Since 1971, the Freudenthal Institute has developed a theoretical approach towards the learning and teaching of mathematics known as ‘Realistic Mathematics Education’. RME incorporates views on what mathematics is, how students learn mathematics, and how mathematics should be taught. The principles that underlie this approach are strongly influenced by Hans Freudenthal’s concept of ‘mathematics as a human activity’. He felt that students should not be considered as passive recipients of ready-made mathematics, but rather that education should guide the students towards using opportunities to reinvent mathematics by doing it themselves.

Study situations can represent many problems that the students experience as meaningful and these form the key resources for learning; the accompanying mathematics arises by the process of mathematization. Starting with context-linked solutions, the students gradually develop mathematical tools and understanding at a more formal level. Models that emerge from the students’ activities, supported by classroom interaction, lead to higher levels of mathematical thinking.

http://www.fi.uu.nl/en/projects/realme.html

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