For school leadership teams

You may be reading this because mathematics teachers at your school have become interested in RME, or because you yourself are looking for ways to develop mathematics teaching in your school.  Particular areas of this website will be of interest to you:

• the ‘Getting started‘ pages explain more about pedagogic techniques, and about how our materials fit into the national curriculum
• the ‘About RME‘ pages explain how Realistic Mathematics Education works, and you might be particularly interested to look at the evidence-based research page
• the ‘For teacher researchers‘ page introduces teachers to ways in which they might research their practice together.

You will probably have some questions about RME from an SLT point of view.  We provide some answers here:

What can I expect to see in an RME classroom?

If you are visiting an RME classroom in order to observe, you may see some differences in comparison to regular mathematics classrooms.  RME can involve significantly more whole class discussion, and students spend less time working through exercises alone.  Typically, you might see:

• A lot of time spent talking about context – a fun run, a shopping trip, and so on. Sometimes discussion can be quite non-mathematical.  This is because RME builds students’ understanding by encouraging them to build their own models of contexts that they can relate to. It’s important that they engage with the context, and the teacher will spend time generating and discussing students’ representations of a context. Although it might appear that students are moving slowly towards formal mathematics, the time spent on groundwork will stand them in good stead later. This not only benefits lower attainers, but also makes space for higher attainers to extend their understanding and make important connections between mathematical ideas.
• Students talking about their strategies for solving even apparently straightforward questions. RME focuses on building students’ understanding of fundamental ideas, so that they have foundations on which to build solutions to more complex problems.
• An emphasis on diagrams and drawings rather than formulae. RME builds on students’ informal strategies for solving problems, and encourages them to draw what they know about a context in order to model it mathematically.  Abstract formulae will eventually appear, but students will understand where these come from and will not need to rely on memory.  RME provides students with a connection between rules and algorithms and the original contexts from which they were generated.
• Teacher questions that are open rather than closed. The aim in RME is not to head straight away for ‘right answers’, but to give students space to think.  This can look like the pace is slow, but students benefit from thinking time and will develop more robust understanding as a result.
• Plenty of student participation. Students will be invited to go to the board to demonstrate strategies and arguments, and to share, question and explain.
• An opportunity to develop mastery. RME fits well with the mastery approach, and shares its emphasis on developing conceptual understanding, the value of articulating thinking and reasoning, and opportunities for deepening knowledge across the whole class rather than accelerating a few.

What is different about pedagogic practice in RME?

In order to encourage students to ‘mathematise’ for themselves, there are some differences in terms of progress and pace, and how teachers deal with misconceptions or answers that are incorrect:

• Progress in mathematics. Progress in mathematics is sometimes seen in terms of procedural understanding and moving quickly to fluency in applying formulae or algorithms.  In RME, progress can be seen in terms of ‘mathematising’ – that is, when students are able to represent a situation diagrammatically, are able to explain their thinking, can find more than one solution to a problem, or are able to make connections between contexts and models.
• The pace may appear to be slower than normal. RME focuses on extended discussion, in order to give students an opportunity to develop their informal models. Although it might appear that they are moving slowly towards formal mathematics, the time spent on groundwork will stand them in good stead later. This not only benefits lower attainers, but also makes space for higher attainers to extend their understanding and make important connections between mathematical ideas.
• RME may start with more complex situations than is usual. RME doesn’t set up learning progression in terms of applying formulae in simpler settings and moving on to larger or more difficult numbers. Often, it starts with complex situations that cannot be easily solved with simple calculation or the application of formulae, in order to encourage students to develop models that they will ultimately be able to apply in numerous mathematical situations.
• Misconceptions or ‘wrong answers’ are not immediately corrected. RME relies on students developing the means to think for themselves and develop mathematical arguments about their models and strategies, and those suggested by other students. Teachers need to hold back on correction, in order to make space for thinking.  Some students, particularly lower attainers, may begin to contribute and engage more than they do in regular lessons as a result.

What about coverage of the curriculum and assessment/homework?

Our RME materials are aligned with the national curriculum and do not introduce new or different mathematical content. Pupils learn the mathematics they need to provide a firm foundation for the GCSE examination and hopefully have a better understanding of it and be able to apply it better.  We find that they often enjoy mathematics more, too. RME takes a ‘bottom-up’ approach which means that the curriculum is covered somewhat differently, and students’ work will look rather different too.

• Variable pace in coverage of the material. Your participating teachers are teaching 5 RME modules (each on a particular topic) in each of year 7 and 8, each one in a two-week block.  Rather than break each module up into individual lessons, we have provided enough material to cover two weeks of work, in the form of a single PowerPoint presentation which is supported by an extensive teacher guide.  Each module provides enough material for students to build their understanding, and teachers are encouraged to decide for themselves how long to spend on any individual slide – they might spend a whole lesson on just 1 or 2 slides in order to enable students to build informal models, but move more quickly through later slides once models are established.
• Curriculum coverage focuses on deepening understanding rather than repetition. Often, teachers find that they need to repeat learning from previous years because students have forgotten the methods they learned. Because RME focuses on building a deeper and more connected conceptual understanding, earlier methods can be connected with the developing understanding rather than being revisited in a repetitive manner. Students are therefore better equipped to solve non-routine problems of the kind now emphasised at GCSE and teachers can spend time fostering problem-solving skills.
• Students may write less in their books. Because they may be working on fewer exercises during RME modules, you might find that students write less in their books. All RME modules are supplemented with activities and worksheets, and the teacher guide suggests possibilities for extension.  Students may be asked to investigate a context during class or for homework, and instead of exercises might write about these in their books, or include photographs of their work.  We will be developing these aspects of practice in the training programme.

How can I support my colleagues?

Teachers embarking on RME are often developing ways of  teaching which are very different for them, and this can be challenging.  Lesson objectives may be more difficult to define than in regular lessons, and teachers may feel pressured to show progress. They may struggle at first to find a way to engage and challenge higher attainers.  Please support them as much as possible by recognising that RME is different, and requires change not only on the teachers’ part, but also in students’ expectations too.  Teachers may benefit from opportunities to share what they are doing with colleagues across the school – not just in mathematics.  Teachers in other subjects which more readily use discussion may have useful input to offer. Researching their own practice in lesson study, for instance, can also help teachers to develop their RME techniques.