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Data Modeling & the Infrastructural Nature of Conceptual Tools

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Abstract

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways of thinking are often out of sync with the situations that we need to understand and explain. We have chosen to discuss data modeling because in mathematics education, future-oriented statements of curriculum standards generally identify data modeling as a topic that should receive priority attention. Several example activities based on the models and modeling perspectives (MMP) are used to support the claims that: (a) statistical techniques are based on models, (b) alternative models often make significantly different assumptions about how to measure even elementary things such as distances and spread. Also, new technologies for computation, conceptualization, and communication are making significant changes in which statistical techniques are easily executed. Moreover, these newly available techniques are often based on assumptions that are more realistic given the relevant quantities and relationships.

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Notes

  1. Unfortunately, completely different lines may satisfy these two conditions. For example, consider three points in a plane. The line that satisfies condition 1 will go through two of the three given points; but, the point that satisfies condition 2 will only go through one of the points.

  2. Even in cases where solutions could be found for least distance curves, the solutions often were not unique—or else there did not exist function-based ways to describe errors.

  3. For the graphs in the fourth row of Fig. 20, we graphed the average rather than the sum because we wanted to avoid having the resulting graph go outside the window of the graph.

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Authors and Affiliations

  1. Indiana University, Bloomington, USA

    Richard Lesh, Elizabeth Caylor & Shweta Gupta

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  1. Richard Lesh
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  2. Elizabeth Caylor
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  3. Shweta Gupta
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Correspondence to Richard Lesh.

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Lesh, R., Caylor, E. & Gupta, S. Data Modeling & the Infrastructural Nature of Conceptual Tools. Int J Comput Math Learning 12, 231–254 (2007). https://doi.org/10.1007/s10758-007-9124-0

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