Relationship of college students' visual preference to use of representations: Conceptual understanding of *functions in algebra

The dissertation presents a study of the implementation of reform efforts particularly related to the use of multiple approaches to problem solving in a college advanced algebra course by considering (1) what types of representations students choose to use when solving algebra problems related to polynomial, exponential, and logarithmic functions with graphing calculator technology, (2) why students choose to use these representations, (3) whether or not visual learning preference is related to students' choice of representation and ability to use multiple representations, (4) whether or not students think that use of multiple representations deepens their understanding, and (5) in what ways students gain an understanding of connections between algebraic (symbolic), graphical, and tabular representations.;Pretest and posttest worksheets asking students to show different ways to solve problems involving various functions, a Mathematical Processing Instrument, student questionnaires and teacher questionnaires, and student interviews were conducted. On the worksheets, students used symbolic algebra and graphs predominantly, with very little use of tables. Influences on why students choose one representation over another when solving problems include students' perception of what is mathematically proper; students' perception of instructors' beliefs about the value of given methods; processes and representations modeled by instructors when giving examples; the nature of a given problem; and the ease, speed, and accuracy in which a representation can produce an answer to a given problem. Chi-square analysis revealed no relationship between students' visual learning preference and initial choice of representation on posttest problems. One-tailed paired t-tests revealed that students were able to use significantly more representations on the posttest than on the pretest, and ANOVA showed that gains from pretest to posttest were not significantly different among visual learning preference groups (visual, harmonic/versatile, and non-visual).;Overall, students thought that using multiple representations deepened their understanding. They made connections between various representations through seeing different approaches demonstrated by different instructors and by other students; through solving problems that require multiple steps and integration of concepts; through practicing using each of the representations and subsequently recognizing similarities and differences between the representations; and through beginning to realize that the representations are linked.