A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

From Concrete to Abstract: Teaching for Transfer of Learning when Using Manipulatives

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

Orchestrating Whole Group Discourse to Mediate Mathematical Meaning

The most common pattern of classroom discourse follows a three-part exchange of teacher initiation, student response, and teacher evaluation or follow-up (IRE/IRF) (Cazden, 2001). Although sometimes described as encouraging illusory understanding (Lemke, 1990), triadic exchanges can mediate meaning (Nassaji & Wells, 2000). This paper focuses on one case from a study of discursive practices of seven middle grades teachers identified for their expertise in mathematics instruction. The central result of the study was the development of a model to explain how teachers use discourse to mediate mathematical meaning in whole group instruction. Drawing on the model for analysis, thick descriptions of one teacher’s skillful orchestration of triadic exchanges that enhance student understanding of mathematics are presented.