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'''MODELING THEORY & INSTRUCTION'''
'''MODELING THEORY & INSTRUCTION'''


Since about 1980, Hestenes has been developing a MODELING THEORY of science and cognition, especially to guide the design of science instruction [33-39]. The theory distinguishes sharply between conceptual models that constitute the content core of science and the mental models that are essential to understand them. MODELING INSTRUCTION is designed to engage students in all aspects of modeling, broadly conceived as constructing, testing, analyzing and applying scientific models [40].
:Since about 1980, Hestenes has been developing a MODELING THEORY of science and cognition, especially to guide the design of science instruction [33-39]. The theory distinguishes sharply between conceptual models that constitute the content core of science and the mental models that are essential to understand them. MODELING INSTRUCTION is designed to engage students in all aspects of modeling, broadly conceived as constructing, testing, analyzing and applying scientific models [40].


To assess the effectiveness of Modeling Instruction, Hestenes and his students developed the Force Concept Inventory [41,42], which has become a standard instrument for evaluating student understanding of introductory physics [43] and translated into more than 20 languages [44].
:To assess the effectiveness of Modeling Instruction, Hestenes and his students developed the Force Concept Inventory [41,42], which has become a standard instrument for evaluating student understanding of introductory physics [43] and translated into more than 20 languages [44].


After a decade of education research to develop and validate the approach, Hestenes was awarded grants from the National Science Foundation for another decade to spread the MODELING INSTRUCTION PROGRAM nationwide. As of 2011, more than 4000 teachers had participated in summer Modeling Workshops, including nearly 10% of the nation’s high school physics teachers. Teachers describe Modeling Instruction as transformative –– a 2010 survey found that 90% of the teachers continue to use it years after their first Workshop. It is estimated that Modeling teachers reach more than 100,000 students each year.
:After a decade of education research to develop and validate the approach, Hestenes was awarded grants from the National Science Foundation for another decade to spread the MODELING INSTRUCTION PROGRAM nationwide. As of 2011, more than 4000 teachers had participated in summer Modeling Workshops, including nearly 10% of the nation’s high school physics teachers. Teachers describe Modeling Instruction as transformative –– a 2010 survey found that 90% of the teachers continue to use it years after their first Workshop. It is estimated that Modeling teachers reach more than 100,000 students each year.


Perhaps the most impressive outcome of the program is that teachers created their own non-profit organization, the American Modeling Teachers Association [45], to continue and expand the mission after government funding terminated. This is the first nationwide community of teachers dedicated to STEM education reform. It promises to be a most effective vehicle for addressing the nation’s STEM education crisis.
:Perhaps the most impressive outcome of the program is that teachers created their own non-profit organization, the American Modeling Teachers Association [45], to continue and expand the mission after government funding terminated. This is the first nationwide community of teachers dedicated to STEM education reform. It promises to be a most effective vehicle for addressing the nation’s STEM education crisis.


Another outcome of the Modeling Program was creation of a graduate program at Arizona State University for sustained professional development of STEM teachers [46]. This provides a validated model for similar programs at universities across the country. Linking such programs to the AMTA will strengthen the pipeline from high schools to university science and engineering schools [47].
:Another outcome of the Modeling Program was creation of a graduate program at Arizona State University for sustained professional development of STEM teachers [46]. This provides a validated model for similar programs at universities across the country. Linking such programs to the AMTA will strengthen the pipeline from high schools to university science and engineering schools [47].


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Revision as of 02:17, 28 March 2012

David Orlin Hestenes
Born1933
Known forGeometric Algebra Conformal Geometric Algebra
AwardsOersted Medal (2002)
Scientific career
FieldsPhysics
InstitutionsArizona State University


David Orlin Hestenes, Ph.D.(born May 21, 1933) is a theoretical physicist and science educator. He is best known as chief architect of Geometric Algebra as a unified language for mathematics and physics [1], and as founder of Modeling Instruction, a research-based program to reform K-12 STEM education [2]. Most recently, he is co-founder of XOTAR Corporation for development of advanced robotic systems.


