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At Preston Park, we have created our personalised curriculum which embeds the mastery approach to mathematics whilst ensuring greater depth is designed in all lessons using SOLO taxonomy.

What is teaching for Mastery?

Preston Park have attended the Central and West London's Maths Hub's Teacher Research Groups, and have developed the teaching of maths mastery across the school. A central component of the NCETM Maths Hubs programmes are the Five Big Ideas which have been drawn from research evidence. The Five Big Ideas underpin the teaching and learning in mathematics.

Overview of the Five Big Ideas:

Coherence: Connecting new ideas to concepts that have already been understood, and ensuring that, once understood and mastered, new ideas are used again in next steps of learning, all steps being small steps

Representation and Structure: Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation

Mathematical Thinking: If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others

Fluency: Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics

Variation: Varying the way a concept is initially presented to students, by giving examples that display a concept as well as those that don’t display it. Also, carefully varying practice questions so that mechanical repetition is avoided, and thinking is encouraged.


How is Greater Depth achieved?

At Preston Park, we have developed the PEER model which is based on John Hattie's SOLO Taxonomy. SOLO, which stands for the Structure of the Observed Learning Outcome, is a means of classifying learning outcomes in terms of their complexity, enabling us to assess students’ work in terms of its quality. It was proposed by John B. Biggs and K. Collis and has since gained popularity. SOLO taxonomy focuses on more the teaching and learning, whereas, Blooms taxonomy focuses more on knowledge. One of the most important things to understand about SOLO is that it describes a journey. You have to progress through the levels and cannot jump straight to deep learning

As Hattie put it recently, “you can’t do the deep stuff until you know the shallow stuff.” You can’t link things together until you have things to link together. This is one of the reasons ‘problem-based learning’ strategies score so poorly in his Visible Learning rankings (0.15 ES where 0.4 is mean average). In Visible Learning, he wrote, “…this is a topic where it is important to separate the effects on surface and deep knowledge and understanding. For surface knowledge, problem-based learning can have limited and even negative effects…” You can’t solve problems until you are fluent in the skills required to solve the problem. It’s like trying to solve a jigsaw without having the pieces. Deep learning is about links. Firstly, links to other things within the same topic, then to things outside the topic. 

How does the PEER model support Mastery in Mathematics?

At first, we pick up only one or few aspects of the task (unistructural), then several aspects but they are unrelated (multistructural), then we learn how to integrate them into a whole (relational), and finally, we are able to generalised that whole to as yet untaught applications (extended abstract). Tasks for each lesson are designed to ensure children move from the concrete to the abtract in each lesson.

What does PEER stand for?

               The prove task (unistructural) is where the task set focuses on just once relevant concept. There is no explanation of thoughts                       and children are able to follow the steps to success to meet the learning objective.


     The explain task (multistructural) should allow children to build upon the prove task where they can offer several relevant                     details. At this point there is not integration of additional knowledge, they simply explain the process to show how well they                                  understand the concept.


      The explore task (relational) should build upon the ideas of variation. This can be procedural or conceptual variation, providing            an opportunity for children to link ideas that relate all the facts from the relevant concept (from the prove task) and at the same            time integrates prior knowledge.  


      The reapply task (extended abstract) is the dong nao ting aspect of Mastery maths, where pupils can recognise the relevant                  concept and recognise other possibilities and abstract principles. Learning goes beyond what has been taught.


Click on the year group below, to view the mathematics coverage for the academic year 2017-18:

   Year 1   Year 2    Year 3   Year 4   Year 5  Year 6

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