Realistic Mathematics Education (RME) was originally developed by the Freudenthal Institute in the Netherlands, and is widely used there.  In RME, mathematics is developed by working with contexts which provide a source for generating mathematical models and hence a deep understanding of where mathematics comes from.  Contexts can be taken from the real world, from fiction or from an area of mathematics that students are already familiar with – the important thing is that students are able to imagine and engage with them.

The RME curriculum uses contexts which have potential for model building, and teachers encourage learners to gradually refine the multiple informal strategies which they naturally bring to a problem. Experience shows that, through staying connected with the context, they are able to continue to make sense of what they are doing, without the need for memorising rules and procedures which have no meaning for them.  When students work in context, rather than in the abstract, they are doing more than learning a particular type of mathematical technique.  They are using mathematics to solve problems.

RME pedagogy supports teachers in enabling students to connect their informal representations of the world to formal mathematics, building from shared understanding of imaginable contexts to recognition of the mathematical sameness of different problems and the ability to choose an appropriate model to solve a problem (Van den Heuvel-Panhuizen, 2003).

Materials are structured so that students at all ages and levels of attainment can engage with the same problem context. Training in the use of RME materials includes helping teachers to develop classroom cultures that feature active mathematising by pupils and discussion and sharing of strategies.  The key features of an RME classroom are:

  • extended discussion of multiple contexts
  • development of students’ representations of contexts
  • focus on multiple strategies for solving problems
  • sharing, explaining and discussing strategies

RME classrooms create a shift in “socio-mathematical norms” (Yackel & Cobb, 1996) which make them more inclusive – students are able to develop ownership of mathematics and engage confidently in discussion. They are encouraged to take their modelling as far as they can, while maintaining links to the context from which they are generated.