Realistic Mathematics Education

Realistic Mathematics Education, usually abbreviated RME, is a domain-specific instructional theory for teaching mathematics developed in the Netherlands from the 1970s onward at what became the Freudenthal Institute, associated above all with the mathematician and mathematics educator Hans Freudenthal. Freudenthal argued that mathematics should be treated as a human activity to be reinvented by students rather than a ready-made body of knowledge to be transmitted to them, so that students are guided to mathematize situations they can imagine, gradually building formal mathematical concepts, tools and procedures out of informal reasoning about problems that make sense to them. The word realistic in the theory's name does not mean strictly real-world or true to life; it traces to the Dutch verb zich realiseren, to imagine, so a realistic problem under RME is simply one a student can picture and engage with, whether or not it describes an everyday situation. Rich problem situations under RME serve a double role, first as the source from which mathematical concepts and procedures are developed and later as a context in which students apply what they have learned, with instruction typically progressing from informal, context-bound strategies toward more formal and general mathematical reasoning. Since its development, RME has spread well beyond the Netherlands and has influenced mathematics curricula and instructional design in countries including the United States, England, Germany, Denmark, South Africa, Brazil and Japan.