# Modeling in K-16 Mathematics Classrooms – and Beyond

## Abstract

The first half of this book focused on research investigating what it means for students to “understand” modeling processes and models that are important in order for students to be able to use mathematics in real life situations beyond school. This second half shifts attention toward investigations about what is needed for modeling activities to be used productively to promote learning in mathematics classrooms. These investigations are not simplistic one-variable experimental studies intended to prove or disprove the success or failure of pre-defined “treatments” and “interventions.” Rather, many of these chapters describe *teaching experiments* (Lesh, 2003) which are investigations designed to show how students’ or teachers’ thinking changes in situations which involve multiple iterative cycles of expressing, testing, and revising initial ways of thinking about (simulations of) “real life” decision-making situations. Or, other chapters describe *design studies* (Kelly, Lesh, and Baek 2008) in which students or teachers design artifacts or tools which need to be powerful (for some specific purpose in some specific situation), sharable (with other people), and reuseable (in other situations). Both of the preceding kinds of studies often involve *model-eliciting activities* in which: (a) one of the most important parts of the products that are produced are the underlying interpretation systems (or models), and (b) the interpretation systems (models) involve concepts that the researcher or teacher judges believe to be among the main “big ideas” that students should learn.

## Keywords

Modeling Activity Modeling Competency Interpretation System Metacognitive Process American Pragmatist## References

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