Starting at a new school is difficult. There are systems to learn, lots and lots of staff and students to get to know, and relationships to build up. And then there’s the actual teaching. I’ve picked up two KS4 classes this year and whilst I know what maths they have theoretically been taught, I need to quickly find out what they actually know – particularly with my top set Y11s. This is where formative assessment comes in. Checking for student understanding is one of Rosenshine’s (2012) “Principles of Instruction” and Dylan Wiliam reminds us that any assessment can be formative, and assessment functions formatively when it improves the instructional decisions that are made by teachers, learners or their peers.
There are a couple of techniques that are helping me to find out what my classes are secure on and what they are not.
- Recall questions at the start of the lesson
I always start by having between 5 and 10 questions on the board. This links well with both retrieval and spaced practice, and they can also be used formatively. These are mostly mixed topic with short answers required, and students complete them (mostly) on their own. I can go round the room whilst they are working looking for any obvious problems, and seeing the methods they are using. We will always talk through the answers together – some questions are very quick to go through, some take longer. I always ask them to explain their thinking which gives me a real insight into how they were taught before and where any gaps might be. I can then address these either right away by modelling the answer on the board, or make a note to come back to the topic later if I feel we need more time on it.
I like the mixed nature of these questions. I think this is increasingly important as students reach the latter part of their GCSE course, as they also give me an opportunity to make connections between topics to help students to build a more complete schema of their mathematical knowledge. A future development could be to make sure these sets of questions contain non-standard examples to really check deep understanding.
- Multiple choice questions to check prior knowledge and understanding
With my year 11s I am now at the most mathematically challenging end of the course, and we will be going on to cover the Level 2 Further Maths topics before the exams. It is vitally important that I know how to pitch these lessons and so I need to know where my starting point is.
“Specific questions allow teachers to diagnose exactly what a pupil’s strengths and weaknesses are, and they make it easy, even obvious, to work out what to do next…” Daisy Christodoulou, Making Good Progress? (2016)
To help with this I often use three or four multiple choice questions which the students answer as a class. I choose questions which will show me whether they have the prerequisite knowledge for the topic I am about to cover, and I usually find them on the www.diagnosticquestions.com site. The beauty of these questions is that the alternative answers purposely highlight misconceptions that students might have and allow me to quickly resolve these and check everyone is starting from the same baseline. I just display one question at a time on the board and after a few minutes silent thinking time I ask the students to show me 1 finger raised for options A, 2 for B etc. They can do this discreetly in front of them so they don’t influence others (thanks to Craig Barton’s How I Wish I’d Taught Maths for this technique).
I can then adapt my teaching straight away depending on what I see. If most are correct, I will ask someone to explain why, check the understanding of any who did get it wrong, and move on. Sometimes there is a real split in the answers. In this case I will usually talk through the concept again, without saying who is correct and who is not – this gives students the chance to rethink before having the chance to vote again. I can see whether they had just forgotten, or made a silly error, and usually this will clear things up. I can then go on to teach the new topic knowing that we have reviewed the basics and all of the class are at the same starting point. On the odd occasion when it is obvious that there are a number of misconceptions, I will have to then rethink and maybe reteach that concept, not the lesson I had originally planned perhaps but far preferable to the alternative of no-one being able to access the new content.
Both of these strategies are really helping me to get to grips with my new classes – formative assessment has become an absolutely vital part of my teaching.
Notes and references:
www.diagnosticquestions.com has over 43000 multiple choice questions on maths topics, and also over 25000 questions on other subjects
How I Wish I’d Taught Maths (2018) – Craig Barton
Making Good Progress? (2016) – Daisy Christodoulou
Making Every Maths Lesson Count (2019) – Emma McCrea
By Deb Friis