Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum
Gwendolyn M. Lloyd, Melvin Wilson
In this study we investigate the content conceptions of an experienced high school mathematics teacher and link those conceptions to their role in the teacher's first implementation of reform-oriented curricular materials during a 6-week unit on functions. The teacher communicated deep and integrated conceptions of functions, dominated by graphical representations and covariation notions. These themes played crucial roles in the teacher's practice when he emphasized the use of multiple representations to understand dependence patterns in data. The teacher's well-articulated ideas about features of a variety of relationships in different representations supported meaningful discussions with students during the implementation of an unfamiliar classroom approach to functions.
Using Transactional Reading Strategies to Support Sense-Making and Discussion in Mathematics Classrooms: An Exploratory Study
Raffaella Borasi, Marjorie Siegal, Judith Fonzi, Constance F. Smith
In this study we explore the potential for mathematics instruction of four reading strategies grounded in transactional reading theory. On the basis of the descriptive study of 18 instructional episodes developed in 4 secondary mathematics classes as a result of collaborative action research, we show that encouraging mathematics students to talk, write, draw, and enact texts can provide them with concrete ways to construct and negotiate interpretations of what they read. In addition to helping students better understand the text read, acting on and acting out a text allow students to use that text as a springboard for sense-making and discussion of important mathematical ideas and issues about the nature of mathematics, especially when these reading experiences are supported by compatible classroom norms and values.
Conceptualizing Belief Structures of Preservice Secondary Mathematics Teachers
Thomas J. Cooney, Barry E. Shealy, Bridget Arvoid
This is a study of the beliefs and belief structures of 4 preservice secondary mathematics teachers as they progressed through a 4-quarter sequence in mathematics education including student teaching. We considered the notions of centrally and peripherally held beliefs and whether beliefs were held dualistically or contextually. The various ways in which the teachers structured their beliefs helped account for the fact that some beliefs were permeable whereas others were not. The nature of the evidence supporting the teachers' beliefs was considered particularly as that evidence related to the voices of significant others or to what the individuals valued. A scheme for conceptualizing the professional development of preservice teachers is posited.
Learning to Estimate in the Mathematics Classroom: A Conversation-Analytic Approach
Michael A. Forrester, Christopher D. Pike
In contrast to contemporary estimation researchers who have focused primarily on children's computational estimation abilities, we examined the ideas surrounding the teaching and learning of measurement estimation in the classroom. Employing ethnomethodologically informed conversation analysis, we focused on 2 teachers' instructions during estimation lessons and on pupils' (aged 9-11 years) talk during small-group follow-up activities. The results indicated that estimation is understood as discursively interdependent with measurement and is associated both with teacher-formulated accountability and with vagueness, ambiguity, and guessing. Furthermore, the meaning of what it is to estimate is embedded in practical action. In concluding comments we consider the advantages of using conversational analysis as a method for highlighting the relationships between language and mathematics in the classroom.