The relationship of aptitude, strategy, and cognitive task performance is explored through the use of mathematical models of performance time. Models of strategy and strategy-shifting on a spatial visualization task were tested individually for 30 male high school and college subjects. For each of three successive task steps (encoding, construction, and comparison), different models applied for different subjects suggesting that different subjects used different strategies for solving the same items. Some of the best fitting models specified that subjects frequently and flexibly switched strategies during the task in keeping with variations in item demands. This was considered a form of adaptive, within-task learning. Three alternative cases of aptitude-strategy relationship were examined. For the encoding and construction steps the most efficient strategy was restricted to subjects with a particular aptitude profile. For the comparison step, strategy selection appeared to be a more casual choice but aptitude differentially mediated performance depending on which strategy had been selected. The importance of strategy-shift models as a means for analyzing more precisely subjects' problem solving processes and for representing the adaptive, flexible quality of intelligent performance is discussed. (Author)