The effect of graphing calculator use on students' understanding of variations on a family of equations and the transformations of their graphs.

The study investigated the use of Casio fx7500 calculators during a five and a half week unit in precalculus. There were one hundred twenty-six participants, eighty-five percent of whom were African-American. The graphing calculators were incorporated into the unit on advanced graphing techniques that focussed on stretches and shrinks, reflections, translations, and forming reciprocals of functions. The role of the graphing calculators was to allow students to observe and analyze the effects of various parameter changes on the graphs of functions and relations. Open-ended mathematical questions were used to assess students' conceptualizations and to assign students to groups representing three levels of conceptual linkage between graphs and equations. Assessment scales were developed to codify these responses. Anecdotal information, obtained through classroom observations and interviews, was also analyzed. Analyses showed that the control group was superior at sketching functions, understanding translations and stretches and shrinks, and describing parameter variations. One of the most important findings of the study was that students with poorly and partially formed conceptual links between graphs and equations were cognitively distracted by also having to learn how to use the graphing utility. In addition, the data suggested that constructing tables of functional pairs of numbers was an essential element needed for students to develop conceptual links between graphs and equations. Students who initially had solidly formed conceptual links between graphs and equations benefitted from the use of the graphing calculator. Understanding of stretches and shrinks and translations was not aided by the use of these graphing calculators. Classroom observations and student interviews suggested that unfamiliarity with certain characteristics of the calculator may have affected its effectiveness as an instructional tool and, initially, student achievement. These characteristics are discussed and suggestions made for introducing graphing calculator technology more effectively into a revised school mathematics curriculum.Ed.D.EducationMathematics educationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128616/2/9116100.pd