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 firstassumes that novice skills are a subset of those of the expert, represented by the samevocabulary of concepts. The second approach emphasizes novices' misconceptions andthe different meanings they tend to attribute to concepts. Our evidence, based onobservations of problem solving behavior of experts and novices in the area ofmathematical programming, reveals both type of differences: while novices are to someextent underdeveloped experts, they also attribute different meanings to concepts. Theresearch suggests that experts' concepts can be characterized as being moredifferentiated than those of novices, where the differentiation enables experts tocategorize problem descriptions accurately into standard archetypes and facilitatesattribution of correct meanings to problem features. Our results are based on twenty-fiveprotocols obtained from experts and novices attempting to structure problemdescriptions into mathematical programming models. We have developed a model ofknowledge in the LP domain that accommodates a continuum of expertise ranging fromthat of the expert who has a highly specialized vocabulary of LP concepts to that of anovice whose vocabulary might be limited to high school algebra. We discuss thenormative implications of this model for pedagogical strategies employed by instructors,textbooks and intelligent tutoring systems.