How is Abstract, Generative Knowledge Acquired? A Comparison of Three Learning Scenarios

How is Abstract, Generative Knowledge Acquired? A Comparison of Three Learning Scenarios Timothy J. Nokes (tnokes@uic.edu) Stellan Ohlsson (stellan@uic.edu ) Department of Psychology The University of Illinois at Chicago 1007 West Harrison Street (M/C 285) Chicago, IL 60607, U.S.A. Abstract Several theories of learning have been proposed to account for the acquisition of abstract, generative knowledge including schema theory, analogical learning and implicit learning. However, past research has not compared these three theories directly. In the present studies we instantiated each theory as a learning scenario (i.e., direct instruction, analogy training and implicit training) and then tested all three training groups on a common problem. Results show that the analogy training groups and one of the direct instruction groups performed significantly better than the other groups on problem solving performance. The findings are interpreted in terms of opportunity to practice generating a response of the relevant type. Theories of Deep Learning In order to solve complex, novel problems one must be able to retrieve previously learned information from memory and apply it to the current situation. For instance, students learning geometry need to be able to apply mathematical formulas acquired during study to novel problems encountered at test. Although surface features of the problems change (e.g., specific values: a=5 to a=15) the abstract operators used to solve the problems stay the same (e.g., the Pythagorean theorem: a + b = c ). Thus, in order for the knowledge gained from study to be helpful on the test it must be both abstract and generative. How such deep knowledge is acquired remains a central question for researchers in psychology, philosophy and education. Several theoretical explanations have been proposed as to the origin of such abstract, generative knowledge including: schema theory (Marshall, 1995; Thorndike, 1984), analogical learning (Gentner, 1983; Holyoak & Thagard, 1988) and implicit learning (Reber, 1989). Research on schema theory has shown that abstract knowledge is constructed during various types of higher- order cognitive activities including text comprehension (e.g., Kintsch & van Dijk, 1978; Thorndike, 1977), problem solving (e.g., Marshall, 1995) and direct instruction (e.g., Ohlsson & Hemmerich, 1999; Ohlsson & Regan, in press). For the purposes of this paper we are not concerned with the induction hypothesis of schema acquisition but instead with whether a schema can be taught directly (Ohlsson & Hemmerich, 1999). Although schema theory has provided much insight into the nature and form of abstract knowledge representations (e.g., Bobrow & Collins, 1975) it has done little to articulate a specific theory for how abstract schemas are acquired. A second major theoretical proposal is the analogical learning hypothesis. Research on analogical learning suggests that one acquires deep knowledge through a systematic process in which a person retrieves an analog from memory and maps the underlying conceptual structure to a novel problem (Gentner, 1983; Holyoak & Thagard, 1988). In a typical analogical learning experiment participants first solve a source problem (e.g., story problems: Gick & Holyoak, 1983; or algebra problems: Reed, 1987) and then solve a test problem that has different surface features (i.e., a different context) but retains the deep relational features of the source problem. When participants are given the hint to use the source problem to solve the test problem they perform better than a control group who did not receive prior training, indicating that explicit knowledge of the prior solution procedure facilitates subsequent problem solving. In contrast to the prior two theories research on implicit learning suggests that knowledge acquisition is a passive, inductive process that is independent of any intention to learn (Reber, 1989; Seger, 1994). In the training phase of artificial grammar learning – a typical implicit learning paradigm – the participants memorize letter strings that are generated from an artificial grammar. Participants are not informed of the rule-based nature of the memorization strings until after the training phase. In the test phase, the participants are given a classification task in which they are asked to judge whether or not new letter strings, half generated by the relevant grammar and half violating one or more of the rules, are like those memorized during the training phase. A large amount of evidence (Reber 1989; Seger; 1994; Stadler & Frensch, 1998) shows that participants perform better than chance in the test phase, indicating that they have acquired some knowledge of the underlying grammar. These three theories present a complicated if not contradictory picture of knowledge acquisition. Each theory has a history of empirical support, experimental paradigms and explanatory problems associated with it. In order to