Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.

Supporting Whole-Class Collaborative Inquiry in a Secondary Mathematics Classroom

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.

Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.