Research School Network: Diagnostic assessment in maths Secondary maths teacher and EEF specialist Simon Cox explains how diagnostic assessment can be utilised effectively in maths.

Mathematics classrooms up-and-down the country are busy places once again. While by no means ​‘back to normal’, with face coverings the norm and teachers often restricted to a taped-out area at the front of the room, the sounds of mathematical discussions and of children getting ​‘stuck’ on interesting problems make a welcome change from Teams notifications and Loom recordings.

Alongside supporting our pupils in reconnecting with the classroom, we will be looking to assess the mathematical progress made by our pupils during a disrupted year: for school-level decision-making, identification of ideas and concepts requiring revisiting or re-teaching, and highlighting misunderstandings or misconceptions which may indicate the need for targeted individual support.

It may be tempting to do this by giving pupils a series of past A‑level, GCSE, or SATs papers, but as these are summative tests which are not written with formative assessment in mind. It is doubtful that these will give us the information we need. Identifying the purpose of our assessment up-front, and designing it around the information that will prove most useful to classroom teachers, is a better bet.

What does effective formative assessment look like?

While setting questions remotely during partial school closures may have been relatively straightforward, genuinely meaningful formative assessment which informs our next steps both at a class level and at an individual pupil level has proven more challenging. 

The 2017 guidance report ​‘Improving Mathematics in Key Stages 2 and 3’ suggests that formal tests have their place in our classrooms, but that low-stakes quizzes, informal observations of pupils, and discussion, are also valuable pieces of the assessment jigsaw. Now, back in the classroom, it might be quick and easy to fall back on a written test, but in reality, a range of different assessment types – conducted over a significant period of time – are needed to build up a picture of a pupil’s mathematical understanding and to identify meaningful gaps.

Strong relationships and a thorough mathematical understanding of our pupils are key to this. It also shouldn’t necessarily be assumed that all teachers are equipped to deliver effective formative assessment without ongoing support and training. It can be challenging, particularly for less-experienced teachers, to manage in practice.

Low-stakes quizzes

Providing opportunities for pupils to demonstrate their mathematical understanding in a safe, supported environment is important. Low-stakes quizzes (which don’t entail the pressure of a test with scores attached) can support this well. Diagnostic hinge-point questions can be useful here too – carefully designed, with the incorrect options (the ​‘distractors’) carefully chosen to uncover common misconceptions, these can be a powerful diagnostic tool as well as an effective prompt for classroom discussions: ​“Why do you think someone might think the answer is B? Discuss in pairs.”

Multiple choice questions can be time-consuming and challenging to write, but they can be re-used year after year and often lead to rich mathematical discussion. There are also some excellent online sources of questions, such as Craig Barton’s Diagnostic Questions site.

Mathematical discussions

We can learn a lot about our pupils’ understanding through carefully constructed opportunities to discuss mathematics with peers, as a class, and with the teacher. This could be through overheard explanations between pairs, opportunities for pupils to share their thinking with the whole class through use of a visualiser, or via expertly-managed teacher-led classroom talk. The questions we ask can be critical here, and sources such as ​‘Thinkers’ from the Association of Teachers of Mathematics can be useful.

Consider, for example, the following task:

Show me an example of a decimal which is between 0 and 1 

Show me an example of a decimal which is between 0 and 1, and is bigger than 0.5

Show me an example of a decimal which is between 0 and 1, and is bigger than 0.5, and rounds to 0.6 to 1 decimal place 

Show me an example of a decimal which is between 0 and 1, and is bigger than 0.5, and rounds to 0.6 to 1 decimal place, and rounds to 0.62 to 2 decimal places

…and so on!

This task would very quickly highlight which pupils had gaps in their understanding of place value and rounding, and would be useful in deciding who might need some additional support in this area.

Whatever format our assessment takes, we should avoid the temptation to rush our pupils through a battery of assessments. The return to school may see some gaps closing very quickly, while other deeper misconceptions may take longer to emerge. As always, the key to effective diagnostic assessment lies in high-quality everyday classroom teaching and practitioners should be supported as much as possible to enable this to happen.

References:

Hodgen, J. & Wiliam, D. (2006). ​‘Mathematics inside the Black Box: Assessment for Learning in the Mathematics Classroom’. London: NFER-Nelson.

Wiliam, D. (2007). ​‘Five key strategies for effective formative assessment’. Reston: National Council of Teachers of Mathematics (NCTM)