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