Diagnostic assessments are exactly what the name suggests – they diagnose a pupil’s understanding of a concept and help the teacher, and pupil, identify the pupil’s strengths and weaknesses. For this reason, they tend to be used at the beginning of a topic but can also be used during a topic to determine if a core concept has been understood.

In addition, diagnostic assessment data can support teachers in adapting a learning sequence by including additional steps/re-teaching where there are gaps in understanding or consolidating steps/allocating less time to steps which are secure. In this way, diagnostic assessments are a great way of adapting a scheme of learning to suit the needs of a specific group of children. 

What does a diagnostic assessment look like and how can they be used?

These assessments can take many forms and can look different. However, generally speaking, a diagnostic assessment is low stakes and is used formatively rather than summatively.

Quite often a diagnostic assessment can be in the form of a multiple-choice question (www.diagnosticquestions.com provides a wealth of examples of these) but the important thing to remember is the assessment should 'diagnose' something, therefore answers should include common misconceptions. It is also worth noting that questions which have been answered correctly may not always reflect a pupil’s understanding but may also be the result of a 'lucky guess'.

I look at a number of examples of diagnostic assessment in this document here [Hyperlink to additional content]

Benefits and challenges

There are a number of things to consider when deciding whether to use diagnostic assessments:

Why do I use diagnostic assessments?

For some pupils, a more formal approach to assessment can lead to anxiety and even a fixed mindset towards mathematics (Boaler, J., 2014). How often do we hear, 'I wasn’t good at maths when I was at school'? I imagine for those that may say this it could stem from a negative experience of maths in an assessment situation, or maybe due to receiving a low grade at some point. Repeatedly failing or performing low on assessment can lead to pupils expecting to perform in the same way next time (Black, P., & Wiliam, D.,1998). Diagnostic assessments, however, are low stakes and informal, so therefore avoid the anxiety that can be associated with other forms. Likewise, as marks or grades are not associated with diagnostic assessments, when used they can avoid pupils repeatedly experiencing failure.

Also, more formal approaches to assessment can often rely on a pupil providing an answer that is marked correct or incorrect – therefore, only assessing what is easy to assess. These types of assessment often lack the opportunity for pupils to show their ability to discuss and unpick the maths, making predictions, conjectures or following a line of enquiry (those key elements of the reasoning strand highlighted in the national curriculum). Diagnostic assessments on the other hand enable you to engage in talk with the pupils to find out why they have answered in that way. They may allow for conjectures to be made and then investigated, thus providing a rich mathematical opportunity.

In addition, by providing pupils with multiple choice answers or multiple responses to a statement, as seen in the concept cartoon, it can support them if they are reluctant to contribute or share their own ideas. Some of the pupils in my current class started the year as shy and afraid of sharing their answers with both me and their partner. Some pupils even resorted to guessing or saying any answer and avoided ‘hard thinking’. Using diagnostic assessments can provide them with an existing idea which quite often may be similar to their own idea without the pressure of their partner thinking it is their own. Alternatively, for those who struggled to develop their own answer, it has scaffolded them and supported them to think why someone has given a particular answer. This has really enabled my pupils to recognise that making mistakes and not always having the correct answer straight away is ok and is key to  becoming a successful mathematician. It has also developed their oracy skills and ability to discuss mathematical ideas.

Over time, my pupils have really developed their resilience and are now open to challenging one another and unpicking ideas together. For me, a successful mathematics classroom is rich in discussion, making conjectures and forming generalisations – diagnostic assessments can provide those opportunities when used in some of the ways discussed.

To see examples of diagnostic questions and how pupil answers can be interpreted, click here [Kate’s supporting document]

References

Barton, C. 2018. On Formative Assessment in Math How Diagnostic Questions Can Help. American Educator 42 (2) pp33-38.

Black, P. and Wiliam, D. (1998). Inside the Black Box, London, UK: GL Assessment.

Dabell, J., Keogh, B. and Naylor, S., 2008. Concept cartoons in mathematics education.

https://arbs.nzcer.org.nz/using-concept-cartoons-assessment

https://www.atm.org.uk/shop/concept-cartoons-in-mathematics---book/exs004

https://educationendowmentfoundation.org.uk/public/files/Diagnostic_Assessment_Tool.pdf