Diagnostic Teaching, Marking and Feedback, Numeracy

Theirs now to reason why: using Exit Tickets to improve pupil reasoning and explanations

Liz Hill – Teacher of Maths

In 2013, reforms to English and Mathematics GCSEs were announced. The aim of the new specification for mathematics GCSEs was to “demand deeper and broader mathematical understanding” whilst also requiring pupils “to apply their knowledge and reasoning to provide clear mathematical arguments.” (Nov 2013 https://www.gov.uk/government/speeches/reformed-gcses-in-english-and-mathematics )

When planning lessons, I not only think about teaching how and when to apply specific mathematical skills, but I also want to teach pupils to be able to offer a written explanation to reinforce their understanding, as per the new specification. Whilst I am aware that many pupils are able to articulate the ‘why’ and the ‘how’ verbally when questioned, the process of writing down the ‘why’ is often a challenge. Add to this that the syllabus is now larger and more demanding – how are you supposed to teach content and have pupils provide written mathematical arguments?

Enter the exit ticket!


I cannot take all the credit for the layout of my exit tickets, I commandeered it from MrBartonMaths and have tweaked it to fit with Sarah Bonnell’s marking policy.

The exit ticket is given out 10 to 15 minutes before the end of the lesson after a series of lessons on a topic has been taught. Pupils are to answer the four questions quietly and independently, although I encourage pupils with support workers to have a go at it alone.

From the pupils’ answers, I aim to learn how well the pupils understand the topic we have been studying. Each question is supposed to be more challenging than the last, and each question is diagnostic (a post to be written on this at a later date!) so I get a clear insight in to any misconceptions before even reading the pupils’ explanations.

On the right hand side pupils are meant to offer an explanation. I often tell them to imagine they are explaining to a martian how to work out the answer to the question. For those who aren’t confident and who struggle to write an explanation I ask for clear working out, since this is also a key skill in gaining marks at GCSE.

Since rolling these out in September, I have noticed that the ability of my pupils in articulating ‘why’ when asked has improved infinitely. My pupils are becoming more confident and detailed when sharing their method and thought process for solving a problem. Even more exciting are my pupils’ improvements when providing written explanations. Exit tickets are being answered faster and faster in classes where they do them regularly. Pupils have gained independence when starting their exit tickets – they are quiet, focused and thoughtful.

I have practised the exit tickets most often with my Year 8 class who are set 5 and often lack the confidence needed to allow themselves to progress. In September, some pupils were unable offer any explanation and I made it clear that they just need to circle A, B, C, or D (as I have said already, the diagnostic question lets me assess their understanding straight away). I mark the tickets with excitement and pride as I see the progress of the class. The same pupils who started the year circling only A, B, C, or D, now offer me working-out and sentences of explanation without assistance, prompts or hints whatsoever. When given further time during the feedback sessions, these same pupils are able to reason with my questions  and improve their answers. This will set them in good stead as they hurtle towards KS4 and start being expected to offer mathematical arguments to access the marks in the higher graded questions.



As my groups’ ability and confidence in explaining has improved, I must confess that my feedback on exit tickets has improved too. Each exit ticket is a marked piece of work with a WWW, EBI and clear questions, so pupils can develop their understanding and reasoning to take themselves to the next step. I am currently working with the Exit Ticket template version 2.0. If you think that you could use it for your lessons, and find ways to improve it, please let us know how it goes!

Diagnostic Teaching, Mastery, Numeracy

Mastery Approach to Teaching and Learning

Kiera McDonnell – Lead Practitioner for Maths

What is Mastery?

More traditional teaching methods assign a set amount of time for coverage of certain topics. However, over the past decade, theory has made a notable move away from teaching to a time constraint, to varying the time to ensure that pupils are confident and proficient in the outcomes and objectives before moving on to new content. To summarise, there is a far greater emphasis upon depth of understanding rather than a thin breadth of understanding.

