Preservice Elementary Teachers' Beliefs about the Role of Definition in the Learning of Mathematics

Answering a call to emphasize the act of defining over the learning of definitions, we have shifted the content of a geometry course for preservice elementary teachers (PSETs) away from comparing and applying pre-written classification structures to classroom episodes centered on authoring definitions for special quadrilaterals. PSETs complete activities using geometry software, and collaboratively create definitions for specific quadrilaterals. In order to fully understand the potential of this curricular shift, we asked preservice elementary mathematics teachers' to share their perceptions of the process of writing mathematical definitions. Data from participant reflections were analyzed for themes related to mathematical definition and the act of defining. The framework that resulted from iterative discussions by the researchers examined beliefs about the nature of definition and mathematical empathy (Araki, 2015). Findings also suggest that beliefs about authority and positioning students as authors of mathematics are associated with mathematical empathy. Experiences related to the process of defining enabled PSETs to see far greater subjectivity in the discipline of mathematics and to consider, perhaps for the first time, that they, too, were both able and deserving of becoming authors of mathematical ideas.