Abstract

=Abstract=

One of the goals of mathematics education is to allow students to understand mathematical ideas from various perspectives. The ability to move among representations allows the student to become better problem-solvers. This study is based on the symbolic mediation model proposed by Kaput, Blanton, and Moreno (2008). In this model, the symbol system used by the learner interacts with the world of the phenomena being developed in a bidirectional manner. As a concept develops, the learner uses symbols to encapsulate the ideas and in turn these ideas and understanding are shaped by the symbol systems used to represent them. Tall and Vinner (1981) would describe this process as bringing together the concept image and concept definition of the mathematical idea. Further, research on the use of data collection devices suggests that real-time connection of representations is essential for students to make linkages among various aspects of the concepts (Lapp, 2000). This study will employ both quantitative and qualitative methodologies to address the following research questions: (1) Do students with access to dynamically connected representations have a greater ability to translate among graphical, algebraic, and numerical representations of algebraic concepts as compared to students with access to only graphing technology without dynamic connection? and (2) What role does technology that integrates a computer algebra system, graphing utility, and spreadsheet play in a student's ability to move fluidly among representations for algebraic concepts? Data will be collected in College Algebra courses during the Autumn and Spring semesters. Data will include written instruments designed to examine students' ability to translate among representations as well as data collected from interviews, fieldnotes, and concept maps.