LIFE AND CAREER

David Orlin Hestenes (eldest son of mathematician Magnus Hestenes) was born 1933 in Chicago Illinois. Beginning college as a pre-medical major at UCLA (1950-52), he graduated from Pacific Lutheran University in 1954 with degrees in philosophy and speech. After serving in the U.S. Army (1954-56), he entered UCLA as an unclassified graduate student, completed a physics M.A. in 1958 and won a University Fellowship. He obtained his Ph.D. from UCLA in 1963 with a thesis entitled Geometric Calculus and Elementary Particles. Shortly thereafter he recognized that the Dirac and Pauli Algebras could be unified in matrix-free form by a device later called a space-time split [3]. Then he revised his thesis and published it in 1966 as a book, Space Time Algebra [4], now referred to as Spacetime Algebra. This was the first major step in developing a unified, coordinate-free Geometric Algebra and Calculus for all of physics.
From 1964-66, Hestenes was an NSF Postdoctoral Fellow at Princeton with John Wheeler. In 1966 he joined the physics department at Arizona State University, rising to full professor in 1976 and retiring in 2000 to Emeritus Professor of Physics.
In 1980, 1981 as a NASA Faculty Fellow and in 1983 as a NASA Consultant he worked at Jet Propulsion Laboratory on orbital mechanics and attitude control, where he applied Geometric Algebra in development of new mathematical techniques published in a textbook/monograph New Foundations for Classical Mechanics [5].
In 1983 he joined with entrepreneur Robert Hecht-Nielsen and psychologist Peter Killeen in conducting the first ever conference devoted exclusively to neural network modeling of the brain. Hestenes followed this in 1987 with appointment as the first Visiting Scholar in the Department of Cognitive and Neural Systems (Boston University) and a period of neuroscience research [6-9].


GEOMETRIC ALGEBRA and CALCULUS

Spacetime Algebra provided the starting point for two main lines of research: on its implications for quantum mechanics specifically and for mathematical physics generally.
The first line began with the fact that reformulation of the Dirac equation in terms of Spacetime Algebra reveals hidden geometric structure [10]. Among other things, it reveals that the complex factor i in the equation is a geometric quantity (a bivector) identified with electron spin, where i specifies the spin direction and /2 is the spin magnitude. The implications of this insight have been studied in a long series papers [11-16] with the most significant conclusion linking it to Schrödinger’s zitterbewegung and proposing a zitterbewegung interpretation of quantum mechanics [17]. Research in this direction is still active.
The second line of research was dedicated to extending Geometric Algebra to a versatile, self-contained Geometric Calculus that can serve the needs of theoretical physics. Its culmination is the book Clifford Algebra to Geometric Calculus [18]. Noteworthy innovations in the book include the concepts of vector manifold, differential outermorphism and vector derivative that enable coordinate-free calculus on manifolds. That provides a foundation for generalizing the theory of differential forms and integration, including an extension of Cauchy’s Integral Theorem to higher dimensions that was actually the initial impetus for the approach [19]. The book follows with a new approach to differential geometry, including a versatile new tool called the Shape tensor.
Subsequently, this work has been applied to Lagrangian field theory [20], formulation of a Gauge Theory of Gravity alternative to General Relativity [21. 22] and spin representations of Lie groups [23]. Most recently, it led Hestenes to formulate Conformal Geometric Algebra as a new approach to computational geometry [24]. This has found a rapidly increasing number of applications in engineering and computer science [25-30].
After a 20- year gestation period beginning in 1966, Geometric Algebra started to grow steadily and flourish. Actually, this should be seen as continuing developments dating back to Euclid (outlined in Fig. 1). Hestenes has placed the contributions of Grassmann and Clifford in perspective [31, 32], arguing that mathematicians have failed to do justice to their vision of a Universal Geometric Algebra. The problem remains today in failure to distinguish Geometric algebra from Clifford algebra. Though the name “Clifford algebra” may be thought to assign due credit to Clifford, it has helped consign Clifford’s contribution to the relative obscurity of a minor mathematical subspecialty for the better part of a century. It overlooks Clifford’s own preference for the term Geometric Algebra and his judgment that it should be regarded as a contribution to Grassmann’s visionary program. With extensive applications to physics and engineering, Geometric Algebra has evolved into a mathematical language that goes far beyond the Clifford algebra that serves as its grammar. Grassmann and Clifford would approve.

