Research School Network: Responsive Teaching: The Effectiveness of Formative Assessment How diagnostic questioning in maths informs responsive teaching at The George Eliot School, Nuneaton.

Stephen Orford is a Teach First NQT in the Maths Department at The George Eliot School, Nuneaton, a Midland Academies Trust school. You can follow him at @Mr_S_Orford and find out more about the work of The George Eliot School at @GeorgeEliotSch.

At The George Eliot School, we have adopted a vision whereby the addressing of misconceptions forms the heart of our lessons. Teachers are encouraged to give live feedback to tackle misconceptions as they occur and the use of formative assessment plays a significant role in being able to do so. This is different from assessment for learning (AFL) as formative assessment proactively informs the next steps in teaching; the students’ learning needs are at the core of the teaching episode. As Dylan William (2006) emphasises, ​‘if you’re not using the evidence to do something that you couldn’t have done without the evidence, you are not doing formative assessment.’[i] This is a significant part of the learning journey in mathematics, as topics often build upon prior learning and students struggle to understand these without a sound and secure knowledge of the basic skills: formative assessment provides an opportunity to address this issue. It is also a fundamental feature of a longer-term spiral curriculum design. Therefore, as a department we have focused much of our CPD time this academic year on how formative assessment and live feedback can enhance the learning of our pupils in lessons.

The EEF’s guidance report ​‘Putting Evidence to Work: A School’s Guide to Implementation’ provided us with a framework whereby we could clearly develop our approach to formative assessment in the mathematics department.[ii] The initial phase of embedding formative assessment more prominently into our lessons was to fully engage staff within the department and to collaborate over how formative assessment would look in the classroom. This collaboration was key to ensure that the teachers in the department were invested in why formative assessment was essential to the development of our curriculum and to ensure staff were confident enough to implement changes. Out of these discussions, came a prominent concern that some teachers felt they may not be able to cover all of the content needed in that given term if they kept going back to plug knowledge gaps which the formative assessment highlighted were evident. However, as a school we put full trust in our teachers being experts of their subject and are confident that they can make informed decisions as to how much lesson time may be required to reteach content. The key premise that we held as a department was that the students’ needs are at the core of our decisions in lessons, and that newer content would be understood at a deeper level if the prior skills needed to conduct the math were secure: this is where our focus needed to be. This maximises our students’ learning and aligns our principle of teaching and learning with that of Doug Lemov (2015), moving away from ​‘I taught it’ towards ​‘they learned it’.[iii] Furthermore, our atomised and retrieval-based curriculum is structured to enable students to revisit topics in their later years which reduces the effect of uncovered content as they will revisit it when meeting newer topics. 

The main method of formative assessment that we decided to use came from Craig Barton and his use of diagnostic questions. These questions focus on why students have got an incorrect answer and goes further than most assessment which would categorise students as having the answer as merely correct or incorrect. The diagnostic questions are comprised of 4 multiple choice answers whereby 3 are common misconceptions, an example of which can be seen below.[i]
What is even more advantageous of diagnostic questions is that Barton has launched them on his website www.diagnosticquestions.com and allowed students to answer the questions; teachers are able to access data from the questions to see what students have previously answered. This allows the teacher to plan ahead for likely misconceptions.

The EFF’s preparation stage, which encourages a development of a clear and logical plan, led to us trialling a variety of ways to ask the diagnostic questions and consequently gather the data in the classroom. Such practical preparation enabled us to understand what our ​‘key ingredients’ of delivery were to be and assess our ​‘readiness for implementation’. We agreed as a department that the point at which diagnostic questions were asked in the lesson was entirely dependent on the teaching episode: for example, to assess prior knowledge or as hinge questions before independent practice. However, we did agree that as a department that the strategy of using ABCD cards for students to indicate their answers to multiple choice diagnostic questions, was an efficient way of the teacher gauging where misconceptions are in the room and to what extent they need addressing. This may be that the teacher uses adaptive teaching methods with a select few whilst the rest continue with independent practice; or it may mean that further modelling and scaffolding is required for the whole class, or that the teacher needs to revisit and strengthen the retrieval mechanisms for some prior knowledge.

There are some caveats to using diagnostic questions, and the delivery stage of EFF encouraged us as a department to notice these and think about ways to support staff to overcome them. These centred around how to use diagnostic questions effectively, rather than the questions themselves. For example, there is a necessity to create a classroom culture whereby fear of mistakes is not apparent and students are discouraged from opting out; this way the teacher gains a true picture of the understanding of the class. We have been lucky enough to have this atmosphere in George Eliot for two academic years and it has come from passionate teaching and high quality teaching and learning strategies that follow those of Doug Lemov. We have a ​“no opt out” policy whereby we probe students with gradually more scaffolded questions to get them to arrive at an answer and we embrace mistakes; even those made by teachers!

We are constantly thinking about ways to make the most of formative assessment and frequently trialling different approaches using diagnostic questions, so that they become a sustainable and systemic part of the department’s teaching practices. A recent CPD read of Barton’s book, ​‘Reflect, Expect, Check, Explain’[i]
has led to us as a department to trial withholding the correct answer from the students and ​”cold calling” a select few from to explain the reasoning behind their answer. We feel that by listening to these reasons from the students, the teacher is able to gain deeper understanding of where the misconception occurred. This then informs the next steps of the teaching: which questions to ask and who to ask them to, what task may need to be conducted next and which examples needed to use on the board to correct the errors. In addition, it benefits other students who listen to reasoning of their peers; by comparing ideas to their own, they are able to highlight where mistakes were made and what the thinking was behind them. These reasoning skills are necessary for the AO2 and AO3 questions which students tend to struggle more with at GCSE.

The continued exploration of diagnostic questions in our lessons makes us very excited for the journey in developing formative assessment within our department.

[i] Williams, D., (2006), Assessment for Learning: why, what and how? (Cambridge Assessment Network Talk).

[ii] EFF’s guidance report, ​‘Putting Evidence to Work: A School’s Guide to Implementation.’

[iii] Lemov, D. (2015) Tech Like a Champion 2.0: 62 techniques that put students on the path to college. Hoboken, NJ: John Wiley and Sons.

[i] Barton, C., (2018), How I Wish I’d Taught Maths, pp. 337 – 387.

[i] Barton, C., (2020), Reflect, Expect, Check, Explain, pp. 287 – 295.

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