The Impact of Instruction Through Models on Preservice Teachers' Understanding of Fraction Multiplication and Division
Open Access
- Author:
- Ervin, Heather Kay
- Graduate Program:
- Curriculum and Instruction
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- None
- Committee Members:
- Andrea Vujan Mccloskey, Dissertation Advisor/Co-Advisor
Edith Frances Arbaugh, Committee Member
Gwendolyn Monica Lloyd, Committee Member
Paul J Riccomini, Committee Member - Keywords:
- preservice teachers' understanding
fraction models
fraction multiplication
fraction division
teaching intervention - Abstract:
- It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers need to have an understanding of rational number and related concepts such as fraction multiplication and division. A conceptual grasp of these concepts is helpful for teachers to be able to teach in ways that will encourage students to learn with understanding. This study reports on a task-based small group teaching intervention and task-based interviews with four preservice elementary and middle school teachers. Analysis focuses on the preservice teachers’ models for fraction multiplication and division tasks and their sense making of models of fraction multiplication and division. Findings shed light on the preservice teachers’ development of understanding from instruction addressing conceptual understanding and procedural fluency using models of fraction multiplication and division. These findings suggest that instruction may be helpful in deepening understanding of these fraction models and that number line models may be more useful in improving understanding of fraction division than area models. Results of this study enable teacher educators to have a better understanding of preservice elementary and middle school teachers’ understanding and use of models in fraction operations. This study may assist me and other researchers in future projects involving how these understandings impact teacher practice, teacher knowledge, and teaching effectiveness. It is my intent to contribute to the field of mathematics teacher education by filling the gap in research explaining why it is beneficial to use fraction models and how to use these models to communicate effectively with others.