Caroline Brayer Ebby

Learning to Teach Mathematics Differently: The Interaction between Coursework and Fieldwork for Preservice Teachers

Understanding how preservice teachers integratecoursework and fieldwork as they learn to teach iscritical to understanding how to prepare teachers toimplement the kind of instruction envisioned bycurrent reforms in mathematics education. This articleexplores the connections that 3 preservice elementaryteachers made between their experiences as learners ofmathematics in a masters-level university methodscourse and their experiences as teachers ofmathematics in the fieldwork classroom. Three casestudies are presented in order to illustrate differentways that the experience of engaging in mathematicalinquiry influences the way in which elementarypreservice teachers construct their understanding ofthemselves as mathematics teachers. Taken together,the case studies suggest that we need to expand ourperspective as teacher educators to encompass learningfrom the fieldwork experience as well as preserviceteacher learning beyond the conclusion of thesemester. In particular, I conclude that the goals ofa methods course should include developing andnurturing particular habits of mind that helppreservice teachers learn from their own teaching.

Conceptualizing Teachers’ Capacity for Learning Trajectory-Oriented Formative Assessment in Mathematics

TASK (Teachers’ Assessment of Student Knowledge) is an online assessment designed to measure teacher’s capacity for learning trajectory-oriented formative assessment in mathematics, specifically through their ability to analyze student work and make instructional decisions based on that work. In this chapter, we begin by articulating the conceptual framework behind learning trajectory-oriented formative assessment and describing the instrument, scoring rubrics, and ongoing development of TASK. We then present the results of a large-scale field test of TASK, both in terms of the overall results and additional studies of the properties of the instrument. Evidence suggests that this new instrument yields reliable and valid scores of teachers’ formative assessment capacity in mathematics, is feasible for widespread use in a variety of settings, provides useful reporting of results, and can be used to better understand specific aspects of teacher knowledge. We draw on the results of this field test to investigate the relationships between various dimensions of teachers’ ability to analyze student work in mathematics and their instructional decision making.