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The Promises of Realistic Math Education
Students in mathematics classrooms should not be considered passive recipients of ready-made math. Instead, students should be guided toward using opportunities to reinvent mathematics by doing it themselves.
That’s one of the principles underlying Hans Freudenthal’s concept of mathematics as a human activity. Students start with a context-linked activity. For example, they could be asked to make drawings to show different ways that a given number of candies, packed in rolls of ten, might be arranged in a storeroom. For example, 143 candies might be packed up into one ten-roll box and four rolls, with three single pieces, or they might be stored as twelve rolls and twenty-three pieces.
Then students gradually develop mathematical tools and understanding at a more formal level. Models emerge from the students’ activities, are supported by classroom interaction, and lead to higher levels of mathematical thinking.
The Freudenthal Institute, founded by Hans Freudenthal in 1971 at Utrecht University in the Netherlands, and WCER have collaborated on research and development over the past 15 years. This relationship has resulted in the establishment of an international research institute for mathematics education: Freudenthal Institute–USA. Its mission is to establish a comprehensive network of collaborating researchers and developers. They call their approach to teaching mathematics Realistic Mathematics Education (RME).
Freudenthal Director Jan de Lange says: The desired competencies, not the mathematical content, are the main criteria for mathematics literacy. And these are different at different ages and for different populations. . . . We all need to understand how important, how essential, mathematics literacy is for every student, and mathematicians in particular need to understand that mathematics literacy will contribute to a better perception about what constitutes mathematics and how important that field is to our lives.
A Realistic Mathematics Education conference held at UW-Madison in November—the first such conference in the US—drew 120 people, including educators from Italy, England, and Ontario. Sponsored by the Freudenthal Institute–USA, the Mathematics in Context Satellite of the Show-Me Center Project, and WCER, the conference showcased RME theory and its applications in classrooms.
Keynote speakers included Gail Burrill, Michigan State University; Eric Gutstein, University of Illinois at Chicago; Cathy Fosnot, City College of New York; and the Freudenthal Institute’s Jo Nelissen, Jan de Lange, and Marja van den Heuvel-Panhuizen. They discussed topics such as the transformation of teaching and learning, the dialectical relationship between teaching mathematics for social justice and teaching Mathematics in Context, ways of increasing students’ access to mathematics, and the role of context in assessment problems in mathematics.
“In a knowledge society everyone shares interest in improving education,” said de Lange. “We need to connect research in different disciplines—cognitive science, neuroscience, mathematics, and math education. Researchers don’t talk with or work with other disciplines enough.” De Lange also encouraged educators to learn to maximize informal learning opportunities and after-school learning using the Web.
One person representing the WCER team at the RME conference was Tom Romberg, whose research over the past 30 years has analyzed young children’s learning of initial mathematical concepts, methods of evaluating students and programs, and integrating research on teaching, curriculum, and student thinking.
“For research to be productive and useful in any discipline,” Romberg said, “it must be conducted within a research community. Mathematics education is a relatively young academic field, and research on the teaching and learning of mathematics is even younger. A research community in mathematics education has only gradually begun to emerge in the past half century, and the process is still ongoing.”
Romberg said much more is known today than was known in the 1960s, however. For example, it is now understood that learning mathematics with understanding involves more than being able to produce correct answers to routine problems. Mathematics should be viewed as a human activity that reflects the work of mathematicians—finding out why given techniques work, inventing new techniques, and justifying assertions. Learning with understanding occurs when students are given time to discover relationships and learn to use their knowledge, and when they reflect about their thinking and express their ideas. Doing mathematics cannot be viewed as a mechanical performance or an activity that solely involves following predetermined rules.
Romberg, who announced his retirement at the RME conference, was a leader in the development of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989). He is former director of WCER’s National Center for Improving Student Learning and Achievement in Mathematics and Science and has become Emeritus Sears Roebuck Foundation–Bascom Professor of Education at the University of Wisconsin–Madison. Despite his retirement, Romberg remains active at WCER and is completing a revision of his Mathematics in Context curriculum.