What I used to think
If a lesson was going well, and I had a sense that my students were understanding the core content of what I was teaching them, I would tend to end the lesson with a bit of a stinker. This could be a past exam question, a question in context, or a question with a particularly nasty twist. This would be the most difficult question I had asked all lesson, and its purpose would be to push my students to the limit – to provide evidence of the progress they had made. I would usually build it up, with something along the lines of: ‘Okay, this is as tough as it gets. Can you do it?’.
More often than not, the result was that some students could and some could not, and I didn’t really have time to go through the answer in great depth. But I was okay with that, as this was an extension question – I didn’t expect all my students to get it right. The most important thing for me was what had happened in the previous 45 minutes.
Thinking back to that lesson later that evening over a cup of Mellow Birds, I was very happy how it went. The question I never considered was if my students were also feeling the same way.
Sources of inspiration
My takeaway
Kahneman et al (1993) discuss how people’s memory of an experience is often dominated by the feelings of pain and discomfort during the final moments, as opposed to what happened during the rest of the experience. They describe an experiment involving people placing their hands into ice cold water for different durations. The authors found that when given a choice between two equally painful experiences, with the second lasting longer but with a less painful ending (the temperature in the water is increased a little), participants preferred the latter, despite having to endure more pain overall. It was the memory of those final painful moments that lingered in their minds.
Now, clearly there are huge issues transferring these findings to the context of a maths lesson – indeed, the icy water could be more or less painful than a twisty exam question on 3D Pythagoras, depending on your view of mathematics – but it certainly has given me food for thought. What was my students’ impression of that lesson, especially the students who could not do the final, challenging question? What will they remember? Will it be the 45 minutes of success they enjoyed at the start, or the 5 minutes of ‘failure’ at the end? According to this research, it may well be the latter.
Many of my students would have judged the lesson as unsuccessful because of that final, tricky problem. This negative emotion could potentially be swirling around in their heads for some time, maybe until their next maths lesson. In Chapter 2 we have seen how important students’ perception of their ability to succeed in maths is for their motivation, and feelings like this can only do harm.
What I do now
The difficult questions now come in the middle of my lesson when I judge students to be ready for them. This gives me adequate time to work through them carefully, identifying and addressing specific issues that students had.
I always end my lesson with a question that is of mid-range difficulty, or maybe even easier. More often than not, it will be a diagnostic multiple-choice question (Chapter 11). The majority of the learning has happened in the first 45 minutes. My objectives in those last 5 minutes are for me to identify any key misconceptions that will inform my future planning and – the importance of this should never be understated – for my students to feel good about themselves ready for their next maths lesson.
Hopefully that wasn’t too painful an ending to this chapter.