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Papers by David Hestenes

European Journal of Science and Mathematics Education

Radical reform in science and mathematics education is needed to prepare citizens for challenges ... more Radical reform in science and mathematics education is needed to prepare citizens for challenges of the emerging knowledge-based global economy. We consider definite proposals to establish: (1) Standards of science and math literacy for all students. (2) Integration of the science curriculum with structure of matter, energy, models and modeling as unifying themes. (3) Pedagogy promoting scientific inquiry and argumentation. (4) Sustained professional development and support for teachers. (5) Institutional support from local universities for continuous upgrades in curriculum and teaching practices. Physics plays a central role in all these reforms.

Advances in Applied Clifford Algebras

Geometric Calculus is developed for curved-space treatments of General Relativity and comparison ... more Geometric Calculus is developed for curved-space treatments of General Relativity and comparison with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein's Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provides mathematical tools that streamline the formulation and simplify calculations. The formalism automatically includes spinors so the Dirac equation is incorporated in a geometrically natural way.

Advances in Applied Clifford Algebras, 2016

Even today mathematicians typically typecast Clifford Algebra as the "algebra of a quadratic form... more Even today mathematicians typically typecast Clifford Algebra as the "algebra of a quadratic form," with no awareness of its grander role in unifying geometry and algebra as envisaged by Clifford himself when he named it Geometric Algebra. It has been my privilege to pick up where Clifford left off-to serve, so to speak, as principal architect of Geometric Algebra and Calculus as a comprehensive mathematical language for physics, engineering and computer science. This is an account of my personal journey in discovering, revitalizing and extending Geometric Algebra, with emphasis on the origin and influence of my book Space-Time Algebra. I discuss guiding ideas, significant results and where they came from-with recollection of important events and people along the way. Lastly, I offer some lessons learned about life and science.

Boston Studies in the Philosophy of Science, 1996

AIP Conference Proceedings, 1997

Scientific practice involves the construction, validation and application of scientific models, s... more Scientific practice involves the construction, validation and application of scientific models, so science instruction should be designed to engage students in making and using models. Scientific models are coherent units of structured knowledge. They are used to organize factual information into coherent wholes, often by the coordinated use of general laws or principles. Therefore, the structure of scientific knowledge can be made more explicit for students by organizing course content around a small number of basic models. The ability of students to make and use models depends on the representational tools at their command. Students learn transferable modeling skills by applying given models to a variety of situations to describe, explain, or predict physical events or to design experiments. These ideas have been incorporated into a methodology for physics teaching and a course for training teachers.

Advances in Applied Clifford Algebras, 1997

The Force Concept Inventory (FCI) 1 is a unique kind of "test" designed to assess student underst... more The Force Concept Inventory (FCI) 1 is a unique kind of "test" designed to assess student understanding of the most basic concepts in Newtonian physics. It can be used for several different purposes, but the most important one is to evaluate the effectiveness of instruction.

The Views About Sciences Survey (VASS) is a survey of student views about science for the purpose... more The Views About Sciences Survey (VASS) is a survey of student views about science for the purpose of assessing the influence of these views on learning. This paper discusses the survey's design, development, results, and implications for science education. The survey assesses student views along seven dimensions with a novel Contrasting Alternatives Design. It was administered in 23 states to about 8,000 high school and college students enrolled in physics, chemistry, and biology courses. Results indicate that students at all levels holi views about knowing and learning science that often diverge from the views of scientists and educators, student views differ according to discipline and across some demographic strata, and student views are hardly affected by traditional science instruction, but they affect what students learn in the course of such instruction. Contains 72 references.

Spacetime Algebra (STA) provides unified, matrix-free spinor methods for rotational dynamics in c... more Spacetime Algebra (STA) provides unified, matrix-free spinor methods for rotational dynamics in classical theory as well as quantum mechanics. That makes it an ideal tool for studying particle models of zitterbewegung and using them to study zitterbewegung in the Dirac theory. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. It attributes to the electron an electric dipole moment oscillating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. A modification of the Dirac equation is suggested to incorporate the oscillating dipole moment. That enables extension of the Dirac equation to incorporate electroweak interactions in a new way.

This book provides an introduction to geometric algebra as a unified language for physics and mat... more This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to ...

An analysis of the conceptual structure of physics identifies essential factual and procedural kn... more An analysis of the conceptual structure of physics identifies essential factual and procedural knowledge which is not explicitly formulated and taught in physics courses. It leads to the conclusion that mathematical modeling of the physical world should be the central theme of physics instruction. There are reasons to believe that traditional methods for teaching physics are inefficient and substantial improvements in instruction can be achieved by a vigorous program of pedagogical research and development.

This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal curren... more This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal current in a circular loop. Analytical expressions for the eddy currents are derived as a power series in the vectorial displacement of the center of the sphere from the axis of the loop. These ...

