
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One Response to Uncritical Thinking

  1. engight says:

    I think I experienced a similar situation of a problem like you mentioned above. That is, there’re different points of views in solving the problem(correct me if I’m wrong.). Perhaps this shouldn’t have been a multiple choice question? Instead the teacher should have told the student to write a sound reasoning as to why they got the answer to the problem.

    Other than that I think the teacher could have wrote more precisely about the problem in order to avoid misunderstanding. But still, every writing you see has some assumptions in it. So, I guess that perhaps it would have been best if it was a free response.

    Anyhow, this a good point you made about how one can derive different answers because of different view points. This happens to me sometimes when solving a problem if I didn’t enter the author’s viewpoint of the problem.

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