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Connectionist Learning and Education: Applications and Challenges

Connectionist Learning and Education: Applications and Challenges Thomas R. Shultz (thomas.shultz@mcgill.ca) Department of Psychology and School of Computer Science, McGill University, 1205 Penfield Avenue Montreal, QC H3A 1B1 Canada Abstract Successful applications of connectionist learning to educational issues include word reading, single-digit multiplication, and prime-number detection. While closely modeling human learning, these applications underscore the importance of practice, feedback, prior knowledge, and well- structured lessons. Among the remaining simulation challenges in educational domains are other reading and arithmetic skills, learner-generated goals, social aspects of learning, and learning by direct instruction. Keywords: Connectionism; education; multiplication; prime-number detection. reading; Introduction Because connectionism has dominated the theoretical study of learning for the last 20 years, it would be surprising if it yielded no useful applications to the field of education, where learning is obviously a key issue. However, most connectionist research is resolutely theoretical with very little effort expended on solving educational problems. The few systematic treatments of applying connectionism to education were written years ago and seem to have barely scratched the surface of possibilities. This paper reviews some of the more promising lines of connectionist research into learning in the key educational domains of reading and mathematics before attempting to abstract some recommendations that might be of interest to educational researchers. First though, modern connectionism is distinguished from the older, behaviorist connectionism, which had been applied to education nearly a century ago. Finally, some of the considerable challenges that education poses for connectionist modeling are discussed. Connectionism Old and New The central idea of modern connectionism is that mental processes can be modeled by interconnected networks of simple units. This is quite different from the older, behavioristic connectionism. Behaviorism emphasized the learning of associations between stimuli and responses and the idea that responses become habitual by being rewarded. Despite some rather minor historical influence on, and superficial similarities with, modern connectionism, the differences are more profound than some critics believe (e.g., Fodor & Pylyshyn, 1988). Whereas behaviorists discussed a single association between a stimulus and a response, modern connectionism deals with large, multilevel, massively parallel networks. Moreover, many contemporary networks are designed with recurrent connectivity which allows for sequential processing and complex network dynamics. Following from these differences, the old knowledge representation schemes were entirely local, whereas modern networks often employ distributed schemes in which each unit represents many different ideas and each idea is represented by many different units. These distributed representations are more efficient and robust, more biologically realistic, and account for a variety of interesting psychological phenomena. Behaviorism was uninterested in mental states, while modern connectionists invest considerable energy into determining what their networks know at various points in learning. Such knowledge-representation analyses often become an essential part of explaining psychological phenomena. The law of effect emphasized that habit formation was controlled by rewards. Contemporary connectionist models have demonstrated the difficulty of learning from evaluative reward signals indicating that an organism is doing well or badly (Hertz, Krogh, & Palmer, 1991). In contrast, many neural networks learn from fully specified target vectors that indicate the correct response to particular inputs, making learning faster and more accurate. Taken together, these differences provide modern networks with vastly more learning power than simple habits possess. A habit implements only a simple linear relation between a stimulus and a response, whereas there are now proofs that a network with a single layer of hidden units can learn any continuous function to any degree of accuracy if this layer has enough hidden units (Hertz et al., 1991). There are also proofs that any function can be learned by a network with two hidden layers, if there are enough hidden units in each layer. Finally, although most of the theoretical work in behaviorism was vague and speculative, contemporary connectionism is characterized by working computational models that enable evaluation of the quality of data coverage and generate testable predictions. Connectionism has been more concerned with establishing a theoretical understanding of learning than with developing applications to education or other practical fields. However, because connectionists have had so much success modeling the learning of reading and elementary mathematics, there is the possibility for applications to educational practice. Models of Reading A debate about whether it is better to teach reading with the rules of letter-to-sound correspondence or by learning to visually recognize whole words began in the 1960s (Foorman, 1994). There are hundreds of such phonic rules, but because letter-to-sound correspondence is only quasi- regular, they are not all that useful to learn as universally