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\nassumes that novice skills are a subset of those of the expert, represented by the same\nvocabulary of concepts. The second approach emphasizes novices' misconceptions and\nthe different meanings they tend to attribute to concepts. Our evidence, based on\nobservations of problem solving behavior of experts and novices in the area of\nmathematical programming, reveals both type of differences: while novices are to some\nextent underdeveloped experts, they also attribute different meanings to concepts. The\nresearch suggests that experts' concepts can be characterized as being more\ndifferentiated than those of novices, where the differentiation enables experts to\ncategorize problem descriptions accurately into standard archetypes and facilitates\nattribution of correct meanings to problem features. Our results are based on twenty-five\nprotocols obtained from experts and novices attempting to structure problem\ndescriptions into mathematical programming models. We have developed a model of\nknowledge in the LP domain that accommodates a continuum of expertise ranging from\nthat of the expert who has a highly specialized vocabulary of LP concepts to that of a\nnovice whose vocabulary might be limited to high school algebra. We discuss the\nnormative implications of this model for pedagogical strategies employed by instructors,\ntextbooks and intelligent tutoring systems.