The use of its techniques in research on pairing representations

Pairing external representations of the same concept is ubiquitous in educational software., 4 study integrating cognitive research and development of an Intelligent Tutoring System (ITS) was undertaken to evaluate the effects of pairing representations of mathematical functions on high school students. The study consisted of (a) the administration of a questionnaire (N = 200) for assessing knowledge of properties of functions displayed separately in graphical and algebraic representations; and (b) a clinical study showing the effectiveness of pairing as an instructional action; (c) the development of an ITS, the Function Characteristics Tutor (FCT), for learning function characteristics by comparing (a special case of pairing) representations; (d) an experiment (N = 60) in which students solved tasks with FCT. Overall results show that comparing graphical and algebraic representations is efficient in learning important function characteristics, not only when the two representations refer to the same object, but mainly when they refer to different objects. FCT reproduced these results, and its degree of efficiency measured the cognitive interpretation drawn from the interviews and the questionnaire.