Secure Foundations: Testing Prerequisite Knowledge with Complete Maths

Thursday, 19 August 2021

In May we posted a blog exploring the importance of secure foundations when preparing pupils to move from primary to secondary school. In this blog, we aim to explore in more detail how teachers can use, and assess, prerequisite knowledge to identify weaknesses in pupils’ foundational knowledge, and to demonstrate how each of our platforms is designed to support this process.

Few teachers would dispute the notion that pupils will be more successful in studying a topic if they have understood the underpinning principles and knowledge behind it. On the flip side, few teachers would argue that large class sizes, mixed-ability sets or age-not-stage curriculums are optimal when it comes to ensuring every pupil has understood the previous step before moving onto the next one. That is not, however, to say it is impossible: with the right tools, and the right training, teachers can take a mastery approach whatever the context in which they are teaching.

In AskMark Volume 2, our founder Mark McCourt wrote that “A key ingredient of a mastery approach is diagnosing and fixing any gaps in prerequisite knowledge before pupils begin to learn a new idea. Done well, this can ensure that pupils with quite different prior attainment can work on new ideas at the same time and at pace.” Several factors need to be in place for this to happen:

  • Teachers need to know the underpinning prerequisite knowledge for the topic they are about to teach
  • Teachers need both the resources and the opportunity to test this prerequisite knowledge before beginning a new topic
  • Teachers need time to explore the results of any prerequisite test
  • Teachers need the freedom and opportunity to adapt what they planned to teach when prerequisite test results tell them it is required
  • Teachers need the confidence and the expertise to know how to deviate from the lesson plan or scheme of work
  • Teachers need the time and resources to differentiate their lesson, and any follow-up interventions, to suit the individual needs of each pupil within their lesson (for a more detailed exploration of what we believe effective differentiation in a maths classroom looks like, see Volume 3 of AskMark)

For non-specialists, NQTs or RQTs, and any teacher whose workload frequently impinges on their planning time (in short: for any teacher!) the list above is bound to pose at least one challenge. Luckily for us, Mark McCourt quite literally wrote the book on mastery and it is under his guidance and leadership that we’ve developed each of our platforms with a view to making it easier for teachers to follow this approach. This blog offers an exploration of how Complete Maths CPD, Complete Maths CLASSROOM and Complete Maths TUTOR can support teachers at every stage in delivering effective, mastery-based lessons.

Understanding Effective Mastery Teaching with

Our online CPD platform currently contains over 200 courses, covering pedagogy relevant to teachers of every age group and at every stage of their career. If you are looking to kickstart your mastery journey, or perhaps to refresh your knowledge and revisit the basics, then we would recommend starting with our hugely popular Mastery Learning course.

For teachers who are confident in the core principles of mastery, and now wish to explore the role of assessment and prerequisite knowledge in more detail, we recommend the following courses:

In Responsive Teaching, Gary Lamb explores different strategies through which teachers can know whether true understanding has taken place, as well as research and models for effective corrective teaching.

Doing the Right Stuff, delivered by Dave Taylor, covers practical exercises classrooms teachers can use to identify the right level of maths to teach, and how to get pupils doing the right stuff from the moment they enter in year 7 through improved curriculum planning.

Getting Teacher Assessment Right, led by Mark McCourt, explores how and why we assess. Originally recorded in light of Centre Assessed Grades, it remains a thought-provoking discussion of the role of assessment within the classroom.

Numerous schools and organisations are now launching what we have nicknamed a ‘CPD Bookclub’ using our online bank of CPD courses. This involves a group of teachers agreeing a focus, selecting relevant courses from Complete Maths CPD, and then either watching and discussing the course together in small chunks, or watching the course at home then meeting to discuss it at a later date. If you’d like to read more about how Sir James Smith’s School in Cornwall implemented a CPD Bookclub, check out their case study on our website.

If you’d like support in creating a CPD plan for your team, we can help by recommending courses and providing a discussion guide to structure your feedback session. Get in touch to discuss your requirements by emailing This email address is being protected from spambots. You need JavaScript enabled to view it.

