Download e-book for kindle: Modeling Students' Mathematical Modeling Competencies: ICTMA by Gabriele Kaiser (auth.), Richard Lesh, Peter L. Galbraith,

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By Gabriele Kaiser (auth.), Richard Lesh, Peter L. Galbraith, Christopher R. Haines, Andrew Hurford (eds.)

Modeling scholars’ Mathematical Modeling knowledge bargains welcome readability and concentration to the foreign learn group in arithmetic, technology, and engineering schooling, in addition to these considering the sciences of educating and studying those subjects.

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Extra info for Modeling Students' Mathematical Modeling Competencies: ICTMA 13

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I submit that this tension is basically about matching structure in mathematical models to observable structure in the world. It can be construed as tension between mathematical and physical intuition, as defined in connection with Fig. 4. In understanding a physical equation, the physicist is always concerned with correlating the mathematical structure in the equation with intuitive structure in a 32 D. Hestenes mental model. This is known as interpreting the equation. The correspondence is a two-way mapping.

Compromise then occurs when both p-prims are seen to have validity. In modeling terms this can be described as tuning the p-prims to fit a coherent mental model. Sherin’s most important finding came from observing students construct equations from ideas of what they want the equations to express. They were appealing to common sense, not just following formal rules. For example, in problems involving 30 D. Hestenes equilibrium of forces Sherin noted activation of balancing p-prims (Fig. 5) and strong linking of these p-prims to equations.

No doubt the central role of objects in cognition derives from perception, for perception organizes sensory input into objects situated in an environment. Though objects are cognitively basic, they are not cognitively primitive; they have substructure. The catalog of cognitive primitives evidently includes p-prims and image schemas. These primitives also have structure; they are best described as structured wholes, or Gestalts, to use a term that suggests their origin in Gestalt perception. Turning from model substructure to superstructure, we note that mental objects are invariably situated in some mental context or frame, sometimes called a script or a scenario when action or change is modeled.

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