Using example-problem pairs in mathematics teaching

I have been a mathematics teacher for 14 years.

For most of these, I was oblivious to research evidence and to what it could tell me about what works in the classroom and about how children learn. It’s not that I ignored the evidence – I just didn’t know it was out there, and it had certainly never featured in my initial teacher training.

In more recent years, and certainly as part of my current role as Blackpool Research School lead, I have spent much more time engaging with research evidence and what it can tell us about what has worked well previously, and what could be worth considering in my classroom.

Worked examples are one such area, one which might be considered a “quick win” in terms of making easy changes to practice. Teacher training stressed the importance of examples in mathematics, and I often gave three or four increasingly difficult examples to my pupils, followed by an exercise for them to try – something like the example below:

Example One

What I didn’t consider (because I didn’t know) is that what I was doing had been shown to contribute to the worst learning outcomes during research trials:

“It was notable that the method of showing students a set of worked examples followed later by a similar set of problems to solve led to the worst learning outcomes.” (Sweller, Kalyuga, and Ayers, 2011)

Intrigued, I obviously wanted to find out what works better. I expected a complex, difficult to implement idea which would massively add to teacher workload. What I found was pleasantly surprising:

“For an example to be most effective, it had to be accompanied by a problem to solve. The most efficient method of studying examples and solving problems was to present a worked example and then immediately follow this example by asking the learner to solve a similar problem.” (Sweller, Kalyuga, and Ayers, 2011)

…which I interpreted to looking something like this:

Example Two

followed by some practice, then introducing negatives then some practice…

And that’s what I now do.

Simple and, initially at least, seemingly very effective.

Reference

Sweller, Kalyuga, and Ayers, 2011: Cognitive Load Theory

9 October, 2017 —