PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Graphs of inequalities in two variables
Page: 1133
In this study, I analyze how preservice secondary teachers represented and explained graphs of three inequalities—a linear, a circular, and a parabolic—in two variables. I then suggest new ways to explain graphs of inequalities, i.e. some alternatives to the solution test, based on the preservice teachers’ thought processes and by incorporating the idea of variation. These alternatives explain graphs of inequalities as collections of rays or curves, which is similar to graphs of functions as collections of points in one variable functions and as collections of curves in two variable functions. I conclude the study by applying the alternatives to the solving of optimization problems and discussing the implications of these alternatives for future practice and research.