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A science need: Designing tasks to engage students in modeling complex data

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Abstract

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaput’s belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in reasoning about data. A Science of Need embodies the utility value of mathematics, and engages students in seeing the importance of mathematics in both their current and their future lives. An extended example of the design of tasks that require students to generate, test, and revise models of complex data is used to illustrate the ways in which attention to the contributions of students can aid in the development of both useful and theoretically coherent models of mathematical understanding by researchers. Tools such as Fathom are shown as democratizing agents in making data modeling more expressive and intimate, aiding in the development of deeper and more applicable mathematical understanding.

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Notes

  1. The reader will note the irony that this is the very goal of instruction: To engineer learning systems so that students will learn more and better than they would in a purely “natural” manner—we just didn’t recognize its value at the time.

  2. This is also partly because the representational tools we use constrain the learner to use only certain forms of reasoning (e.g., graphical representations of functions), and groups to engage in only certain kinds of discursive activity. This is how designed features of activities can be generalized with some fidelity across people and situations (de Corte 1999).

  3. This is not technically correct usage mathematically. For pedagogical reasons, we used the intuitive notion of stretching and moving to give the students a feel for the covariational features of the general model (see Carlson et al. 2002 for a good discussion of covariational reasoning if you are bothered by our choice).

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Authors and Affiliations

  1. School of Education, Indiana University, Bloomington, IN, USA

    Richard Lesh, Elizabeth Caylor & Shweta Gupta

  2. Division of Curriculum and Instruction, Arizona State University, Box 871011, Tempe, AZ, 85287-1011, USA

    James A. Middleton

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  1. Richard Lesh
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Correspondence to James A. Middleton.

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Lesh, R., Middleton, J.A., Caylor, E. et al. A science need: Designing tasks to engage students in modeling complex data. Educ Stud Math 68, 113–130 (2008). https://doi.org/10.1007/s10649-008-9118-4

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