Read my mind!

Posted by Kevin Houston on Mar 20, 2019 in How To Think Like A Mathematician, Mathematical thinking, Mathematics education | 0 comments

Asking student questions is an art. In any reasonably sized class student ability will be very variable and so it is difficult to pitch a question which is hard enough to not be insultingly trivial and easy enough to be answered by most. The sweet spot is where the level of difficulty is just hard enough to stretch them.

One method is to start with a difficult question and then keep simplifying it (bit like a Dutch auction — start high and progress downwards). This can be a good approach but if there is a specific answer in my head and I am merely indulging in a guessing game, then that is a mistake. I call this the “Read my mind” error. For example, let’s say that in a tutorial I want them to tell me that we should use the simplex method to solve a particular question. I may start with “How can we answer this?” and when greeted by silence or blank stares I try something simpler. “What methods do we know to answer this type of question”. Blank stares. This then continues “What method did we do last week? … The what method’? … The simp… method? … No one? The simplex method perhaps?”

There are two mistakes occurring with the read-my-mind error. First, there is a right answer in my head and I am going to keep questioning until students find it. (Students often believe that there is always a right answer anyway and, to be honest, that is regularly the case in mathematics.) The other mistake is that it conditions students to expect the question to be simplified and besides “he’s going to give us the answer anyway” so there is no point in answering.

If I find myself making this mistake, I stop and try to find a different way forward. For example, changing the question to an instruction, “Find a method in your notes” or “In pairs or threes, come up with suggestions for methods”.

The latter is a very good change of tack. Students avoid answering questions as they do not wish to look foolish in front of their peers. (Sometimes when they do talk in class, they get the self-criticism in first, “I know that this might be a stupid question/answer…” ) Students in pairs are more likely to propose what they perceive as a possibly stupid answer to their friends — the stakes are lower than saying it in front of everyone. Hence, this changing the question to an instruction means that the original question is more likely to be successfully answered.

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