MASTERY MATHEMATICS AT THE EDRON ACADEMY PART 2

Coherence

We must work at a pace and within a structure that allows children to master every step of the journey. Small steps are vastly more accessible than giant leaps, and a rushed block of teaching is far less impactful than a measured curriculum that reinforces understanding at regular intervals.

Fluency

Central to a mastery of mathematics is the ability to rapidly recall and manipulate number facts. If a child must stop to calculate when asked to multiply 7 by 8, they are going to struggle to solve a complex word problem involving multiplication. If, however, they instinctively know that 7 times 8 yields 56, or if you can quickly sum up in their head that 19 plus 23 gives us 42, they can begin to tackle more difficult problems safe in the knowledge that they can focus on the problem itself, rather than the accuracy of their arithmetic. When we fear numbers, we shy away from them. When we understand them, that confidence to take on new challenges grows exponentially. For this reason, at the Edron Academy we dedicate time at the start of every lesson to mathematical fluency. In addition to this, we regularly conduct low-stakes testing to measure children’s arithmetical progress and identify areas where we need to focus our attention.

Representation & Structure

There is considerable research around the acquisition of abstract mathematical concepts (eg. Piaget, 1977, or Gifford, 2004). Since a number is not a real thing in and of itself, but rather a representation of a quantity, it can be tricky for children to make sense of number sentences in the abstract. That is to say, the question “What is the remainder when you divide 19 by 4?” is a lot easier to answer if you have material objects with which to make the abstract a reality. If I divide 19 blocks into 4 equal piles, I will find that I have 3 blocks left over. Therefore, our teachers help children to build a conceptual understanding through visual and kinaesthetic models, ensuring a solid foundation for their mathematical understanding, and enabling them to construct upon this foundation a contextual understanding of the problems they encounter.

Mathematical Thinking

To think mathematically is to understand the rules that govern numbers and to work creatively to make sense of those rules in the context of a problem. Therefore, we can say that at the heart of mathematical thinking lies reasoning, the ability to methodically work through and justify the necessary steps to reach a conclusion. We teach reasoning through discussions, group work and partner activities, with teachers constantly modelling the mathematical process and the justification behind each step that we take.

Variation

Our teachers vary their approach, representing concepts in more than one way to develop a deep and holistic understanding (NCETM, 2016). Variation keeps the learning fresh and exciting, and enables children to make connections, drawing attention to mathematical relationships and structure.

With this holistic approach to teaching and learning in mathematics, we foster a culture of excellence in which children feel inspired towards mastery, no matter their starting point. We make maths fun, accessible and rewarding for all students. We show our students that maths is more than a rigid set of rules governing numbers. Pythagoras was a keen musician, Bertrand Russell an innovative philosopher, and Nicholas Copernicus a visionary astronomer. In delivering a curriculum based on mastery of mathematics, we aim to give children the creative thinking and robust reasoning skills they need to succeed, no matter what avenues they pursue in their future lives.

James Hughes, Head of Primary