Tom Oakley
- Jul 3, 2021
- 3 min read

Thinking Primary Mathematics Assessment (2)

Updated: Jul 4, 2021

[This post focuses predominantly on KS1 and KS2 maths lessons in mainstream settings, but some aspects may translate to other key stages and settings.]

Maths lessons provide many opportunities for formative assessment, but even then it can be hard to know whether progress is genuinely taking place… after all what does progress look like?

One problem we can have in judging progress is that improved performance can look like learning, when it’s actually more like ‘good instruction-following’. And the opposite can also be true - what can seem like under-performance can mask deep thinking.

Unfortunately, whilst improved performance is easier to spot (see below), progress in mathematical thinking is harder to ascertain because, if it’s taking place, it’s happening in the student’s mind.

This is frustrating because if we could just measure progress by performance alone, it wouldn’t be so hard to do. After all, improved performance is often observable through the way children find solutions - i.e. with increased efficiency, accuracy, independence, confidence etc. Using mini-whiteboards* and recording calculations in exercise books can be great for showing proficiency at whatever it is a student is ‘doing’, but they’re often insufficient for showing what the student is thinking.

That’s why formative assessment is just as much (if not more) about inferring how the children did, as it is about judging what the children did. Developing the art of formative assessment (or responsive teaching) can be incredibly complex, but I’m convinced that two of the crucial ingredients are a) knowing what you need to find out about the students’ thinking to inform the next ‘step’; and b) knowing how you can find that out in a way that leads to valid inferences - which in-turn supports good decision making.

Even with a toolkit of assessment strategies (see below), it’s important to consider what (if anything) will be recorded by the end of the lesson and how it will be used to a) support thinking during the lesson, and b) inform learning that will happen later. Designing activities which both support and capture thinking is a key element of task design - a blog for another day perhaps.

Implications

# Adults need to understand where this lesson fits in the learning sequence and what progress is likely to look like within/after this lesson(s).

# Adults should aim to assess improvement in mathematical thinking as well as performance.

# Choice of purposeful assessment strategies should be made based on their usefulness for informing decision making.

Notes and further reading

Notes

*Using mini dry-wipe whiteboards (https://my.chartered.college/wp-content/uploads/2018/08/9.-Mini-Whiteboards.pdf) is a popular way to observe performance. My recommendation is, in case you don’t already do this, to do ask students to share their responses ‘Mexican Wave style’ i.e, group by group, with short pauses between each group - ideally the pauses are just long enough for the teacher to take in what’s being shown, but not long enough for other students to copy a friend’s response.

Thinking Primary Mathematics Assessment (2)

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