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Date of Award
Curriculum and Instruction
S. Asli Özgün-Koca
REPRESENTATIONAL CONFLICT AND ITS IMPACT ON STUDENTS’ LEARNING MATHEMATICS WITH UNDERSTANDING
SARAH G. ISAKSEN December 2018
ADVISOR: Dr. S. Asli Özgün-Koca
MAJOR: Curriculum and Instruction (Mathematics Education) DEGREE: Doctor of Philosophy
For many years, multiple representations have played a major role in the teaching and learning of mathematics (NCTM, 2014). The present study defined and investigated a particular phenomenon called representational conflict, which can arise when students simultaneously use multiple representations on the same mathematical task. Representational conflict is a type of cognitive conflict that students experience when mathematical productions or results from multiple representations do not appear to be compatible with one another. The present study investigated what triggers representational conflict, how students reconcile representational conflict, and whether and how students are learning mathematics with understanding as a result of reconciling representational conflict.
A blended theoretical framework was used to carry out the research. The blended framework encompassed constructivist theory’s cognitive disequilibrium, the sociocultural approach, and the theory of technology as more knowledgeable other. This blended framework served as the foundation for moving from theory to the classroom practice of learning with understanding according to Hiebert (1997). Participants in the
study were students enrolled in a Calculus I course at a 4-year university. Digital recordings of the mathematical activity of the participants were collected to serve as the data source. The students simultaneously used dynamic mathematics software (GeoGebra) as well as paper-and-pencil when collaboratively working on their mathematical activities. A grounded theory approach was used for data analysis.
Findings include the following triggers of representational conflict: students’ struggling with procedural fluency; students’ struggling with conceptual understanding; and mathematical oversights. These triggers were found to be expressed in either the GeoGebra environment or the paper-and-pencil environment. When representational conflict was triggered, it was found that students always worked to reconcile the conflict with the use of more knowledgeable other pathways (a single more knowledgeable other, or a combination of more knowledgeable others). In addition to reconciling representational conflict with a more knowledgeable other pathway, a verbally expressed mathematical explanation was almost always part of the reconciliation process. Finally, there was some evidence of the potential for reconciling representational conflict to lead students’ to learn mathematics with understanding.
Isaksen, Sarah, "Representational Conflict And Its Impact On Students' Learning Mathematics With Understanding" (2018). Wayne State University Dissertations. 2107.