Luke Rolls is an Associate Headteacher at the University of Cambridge Primary School. Luke recently co-edited the book Re-imagining Professional Development in Schools as part of the Routledge Unlocking Research series.
1. If you had to sum up your school’s view of mathematics as a subject in one sentence, what would it be?
In spirit, maths is fundamentally about problem solving and possibility thinking.
2. How does your school embed numeracy across the curriculum?
Our STEM leader Lucy Bullen-Smith has this year been trialling using multidisciplinary STEM projects in the curriculum. The purpose of these has been to develop knowledge, understanding and skills in science, technology and maths as parallel threads of learning that then culminate in enrichment weeks. These allow children to bring together their understanding, apply new thinking and make connections in an interdisciplinary way.
Rather than mathematics being just a lesson they take once a day, we try to support children to think of maths as a lens through which they can interpret the world. This means that whether we are lining up in pairs, sorting scissors in the storing block or solving measuring problems when cooking, children get to “see” the maths all around them.
To inspire children in the wider field of STEM, we regularly invite speakers who are specialists in their fields. We have welcomed astrophysicists, epidemiologists, mathematicians, robotics engineers, environmental scientists and university students. We strategically plan these inter- and trans-disciplinary experiences into sequences of learning so that children experience maths that goes beyond the expectations set out in the National Curriculum. Through children making meaning of maths in the context in which they live and experience the world, we want them to relate what they learn to the much larger fields of human experience and knowledge.
Alongside these, we promote ways in which we can integrate maths in different subjects; for instance, in computing, through coding Sphero robots, children learn practical problem-solving and logical reasoning skills whilst engaging with curriculum geometry objectives in position and direction and angles.
3. What is your view of mathematical ability and how is that supported by your school policies?
Our school was founded on the ethos that we do not label children as being of a certain “ability.” We hold values of inclusion at the heart of what we do: giving the time, space and support for children to flourish and surprise us. One child for example who joined my class five years ago in Year 2 was working well below age-related expectations and presented with little number sense. Had they been set by so-called “ability,” I don’t believe they would have achieved the trajectory they did. They transitioned to secondary school with an in-depth grasp and fluency of maths, and on standardised assessments as one of the highest performing children in the year group.
For me, children are born mathematicians with what John Mason refers to as natural “mathematical powers.” When a toddler picks up a shape toy, they are motivated to make it fit through the corresponding space in the box. They persevere and want to solve the problem. The feeling of “aha” that comes with overcoming a cognitive obstacle is something that is inherently satisfying; it gives us a sense that by working through perplexity, we can break through and resolve order out of disorder. Before formal education, children experience maths all the time in these intuitive, exploratory ways. I think it is when maths learning becomes experienced in a way that is unreasonably difficult to make sense of that both achievement and a learner’s sense of self-efficacy can then be negatively impacted. While we can never be fully sure of the many cultural and social effects of meaning-making on these journeys, skilful and inclusive teaching seems to bring an equalising effect so that children are not limited. For me, this is why it is crucial that professional development is a protected entitlement for all teachers and teaching assistants – for the extremely important work they do.
4. If I came into a maths lesson at your school, what would I always see? Sometimes see? Never see?
You would likely see different forms of learning depending on the stage of a lesson. Children might be engaging in:
- a collaborative problem-solving task in their stable triad groups;
- sitting altogether as a class community and sharing their representations and solutions for a problem where children are querying and elaborating on each other’s thinking;
- reviewing previous learning;
- a maths story that leads them to mathematical role-play;
- a maths game that develops their fluency and strategic thinking;
- listening to a teacher teaching from the front;
- practising questions and journaling independently;
- challenging themselves with questions like “What if…?”
We think that when implemented well, these types of learning structures can give children a balanced diet of maths that has meaning and purpose and that works on targeting the sweet spot of challenge.
What would you never see? I would say a dull-feeling classroom where everyone is going through the motions without any heart or interest. Hopefully, what you would always see is children visibly enjoying maths and relishing both struggling and succeeding. We often notice that in maths lessons across the school, we can hear many indicators of play such as laughter, wonder and excitement. In a maths lesson…! I know!
5. What are your favourite mathematical tools, objects or manipulatives and why do you like them?
Cuisenaire rods, because of their versatility. Children are naturally motivated to play with them and they powerfully help children see the structures of the maths they are looking at. When we help children not to become fixated on a rod being equivalent to a unique value, they start to attend to relational thinking. I enjoy blowing their minds with cuisenaire rods: the way of zen videos where the rods are shown to represent amounts from 37 to a trillion.
6. How does your school support professional development of teachers in mathematics?
We engage teachers in professional learning in several ways. A simple one, though sometimes not always thought of as professional development, is weekly collaborative lesson planning. We do not follow one scheme of work, but we do actively provide teachers with access to the best teaching materials we can find – from countries such as Japan, China and Singapore as well as the UK. The process of exploring the space between the intended and implemented curriculum asks us to consider how we will sequence a unit of learning, what the misconceptions are, how we will attend to these, what the most powerful representations and manipulatives will be, and what language structures will support children’s thinking. We have iterated our planning now for over five years, and year on year teachers work to improve what went before.
We have also introduced a coaching cycle per term. Each teacher has the opportunity to work with our leadership team who focus on modelling, team-teaching or observing lessons using an appreciative enquiry model called “Observations for Success.” Through coaching, teachers identify an area they would like to focus on in their practice and the coach supports them by collecting data against the area of focus. We find that teachers respond very positively and are motivated to engage in following up with the findings of the coaching cycle, adapting and integrating new aspects to their practice.
As a member of the Collaborative Lesson Research Group, we are running a lesson study this year in Key Stage 2 with Professor Mike Askew and Dr Julie Alderton, who are guiding us to look into effective ways to teach multiplication as scaling. As part of that project, we have six planning sessions exploring the subject, pedagogical content knowledge and progression of multiplicative reasoning. At first, we baseline children’s understanding, analyse their responses and then use that information to plan a medium- and short-term sequence of learning. At the end, we will come together to watch the lead teacher Ellen Millar deliver the lesson and observe children’s responses. Last year, we carried out a similar project investigating the teaching of fractions on a number line. We are always amazed at how our findings can contradict common practices and thinking.
We publish our staff meeting professional development sessions on the Unlocking Research website – these talks are not always maths-specific, but they are often relevant to maths teaching and look at pedagogical areas such as developing metacognitive thinking or supporting children with working memory difficulties.
7. What is your favourite quote about mathematics?
I will go with “mathematics is not a spectator sport” by George Pólya. I think it sums up why people do not always have a favourable experience of learning maths; it is something which can be felt as being done to them rather than as something inspiring and energising. To be a good learner, you need to be a good listener and open-minded, but you also need to have a chance to have a go, to get it wrong, and the space to be curious and find out more. For children, they know what they are likely to expect and how they feel about it when they walk into a lesson. As Paul Lockhart said, mathematics needs to be experienced as “an adventure.”
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