- Tom Oakley
Thinking Primary Mathematics Assessment (3)
Updated: Jul 17, 2021
This is the third of three posts focusing on assessment of primary mathematics. In this post, the subject is summative assessment in Key Stage 2 - including end of block, end of term, end of year and end of key stage tests. Although this post focuses predominantly on summative assessment of KS2 maths, in mainstream settings, some aspects may translate to other key stages and settings.
Because assessments are so prevalent – because they often just seem like part of school life – we often forget that they are conducted for particular reasons. Specifically, assessments are conducted in order to draw conclusions. Dylan William, 2014 (Principled Assessment Design)
Summative maths assessments are a part of common practice in many primary schools - such as finishing each unit of work, or each term, with one or more tests. If you use different forms of summative assessments in maths how do you know they’re all ‘working’? Does your use of summative assessments lead to better learning?
To help you, here’s some questions to guide your thinking?
Q1. How many assessments do your students do and are all of them necessary?
While there is evidence to support the benefits on learning through testing, how many tests is enough and when does it become too many?
Just take a moment to think about how many tests your students will do in one school year. Now take a moment to think of the number of lessons taken by administering these tests and going through the answers. How many lessons would that be for all of Key Stage 2?
Whether it’s 15 or 50, if the outcomes of the tests only partially influence future curriculum provision, it’s worth asking if teachers know why the children are spending so much of their time being tested.
Q2. Are teachers aware of why we are doing each assessment?
Whenever an assessment is carried out it should be because (a) there is something specific you need to find out, (b) the assessment task has been chosen because it is the most reliable way to gather that information and (c) we are confident that the results will support us in making valid inferences about each student’s learning.
Consider what it is that you want to learn from each type of assessment that you use. For example, do you want to learn something different from end of unit assessments than you do from end of term assessments?
End of block assessments should help you to find out whether children can apply the knowledge they’ve recently acquired in various contexts and give some indication of confidence. Whereas for end of term assessments, that might not be the case, as you’re likely to assess several units of work, and what you want to find out might differ depending on the time of year. As an example, at the end the autumn term in Year 2 you may be most interested to learn more about students’ understanding of place value and comparison of number - especially as this knowledge is required for the upcoming measurement and statistics units in spring.
I believe that it is more productive to focus on decision-driven data-collection, rather than on data-driven decision- making. By focusing on the decisions that need to be made, rather than the data, we are far more likely to collect the right data, the right amount of data, in the right way, for the need at hand. Dylan William, 2014 (Principled Assessment Design)
Q3. How and when will you gather the information you need to know?
When you have identified what it is you need to find out, consideration should be given to how you will collect it. Clearly what’s age-appropriate for Year 6 summer term, isn’t appropriate for Year 3 autumn term.
If you've chosen to use a written test, that includes deciding the number of questions, amount of time and whether the children can have resources or other support. And I ought to add that assessment questions should ideally come from a trusted source - somewhere they’ve been trialled many times in the past. Testbase is one such place, for example.
We should also consider when the tests happen. Is an “Assessment Week” in mid-December, or the week of Sports Day, really the best time to do this? Probably not if I know I don’t have capacity to mark and analyse the assessments meaningfully. Just because we’ve always done it then, that doesn’t make it the right thing to do.
Q4. How will you mark the assessments?
Have you ever considered whether it’s best to mark paper-by-paper (one whole test each student after the other), or question-by-question (marking every response to each question, before then going to the next question)? Or whether it’s more appropriate to mark the papers with the children? In my experience each approach serves a different purpose and can highlight different things.
It‘s likely that different members of your teaching team will do this differently. Have you ever discussed what you do any why?
Equally, have you thought about what you will do with the students’ scores when you have them? I assume you probably don’t need a standardised score or maths age every term, or half term. Do you?
Arguably the most important thing to find out is which questions the children found most difficult and why. How will you find out if their incorrect answers were the result of a mistake, a misinterpretation of the question or a misconception? I’d suggest that it’s hard to know this without talking to the children and gaining their feedback.
Q5. How will you give and receive constructive feedback after the assessments?
I’m convinced that marking the answers right or wrong is only one part of the information gathering process. It’s important to think further than ‘How many did the student get right?’ and instead try to establish ‘What support does each student need to be able to successfully answer questions like these in the future?’
It’s for this purpose that we have post-assessment conversations with children. This is more than just ‘going through the test’, but creating an opportunity for students to feedback to the adult. How you do this depends on what you want to learn and what you want the children to learn.
Sometimes a 1:1 conversation will work best, other times it could be a large-group discussion, or it might be a case of asking children to discuss questions with a Response Partner. It depends on the number of questions you need to discuss and the number of students you need this discussion with.
From my experience, I’d prefer not to go through too many questions and I don’t want students concentrating more on who scored what than which strategies were used and why. For this reason, if I know I’m going to share their papers back with students, I prefer to record the children’s marks on an assessment grid and not on the test papers. Their paper therefore won’t have scores on, but instead students can annotate the papers to indicate their confidence, add any comments and their scores if they wish.
Something to think about
There really is a lot more to summative assessments and the subsequent analysis than you might first assume. Please bear that in mind if you’re asking an inexperienced teacher to use tests to inform their practice.
This post only just scratches the surface so if you have any questions or comments about summative assessment, start a conversation on Twitter by tweeting @thinkingcpd or use #thinkingsummative For more food for thought, check out one or more of the suggested reads below.
Suggested Reading relating to Assessment in Maths
J Hodgen and D Wiliam - Mathematics Inside The Black Box, 2006. This is an excellent place to start if you’re interested in maths assessment. A short read, packed with lots to think about.
D Wiliam - Principled Assessment Design, 2014. This is a really thorough paper into how assessments are designed and used. If you’re interested in thinking deeply about how assessments are put together, this is a must-read. However, it’s not short.
T Sherrington - Get Assessment Right and Reduce Workload at the Same Time
J Dabell, Maths No Problem - Re-evaluating the place for summative assessment in the classroom
Mary Mayatt on testing
Daisy Christodoulou, Bias in teacher assessment - https://daisychristodoulou.com/2019/09/even-reliable-assessments-can-be-biased/
Alex Quigley https://www.theconfidentteacher.com/2021/04/does-reading-really-matter-in-mathematics/