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Foundations for the Future in Math Ed – Research Methodologies for Getting Beyond Traditional Conceptions of Competence


Richard Lesh & Tom Fennewald, Indiana University




Research methodology, Evolving expert studies, Mathematics Curriculum, , Modeling, Engineering education


Beyond school, problem solving is changing! The kinds of mathematical understandings and abilities that are most useful are changing! And, in businesses and professions where some kind mathematical thinking is critical for success, people with new types of understandings and abilities are being sought! … Yet, research and theory development in mathematics education is failing to keep pace with such changes.

Recently, two books represent next steps in a research agenda whose foundations were described in Beyond Constructivism – Models & Modeling Perspectives on Mathematics Problem Solving, Learning & Teaching (Lesh & Doerr, 2002).

o Models & Modeling as Foundations for the Future in Mathematics Education (Lesh, Hamilton & Kaput) describes research investigating: (a) new kinds of problem solving situations and (b) new kinds of mathematical understandings and abilities that are becoming especially important in a technology-based age of information.

o Models and modeling in Engineering Education: Designing experiences for all Students (Zawojewski, Diefes-Dux & Bowman (2008) describes answers to the preceding questions in engineering – and in other fields populated by heavy users of mathematics, science, and technology.

The voices of people who are heavy users of mathematics are seldom heard in debates about what should be emphasized in a future-oriented mathematics curriculum. … What if the opinions of such people were taken seriously? What if we didn’t begin with the assumption that next-generation goals must be restricted to incremental changes in what has emphasized in textbooks and standardized tests? How can such questions be investigated without relying exclusively on consensus-building political processes which assume that someone or some community already knows that answers?

This paper focuses on a new category of design research methodology called evolving expert studies – because the results of such studies often represent significant extensions or revisions in the thinking of participants (Kelly, Lesh & Baec, 2008; English, 2008). Such methodologies respect the opinions of diverse groups of stake holders whose views should be considered. Yet, nobody (including especially the researchers) is considered to have privileged access to the truth. Everybody’s prejudices are subjected to a series of iterative express -> test -> revise cycles in which the researchers develop models of students modeling abilities.

English, L. (Ed.) (2007) International Handbook of Research in Mathematics Education (2nd Ed.) NY: Taylor & Francis.

Kelly, A. E., Lesh, R. A., & Baek, J. Y. (2008). Handbook of innovative design research in science, technology, engineering, mathematics (STEM) education. NY: Taylor & Francis.

Lesh, R. & Doerr, H. (2002) Beyond Constructivist: A Models & Modeling Perspective on Mathematics Teaching, Learning, and Problems Solving. Hillsdale, NJ: Lawrence Erlbaum Associates.

Zawojewski, J. Diefes-Dux, H. & Bowman, K. (Eds.) (2008) Models and modeling in Engineering Education: Designing experiences for all students. Rotterdam: Sense Publications.