Figure 1 (from [32])

MODELING THEORY & INSTRUCTION

Since about 1980, Hestenes has been developing a MODELING THEORY of science and cognition, especially to guide the design of science instruction [33-39]. The theory distinguishes sharply between conceptual models that constitute the content core of science and the mental models that are essential to understand them. MODELING INSTRUCTION is designed to engage students in all aspects of modeling, broadly conceived as constructing, testing, analyzing and applying scientific models [40].
To assess the effectiveness of Modeling Instruction, Hestenes and his students developed the Force Concept Inventory [41,42], which has become a standard instrument for evaluating student understanding of introductory physics [43] and translated into more than 20 languages [44].
After a decade of education research to develop and validate the approach, Hestenes was awarded grants from the National Science Foundation for another decade to spread the MODELING INSTRUCTION PROGRAM nationwide. As of 2011, more than 4000 teachers had participated in summer Modeling Workshops, including nearly 10% of the nation’s high school physics teachers. Teachers describe Modeling Instruction as transformative –– a 2010 survey found that 90% of the teachers continue to use it years after their first Workshop. It is estimated that Modeling teachers reach more than 100,000 students each year.
Perhaps the most impressive outcome of the program is that teachers created their own non-profit organization, the American Modeling Teachers Association [45], to continue and expand the mission after government funding terminated. This is the first nationwide community of teachers dedicated to STEM education reform. It promises to be a most effective vehicle for addressing the nation’s STEM education crisis.
Another outcome of the Modeling Program was creation of a graduate program at Arizona State University for sustained professional development of STEM teachers [46]. This provides a validated model for similar programs at universities across the country. Linking such programs to the AMTA will strengthen the pipeline from high schools to university science and engineering schools [47].


AWARDS AND FELLOWSHIPS

2003 Award for excellence in educational research by the Council of Scientific Society Presidents
2002 Oersted Medal by the American Association of Physics Teachers
Fellow of the American Physical Society
Overseas Fellow of Churchill College (Cambridge University)
Foundations of Physics Honoree (Sept.-Nov. issues, 1993)
Fulbright Research Scholar (England) 1987-1988
NASA Faculty Fellow (Jet Propulsion Laboratory) 1980, 1981.
NSF Postdoctoral Fellow (Princeton) 1964-1966.
University Fellow (UCLA) 1958-1959.


