Jean-Claude Falmagne
Encyclopedia
Jean-Claude Falmagne is a mathematical psychologist whose scientific contributions deal with problems in reaction time theory, psychophysics, philosophy of science
, measurement theory, decision theory
, and educational technology. Together with Jean-Paul Doignon, he developed Knowledge Space Theory
, which is the mathematical foundation for the ALEKS
software for the assessment of knowledge in various academic subjects, including K-12 mathematics, chemistry, and accounting.
While working on his doctoral dissertation, which dealt with reaction times, Falmagne became interested in the applications of mathematics to the cognitive sciences. In 1964, he was invited by Patrick Suppes
to spend the summer at Stanford University
. He presented the results of his dissertation at a conference there and met several prominent mathematical psychologists, including Bill Estes, Dick Atkinson
, and Duncan Luce, and the mathematician János Aczél
. Suppes, Luce, and Aczél had a strong influence on Falmagne’s choice of scientific career and on his approach to solving scientific problems. His visit to Stanford convinced him that he needed to continue his education in the United States.
With the support of Fulbright and FNRS fellowships, Falmagne held post-doctoral positions at the University of Pennsylvania, the University of Wisconsin-Madison, and the University of Michigan between 1966 and 1969. His interests grew to include psychophysics, measurement theory, and probabilistic models of ordering and algebraic measurement. After short teaching stints back in Europe at the University of Brussels and the University of Paris, he returned to the United States in 1971 as a Professor of Psychology at New York University.
In 1989, he joined the faculty of University of California, Irvine, accepting an appointment at the Department of Cognitive Sciences and the Institute for Mathematical Behavioral Sciences. He remained there until his retirement in 2004.
Currently, Falmagne is Chairman of ALEKS Corporation, a web-based educational software company that he founded with some of his graduate students. He is also a Professor Emeritus at the University of California, Irvine
.
in their article "Random Orderings and Stochastic Theories of Responses", concerning the representation of choice probabilities by random variables and published his findings in the Journal of Mathematical Psychology.
, their work on the stochastic
framework led to the creation of the web-based system ALEKS for the assessment and learning of mathematics and science. Falmagne and Doignon's 2011 book, Learning Spaces, contains the most current presentation and development of the stochastic framework for the assessment of knowledge. Learning spaces are specific kinds of knowledge spaces, whose best applications are to situations where assessments guide efficient learning. Learning spaces are a part of the concept of Media Theory, which explores the modeling of knowledge structures and knowledge states. More generally, these lines of research are collectively called Knowledge Space Theory and are being pursued by many investigators, mostly in Austria, Germany, and the Netherlands.
argue that the requirement of invariance, which they call "meaningfulness" should be part of the axioms or theory establishing the law, rather than result from them. They proposed a more powerful framework making this invariance explicit in the notation. This approach was generalized by Falmagne in "Meaningfulness and Order Invariance: Two Fundamental Principles for Scientific Laws", and applied to several exemplary laws of physics.
. He is also a fellow of the Society of Experimental Psychologists
. He received an Innovation Award from the University of California, Irvine in 2004 and a doctoris honoris causa degree in science from the University of Graz in 2005.
In celebration of Falmagne's 70th birthday in 2004, a "Falmagne Symposium" was held at the annual meeting of the European Mathematical Psychology Group (EMPG) in Ghent, Belgium, and a "Falmagne Festschrift Meeting" was held at the University of Michigan, Ann Arbor. Two special issues of the Journal of Mathematical Psychology were published in 2005 with the papers presented at two meetings organized to honor his 70th birthday.
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
, measurement theory, decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
, and educational technology. Together with Jean-Paul Doignon, he developed Knowledge Space Theory
Knowledge space
In mathematical psychology, a knowledge space is a combinatorial structure describing the possible states of knowledge of a human learner.To form a knowledge space, one models a domain of knowledge as a set of concepts, and a feasible state of knowledge as a subset of that set containing the...
, which is the mathematical foundation for the ALEKS
Aleks
ALEKS is an Internet based interactive mathematics and science tutoring and assessment program for subjects in mathematics, the sciences, and business....
software for the assessment of knowledge in various academic subjects, including K-12 mathematics, chemistry, and accounting.
Early life and career
After finishing high school, Falmagne spent two years in the Belgian army, where he became an officer. Military service was mandatory in Belgium at the time. In 1954, he enrolled at the University of Brussels (Université Libre de Bruxelles) as a student in the psychology department. He received his undergraduate degree in 1959 and was hired as an assistant at the University of Brussels, which is a faculty position in the Belgian system. He obtained his Ph.D. degree in 1965 from the same institution.While working on his doctoral dissertation, which dealt with reaction times, Falmagne became interested in the applications of mathematics to the cognitive sciences. In 1964, he was invited by Patrick Suppes
Patrick Suppes
Patrick Colonel Suppes is an American philosopher who has made significant contributions to philosophy of science, the theory of measurement, the foundations of quantum mechanics, decision theory, psychology, and educational technology...
to spend the summer at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
. He presented the results of his dissertation at a conference there and met several prominent mathematical psychologists, including Bill Estes, Dick Atkinson
Richard C. Atkinson
Richard Chatham Atkinson is an American professor of psychology and academic administrator. He is the former president and regent of the University of California system, and former chancellor of U.C...
, and Duncan Luce, and the mathematician János Aczél
János Aczél (mathematician)
János D. Aczél is a Hungarian-Canadian mathematician, specializing in functional equations.-Affiliations:* Professor Emeritus in the Department of Pure Mathematics, University of Waterloo...