The Mastery approach, first proposed by Benjamin Bloom in 1968, considers the critical links that pupils must make in their learning and that without certain concepts and processes true understanding is not possible. It would be unrealistic to think that a student could understand division without a deep understanding of multiplication. If the bedrock of understanding is not secure, any additional content or learning will not be either.

blur book stack books bookshelves
Photo by Janko Ferlic on Pexels.com

Mastery is less effective if high prior attaining students are accelerated through the curriculum, thus widening the attainment gap. Stretch and challenge are, instead, achieved through deep questioning, both by the teacher and by the student, and a demand for greater precision. In the same way, support is provided through strategies such as varied and multiple representations. Promoting a growth mindset mentality, the Mastery approach is built upon the belief that all students can reach a desired outcome with the right support.

How effective is it?

Due to the targeted and individualised nature of this teaching and learning approach, research clearly shows that Mastery has a very positive effect on student learning. Studies also show that, not only has there been a positive impact on attainment but that student enjoyment, confidence and sense of achievement is also augmented; this student confidence and enjoyment is also transferred to other school learning. The impact of Mastery as a Teaching and Learning strategy has also been found to be particularly effective when pupils work collaboratively, either in pairs or small groups. Learning from peers and supporting classmates in their learning not only improves cognitive understanding but, again, can also increase overall enjoyment. Finally, research evidence also shows that the process yields improvements in students’ confidence in learning situations, school attendance rates, involvement in class sessions and attitudes toward learning.

What are the implications for day-to-day practice?

Moving towards a more Mastery based approach in your classroom clearly requires planning. The need for continual, meaningful in-class feedback in order to effectively respond to the particular needs of your pupils is key. The provision of additional and alternative representation and models, alongside deep questions and problem-solving tasks that challenge students’ understanding, all require rigorous and careful planning. However, through implementing these strategies and introducing the idea of Mastery to your students you have the potential to instil in them the belief that they are capable of learning, and learning well, which, in turn will support them in their journey to reaching their full potential at school and beyond.


Diagnostic Teaching, Numeracy, Time saving teaching, Work/Life balance

Question Level Analysis

Hafsa Farhana – Lead Practitioner for Maths

Teaching a year 11 class can be daunting, especially when you know very little about them. This was one of the challenges I faced when I started teaching two year 11 classes at Sarah Bonnell. I wanted to get an overview of their strengths and weaknesses and use that to plan my teaching for the rest of the year. I needed to make sure that all of my lessons were effective in order to maximise learning in a short amount of time. To do this I used question level analysis (QLA) tables from the beginning of the academic year. This helped me devise a Scheme of Learning catered to my class.

QLAs are all readily available from exam boards websites with conditional formatting so you can see the Red, Amber and Green (RAG) scores for each student. I would also calculate the average as a class and RAG each topics. This is now a method employed by the Maths department for our year 11s to ensure we use the build up to the summer exam effectively and can have a systematic approach to revision.

A comment I often heard from students is that they didn’t know where to begin with their revision so I always share the analysis with the class and individual students. The feedback from students is that they found QLAs useful as they were able to hone in on their weakness so that their revision was purposeful.


The QLAs enable me to give whole class feedback, for example, anything that is Red as a class average, I will need to reteach as a priority. This could be as a whole lesson or part, a starter, homework or a flipped learning activity. The Amber topics can be addressed through starters in lesson or using experts in the class to support the learning of those who weren’t as successful as them in those particular topics. Anything above 75% are the strengths of my class and therefore not a priority to revisit.


When I first started doing this the downfall was that it was very time consuming to enter the data myself. Asking students to fill in the google sheet posed a problem as some students did not want their classmates to see their results. However, I recently discovered how easy it was to do using Google Forms.

I created a Google Form so that I could collect individual scores of my students and shared the form onto the Google Classroom. Within minutes my I collected all their results; I couldn’t believe how quick and easy it was!


This populates a Google Sheet which I then export and copy into the QLA file.

QLAs are not restricted to just exams, but they are very effective when used with diagnostic questions. Another way I use QLAs is by create a sub-SOL, where I can address the topics identified as starters for the term, thereby ensuring students are making progress without deviating from the department SOL so all topics are taught. The next thing I am keen to try is to use the QLAs to support my class in creating a revision timetable.