Creating exercises: Don’t give all the information

Posted by Kevin Houston on Mar 30, 2019 in How To Think Like A Mathematician, Mathematical thinking, Mathematics education | 5 comments

One problem with setting routine exercises is that students will often develop what might be called a `plug and play’ approach to solve them. That is, they look for the common features with a worked example they already know and look for some data in the question. You know the sort of question: “A radioactive material has a half life of . Currently there are 25g. How many grammes are left after 4 days?”, “A tap fills a barrel at a rate of …” or “A bacterial colony grows at a rate…”. The student knows that they have to grab the specific parameters from within the question and stick them into a formula. The exercise has become more about decoding exercises rather than solving a problem.

One way to stop this behaviour is to not give all the information. For example, I once set a geometry question that required students to use the lengths of the semi-axes of the elliptical orbit followed by the Earth going round the sun. I deliberately left this information out of the question and chaos ensued. Many students couldn’t answer the question despite the fact that it takes seconds to find the relevant numbers online. One of the tutors on my module even told the students that the question was unanswerable! To me this showed that the standard way to set mathematical problems is broken. Any question where there is ambiguity — even if it can be resolved by a quick information search — causes problems.

How can we create more of these questions? Well, we could rewrite the radioactive material question as “We have 25g of Fermium-252. How many grammes are left after 4 days?”. The required information is easily accessible via the internet and so the exercise becomes one in which the students need to work out what they need to know. This is a more realistic type of question. Rarely do we get a real-life problem in which we have immediate access to all the required information.

One can go a lot further and remove all the information. See for example Dan Meyer’s talk:

The video is an excellent explanation of how to make exercises into problems so is well worth a watch.

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