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Introduction to the Special Issue: Modeling as Application versus Modeling as a Way to Create Mathematics

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Notes

  1. Roy Pea used this term to describe Kaput during a testimonial session during the 2006 conference for AERA.

  2. Even though articles in this volume emphasize both the noun and the verb meanings of the term model, we wish to avoid the meanings associated with the adjective model which treats it as being synonymous with terms like ideal, exemplary, or good.

  3. A “real life” problem is not just a textbook word problem which is acted out with real objects; nor is a problem that is designed for a team just a problem that was designed for an individual which happens to be given to a group; and, solving a problem when realistic tools are available is not the same as being required to solve a problem when it is understood that specific tools is to be used.

  4. This does not mean that we believe that no significant differences exist between the functioning of individuals and groups. It simply means that research on one often can inform research on the other—in much the same way that research on experts (or gifted students) can inform understandings of novices (or average ability students). Also, because our research focuses on investigating how important mathematics and science concepts evolve—currently as well as historically—it is often irrelevant whether the understandings and abilities develop in the thinking of individuals or groups. In general, our goal is to make claims about the development of ideas and abilities—not individuals or groups.

  5. If problem solvers’ educational experiences focus on word problems in which most of the relevant information is presented in a pre-mathematized form, and if students are able to avoid making meaning out of these symbolic descriptions because the problems are presented in sections of a textbook where all of the problems involve the same kinds of solution processes, then it should be no surprise that such students seldom learn the opposite kinds of processes which focus on modeling—or generating their own symbolic descriptions of the situations.

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  1. Indiana University, Bloomington, IN, USA

    Richard Lesh & Beth Caylor

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  1. Richard Lesh
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  2. Beth Caylor
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Correspondence to Richard Lesh.

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Lesh, R., Caylor, B. Introduction to the Special Issue: Modeling as Application versus Modeling as a Way to Create Mathematics. Int J Comput Math Learning 12, 173–194 (2007). https://doi.org/10.1007/s10758-007-9121-3

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