“Oh no – are we doing a test, Sir?”

When we think of ​‘assessment’ in mathematics, it can bring to mind exam halls full of nervous teenagers sat at distanced desks, classrooms of pupils sat in silence while working through a written task, and that sinking feeling we remember from school when faced with a question we just couldn’t tackle.

But often we don’t need the formality of a written assessment – and the associated marking that goes with it – to provide us with the information we seek. Indeed, GCSE and SATs mathematics papers are not composed with ​‘next steps’ in mind, being a tool designed to summarise a pupil’s learning rather than add to it.

Diagnostic assessment strategies provide frequent, quick opportunities for us to reflect on our pupils’ thinking, strengths, and weaknesses: interpreted with skill, they can give useful insights into pupil learning and the next steps we should take as teachers.

Five ways to use diagnostic assessment in the mathematics classroom

Hinge questions

These are multiple-choice questions which provide an immediate check of initial understanding and, when well designed, have wrong answers based upon common misconceptions. Rich discussion opportunities can follow (“What mistake might a pupil have made if they had chosen Answer A?”). Craig Barton’s ​‘Diagnostic Questions’ website is a good source of these, and Ben Gordon at Montgomery Academy in Blackpool has detailed his team’s approach to using these in this EEF case study.

Quizzing

Low-stakes retrieval activities provide a quick way of checking understanding prior to attempting more complex tasks. These could be four quick questions at the start of a lesson (perhaps from last lesson, last week, last term, and last year – such as these ones from ​‘Maths Bot’), or simply targeted verbal questions.

Mini whiteboards

A staple of most mathematics classrooms, these can provide a quick way of assessing immediate understanding of the class at a glance. Combined with hinge questions, targeted questioning, or other strategies they are a simple yet effective tool. The key is in using them well, and Tom Sherrington blogs here with some tips for maximizing their impact.

Questioning

The questions we ask in lessons can provide us with rich information about the level of pupils’ understanding and can be a very powerful diagnostic tool when used effectively. ​“Give me an example of…”, ​“Which is the odd-one-out and why?”, ​“Is this always, sometimes, or never true?” are all example of question stems which can provide useful information to teachers – more can be found in the excellent publication, ​‘Thinkers’, from the Association of Teachers of Mathematics.

Online question banks

During the pandemic, many schools have invested time or money in implementing the use of software packages which include built-in assessment opportunities. Many of these can be used to provide information about pupils’ understanding of a particular mathematical skill (such as expanding a double bracket) and may give teachers pointers as to which questions their pupils are struggling with (for example, brackets with the ​‘x’ term at the end, or brackets containing two negative values).

Next steps?

Regardless of what form diagnostic assessment takes, it is important that we consider why we are conducting it, what information the assessment is being designed to produce, and how this information will inform our subsequent decision making

With the information diagnostic assessments provide, we might:

• decide to adjust the level of challenge of our lesson activities;
• reteach specific concepts or topics to the whole class or to small groups within the class;

• adjust our curriculum content in the medium or long term to prioritise certain topics;
• address mathematical misconceptions which are causing issues;
• decide which pupils may need additional, targeted academic support (such as tutoring).