The main objective of this study is to construct models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions similar to what the history of science refers to as progressive “problemshifts” that increase the explanatory/heuristic power of the models. Results obtained show the considerable difference in student performance on chemistry problems (mol, gases, solutions, and photoelectric effect) that require algorithmic or conceptual understanding. The difference between student performance on algorithmic and conceptual problems can be interpreted as a process of progressive transitions (models) that facilitate different degrees of explanatory power to student conceptual understanding. A parallel is drawn between the methodology of idealization (simplifying assumptions) used by scientists and the construction of strategies (models) used by students to facilitate conceptual understanding. A major educational implication of this study is that the relationship between algorithmic and conceptual problems is not dichotomous, but rather characterized by a continuum that consists of sequences of models that facilitate greater conceptual understanding. This reconstruction of student strategies to solve problems (progressive transitions) can provide the teacher a framework to anticipate as to how student understanding could develop from being entirely algorithmic to conceptual. © 1995 John Wiley & Sons, Inc.