Using Complete Mathematics to Support Implementing a Mastery Curriculum
Written by Chris McGrane Thursday, 19 September 2019
Mastery learning is a well-defined approach to schooling. It originated in the work of Carelton Washburne and was later developed by John B. Carroll and Benjamin Bloom. Mastery is a model of schooling which has, at its heart the belief that every pupil can learn the school curriculum.
Thomas Guskey further developed the work of Washburne, Carroll and Bloom and codified the core elements of mastery learning:
- Diagnostic Pre-Assessment with Pre-Teaching
- High-Quality, Group-Based Initial Instruction
- Progress Monitoring Through Regular Formative Assessments
- High-Quality Corrective Instruction
- Second, Parallel Formative Assessments
- Enrichment or Extension Activities
Mark McCourt, the UK’s leading expert on mastery learning and CEO of La Salle education has gathered these core elements into the following mastery learning cycle.
Implementing a Mastery Curriculum
Moving to a mastery curriculum is not a trivial process. Succeeding with implementing a mastery curriculum depends upon the following:
- A rigorously designed curriculum – this is essential such that the development of the key skills, ideas and relationships are coherently planned for.
- A well-resourced curriculum – with quality resources, teaching notes and assessment tools.
- Expert teachers – teachers who have the understanding of pedagogy, didactics and reactive assessment processes.
Complete Mathematics subscriptions can support the implementation of a mastery curriculum in your school by addressing all three of these concerns.
A rigorously designed curriculum
Our curriculum is not based upon that of any one nation. Instead it has been developed with the best of mathematics education research and professional knowledge in mind. From the early learning of number through to advanced level ideas such as calculus, the entire curriculum has been planned out. It is broken down into units, each of which is made up of various key mathematical ideas. Each idea contains 'granules', with each granule representing one step towards the mathematical idea that is being learnt.
There are 204 units, containing 320 big mathematical ideas. These ideas appear many times in different units over the years as the curriculum deliberately spirals and pupil understanding strengthens. Each idea is scaffolded carefully as a journey to building the idea; these carefully sequenced steps gradually build up each idea. There are over 1600 steps in Complete Mathematics.
A well-resourced curriculum
The Complete Mathematics platform contains all of the resources you need to plan and implement a mastery curriculum in your school. It includes tools for planning, assessing and reporting. Every granule has a full set of supporting materials and teaching aides for use when planning as well as content to use with your pupils.
Subscription to our Teacher CPD College entitles each teacher to unlimited access to our CPD courses, accessible anytime, anywhere. These high quality CPD courses develop teachers practical and theoretical understanding of how to teach mathematics effectively – be it in the primary, secondary of post-16 sector. Teachers who subscribe to the CPD College have exposure to a vast array of professional learning.
Using Complete Mathematics to Implement the Mastery Learning Cycle
For every single granular step of the Complete Mathematics Curriculum there is a wealth of material to support your teaching.
You can view the pre-requisite knowledge for this granule and view the subsequent ideas which depend upon fluency and understanding with this idea. There are extensive pedagogical notes and lists of common misconceptions for every granule. These notes are drawn from both the literature on effective teaching of this idea and from the experience of the expert team at Complete Mathematics.
Importantly there are example questions for each of the granules. These are split into typical, probing or hard question types. These indicate the sorts of questions that pupils, who have understanding of the idea should be able to answer correctly.
For each of the granules there is a resources and tutorials section. This includes resources associated to this granule which have either been created by the team at Complete Mathematics or uploaded by our members. These resources can help to simplify the planning process for teaching each granule. The tutorials section contains links to videos which explain the ideas and skills related to each granule.
Also, for each granule there is a summary of 'Key Learning Points', 'I Can...' statements for pupil self-evaluation and a breakdown of key vocabulary. It is important that pupils are exposed to the correct terminology and can become fluent in their description of mathematics.
With this array of supporting materials available at every step within a unit, a teacher can spend less time searching for guidance or content and more time perfecting their methods of teaching this piece of maths. If corrective teaching is needed, a teacher can dip back in the curriculum via the listed pre-requisites and find the right support and content immediately. Additionally, with the more advanced materials found in the example questions and resources sections of a granule, there is great scope for topic enrichment and enhancement activities.
At the start of a new episode of learning we need to ensure that we are teaching pupils the correct mathematics. We know that pupils must be secure in the prerequisite ideas or else subsequent learning will not be possible. There is no such thing as a weaker pupil, only a pupil to whom we are teaching the wrong mathematics.
The assessment creation tool on the platform generates a pre-teaching diagnostic for the current topic. Pupils can do this on their own devices or you can generate a PDF and print this out.
The platform will generate a question by question analysis for this assessment to let you plan next steps for your class. For those pupils who need some re-teaching of this prerequisite work you can view the granules on the platform to plan for this and to find appropriate tasks and exemplar questions etc. For pupils who have demonstrated fluency the hard questions on the prerequisite granule can be used to offer challenge and further depth.
Similarly, as your class are working through the curriculum it is possible to generate quizzes, to formatively assess their learning. A powerful assessment tool which is built into the platform allows us to assess what pupils have been working on in class over a specific time period. This means we can think about retention and the long-term durability of the learning, rather than just instantaneous performance at the time of teaching. This also allows us to utilise key aspects of cognitive science such as the testing effect and interleaving effect to enhance learning.
Continuing round the Mastery Learning Cycle — following the completion of our teaching for each part of a particular Unit and having identified through our regular formative quizzes that no-one in the class requires further remediation, we use the Custom Diagnostic Test creator on the CM platform to create a Summative test on the whole of the Unit.
If the assessment markbook identifies further required remediation, we proceed to some corrective teaching, once more using the available support materials, resources and pedagogical advice found in each granular objective. If however everyone in the class scores appropriately on the summative assessment, then we move forwards onto the planning of the next Unit, and restarting the cycle, with the knowledge that we a building on strong foundations of understanding across the class.
The Complete Mathematics platform continues to evolve to help teachers implement a mastery approach. If you are interested in learning more about the work we're doing, or how you and your institution could benefit from Complete Mathematics subscription then do please get in touch. Our school support team would be happy to arrange a complimentary visit, webinar or phone call to discuss this — book your free demo.
Part of our Teacher CPD College is our hugely popular Mastery Learning course. This is also available as a stand-alone course, and you can find out more details here.
About the Author
Chris has 13 years of teaching experience, spread across 3 very different schools. Before becoming Mathematics Lead for La Salle in Scotland he was Principal Teacher of Maths at Hillhead High School and oversaw the design and implementation of a mastery curriculum - the first of its type in Scotland. The work was been hailed as sector leading, while attainment improved over this time. Chris is an avid reader of literature relating to mathematics education and has shared both this learning and practice from his own classroom regularly at conferences, where has been a popular speaker. Chris has appeared on recent episodes of Craig Barton's podcast and is scheduled to appear for an extended interview in the coming year.
Chris has played a role in moving forward professional dialogue regarding mathematics education in Scotland. In addition to conference presentations he uses Twitter daily to share insight, ideas and opinion. He regularly publishes articles on his blog. Chris is the lead of the Glasgow branch of the Association of Teachers of Mathematics (ATM), which regularly puts on events with expert speakers. Recently, reflecting his interest in effective task design, Chris launched the website startingpointsmaths.blogspot.com which shares tasks he has written and collated from colleagues.