Thinking Primary Mathematics Assessment (1)
Updated: Nov 12, 2021
This is the first in a series of posts relating to assessing primary mathematics.
Pre-Topic Diagnostic Assessment
Ausubel (1968): “If I had to reduce all of educational psychology to just one principle, I would say this: The most important single factor influencing learning is what the learner already knows; ascertain this and teach him [or her] accordingly”.
Using pre-topic diagnostic assessments is a useful way for teachers to learn about children’s starting points. By this I certainly don’t mean using “cold tasks” where children are tested on content they haven’t learnt yet. I mean assessing prior curriculum content. After all, just because something was taught it doesn’t mean that it was learnt.
What is a diagnostic assessment and how can it help? A diagnostic assessment helps you to find out what is, and crucially what isn’t, well understood; and which aspects will need addressing before new content is taught.
A key feature of any diagnostic task is that it should go beyond revealing which questions a child can or can’t answer, it should also be clear what the child is thinking so that the teacher can ascertain what the gaps are and how to address them.
But, as with many things, “it ain’t what you do, it’s the way that you do it”. Just doing a diagnostic assessment isn’t enough. The results of the assessment must inform future teaching and learning and, ideally, that includes addressing gaps and misconceptions before (or at the beginning of) the upcoming unit.
You can read about pre-topic diagnostic assessments here:
The Education Endowment Foundation - https://educationendowmentfoundation.org.uk/tools/assessing-and-monitoring-pupil-progress/developing-whole-school-assessment/diagnostic-assessment/
The Education Endowment Foundation mathematics guidance reports for EYFS&KS1 and KS2&KS3 both recommended finding out about children’s starting points and using this to inform plans for teaching (and pre-teaching) https://educationendowmentfoundation.org.uk/school-themes/mathematics/
Beth Smith, from White Rose Maths, wrote a piece for TeachWire here: https://www.teachwire.net/news/the-5-basics-of-primary-maths-assessment
DfE non-statutory guidance contains suggestions or prerequisite learning for each of the Ready to Progress Criteria - https://www.gov.uk/government/publications/teaching-mathematics-in-primary-schools
What could a pre-topic diagnostic assessment look like?
It could involve asking multiple choice questions based, such as those found at www.diagnosticquestions.com/whiterose - if I was teaching Y3, I would use the Y2 questions for example. These are particularly good because the tasks include well-chosen incorrect options that can reveal misconceptions. (free with log in)
Alternatively, it could involve undertaking a test, based on prior content, then discussing the answers given and identifying whether incorrect responses were simply mistakes or misconceptions. One way of doing this is using an ‘end of block assessment’ from the previous year - like these on White Rose Maths https://whiterosemaths.com/resources/assessment/primary-assessment/end-of-block-assessments/ (free without log in)
Or, and this is my preference (but I am biased), it could involve a practical dialogic activity which has been designed to discover potential misconceptions and elicit key vocabulary - such as these produced by my colleagues (and me) in the Cambs Maths Team https://www.cambslearntogether.co.uk/cambridgeshire-school-improvement/cambridgeshire-english-and-maths/cambridgeshire-diagnostic-assessment-toolkit (free samples available)
This post is just a starting point, so if you’re interested in finding out more about pre-topic diagnostic assessment, or have questions such as: a) which children should I assess?, b) when should this assessment take place? and c) what should I do if I discover gaps? then get in touch and start a conversation @thinkingcpd on Twitter - use the hashtag #thinkingdiagnostic