Modeling

Modeling Theory aims at elucidating the roles of models and modeling in scientific knowledge and practice. It provides a foundation for a realist philosophy of science and a constructivist teaching methodology. Modeling pedagogy and its implementation in physics teaching is addressed at the Modeling Instruction Program site.

Conceptual Modeling in physics, mathematics and cognitive science

Abstract. Scientific thinking is grounded in the evolved human ability to freely create and manipulate mental models in the imagination. This modeling ability enabled early humans to navigate the natural world and cope with challenges to survival. Then it drove the design and use of tools to shape and control the environment. Spoken language facilitated the sharing of mental models in cooperative activities like hunting and in maintaining tribal memory through storytelling. The evolution of culture accelerated with the invention of written language, which enabled creation of powerful symbolic systems and tools to think with. That includes deliberate design of mathematical tools that are essential for physics and engineering . A mental model coordinated with a symbolic representation is called a conceptual model. Conceptual models provide symbolic expressions with meaning. This essay proposes a Modeling Theory of cognitive structure and process. Basic definitions, principles and conclusions are offered. Supporting evidence from the various cognitive sciences is sampled. The theory provides the foundation for a science pedagogy called Modeling Instruction, which has been widely applied with documented success and recognized most recently with an Excellence in Physics Education award from the American Physical Society.

D. Hestenes, SemiotiX, November 2015.
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Modeling Theory for Math and Science Education

Abstract. Mathematics has been described as the science of patterns. Natural science can be characterized as the investigation ofpatterns in nature. Central to both domains is the notion of model as a unit of coherently structured knowledge. Modeling Theory is concerned with models as basic structures in cognition as well as scientific knowledge. It maintains a sharp distinction between mental models that people think with and conceptual models that are publicly shared. This supports a view that cognition in science, math, and everyday life is basically about making and using mental models. We review and extend elements of Modeling Theory as a foundation for R&D in math and science education.

D. Hestenes, Modeling Theory for Math and Science Education, In R. Lesh, P. Galbraith, C. Hines, A. Hurford (eds.) Modeling Students' Mathematical Competencies (New York: Springer, 2010).
© American Institute of Physics (http://www.aapt.org).

Notes for a Modeling Theory of Science, Cognition and Instruction

Abstract. Modeling Theory provides common ground for interdisciplinary research in science education and the many branches of cognitive science, with implications for scientific practice, instructional design, and connections between science, mathematics and common sense.

D. Hestenes, Notes for a Modeling Theory of Science, Cognition and Instruction, In E. van den Berg, A. Ellermeijer & O. Slooten (eds.) Modelling in Physics and Physics Education, (U. Amsterdam 2008).
© American Institute of Physics (http://www.aapt.org).

Modeling Games in the Newtonian World

Abstract. The basic principles of Newtonian mechanics can be interpreted as a system of rules defining a medley of modeling games. The common objective of these games is to develop validated models of physical phenomena. This is the starting point for a promising new approach to physics instruction in which students are taught from the beginning that in science "modeling is the name of the game." The main idea is to teach a system of explicit modeling principles and techniques, to familiarize the students with a basic set of physical models, and to give them plenty of practice in model building, model validation by experiment, and model deployment to explain, to predict and to describe physical phenomena. Unfortunately, a complete implementation of this approach will require a major overhaul of standard instructional materials which is yet to be accomplished. This article lays down physical, epistemological, historical, and pedagogical rationale for the approach.

D. Hestenes, Am. J. Phys., 60: 732-748 (1992).
© American Institute of Physics (http://www.aapt.org).

Modeling Software for Learning and Doing Physics

Abstract. This is the initial report of a long term research program on the design of integrated computer software systems for physics education specifically, and math-science education generally. The program is grounded in a theory of instruction which is centrally concerned with the construction, validation and use of scientific models for objects and processes in the real world. It aims to develop a detailed theory of software design which supports and coordinates all aspects of conceptual and computational modeling. The theory is applied to the design of a versatile Modeling Workstation for learning and doing physics by computer, including the coordination of both experimental and theoretical activities.

Foundations of Mechanics

Philosophy is written in that great book which ever lies before our eyes - I mean the Universe - but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
-- Galileo Galilei

1.	Models and Theories
2.	The Zeroth Law of Physics
3.	Generic Laws and Principles of Particle Mechanics
4.	Modeling Processes