IMPOSING STRUCTURE ON LINEAR PROGRAMMING PROBLEMS: AN EMPIRICAL ANALYSIS OF EXPERT AND NOVICE MODELS

Abstract

Research on expert-novice differences falls into two complementary classes. The first assumes that novice skills are a subset of those of the expert, represented by the same vocabulary of concepts. The second approach emphasizes novices' misconceptions and the different meanings they tend to attribute to concepts. Our evidence, based on observations of problem solving behavior of experts and novices in the area of mathematical programming, reveals both type of differences: while novices are to some extent underdeveloped experts, they also attribute different meanings to concepts. The research suggests that experts' concepts can be characterized as being more differentiated than those of novices, where the differentiation enables experts to categorize problem descriptions accurately into standard archetypes and facilitates attribution of correct meanings to problem features. Our results are based on twenty-five protocols obtained from experts and novices attempting to structure problem descriptions into mathematical programming models. We have developed a model of knowledge in the LP domain that accommodates a continuum of expertise ranging from that of the expert who has a highly specialized vocabulary of LP concepts to that of a novice whose vocabulary might be limited to high school algebra. We discuss the normative implications of this model for pedagogical strategies employed by instructors, textbooks and intelligent tutoring systems.