. Suppes, Luce, and Aczél had a strong influence on Falmagne’s choice of scientific career and on his approach to solving scientific problems. His visit to Stanford convinced him that he needed to continue his education in the United States.
With the support of Fulbright and FNRS fellowships, Falmagne held post-doctoral positions at the University of Pennsylvania, the University of Wisconsin-Madison, and the University of Michigan between 1966 and 1969. His interests grew to include psychophysics, measurement theory, and probabilistic models of ordering and algebraic measurement. After short teaching stints back in Europe at the University of Brussels and the University of Paris, he returned to the United States in 1971 as a Professor of Psychology at New York University.
In 1989, he joined the faculty of University of California, Irvine, accepting an appointment at the Department of Cognitive Sciences and the Institute for Mathematical Behavioral Sciences. He remained there until his retirement in 2004.
Currently, Falmagne is Chairman of ALEKS Corporation, a web-based educational software company that he founded with some of his graduate students. He is also a Professor Emeritus at the University of California, Irvine
University of California, Irvine
The University of California, Irvine , founded in 1965, is one of the ten campuses of the University of California, located in Irvine, California, USA...
.
Research
In 1978, Falmagne solved a well-known problem, posed in 1960 by the economists H.D. Block and Jacob MarschakJacob Marschak
Jacob Marschak was an American economist of Ukrainian Jewish origin.- Life :...
in their article "Random Orderings and Stochastic Theories of Responses", concerning the representation of choice probabilities by random variables and published his findings in the Journal of Mathematical Psychology.
Knowledge spaces, media theory, learning spaces and the ALEKS software
In 1985, Falmagne, along with Jean-Paul Doignon, wrote “Spaces for the Assessment of Knowledge”. In this article, they presented a formal framework for the assessment of knowledge in various academic subjects, such as arithmetic, algebra, and chemistry. This early framework was combinatoric in character, and as such insufficient for a practical assessment, which is unavoidably plagued by careless errors on the part of the test takers. In time, they created a stochastic framework for the description of the evolution of an assessment, question by question. With extensive financial support from the National Science FoundationNational Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
, their work on the stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
framework led to the creation of the web-based system ALEKS for the assessment and learning of mathematics and science. Falmagne and Doignon's 2011 book, Learning Spaces, contains the most current presentation and development of the stochastic framework for the assessment of knowledge. Learning spaces are specific kinds of knowledge spaces, whose best applications are to situations where assessments guide efficient learning. Learning spaces are a part of the concept of Media Theory, which explores the modeling of knowledge structures and knowledge states. More generally, these lines of research are collectively called Knowledge Space Theory and are being pursued by many investigators, mostly in Austria, Germany, and the Netherlands.
The meaningfulness of scientific laws
A common practice in the statement of scientific laws ensures that the mathematical expression of the law is invariant with respect to changes of units of its variables—except for the values of dimensional constants. In dimensional analysis, this invariance is implicit and captured by the concept of "quantities". In "Scales and Meaningfulness of Quantitative Laws", Falmagne and NarensLouis Narens
Louis Narens is Professor in the Department of Cognitive Sciences and the Department of Logic and the Philosophy of Science at the University of California, Irvine.He is one of the major exponents of measurement theory in mathematical psychology...
argue that the requirement of invariance, which they call "meaningfulness" should be part of the axioms or theory establishing the law, rather than result from them. They proposed a more powerful framework making this invariance explicit in the notation. This approach was generalized by Falmagne in "Meaningfulness and Order Invariance: Two Fundamental Principles for Scientific Laws", and applied to several exemplary laws of physics.
Other work
The monograph Elements of Psychophysical Theory presents the mathematical foundation of psychophysics and includes an introduction to measurement theory and functional equations. Falmagne's work in philosophy of science concerns foundational issues in algebraic measurement and in probabilistic measurement. A distinctive feature of his research lies in the use of functional equations in order to achieve generality.Awards and honors
Falmagne is the recipient of Fulbright and Guggenheim Fellowships and of a von Humboldt Award. In 1994, he was recognized as a "Friend of NSERC" by the Natural Sciences and Engineering Research Council of Canada and János D. Aczél . That same year, he was elected as a member of the New York Academy of SciencesNew York Academy of Sciences
The New York Academy of Sciences is the third oldest scientific society in the United States. An independent, non-profit organization with more than members in 140 countries, the Academy’s mission is to advance understanding of science and technology...
. He is also a fellow of the Society of Experimental Psychologists
Society of Experimental Psychologists
The Society of Experimental Psychologists , originally called the Society of Experimentalists, is an academic society for experimental psychologists. It was founded by Edward Bradford Titchener in 1904 to be an ongoing workshop in which members could visit labs, study apparatus, and hear and...
. He received an Innovation Award from the University of California, Irvine in 2004 and a doctoris honoris causa degree in science from the University of Graz in 2005.
In celebration of Falmagne's 70th birthday in 2004, a "Falmagne Symposium" was held at the annual meeting of the European Mathematical Psychology Group (EMPG) in Ghent, Belgium, and a "Falmagne Festschrift Meeting" was held at the University of Michigan, Ann Arbor. Two special issues of the Journal of Mathematical Psychology were published in 2005 with the papers presented at two meetings organized to honor his 70th birthday.
External links
- ALEKS Corporation
- Falmagne's Profile and Bibliography at University of California, Irvine
- John Simon Guggenheim Memorial Foundation
- Bibliography of Knowledge Spaces - Maintained by Cord Hockemeyer at the University of Graz
- National Science Foundation
- 2011 Meeting of the European Mathematical Psychology Group