The effect of hand held calculators on learning about: functions, functional notation, graphing, function composition, and inverse functions

摘要

The purpose of this investigation was to determine if a unit about functions in a Basic Collegiate Mathematics class where use of calculators was integrated into the instruction was more effective than a unit about functions where use of calculators was allowed but not integrated into the instruction;The investigator with the assistance of the Department of Mathematics at the University of Northern Iowa (UNI) developed a unit on functions and a thirty-item achievement test (two forms). The total test was to measure unit achievement. Five non-intersecting subsets of five or six items each were to measure achievement in: (1) The idea of a function sub-unit, (2) Functional notation sub-unit, (3) Graphing sub-unit, (4) Composition of functions sub-unit and (5) Inverse functions sub-unit;One form of the test was administered as a pretest. Eleven days of instruction took place. The second form was administered as a posttest. There were 164 Basic Collegiate Mathematics students from UNI at Cedar Falls, Iowa involved in the study. Enrollment procedures did not allow random assignment of students. Class 1 (76 students) and class 3 (50 students) were randomly assigned to be experimental groups. Everyday, in these classes, the calculator was used in demonstrations and/or discussions as an aid to learning about functions. Class 2 (38 students) was the control group. In this class, although calculator use was allowed, instruction did not require nor encourage calculator use and no in-class calculator demonstrations occurred;The pretest scores were used as convariates in an analysis of covariance. No significant differences were found between groups in student achievement in the functions unit. No significant differences were found between goups in any of the five sub-units;The findings led to the following conclusions: (1) The integration of the calculator into a unit on functions did not cause more effective learning about functions. (2) The integration of the calculator into a unit on functions did not cause more effective learning in any of the five sub-units.