Moving Forward with Formative Assessment

Dr Colin Foster

8 October 2019

Many people have said for some time that formative assessment, or responsive teaching, is one of the most important aspects of the mathematics classroom. When I was a new mathematics teacher, I attended a CPD event on formative assessment, when formative assessment was less widely known than it is today. The presenter began by asking, “Could you put your hand up if you already know quite a bit about formative assessment?” A pretty vague question. About half of the room raised their hands. The presenter looked a little uncomfortable, and said, “OK, I’ll go fairly quickly through the first part of this”. I remember thinking, even back then, that this response was problematic. For those who had never heard of formative assessment, the fast version might be too fast; for those who already knew lots about it, even the fast version might be too slow.

‘Doing formative assessment’ often seems to focus on developing a repertoire of strategies for discovering how your students are doing, preferably using approaches that take account of the whole class, rather than just a few confident responders. This is very important, and mini-whiteboards and hands-down protocols can really help. These sorts of strategies certainly take us beyond the rhetorical tics of “Does that make sense?” and “Is everyone OK with that?”, where it is very obvious what answer the teacher wants! And, instead of asking students to red-amber-green whether they think they can do something or feel good about it, it is usually much more helpful to ask them a question that requires that knowledge, and see if they can do it. It is easy to think or say that you can do something until you are challenged to actually do it!

But, even with the best formative assessment tools, the easy bit is always going to be finding out the differences among your audience; the much harder bit is doing something about it. Any well-pitched question is likely to divide the crowd. If everyone is OK, or everyone is not OK, that could be very important to know, but the most informative questions are the ones that expose differences. And then dealing with those differences can be hard.

We wrestled with these issues when I worked with Malcolm Swan and other colleagues at the Shell Centre in Nottingham on the Mathematics Assessment Project, where we designed 100 formative assessment lessons across the secondary mathematics curriculum. The aim was always to make visible students’ conceptual difficulties and then address them with a variety of strategically-designed tasks. The lessons are completely free and have been downloaded over 8 million times so far.

In my work on Mathematical Etudes, I have tried to design tasks which operate at multiple levels, so that students who need routine practice of a technique get plenty of that, but, as their fluency in the particular process develops, their attention can shift increasingly to the wider problem or question that is generating all this practice (click here for an example). So, even someone who is already extremely fluent with the technique that is the focus of the task should find much to be engaged with and benefit from.

Here at Loughborough, I am setting up a network called LUMEN, linking researchers in the Mathematics Education Centre here with mathematics teachers in schools and colleges through a series of completely free CPD events run both in Loughborough and in London. I am very excited that the first events (7 November in Loughborough and 14 November in London) will be led by Craig Barton (Mr Barton Maths) and will dig deeply into formative assessment, exploring how we can go beyond just diagnosing to really supporting students powerfully in their learning of mathematics. Craig’s Diagnostic Questions are a hugely-valuable resource for supporting formative assessment in mathematics, and I am really looking forward to hearing him talk about the most effective ways of making use of this to support the teaching of mathematics.

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Colin Foster

Director of LUMEN (Loughborough University Mathematics Education Network)

Reader in Mathematics Education, Mathematics Education Centre, Loughborough University