European Journal of Science and Mathematics Education

Radical reform in science and mathematics education is needed to prepare citizens for challenges ... more Radical reform in science and mathematics education is needed to prepare citizens for challenges of the emerging knowledge-based global economy. We consider definite proposals to establish: (1) Standards of science and math literacy for all students. (2) Integration of the science curriculum with structure of matter, energy, models and modeling as unifying themes. (3) Pedagogy promoting scientific inquiry and argumentation. (4) Sustained professional development and support for teachers. (5) Institutional support from local universities for continuous upgrades in curriculum and teaching practices. Physics plays a central role in all these reforms.

Advances in Applied Clifford Algebras

Geometric Calculus is developed for curved-space treatments of General Relativity and comparison ... more Geometric Calculus is developed for curved-space treatments of General Relativity and comparison with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein's Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provides mathematical tools that streamline the formulation and simplify calculations. The formalism automatically includes spinors so the Dirac equation is incorporated in a geometrically natural way.

Advances in Applied Clifford Algebras, 2016

Even today mathematicians typically typecast Clifford Algebra as the "algebra of a quadratic form... more Even today mathematicians typically typecast Clifford Algebra as the "algebra of a quadratic form," with no awareness of its grander role in unifying geometry and algebra as envisaged by Clifford himself when he named it Geometric Algebra. It has been my privilege to pick up where Clifford left off-to serve, so to speak, as principal architect of Geometric Algebra and Calculus as a comprehensive mathematical language for physics, engineering and computer science. This is an account of my personal journey in discovering, revitalizing and extending Geometric Algebra, with emphasis on the origin and influence of my book Space-Time Algebra. I discuss guiding ideas, significant results and where they came from-with recollection of important events and people along the way. Lastly, I offer some lessons learned about life and science.

Boston Studies in the Philosophy of Science, 1996

AIP Conference Proceedings, 1997

Scientific practice involves the construction, validation and application of scientific models, s... more Scientific practice involves the construction, validation and application of scientific models, so science instruction should be designed to engage students in making and using models. Scientific models are coherent units of structured knowledge. They are used to organize factual information into coherent wholes, often by the coordinated use of general laws or principles. Therefore, the structure of scientific knowledge can be made more explicit for students by organizing course content around a small number of basic models. The ability of students to make and use models depends on the representational tools at their command. Students learn transferable modeling skills by applying given models to a variety of situations to describe, explain, or predict physical events or to design experiments. These ideas have been incorporated into a methodology for physics teaching and a course for training teachers.

Advances in Applied Clifford Algebras, 1997

The Force Concept Inventory (FCI) 1 is a unique kind of "test" designed to assess student underst... more The Force Concept Inventory (FCI) 1 is a unique kind of "test" designed to assess student understanding of the most basic concepts in Newtonian physics. It can be used for several different purposes, but the most important one is to evaluate the effectiveness of instruction.

The Views About Sciences Survey (VASS) is a survey of student views about science for the purpose... more The Views About Sciences Survey (VASS) is a survey of student views about science for the purpose of assessing the influence of these views on learning. This paper discusses the survey's design, development, results, and implications for science education. The survey assesses student views along seven dimensions with a novel Contrasting Alternatives Design. It was administered in 23 states to about 8,000 high school and college students enrolled in physics, chemistry, and biology courses. Results indicate that students at all levels holi views about knowing and learning science that often diverge from the views of scientists and educators, student views differ according to discipline and across some demographic strata, and student views are hardly affected by traditional science instruction, but they affect what students learn in the course of such instruction. Contains 72 references.

Spacetime Algebra (STA) provides unified, matrix-free spinor methods for rotational dynamics in c... more Spacetime Algebra (STA) provides unified, matrix-free spinor methods for rotational dynamics in classical theory as well as quantum mechanics. That makes it an ideal tool for studying particle models of zitterbewegung and using them to study zitterbewegung in the Dirac theory. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. It attributes to the electron an electric dipole moment oscillating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. A modification of the Dirac equation is suggested to incorporate the oscillating dipole moment. That enables extension of the Dirac equation to incorporate electroweak interactions in a new way.

This book provides an introduction to geometric algebra as a unified language for physics and mat... more This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to ...

An analysis of the conceptual structure of physics identifies essential factual and procedural kn... more An analysis of the conceptual structure of physics identifies essential factual and procedural knowledge which is not explicitly formulated and taught in physics courses. It leads to the conclusion that mathematical modeling of the physical world should be the central theme of physics instruction. There are reasons to believe that traditional methods for teaching physics are inefficient and substantial improvements in instruction can be achieved by a vigorous program of pedagogical research and development.

This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal curren... more This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal current in a circular loop. Analytical expressions for the eddy currents are derived as a power series in the vectorial displacement of the center of the sphere from the axis of the loop. These ...