The Other Side of “Open-Ended”

This is a sequel of sorts to my recent post When Open-Ended Goes Awesome. Check that one out if you want. 

Many years to Jennswondering for inspiring this post and for giving me permission to reference her post Why My Son Failed His Math Test. Check that out if you want. I enjoyed it and wanted to discuss it a bit.

You see, I am a math reform advocate. I am actually a big fan of the math essay. I think that there is a ton that we can do to support students by making them write. We can learn their misconceptions. We can learn their thoughts and we can give those whose algebra skills might be lacking a chance to approach subjects like Geometry and Statistics.

However, not all math writing is created equal. Exhibit A: Why My Son Failed His Math Test.

In this wonderfully-told anecdote, a mother is remarking on her son’s failed math test. His homework scores were coming back high. As she investigated more, she found that the homework was very open-ended, but… well.. I’ll just let her tell the story.

“On the Put Your Thinking Cap section of the math packet, the teacher asked the kids to write whether they would use a line, bar or picture graph to show the following and why. My son’s initial answers were:

1) The number of people at an amusement park who chose different rides?

“I would do a line graph because it makes me feel like I’m at an amusement park.”

The implication from the mother is that the student received 100% on this paper. Obviously there is a ton going on in this situation that isn’t written, so this isn’t an indictment of the teacher…

BUT, it does highlight a risk with writing in mathematics. The goal of math literacy isn’t to write for writing’s sake. The goal of math literacy is to use reading and writing to support rich mathematical understanding.

This student’s homework question was a pretty good question, but his answer doesn’t give a lot of evidence of rich understanding of the strengths and weaknesses of the different ways of representing a data set. Further, because of the title of the post, it seems that the confusion wasn’t addressed before the test. This student may have been allowed to think that what he wrote was an effective support for choosing a particular representation. So, the student was worse that confused. A confused student at least knows to ask. This student may have been led to believe that his thought process was correct and so, there was no need for questions.

And so it is: open-ended questions aren’t a universal good or bad. They can create some fantastic opportunities, but they can also open a world of confusion that drains a math class of valuable rigor.

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