By Gabriele Kaiser (auth.), Richard Lesh, Peter L. Galbraith, Christopher R. Haines, Andrew Hurford (eds.)
Modeling scholars’ Mathematical Modeling skills bargains welcome readability and concentration to the overseas learn neighborhood in arithmetic, technological know-how, and engineering schooling, in addition to these all for the sciences of training and studying those subjects.
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Additional info for Modeling Students' Mathematical Modeling Competencies: ICTMA 13
Example text
The object of the game is to construct valid models of real objects and processes. Such models comprise the content core of scientific knowledge. To understand science is to know how scientific models are constructed and validated. The main objective of science instruction should therefore be to teach the modeling game. (Hestenes, 1992) Modeling Theory has been developed with that purpose expressly in mind. Its implications for the design of curriculum and instruction have been thoroughly discussed in the literature reviewed in Hestenes (2007).
4 Intuition of structure Physical intuition matches structure in mental models with structure in physical systems. Mathematical intuition matches mental structure with symbolic structure. Thus, structure in the imagination is common ground for both physical and mathematical intuition. 3 Modeling Theory 23 I surmise that physical intuition is highly developed among experimental physicists, where they develop detailed mental images of experimental design, equipment, measurement procedures and data analysis.
I submit, however, that their intuitions of geometry gradually diverge as they employ geometry in different ways. The mathematician concentrates on construction and analysis of formal structures. The physicist uses geometry for modeling rigid bodies and measurement of length, which is the foundation for physical measurements of every kind. Such developments in mathematics and physics do not have to go far before their common ground in Euclidean geometry is no longer obvious. With respect to the Kantian category of causality, intuitions of physicists and mathematicians diverge even more strongly, as we shall see.