Subgoal Learning and the Effect of Conceptual vs. Computational Equations on Transfer

Subgoal Learning and the Effect of Conceptual vs. Computational Equations on Transfer Robert K. Atkinson ( atkinson@ra.msstate.edu ) Department Counselor Education and Educational Psychology; Box 9727; Mississippi State, MS 39762, USA Richard Catrambone ( rc7@prism.gatech.edu ) School of Psychology Georgia Institute of Technology Atlanta, GA 30332-0170, USA Abstract Subgoal learning is examined through the use of equations that are designed to encourage a conceptual rather than computational approach to solving problems (conducting statistical tests). Learners who studied conceptually-oriented examples transferred more successfully to novel problems compared to learners who studied computationally-oriented examples. These results extend prior work on subgoal learning by demonstrating another technique for aiding subgoal learning. Introduction Research suggests that learners typically struggle when they are obligated to solve problems that have different procedural requirements than those demonstrated by training problems or worked-out examples, even if those differences are relatively slight (e.g., Catrambone, 1995, 1996, 1998; Novick & Holyoak, 1991; Reed, Dempster, & Ettinger, 1985). This difficulty may stem in part from the fact that learners often represent the problem solving procedures of training problems or worked-out examples as a set of linear steps rather than forming a hierarchical representation that could permit them to successfully solve novel problems (Dufresne, Gerace, Hardiman, & Mestre, 1992; Singley & Anderson, 1989) Educators and researchers alike are concerned with this problem. In fact, the Committee on Developments in the Science of Learning (1999) recently suggested that “a major goal of schooling is to prepare students for flexible adaptation to new problems and settings [and that] students’ abilities to transfer what they have learned to new situations provides an important index of adaptive, flexible, learning” (pp. 223). Research indicates, however, that this goal is rarely achieved (Chi, Feltovich, & Glaser, 1981; Larkin, McDermott, Simon, & Simon, Presumably, emphasizing the structure of an example through instruction will increase flexible transfer by helping the learner look beyond the surface features of the example and test problem to find the goal-related features that can be used to solve the problem. Thus, instead of committing to memory the details of equations as the basis for one’s problem solving knowledge, a more productive approach would be to organize this knowledge in such a way that it could support generalizations across problems in a domain. One type of knowledge structure that appears to offer the promise of enhancing this type of procedural generalization is one organized around subgoals. Subgoal-Oriented Instruction As used in the present paper, a subgoal denotes a meaningful conceptual piece of an overall solution procedure. Subgoals are particularly useful to learners because they can assist them in solving novel problems since problems within a domain often share a common set of subgoals, albeit the steps for achieving the subgoals vary from problem to problem within a domain. Once learners become familiar with the typical subgoals in a domain, this knowledge can assist them in identifying which part of a previously-learned solution procedure needs to be modified in order to solve a novel problem (Catrambone, 1996, 1998). Recently, a line of research has emerged examining the efficacy of subgoal-oriented instruction (Catrambone, 1995, 1996, 1998). In particular, this line of research has explored several techniques for designing examples that help learners to form subgoals to represent the purpose of steps in an example’s solution. Across a series of studies, Catrambone investigated the impact of making the goal structure of an example’s solution explicit by using manipulations such as the use of solution step labels or visually isolating parts of example solutions. These studies indicated that if examples are designed in such a way as to encourage subgoal learning, then learners are more likely to correctly solve new problems that involve the same subgoals but require new steps for achieving them. These studies also suggest that example solutions that are segregated or labeled encourage learners to self- explain how the steps go together. One result of his self- explanation process is the formation of subgoals (Catrambone, 1998). This work parallels research in the text-comprehension literature on the effects of signals