RME Conference for teachers, July 2022

Starting from somewhere

The theme for the day was ‘starting from somewhere’.  In RME, we work on the premise that all students come to mathematics classes with ideas that we can work on.  So starting with where students are is key to how we aim to teach.

We start by looking closely at how students approach a familiar situation – like swimming races or filling a school hall.  So the conference focused on thinking about how to listen to students and build on their informal understandings…

BUT

Major change isn’t always an option in today’s schools. So we focus on starting from somewhere – what can you do on Monday morning?

The sessions in the conference focused on showcasing RME in a model lesson from ‘Exploring Space’ (G2) led by trainer Jo Kennedy, followed by a deeper dive by Sue Hough, Steve Gough and Kate O’Brien into how context works in RME, how we use the bar model and the ratio table, problem-solving approaches, and research and RME.  We also shared ideas with a range of RME practitioners from around the country, who contributed a panel session on various topics including establishing  a classroom culture, carrying on with RME up to GCSE, and the RME fit with mastery approaches.

Notes on the presentations

Exploring context in RME

This talk focused on how materials designers use context to stimulate the development of informal strategies which can then be built on in the classroom.  Sue talked about the selection of images which evoke a context, and how the related text is designed to encourage learners to not only imagine the situation but also study the image very closely.  Looking carefully supports the generation of solutions which don’t require formal mathematical knowledge.  As well as providing support for the process of emergent mathematics, this enables all learners in the classroom to participate.  We zoomed in on the use of comparison questions in particular.  In RME these are not about working out ‘right’ answers to mathematics questions: instead, they promote relational understanding and students’ own mathematisation of a situation.  Context in RME isn’t a question of providing a ‘hook’ or an application: it’s about generating mathematical thinking itself.  This means that sometimes the context itself is mathematical, where the aim is to look closely at  patterns, structures and the links between strategies.  The PowerPoint includes many examples from our materials.  For more on context watch materials designer Steve Gough building on context, and read more about going back to context as a teaching strategy.  You can also read about the role of context in making sense of mathematics with RME.

Using models in RME

Thinking about how models work in RME follows on naturally from a focus on context in RME.  A major difference between RME and other approaches is that, in RME, models emerge as students engage with the context and think about questions like ‘how can we make this recipe for 8 enough to feed 20?’.  In this talk, Steve demonstrated how the informal jottings we might make in a cookery book to adjust a recipe for our particular needs leads to a more formal structuring of information in a ratio table. Similarly, making a realistic drawing of a subway sandwich in order to work out how much 3 people get if it is shared ultimately moves to a more formal bar model and a double number line. These emergent models enable students to keep hold of meaning even when dealing with contexts which have moved away from being visually bar-like, and many students begin to recognise that the ratio table is a bar model – but it pays little or no attention to scale.  It enables greater flexibility and efficiency, enabling students to answer a variety of questions, including at GCSE level.  Read more about the bar and the ratio table on the using models pages, and about the role of contexts and models in emergent mathematics on the RME concepts for research page.

Problem-solving in RME

This session focused on RME as a way of developing problem-solving approaches for all learners. Sue began by thinking about how real life problems compare with those we ask students to do in mathematics classrooms: in real life the problems matter to us; we might try to fix them ourselves; we have some confidence in trying our own solutions (although we might eventually need to get outside help); and we know that we need to be patient in finding a solution. This is very different to standard classroom problem-solving where students know that it is highly likely that their teacher will simplify the problem and indicate how they might go about it. And they are under time pressure. Students don’t develop confidence in their ability to solve problems, or experience in sitting with the problem or trying out ideas.  In contrast, RME pedagogy involves a number of strategies for promoting classroom cultures in which students expect, and are expected to, solve problems for themselves.  In her talk, Sue modelled the strategy of ‘Say what you see’ and asking ‘What else do you know?’ as ways of helping students to notice what is going on in a particular context or question and think creatively about it. She showed how, applied to GCSE questions, these approaches not only make a question more accessible, but also create opportunities for more challenging mathematical thinking.  Find out more about ‘Say what you see’ and related strategies ‘What’s the same? What’s different?’ and ‘Make time for thinking’ on our teaching strategies pages.

RME and research

Continuing the theme of noticing, but this time in research, Kate led a session focusing on how we research and what we can learn from it.  She pointed out that there are numerous concepts of interest in RME which present opportunities for noticing what students are doing when they engage with mathematics – the role of context in how they approach a problem, how they use informal models, how teachers can guide emergent mathematics.  While much conventional research focuses on contrasting pre-test and post-test results with large samples, smaller scale exploration of student thinking in classrooms is a rich source of learning for both teachers and researchers. New opportunities arise too when we begin to consider issues in including all students in mathematics, or how important mathematics is in understanding global issues like climate change.  We encourage teachers to start from somewhere and to keep in contact with us as they undertake their own research.  Find out more about research on RME and related literature, and think about noticing and other research techniques on our teacher researcher page.

Emergent theme of the day?  How much we use gesture in mathematics!