Constructionism and Reductionism: Two Approaches to Problem-Solving and Their Implications for Reform of Statistics and Mathematics Curricula

Abstract

The First International Conference on the Teaching of Mathematics was held in Samos, Greece, in July 1998. Presentations by the attendees reflected a recent debate on reforms of the mathematics curriculum and related pedagogy. Chief among these was a greater emphasis on connecting the mathematics curriculum with applications, to make courses in mathematics more "relevant" to students. This manuscript notes that mathematicians tend to teach students to approach data analysis in a constructive manner, proceeding from an understanding of the basic science, while statisticians concentrate on reductive approaches, whereby models are generated upon consideration of the data themselves. It is suggested that departments of mathematics and statistics will need to adopt a new spirit of cooperation, and partner with colleagues in application areas, if curricular enhancements in either domain are to have a reasonable chance at success.

Keywords:

• Applied statistics
• Curriculum reform
• IJssel lake
• Modeling

Acknowledgments

This work was partially supported by National Institutes of Health Grant 1-R03-AG15180-01. The author thanks Jerry Uhl, Bruce Pollack-Johnson, and Deborah Hughes-Hallett for helpful comments.