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Last week saw Ofsted criticising boring teaching. A common response was that if you want more engaging lessons, you need to allow teachers to take more risks. More creative lessons might be great, but, they argue, a greater number of lessons will fall flat, and we need to be ok with that.

Last week saw Ofsted criticising boring teaching. A common response was that if you want more engaging lessons, you need to allow teachers to take more risks. More creative lessons might be great, but, they argue, a greater number of lessons will fall flat, and we need to be ok with that.

Engaging students with more interesting lessons is one reason to take risks, but there are others...

In the context of major challenges like climate change and a contracting economy, the RSA has been emphasising the importance of action by each of us. These aren't problems that will be solved just by government, big business, but rather require most people to change their behaviour. Change is less about them and more about us.

When thinking about schools, I would argue, in short, that our concern should be not only that young people are knowledgeable, but that they are able to act.

That's why when I met a university admissions tutor for a maths department the other day, I asked him what he thought about using projects or practical problems as a vehicle for learning content in a subject like maths. As it is one of the subjects least often integrated into project work in Opening Minds' schools, I was expecting a fairly firm rejection of the idea.

His response was far more subtle. It was, he said, potentially worth pursuing, but in pursuit of a better outcome, we could lose what's worthwhile in what we already do. It was, in short, fragile.

In the ensuing discussion, he gave the excellent example of an exercise he had run with students where, rather than ask an individual a straight maths question, he presented a group of students with a problem and asked them to present a reasonable solution.

In this case the problem was ' predict how many people could you fit on a football pitch'?

This problem has several possible solutions. One is to take the area of the pitch, assume everyone is shaped like a rectangle of a regular size, and go from there. Another is to refine that approach for a more accurate answer by assuming the space people take up is not rectangular, but hexagonal. Then tessalate the hexagons. You can refine further by assuming different sized hexagons based on, say, the average area taken up by adults and children. You can further refine it by acknowledging that the area taken up is better represented by a circle, and attempting to tessalate those.

To get the most useful answer, the group must realise rectangles aren't very accurate, that to work with circles involves using maths that hasn't been invented yet (according to my source). The best solution in practice is therefore going down the hexagon route.

He argued that many students were arriving at university who knew the formulas, but not when or how to use them to solve a problem. Classroom teaching and individual coaching got them so far, but no further.

So, using a practical problem in this way could be better. Students can delve more deeply into the maths and grapple with the formulas, while at the same time having to imagine a solution, manage group discussion and decision processes and so on.

But there is a price...the FA say football pitches can be different sizes. What happens if the students just argue about what size the pitch is? In other words, if the facilitation of the group processes is poor it can lead to dealing with content in a very shallow way.

We might decide change is needed for a number of reasons: engaging students, helping students learn how to use knowledge, and or how to work with others are just a few. However, if we move on from 'delivering content' as many schools have begun to, we must realise the risks involved and consider how far we should go, how we can improve the chances of success, and do we have the people that can get results in this way?

In short, we need to remember it's fragile.

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