| Last updated March 28, 2019 |
Welcome and Overview
Welcome and thank you for visiting my home page. I am a Professor in the
Psychology Department and Director of the Center for Mind, Brain,
Computation and Technology at Stanford. My research addresses a broad
range of topics in cognitive science and cognitive neuroscience, including
perception and perceptual decision making; learning and memory; language
and reading; semantic and mathematical cognition; and cognitive
development. I view cognitive functions as emerging from the parallel,
distributed processing activity of neural populations, with learning
occurring through the adaptation of connections among participating
neurons, as discussed in Parallel Distributed
Processing (Rumelhart, McClelland, and the PDP Research Group, 1986).
Research in my lab revolves around efforts to develop explicit
computational models based on these ideas; to test, refine, and extend the
principles embodied in the models; and then to apply the models to
substantive research questions through behavioral experiment, computer
simulation, and mathematical analysis.
My career highlights are listed below. A full list
of relevant publications is available on my
publications page, and links to other resources are provided next to
my photograph above.
Mathematical Cognition
Recently, I have begun what I expect will be a broad-ranging and
long-term program of research in mathematical cognition (watch
this video or rea
d this
paper for a description of the approach). The work grows out of my
long-standing interest in developmental transitions and in readiness to
learn from new experiences as well as from the hope that a
Parallel-Distributed Processing approach may shed light on some of the
most awe-inspiring achievements of human thought --- the insights and
structured reasoning systems that have been created by mathematicians. In
this effort, we are combining experimental studies and computational
modeling studies. The lab is seeking to recruit experimentally and/or
computationally oriented students interested in contributing to this
effort.
The goal is to understand the development of human abilities in
mathematics at all levels, from numerosity and the initial stages of
counting to arithmetic, algebra, geometry, and even multivariate
mathematics and calculus. At the heart of the effort is the belief that
mathematics is best viewed as a matter of learning a set of models that
characterize the objects of mathematical thought and their properties, and
to carry out operations on expressions that have meaning in terms of
objects represented with such models. On this view, mathematics can be
thought of as providing a way of seeing properties of (real or imagined,
often idealized) objects or sets of objects that bring out useful
relationships that are captured in symbolic expressions but that are often
understood in terms of intuitively grasped relationships that gives these
expressions their meaning. There is also an emphasis on understanding how
gradual learning processes can eventually lead to insight and
qualitatively different levels of understanding and mathematical ability,
and on determining how best to support learners as they attempt to acquire
such models.
The approach contrasts with rule-based approaches to mathematics in two
ways: First, it treats formal systems of symbolic representation as ways
of notating elements of a structured system for representing properties of
objects and their relations, rather than simply as arrangements of symbols
subject to processing according to structure-sensitive rules. Second, it
distinguishes between the explicit knowledge of a formal rule and implicit
knowledge embedded in acquired ways of perceiving and deriving
inferences. For example, we can consult an explicit rule corresponding to
the commutativity principle (for all a and b, a+b=b+a), or we may possess
the implicit knowledge that the total quantity resulting from the additive
combination of two part quantities is the same regardless of the order in
which the part quantities are combined. I adhere to the view that an
explicit rule is useful as a part of a system for formally establishing
the validity of an understanding or insight, but that the understanding
itself may come from the implicit knowledge, rather than from the
manipulation of symbolic expressions in accordance with explicit
rules. Thus, an essential part of teaching mathematics is finding ways to
reinforce students' acquisition of the relevant models, rather than simply
encouraging them to memorize a list of formulas.
Specific projects currently underway in the lab include: (a) an
extension of deep learning that captures the gradual emergence of a
representation of the numerosity of items in a visual scene, capturing
the development of increasingly precise representations of numerosity
across the first two decades of life; (b) a learning-based model aimed
at capturing the graded, magnitude-dependent performance of children
in tasks tapping their knowledge and ability to perform correctly in
simple exact number tasks thought to tap the so-called 'cardinality
principle'; (c) empirical and model-based assessment of mechanisms of
numerical magnitude comparison, applied to comparison of fractions and
both negative as well as positive numbers; and (d) investigations of
the role of visuospatial representations in trigonometric reasoning.
Papers on several of these topics are in the pipeline. In addition I
have the long-term plan to create a simulated agent based on a neural
network that can learn the principles of number, algebra, and geometry
well enough to pass the New York State Regent's exam in Geometry.
Some elements of this work are described in the lecture mentioned above.
Career Highlights
James L. (Jay) McClelland received his Ph.D. in Cognitive Psychology from
the University of Pennsylvania in 1975. He served on the faculty of the
University of California, San Diego, before moving to Carnegie Mellon in
1984, where he became a University Professor and held the Walter Van Dyke
Bingham Chair in Psychology and Cognitive Neuroscience. He was a founding
Co-Director of the Center for the Neural Basis of Cognition, a joint
project of Carnegie Mellon and the University of Pittsburgh. In 2006
McClelland moved to the Department of Psychology at Stanford University,
where he founded the Center for Mind, Brain, and Computation in 2007 and
served as department chair from fall 2009 through summer 2012. He is
currently the Lucie Stern Professor in the Social Sciences and
Co-Director of the Center for Mind, Brain, Computation and Technology.
Over his career, McClelland has contributed to both the experimental and
theoretical literatures in a number of areas, most notably in the
application of connectionist/parallel distributed processing models to
problems in perception, cognitive development, language learning, and the
neurobiology of memory. He was a co-founder with David E. Rumelhart of
the Parallel Distributed Processing (PDP) research group, and together
with Rumelhart he led the effort leading to the publication in 1986 of the
two-volume book, Parallel Distributed Processing, in which the
parallel distributed processing framework was laid out and applied to a
wide range of topics in cognitive psychology and cognitive neuroscience.
McClelland and Rumelhart jointly received the 1993 Howard Crosby Warren
Medal from the Society of Experimental Psychologists, the 1996
Distinguished Scientific Contribution Award (see
citation) from the American Psychological Association, the 2001
Grawemeyer Prize in Psychology, and the 2002 IEEE Neural Networks Pioneer
Award for this work.
McClelland has served as Senior Editor of Cognitive Science, as
President of the Cognitive Science Society, as a member of the National
Advisory Mental Health Council, and as President of the Federation of
Associations in the Behavioral and Brain Sciences (FABBS). He is a member
of the National Academy of Sciences and a corresponding Fellow of the
British Academy. He has received the APS William James Fellow Award for
lifetime contributions to the basic science of psychology, the David
E. Rumelhart prize for contributions to the theoretical foundations of
Cognitive Science, the NAS Atkinson Prize in Psychological and Cognitive
Sciences, and the Heineken Prize in Cognitive Science.
McClelland currently teaches on the PDP approach to cognition and its
neural basis in the Psychology Department and in the Symbolic Systems
Program at Stanford and conducts research on learning, memory,
conceptual development, langauge processing, and mathematical cognition
at Stanford and as a consulting research scientist at DeepMind.