Embedding Prerequisites into Lessons with

Earlier this year we launched our new lesson page, which provides teachers with the prerequisite knowledge for every objective added to a lesson. The video below demonstrates how CLASSROOM can be used to create readiness quizzes for pupils to complete either at home or on devices in lesson before beginning a new topic, with the level of depth specified by the teacher in advance:

Even if you don’t have access to devices in school, the prerequisite strands can be a valuable tool in lesson planning. Fiona Wilmot from Bewdley School talks about this in depth in her school’s case study, also available on our website. In the case study, Fiona describes how “[One of our staff] was using it as a very detailed diagnostic: ‘This is what they need to know beforehand. Do they?’ Testing that they were okay before moving on. And it made his teaching far more effective and far more secure.” Each objective is also supported by detailed teaching notes including common misconceptions, which non-Maths specialists in particular report finding incredibly useful when following a mastery approach.

It is also worth noting that these readiness quizzes can be exported as a pdf and printed off – schools have then used them as revision resources, sources for quiz questions, or as the backbone to readiness work in lessons.

New and existing CLASSROOM subscribers have access to free platform training as part of their subscription; if this applies to you we would encourage you to take advantage of the offer if you haven’t already and see how the new lesson page, and especially the readiness quizzes, could work in your school.

Testing and Fixing Prerequisite Knowledge with

Private tuition is considered the gold standard simply because a tutor’s modus operandi is finding out what a pupil doesn’t know and then addressing this, something that becomes far more challenging in a group. TUTOR was built to ensure every single pupil could have access to bespoke maths teaching, delivered by an expert, and thus providing the benefits of tuition without the sometimes prohibitive cost.

There are two ways in which pupils can approach learning on TUTOR: the first is to allow the platform to assess them and pinpoint a starting point in the maths universe. From here, pupils will have a bespoke course mapped out in front of them, which responds to and re-charts their journey following every completed quiz. This iteration of TUTOR is in its final stages of development at the time of writing, and will be available to pupils very soon.

The second option is for pupils to enrol themselves on, or for teachers to enrol pupils on, a ready-made course. Each course is made up of ideas, and each idea is broken into a number of goals; each goal in turn begins with pupils being shown the prerequisite knowledge required, and prompted to take a short quiz testing this knowledge. At the end of the readiness quiz, if pupils score less than 80%, they will be prompted to ‘fix’ any gaps and directed to Learn and Do videos exploring the specific topic in more depth.

In both cases, the testing of and response to prerequisite knowledge is key. In an earlier blog post, we explored the ways in which TUTOR could be used to support teaching and learning in and out of the classroom. When it comes to prerequisites, our focus today, TUTOR is most valuable as a resource not just for assessing the readiness of a pupil to move on to a new topic, but also as a form of intervention after the lesson if a teacher believes gaps remain.

Many schools have told us they plan to use TUTOR this year in place of normal lunchtime or after-school intervention — rather than have one maths teacher deliver the same lesson to a slightly smaller group, a member of staff from any team or department will instead supervise pupils working on TUTOR. Pupils working from home can similarly benefit, meaning those not included in school-based interventions won’t miss out. In this way, even teams made up of non-specialists, or with lower levels of experience, can ensure every pupil’s knowledge of prerequisites is continually checked and, when needed, addressed.

Putting Prerequisites at the Heart of the Curriculum

Prerequisite knowledge is core to what we do at Complete Maths: we want to map it, test it, and help teachers react to it at every possible opportunity. If your team feels the same, or if you want our help moving your team in this direction, then we want to hear from you.

  • Could you collaborate with us on a retrospective case study, sharing with other schools how you used our platforms to embed the testing and teaching of prerequisites in your school?
  • Would you like to collaborate with us on a forward-facing case study, in which we work together to help your team use our platforms to develop your use of prerequisites?
  • Could you deliver a workshop at our next MathsConf sharing how you use prerequisites in your classroom?

We mean it when we say our work is driven by what teachers need, and by what will help improve the mathematical education of all pupils. We can’t do it without you, our Complete Maths community, so if you think you can help, or if you think we can help you, then get in touch: This email address is being protected from spambots. You need JavaScript enabled to view it.

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