Building concept images--supercalculators and students' use of multiple representations in calculus

Graduation date: 1992This study investigated how the use of supercalculators\ud (HP 28S and HP 48SX) affects students' conceptual understanding of\ud differential and integral calculus. Students (n = 324) from 12\ud institutions throughout the United States studied an experimental\ud curriculum emphasizing multiple representations (symbolic,\ud numerical, graphical). (The curriculum was developed through the\ud Oregon State University Calculus Project supported by the National\ud Science Foundation.) In particular, these students were taught\ud graphical and numerical methods for analyzing and solving problems\ud with the aid of supercalculators.\ud The specific research questions concerned: student's\ud representational knowledge and concept image (representational\ud facility, connection among representations, management of\ud representations) and student's calculator usage and interpretation\ud of calculator results (management of the calculator, conflict\ud resolution and confidence in the calculator). The theoretical\ud framework for the study is a concept image theory put forward by\ud Tall and Vinner (1981). Paper-and-pencil tasks were administered to the\ud experimental students as well as 30 students from traditional\ud calculus classes (18 from Oregon State University and 12 from a\ud parallel class at a project site). Audio-taped task-based\ud interviews were conducted with 33 experimental students and 31\ud traditional students.\ud Results indicated that:\ud Experimental students showed greater facility with\ud graphical and numerical representations and exhibited\ud better ties among the three representations than\ud traditional students.\ud Individual students do show definite preferences for\ud certain representations but different factors influence\ud their choices.\ud More evidence of compartmentalization was observed\ud among the traditional students than among the\ud experimental students.\ud Grades do not appear to be a good predictor of the quality\ud of the connections among the representations.\ud Students use of the calculator is closely tied to their\ud management of representations.\ud Students who lack confidence in their symbol manipulation\ud skills appear to use the calculator more readily than those\ud who are confident in their symbol manipulation skills.\ud When a device (machine or a formula) is used to perform a\ud computation in a routine fashion, those are results\ud students look at least critically.\ud Students' confidence in graphical information appearing on\ud the screen is tied to having a priori information.\ud In addition, the role of the instructor appears to be particularly\ud important in terms of management of representations and of the\ud calculator