Last November, the online Atlantic published an article that Katherine Beals and I wrote on the current trend to have students explain their work in math.
Our main point was that doing so was in many cases superfluous to the mathematical process. That is, showing one’s work in solving a problem can be the explanation itself. Asking for more tends to be make-work and for students in lower grades whose articulation skills are still developing, a waste of time.
There was quite a flurry of both agreement and protest about this article. (Despite all the complaints, however, it will resurface in the annual anthology “Best Math Writing of 2016” which will be released around December.)
There is a back-story to the article. In the article there is a sample of a student’s explanation of a particular problem. I had solicited such explanations while I was assisting math teachers at a middle school. I had given students some instruction on how to solve particular types of percent problems, and then gave them a problem, asking them to explain their answer. I had them use a template that the school was recommending: “Need/Know/Do”.
There was only one student who got the answer right; and that was the one I used and which appears in the article. It turns out that I really should have also used an example of a wrong answer–complete with incorrect explanation, which might have better made the point. (Though I doubt that there would have been any less criticisms of the article).
I say this because of a meta-study conducted by psychologist Bethany Rittle-Johnson of Vanderbilt University. Rittle-Johnson examined 85 studies and one of her conclusions was “If kids are just off explaining their own thinking without guidance, then they can be spending their time essentially justifying stuff that’s wrong.”