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Maths is a journey not a destination | Maths in the Prep School

15 May 2019

Robert Hicks

Assistant Head (Academic) Prep School Director of Academic Systems

  From Wellington’s opening year, we have always worked very hard to foster the idea among all our pupils that maths is nobody’s enemy. In more traditional educational setups, maths has often suffered something of a negative reputation for being a dull, non-creative subject that is all about completing reams of problems with no deeper purpose than acquiring a familiarity with numbers and formulae. At Wellington, this is fundamentally not the approach we take to teaching maths to any age group. Instead, we aspire to make maths a much more interesting, investigative subject that gives pupils the tools they need to better understand the world around them.  
Freedom to explore, to experiment, to fail and to try again
A big part of this process is to give pupils the freedom to use different methods to the mathematical problems we set them. They’re encouraged to try different approaches, even to get things wrong as part of the process then reflect on why and how they can improve their method before discussing their efforts with each other and their teachers. While this can prove to be an adjustment for some pupils, they almost always warm to it quickly. The end result is that we produce mathematicians who care much more about the process, the ‘journey’, than the final answer, which is usually just a number and isn’t inherently all that interesting. This is an essential part of fully engaging with maths and it’s equally essential that this way of thinking starts as early as possible, which is why we instil it in our Prep School pupils.  
Enjoying maths as a journey
Approaching any mathematical problem becomes much more interesting when pupils are faced with a number of different journeys they can take to get to the destination. They might take a path that is simple but laborious, or they might try a different approach that is technically more tricky but also more efficient. Perhaps they might even take a sort of ‘scenic route’, where they use a combination of various techniques and subsequently discover more about the question and other supporting mathematic principles as they answer it. Pupils are also encouraged to work in different ways to discover what suits them best. Our general classroom practice in the Prep School is to start off by setting pupils a difficult problem, and with minimal guidance we see how far they can get on their own. They can work individually, in pairs or small groups, they can work in their books or on mini whiteboards, or using computers if they prefer. What’s important is that they have the autonomy to decide how they want to approach the set problem. Whatever they decide, our expectation is that they must be prepared to justify their approach and then explain their investigations to the rest of the class. Often this will inspire pupils to try different ways of working and approaching problems when they see their peers delivering a good explanation of their work. Nobody is afraid to get things wrong, in fact, pupils can sometimes learn as much from failed approaches as successful ones, as they learn to refine their method or decide that another one might be more appropriate for the current task. In every case, we can see Prep pupils engaging with the task at hand, eager to try out their ideas and unafraid of the outcome.  
Applying maths in a wider context
Another way in which we try to make maths as engaging as possible early on in pupils’ academic lives is to continually link what they learn in the classroom to the wider world. Pupils can explore maths in the tessellation of Islamic tile patterns, in the formation of features of the natural world, in the trajectory arc of a kicked football. The main message we aim to reinforce as much as possible is that maths is everywhere; it doesn’t exist purely as a line of numbers on a page. This concept is also closely linked with our efforts around instilling global citizenship. For example, we might contextualise Pythagoras’ Theorem by briefly exploring his life and its impact on Ancient Greece’s society as they applied mathematics to create a wondrous building previously undreamt of. Or when we talk about place value, we can discuss the invaluable contribution that India made by inventing the digit ‘0’, number system. Or, whenever we use statistical graphs and charts, we will aim to utilise real-life relevant data, such as population figures or political affiliation percentages in various countries. In each case, we are able to make these real-world links clear to our pupils and show them how maths can help them navigate what’s going on today, as well as yesterday and maybe even tomorrow.  
Throwing down the gauntlet, maths-style
Another important part of making maths engaging is to make it sufficiently challenging. Not only do we aim to do this in every lesson with appropriately challenging problems based upon genuinely interesting contextual scenarios, we also introduce pupils to other mathematical challenges that go beyond the classroom. A prime example would be Wellington’s annual participation in the UK Junior Mathematical Challenge, which is aimed at younger pupils from year 8 and below. It’s a global competition and thousands of schools around the world take part. Each year we usually score in the top 10-15% of the competing schools and many of our pupils perform well enough to receive bronze, silver and even gold medals. It’s a fascinating competition: not only are its questions very challenging, but in later rounds each wrong answer incurs penalty points. This means that pupils have to be strategic; they have to assess each question and decide if they’re confident enough to answer it correctly or if it’s just not worth the risk! While it’s a prestigious competition, it’s also just for fun, which makes it potentially be useful in desensitising pupils to the fear of future examinations. Another fun annual event we always look forward to in the Prep School is the House Maths Challenge, held during ‘Wow Week’, which is the final week of the summer term. Previous years have been sci-fi themed, as I’ve played various alien baddies with our pupils having to solve maths problems in order to save the world. This year we hope to ‘go big’ and make it a whole theatre production complete with the ability for pupils to log into the event on their personal tech devices. This will allow them to contribute to the competition happening on stage in ‘ask the audience’ and other audience participation scenarios. Watch this space for more details!  
Preparing pupils for the next step of the journey
If maths is a lifelong journey, then it’s essential that pupils have the right tools and supplies early on. That’s what we aim to give them in Prep School. We want each pupil to not only have sufficient grounding in various mathematical principles and techniques, but also a highly enquiring and experimental mind that isn’t afraid to try different paths to see where they lead. To finish, I would like to hand over to Kate McNeil, who has done a fantastic job as Head of Prep Maths since joining us this year. Not only is she fantastic with the pupils, she is also full of ideas about how we can keep improving our maths offering and subsequently keep it as relevant, engaging and exciting as possible.
As an educator who has a great passion for the subject, it is a privilege to be leading an inspirational team as we move along this journey. Wellington Prep pupils not only have the aptitude to succeed but also the determination to continually build on their knowledge and understanding through the experiences that Rob has described.In continuing this journey, it is important to view mathematics not as a stand-alone subject, but one where our pupils will develop their cross-curricular learning and life skills. In the upcoming year, we will continue to take pupils out of their comfort zone, building resilience and encouraging creative thought through ‘mastery’ approaches; developing their strategies for tackling the unknown.Further focus on evolving the levels of oracy required to effectively convey reasoning and depth of metacognition with fluency will benefit our pupils holistically. With a wider range of competition opportunities ahead next year, we look forward to watching them shine!