RYSK: Cobb, Zhao, & Visnovska's Learning From and Adapting the Theory of Realistic Mathematics Education (2008)

This is the 21st in a series describing "Research You Should Know" (RYSK).

It's Open Access Week (#OAweek) so I thought it would be fitting to use this "research you should know" post to highlight one of my favorite open access articles in mathematics education, Learning From and Adapting the Theory of Realistic Mathematics Education by Paul Cobb, Qing Zhao, and Jana Visnovska. Because the article is open access, I get to be less interested in summarizing it and more interested in giving you a reason to read it.

Realistic Mathematics Education (RME) is a theory for the design and development of mathematics curriculum. It is still deeply rooted in the Netherlands, where Hans Freudenthal greatly influenced mathematics instruction there with his belief that mathematics was a human activity, and that activity was characterized by mathematizing the real or readily imagined world. ("Realistic" comes from the Dutch phrase "zich realiseren," which in English means "to imagine.") This mathematization can be thought of in two ways, horizontal and vertical: "horizontal mathematization involves going from the world of life into the world of symbols, while vertical mathematization means moving within the world of symbols" (Freudenthal, 1991). Hans Freudenthal died in 1990 but his work continues, primarily at the Freudenthal Institute for Science and Mathematics Education at the University of Utrecht in the Netherlands.

There have been four primary avenues where RME has established itself in the United States. The first is with the middle school curriculum series Mathematics in Context, which grew from a partnership between mathematics education researchers at the University of Wisconsin (primarily Thomas Romberg) and researchers at the Freudenthal Institute. The second is the K-8-focused work of Mathematics in the City, which primarily brought together Cathy Fosnot from the City College of New York and Maarten Dolk of the Freudenthal Institute. The pair also wrote most of the Young Mathematicians at Work book series. The third place where RME is established in the U.S. is here at CU-Boulder, home of Freudenthal Institute US and its director, David Webb. David worked on the Mathematics in Context project at Wisconsin, and brought FI-US with him to CU-Boulder. The fourth place I recognize RME having a significant influence in the United States is in the work of Paul Cobb, particularly in his long research partnership with Koeno Gravemeijer, a researcher from the Freudenthal Institute. Cobb and Gravemeijer spent more than a decade working and publishing together, and that work did a lot to strengthen ties between RME as a design theory and theories in the learning sciences.

Like any idea or theory, RME has limitations. Over its 40+ years of existence it's proven to not be a static thing (van den Heuvel-Panhuizen, 2002), and this article by Cobb, Zhao, & Visnovska describes some of the important ways their work has both informed and been influenced by RME. They describe three adaptations: the first involves accounting for classroom activity and discourse in RME, the second acknowledges the mediating role of the teacher in making curriculum modifications and adaptations, and the third looks at how RME can focus on teacher learning, not just student learning. For details, I'll let you read the article for yourself at http://educationdidactique.revues.org/276. If you have any questions about the article or RME, leave a comment, find me on social media, or email me. We RME folks want to spread the word!


Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Dordrecht: Kluwer.

van den Heuvel-Panhuizen, M. (2002). Realistic Mathematics Education as work in progress. In F. L. Lin (Ed.), Common Sense in Mathematics Education: Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education (pp. 1–39). Taipei, Taiwan.