Last updated March 28, 2019 
James L. (Jay) McClelland

Lucie Stern Professor in the Social Sciences Director, Center for Mind, Brain and Computation Department of Psychology Stanford University
344 Jordan Hall, Bldg 420
Curriculum Vitae and Career Highlights.

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.
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 rulebased 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 structuresensitive 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 learningbased model aimed at capturing the graded, magnitudedependent performance of children in tasks tapping their knowledge and ability to perform correctly in simple exact number tasks thought to tap the socalled 'cardinality principle'; (c) empirical and modelbased 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 longterm 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.
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 cofounder 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 twovolume 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.