Models & Modeling as Foundations for the Future in Mathematics Education

Project Director: Richard Lesh

This project is one component of a much larger collection of projects which Dr. Lesh is conducting with colleagues at several universities throughout the United States, Mexico, and Australia. The general questions being addressed by this research were stimulated by the following kinds of observations. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem solving activities has changed dramatically during the past twenty years. For example, powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. These observations raise the following questions.

What is the nature of typical problem-solving situations where elementary-but-powerful mathematical constructs and conceptual systems are needed for success in a technology-based age of information? What kind of "mathematical thinking" is emphasized in these situations? What does it mean to "understand" the most important of these ideas and abilities? How do these competencies develop? What can be done to facilitate development? How can we document and assess the most important (deeper, higher-order, more powerful) achievements that are needed: (i) for informed citizenship, or (ii) for successful participation in the increasingly wide range of professions that are becoming heavy users of mathematics, science, and technology?

We also ask:

Why do students who score well on traditional standardized tests often perform poorly in more complex "real life" situations where mathematical thinking is needed? Why do students who have poor records of performance in school often perform exceptionally well in relevant "real life" situations?

One primary venue for investigating such questions is a "design laboratory" in which participants engage in activities that are simulations of "real life" problem solving situations which occur beyond school. In addition to researchers in the learning sciences, we also believe that researchers with broad and deep expertise in mathematics and science should play significant roles in such research Ð and that input should be sought, not just from creators of mathematics (i.e., "pure" mathematicians), but also heavy users of mathematics (e.g., "applied" mathematicians and scientists). This is because the questions listed above are about the changing nature of mathematics and situations where mathematics is used; they are not simply questions about the nature of students, human minds, human information processing capabilities, or human development.