The purpose of this investigation was to identify and describe the differences in the methods used by experts (university chemistry professors) and nonscience major introductory chemistry students, enrolled in a course at the university level, to solve paired algorithmic and conceptual problems. Of the 180 students involved, the problem-solving schema of 20 novices were evaluated using a graphical method to dissect their think-aloud interviews into episodes indicative of solutions to paired problems on density, stoichiometry, bonding, and gas laws. These interviewed novices were classified into four different problem-solving categories (high algorithmic/high conceptual, high algorithmic/low conceptual, low algorithmic/high conceptual, and low algorithmic/low conceptual). Results of these comparisons indicated that there is an indirect relationship between a subject's ability to solve problems, and the time and number of transitions required. As the subjects' ability to solve both algorithmic and conceptual problems improved, less time and fewer transitions between episodes of the problem-solving schema were required to complete the problems. Algorithmic-mode problems always required more time and a greater number of transitions for completion than did conceptual-mode problems, but algorithmic-mode problems were more frequently solved correctly. (Author)