Education Commons^™

Developing & Describing The Use & Learning Of Conceptual Models For Integer Addition And Subtraction Of Grade 5 Students, Nicole Marie Wessman-Enzinger

Theses and Dissertations

This dissertation reports the results of a teaching experiment, which explored student thinking about integer addition and subtraction. Through the lens of commognitive theory (Sfard, 2008), interpreting negative integers as secondary intuitions (Fischbein, 1987), and employing teaching experiment methodology (Steffe & Thompson, 2000), this study was a first step in developing more robust descriptions of students' conceptual models for integer addition and subtraction. I investigated: (a) the conceptual models that students exhibited, (b) the various ways that students utilized conceptual models while learning about the addition and subtraction of integers, and (c), the ways that students' conceptions evolved over the …

Preservice Secondary Mathematics Teachers' Knowledge Of Generalization And Justification On Geometric-Numerical Patterning Tasks, James Vincent Kirwan

Theses and Dissertations

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 …