Winston Churchill’s early encounters with mathematics were not especially positive. In his biography, he recalled that the numbers he was confronted with seemed to be ‘tied into all sorts of tangles and did things to one another which it was extremely difficult to forecast with complete accuracy.’ Much later, when he was at Harrow, Churchill resolved to get to grips with mathematics – he had no choice if he wanted to pass into Sandhurst. The rapid progress he made was in part a consequence of his own single-minded determination, but Churchill gave much of the credit to a particular master at Harrow who convinced him ‘that mathematics was not a hopeless bog of nonsense, and that there were meanings and rhythms behind the comical hieroglyphs’.
The ‘meanings and rhythms’ that Churchill became aware of are fundamental to understanding mathematics. Learning mathematics is primarily about noticing and explaining patterns. At Vinehall, we want children who know that 8 + 7 = 15 to recognise that if they know this simple addition fact they also know the answer to 15 – 8 and 68 + 7 and 80 + 70 and 1500 – 700 and a whole host of related sums. Fundamentally, we want the children to appreciate that mathematics is not a vast collection of discrete and disparate results to be memorised but a web of interrelated and overlapping ideas.
At Vinehall, a mastery approach to learning maths is used throughout the pre-prep and into the prep school. Teaching maths for mastery means that a greater emphasis is placed on children using visuals to aid their understanding of mathematical concepts. Mastery lessons are also structured differently as they begin with an exploratory phase during which children are presented with a problem and given time to investigate the question collaboratively, before coming together as a whole class to take part in a structured discussion.
Utilising a mastery approach, it is our intention at Vinehall to ensure that all children become proficient with the fundamentals of mathematics, preparing them for their future schooling as well as the world beyond. Alongside this aim, it is also hoped that the children will derive pleasure from mathematics and will learn, as George Polya remarked, to ‘experience the tension and enjoy the triumph of discovery’ that solving problems entails.
Finally, and perhaps most importantly, throughout the school the prevailing philosophy is that children learn maths by doing maths.