## Uncritical Thinking

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

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:

O O O K R J O O O O

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,

or

J O R K O,

or

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.