Mathematics Content Course For Teachers Research Articles

Inviting Prospective Teachers to Share Rough Draft Mathematical Thinking

Engaging prospective elementary teachers (PTs) in participating productively by making their exploratory (rough draft) thinking public during class discussions remains a constant challenge for instructors of mathematics content courses for teachers, in part because of perspectives incoming PTs may hold about interacting in academic settings. In this article, we share the effects of an intervention designed to confront PTs' incoming perspectives. PTs were provided with opportunities to label the level of completeness and correctness of their thinking before they displayed and discussed their written work publicly during a mathematics content course for teachers. Results indicated that labeling their work increased PTs' level of comfort with sharing their thinking and awareness of the value of doing so. PTs also reported that the label served as a reflection tool. The label increased the PTs' productive disposition in terms of comfort level with taking intellectual risks when doing mathematics and reflecting on their work.

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

The purpose of this study was to examine and elaborate upon elementary prospective teachers’ (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs’ conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs’ performance on tasks to elaborate upon PSTs’ conceptions of the operation of partitive division. This study contributes new insights into PSTs’ conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.

Prospective elementary teachers’ motivation to participate in whole-class discussions during mathematics content courses for teachers

Prospective elementary teachers’ (N = 148) motivation to participate in whole-class discussions during mathematics content courses for teachers, as expressed in their own words on an open-ended questionnaire, were studied. Results indicated that prospective teachers were motivated by positive utility values for participating (to achieve a short-term goal of learning mathematics or a long-term goal of becoming a teacher), to demonstrate competence (to achieve performance-approach goals), or to help others (to achieve social goals). Negative utility values for participating were expressed by those who preferred to learn through actively listening. Five motivational profiles, as composed of interactions among motivational values, beliefs, goals and self-reported participation practices, were prevalent in this sample. Self-reported variations among participants’ utility values and participation practices suggested that prospective teachers engaged differentially in opportunities to learn to communicate mathematically. Results provide pedagogical learner knowledge for mathematics teacher educators.