PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
The role of visual reasoning in evaluating complex mathematical statements: A comparison of two advanced calculus students
Page: 536
The purpose of this study is to examine the role of visual reasoning while students evaluate complex mathematical statements about real-valued functions. We conducted clinical interviews with nine undergraduate students from mathematics courses at different levels. In the interviews, we asked these students to evaluate several mathematical statements alone and then using various graphs. In this paper, we focus on the cases of two students who had completed Advanced Calculus to highlight the contribution of their visual reasoning about several graphs. We found that student’s graphical interpretation of “between” in these statements affected their evaluation of the statements. Even at advanced levels, students’ visual cues dominated their reasoning about the statements. Our findings indicate that students’ visual reasoning contributes to their evaluation of mathematical statements and helps to account for differences between students’ meanings of statements.