Does Time Matter in Improving Mathematical Discussions? The Influence of Mathematical Autonomy

Abstract

Facilitating students’ transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers such transitions take time to manifest. The present study examined students' perceived mathematical autonomy and perceived engagement in mathematical discussions over a half year of school. Using hierarchical linear growth-curve modeling, the authors found that although it may take time for students to transition into more mathematically productive engagement in discussions, it may be the development of their mathematical autonomy, rather than mere exposure over time, that facilitates this transition.

Keywords:

• autonomy
• growth-curve model
• HLM
• mathematical discussion
• self-determination theory

Notes

Kosko (2012b) quantitatively examined the longitudinal effect of student enrollment in classrooms with more frequent discussion. However, Kosko (2012b) does not account for quality of discussion (perceived or observed) or students’ mathematical autonomy.

Data for the second semester was not included because of an incident that required students and teachers to vacate their school building for the majority of that semester. Preliminary analysis of second semester data depicts a different pattern regarding growth, primarily because of the events at the time. Therefore, these data were not included for the present analysis because they deviate from the primary purpose of this study.

While we do not discuss the results here in depth, we also adapted other measures. For each time point, we found statistically significant and positive correlations for students’ perceived mathematical autonomy with their perceived: mathematical competence (3 × =.88, =.56, =.07), social relatedness (3 × =.82, =.45, =.08), and math discussion competence (3 × =.74, =.54, =.15). While some items were originally developed, many items were adapted from multiple sources (Deci & Ryan, 2008; International Association for the Evaluation of Educational Achievement, 2003; Kosko & Wilkins, 2012; National Center for Education Statistics, 2002).

Additional information

Notes on contributors

Karl W. Kosko

Karl W. Kosko is an assistant professor in mathematics education at Kent State University. His program of research centers on mathematical communication with a focus on student engagement in and teacher facilitation of whole class mathematical discussion, and students' mathematical writing.

Jesse L. M. Wilkins

Jesse L. M. Wilkins is a professor of mathematics education at Virginia Tech. His current research focuses on the assessment and promotion of quantitative literacy, and children's development of fraction concepts.