Selected writings

[1] D. Hestenes, A Unified Language for Mathematics and Physics. In J.S.R. Chisholm/A.K. Common (eds.), Clifford Algebras and their Applications in Mathematical Physics (Reidel: Dordrecht/Boston, 1986), p. 1-23.
[2] Home page on Modeling Instruction http://modeling.asu.edu/
[3] D. Hestenes, Spacetime Physics with Geometric Algebra, American Journal of Physics 71: 691-714 (2003).
[4] D. Hestenes, Space-Time Algebra (Gordon & Breach: New York, 1966).
[5] D. Hestenes, New Foundations for Classical Mechanics (Kluwer: Dordrecht/Boston, 1986), Second Edition (1999).
[6] D. Hestenes, How the Brain Works: the next great scientific revolution. In C.R. Smith and G.J. Erickson (eds.), Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems (Reidel: Dordrecht/Boston, 1987). p. 173-205.
[7] D. Hestenes, Invariant Body Kinematics: I. Saccadic and compensatory eye movements. Neural Networks 7: 65-77 (1994).
[8] D. Hestenes, Invariant Body Kinematics: II. Reaching and neurogeometry. Neural Networks 7: 79-88 (1994).
[9] D. Hestenes, Modulatory Mechanisms in Mental Disorders. In Neural Networks in Psychopathology, ed. D.J. Stein & J. Ludik (Cambridge University Press: Cambridge, 1998). pp. 132-164.
[10] D. Hestenes, Real Spinor Fields, Journal of Mathematical Physics 8: 798-808 (1967).
[11] D. Hestenes and R. Gurtler, Local Observables in Quantum Theory, American Journal of Physics 39: 1028 (1971).
[12] D. Hestenes, Local Observables in the Dirac Theory, Journal of Mathematical Physics 14: 893-905 (1973).
[13] D. Hestenes, Observables, Operators and Complex Numbers in the Dirac Theory, Journal of Mathematical Physics. 16 556-572 (1975).
[14] D. Hestenes (with R. Gurtler), Consistency in the Formulation of the Dirac, Pauli and Schroedinger Theories, Journal of Mathematical Physics 16: 573-583 (1975).
[15] D. Hestenes, Spin and Uncertainty in the Interpretation of Quantum Mechanics, American Journal of Physics 47: 399-415 (1979).
[16] D. Hestenes, Geometry of the Dirac Theory. Originally published in A Symposium on the Mathematics of Physical Space-Time, Facultad de Quimica, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico (1981), p. 67-96.
[17] D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Foundations of Physics 20: 1213-1232 (1990).
[18] D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics and physics (Kluwer: Dordrecht/Boston, 1984).
[19] D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313-325 (1968).
[20] A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295-12327 (1993).
[21] A. Lasenby, C. Doran, & S. Gull, Gravity, gauge theories and geometric algebra, Philosophical Transactions of the Royal Society (London) A 356: 487–582 (1998).
[22] C. Doran & A. Lasenby, Geometric Algebra for Physicists (Cambridge U Press: Cambridge, 2003)
[23] C. Doran, D. Hestenes, F. Sommen & N. Van Acker, Lie Groups as Spin Groups, Journal of Mathematical Physics 34: 3642-3669 (1993).
[24] D. Hestenes, Old Wine in New Bottles: A new algebraic framework for computational geometry. In E. Bayro-Corrochano and G. Sobczyk (eds), Advances in Geometric Algebra with Applications in Science and Engineering (Birkhauser: Boston, 2001). p. 1-14.
[25] L. Dorst, C. Doran and J. Lasenby (Eds.), Applications of Geometric Algebra in Compute Science and Engineering, Birkhauser, Boston (2002).
[26] L. Dorst, D. Fontjne and S. Mann, Geometric Algebra for Computer Science (Elsevier: Amsterdam, 2007)
[27] D. Hestenes & J. Holt, The Crystallographic Space Groups in Geometric Algebra, Journal of Mathematical Physics 48: 023514 (2007).
[28] H. Li, Invariant Algebras and Geometric Reasoning. (Beijing: World Scientific, 2008)
[29] E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric Algebra Computing for Engineering and Computer Science. (London: Springer Verlag, 2009).
[30] L. Dorst and J. Lasenby, Guide to Geometric Algebra in Practice (Springer: London, 2011).
[31] D. Hestenes, Grassmann's Vision. In G. Schubring (Ed.), Hermann Günther Grassmann (1809-1877) –– Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996). p. 191-201.
[32] D. Hestenes, Grassmann’s Legacy. In H-J. Petsche, A. Lewis, J. Liesen, S. Russ (Eds.) From Past to Future: Grassmann’s Work in Context (Birkhäuser: Berlin, 2011).
[33] D. Hestenes, Wherefore a Science of Teaching? The Physics Teacher 17: 235-242 (1979).
[34] D. Hestenes, Toward a Modeling Theory of Physics Instruction, American Journal of Physics 55: 440-454 (1987).
[35] D. Hestenes, Modeling Games in the Newtonian World, American Journal of Physics 60: 732-748 (1992).
[36] D. Hestenes, Modeling Software for learning and doing physics. In C. Bernardini, C. Tarsitani and M. Vincentini (Eds.), Thinking Physics for Teaching, Plenum, New York, p. 25-66 (1996).
[37] D. Hestenes (1997), Modeling Methodology for Physics Teachers. In E. Redish and J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics Part II. p. 935-957.
[38] D. Hestenes, Notes for a Modeling Theory of Science, Cognition and Physics Education, In E. van den Berg, A. Ellermeijer and O. Slooten (Eds.) Modelling in Physics and Physics Education, (U. Amsterdam 2008).
[39] D. Hestenes, Modeling Theory for Math and Science Education. In R. Lesh, P. Galbraith, Hines, A. Hurford (Eds.) Modeling Students’ Mathematical Competencies (New York: Springer, 2010).
[40] M. Wells, D. Hestenes, and G. Swackhamer, A Modeling Method for High School Physics Instruction, American Journal of Physics 63: 606-619 (1995).
[41] I. Halloun and D. Hestenes, The Initial Knowledge State of College Physics Students, American Journal of Physics 53: 1043-1055 (1985).
[42] D. Hestenes, M. Wells, and G. Swackhamer, Force Concept Inventory, The Physics Teacher 30: 141-158 (1992).
[43] R.R. Hake, "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," American Journal of Physics 66: 64- 74 (1998).
[44] http://modeling.asu.edu/R&E/Research.html
[45] AMTA home page: www.modelingteachers.org/
[46] D. Hestenes, C. Megowan-Romanowicz, S.Osborn Popp, J. Jackson,and R. Culbertson, A graduate program for high school physics and physical science teachers, American Journal of Physics 79: 971-979 (2011).
[47] D. Hestenes and J. Jackson (1997), Partnerships for Physics Teaching Reform ––a crucial role for universities and colleges. In E. Redish & J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics. Part I p. 449-459.


See also

References

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