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.
# 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
*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.
# Learning vs Performance - Soderstrom and Bjork, 2015. https://www.researchgate.net/publication/275355435_Learning_Versus_Performance_An_Integrative_Review
# Formative Assessment - if you want to know more about formative assessment, try and make time with ‘Inside the black box’ by Black and William https://www.researchgate.net/publication/44836144_Inside_the_Black_Box_Raising_Standards_Through_Classroom_Assessmentand I know that Tom Sherrington recommends Wiliams’ Embedded Formative Assessment book - https://www.amazon.co.uk/dp/193400930X/ref=cm_sw_em_r_mt_dp_81H6B7WV0RKBMHWF2CGG but I’ve not read it myself.
# Assessing Pupil Progress - https://educationendowmentfoundation.org.uk/tools/assessing-and-monitoring-pupil-progress/ is the EEFs toolkit for understanding assessment and monitoring.
# Understanding is complicated and contested, but if you’re looking for a nice head-scratcher read about ‘procepts’ from Tall and Gray https://homepages.warwick.ac.uk/staff/David.Tall/themes/procepts.html
Toolkit strategies you could use to assess performance and mathematical thinking
Observing learning in action - something to think about here from Jayne Carter - https://www.nexus-education.com/what-if-we-used-the-characteristics-everywhere/
Example problem pairs - lots to consider about worked examples here by Craig Barton http://mrbartonmaths.com/teachers/research/worked.html plus something extra to think about here from Greg Ashman - https://gregashman.wordpress.com/2016/02/09/example-problem-pairs/
Cold Calling - coined by Doug Lemov in Teach Like A Champion, but also referred to here by Mary Mayatt - https://www.marymyatt.com/blog/thoughts-on-assessment
Hinge questions and Exit tickets - both neatly described by Emma McCrea in Making Every Maths Lesson Count www.amazon.co.uk/dp/1785833324/ref=cm_sw_em_r_mt_dp_K31HG9GS02HKECSFAFJJ