Regular formative assessment of pupils’ developing mathematical skills does not need to be laborious; this article aims to introduce some simple ideas and strategies that require little extra work but can be highly effective ways of assessing pupils’ maths skills as you teach.
How can developing mathematical language help?
When children can use the right vocabulary to explain their thinking, diagnostic assessment of their level of understanding can be far easier. Teaching pupils the vocabulary that will be used when learning a new mathematical concept, perhaps displaying it on the wall so that it can be referred back to during the lesson, can encourage them to talk about their learning and promote focused dialogue between teacher and pupil. Recommendations from the Education Endowment Foundation highlight the importance of teaching metacognitive strategies within a lesson in order to build on prior subject knowledge. The use of specific sentences that will be repeated throughout a topic can also be modelled for the pupils; for example, “the greater the denominator the smaller the parts” so that when asking a question such as “how do you know that ½ is bigger than ¼?”, they can use the key vocabulary to explain their thinking, either written down or orally.
This can also be useful during peer assessment, when pupils can provide detailed, specific feedback to each other. Asking a learning support assistant to write down responses or snippets of pupils’ feedback conversations on labels that can be stuck in books can also be an effective way of capturing the children’s thinking as they articulate it during a lesson, so that the teacher can clearly see an individual pupil’s grasp of a topic.
How can I identify exactly what pupils are struggling with?
Breaking down a mathematical concept into “tiny steps” can help to pinpoint exactly where pupils are going wrong and specifically address any misconceptions. It also gives pupils a chance to explore a concept fully and in greater depth before moving onto the next step. For example, at the start of a fractions unit, spending a whole lesson on the concept of parts and wholes before moving onto equal parts will build a firm foundation for the introduction of what a fraction represents.
How can I structure my lessons to maximise assessment opportunities?
The structure of a lesson is equally as important as the activities planned within it. Rather than one teacher-led input followed by practice, varying this with multiple, shorter teaching inputs interspersed with group, partnered or independent learning provides opportunities to identify and unpick misconceptions as they happen. Building in structured self and peer assessment opportunities, including self-checking, is also recommended, allowing pupils time to reflect on their own and others’ work and engage critically with the processes that they are using.
There is a lot of curriculum to cover in what always seems like a very short space of time, so finding ways to assess more than one thing at once can be very beneficial. A leading expert in the teaching of Singapore Maths, Yeap Ban Har says, “It’s better to solve one thing five ways than it is to solve five things one way.” Planning one activity that allows pupils to demonstrate multiple skills is a lot less time consuming than planning lots of different activities that each assess only one skill and means that you will be able to gather evidence of how pupils can apply their knowledge to problem solve in a variety of ways.
|Assessing four skills with one activity|
Ask pupils to pick a calculation from their times tables. From a starting point of 4 x 6 = 24, for example, the following questions can be asked:
How else can you represent this calculation?
This could be writing the inverse, writing as repeated addition, or drawing a bar model or an array. Once pupils have drawn the bar model, can they see the connection between multiplication, division and fractions? Can they explain what the number sentence actually means, i.e. four groups of six equals twenty four?
Using your understanding of place value, what other calculations do you know the answer to?
4 x 60 = 240, or 0.4 x 0.6 = 0.24. What about one hundred times bigger / smaller?
What nearby facts can you see?
If you know 4 x 6, you know 3 x 6 and 5 x 6. Pupils can then use their place value facts for these new facts – the possibilities are almost endless!
Can you write word problems for your calculations?
This is yet another chance for pupils to show off their understanding and to be creative.
|Other easy in-class assessment strategies|
Model solving a calculation on the board, and ask pupils to explain what you are doing at each step. Capture the explanations on sticky labels.
Get it wrong
When modelling, make mistakes. Ask pupils to explain the mistake, and perhaps even why they think that the mistake was made at that specific point!
Be the teacher
Many children love writing on the board, so ask them to explain their thinking as they’re solving a problem in front of their classmates.
How many different ways
How many different ways can you solve a calculation? And what’s the most efficient way of solving it? More able pupils may suggest solving 15 x 3 by partitioning 15 into 10 and 5, or rounding 15 up to 20, calculating 20 x 3, then subtracting 15 at the end.
Providing pupils with the answers to all the maths problems they have to solve upfront is one easy way to facilitate self-checking. Once a pupil has worked out their answer they can check to see if it is included in the possible answers; if it isn’t there they know they need to re-think their approach or check their working out.
Confidently monitor pupils' attainment and progress in Maths assessments
The NFER Tests range includes maths assessments for use across years 1-6. These tests have been developed by our assessment experts, in collaboration with teachers, and standardised with over 60,000 pupils. NFER Tests provide reliable standardised and age-standardised scores to confidently monitor attainment and progress.