Date of Award
Doctor of Philosophy (PhD)
Department of Mathematics: Mathematics Education
David D. Barker
Generalization is essential to mathematical thinking (Kaput, 1999), and justification is its inseparable twin (Lannin, 2005). If students will be expected to generalize and justify, then it is important to develop an understanding of teachers' thinking about these concepts. This study examined secondary preservice teachers understanding of generalization, justification, and the interaction between these concepts.
Data were collected from three quadratic geometric-numerical patterning tasks administered during a single interview. Data reduction (Miles & Huberman, 1994) and constant comparative (Glaser & Straus, 1967) methodology was used to analyze written transcripts of the interviews.
The results of this analysis indicated that participants developed or attempted to develop a variety of explicit, recursive, and hybrid rules that appealed to figural, numerical, and symbolic characteristics. The participants justified by verifying and explaining their generalizations through numerical, figural, and algebraic arguments. Participants appeared to encounter the most success generalizing when appealing to figural characteristics and verifying their generalizations.
Kirwan, James Vincent, "Preservice Secondary Mathematics Teachers' Knowledge of Generalization and Justification on Geometric-Numerical Patterning Tasks" (2015). Theses and Dissertations. 392.