Laura R. Van Zoest

Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program

The study compared beliefs about mathematics teaching of four pre-service elementary teachers involved in an intervention experience with those of their non-involved peers. During this intervention, which was based on a socio-constructivist approach to mathematics instruction, the intervention group participated in regular, small-group teaching experiences supported by on-going seminars. The study also examined the relationship between professed beliefs and observed actions for the intervention group.Although most pre-service teachers in this study seemed to attach some importance to children building their own knowledge through social interaction, the intervention group professed significantly stronger beliefs in a socio-constructivist instructional environment than the comparison group. Even though the intervention group strongly espoused socio-constructivist beliefs, they were not uniformly successful in translating these beliefs into instructional actions. Their actions appeared to be most consistent with a socio-constructivist perspective during the initial phase of an instructional episode, but in later phases their actions reflected more traditional beliefs about teaching mathematics.

The Role of Reform Curricular Materials in an Internship: The Case of Alice and Gregory

This report describes a case study of asecondary school mathematics internship wheremost of the elements of the internship ecologywere aligned with calls by the National Councilof Teachers of Mathematics [NCTM] for reform.Much research has been done on the lack ofimpact of teacher education programs on teacherclassroom behavior. Often this results fromdissonance between the philosophy and goals ofuniversity teacher education programs and thoseof schools. The case documented here offers aninstance of alignment between the universityprogram and the school internship site. Thefindings showed that within this supportiveatmosphere the reform curricular materialsbeing used in the classroom had a strong andlargely positive influence on the character ofthe internship experience, and on the internslearning. The form and content of the materials– Core-Plus Mathematics ProjectsContemporary Mathematics in Context –supported reform-oriented development for theintern by providing particular foci to theplanning discussions between the intern and thementor. These areas of focus were: (a) themathematics content itself, (b) conceptualunderstanding as a main goal for instruction,and (c) the use of questioning as the bestmeans of guiding students to thatunderstanding. The findings highlight theimportance of developing reform-supportiveenvironments for intern teaching placements.

Mathematics Teacher Identity: a framework for understanding secondary school mathematics teachers’ learning through practice

Abstract The United States has engaged in intensive reform efforts in school mathematics education in the decade since the publication of the National Council of Teachers of Mathematics’ Standards for School Mathematics. This context has generated interest in how to best develop reform–oriented teachers. In this article the authors describe their thinking towards the development of a framework for the qualitative study of secondary school mathematics teachers’ learning to teach through practice. Their need for such a framework occurred in the context of their work with teachers who during their teacher preparation program participated in multiple communities where individuals shared a common goal of reforming instruction. The framework combines the following theoretical constructs: (a) Shulmans heuristic of important teacher knowledge, (b) Wengers conception of learning as identity development in social situations, and (c) cognitive notions of thinking as residing in ones head.

Attributes of Instances of Student Mathematical Thinking that Are Worth Building on in Whole-Class Discussion

ABSTRACT This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making). Findings illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of these high potential instances that could be used to help teachers more easily recognize them. Implications for researching, learning, and enacting the teaching practice of building on student mathematical thinking are discussed.

Noticing Distinctions Among and Within Instances of Student Mathematical Thinking

In this chapter, we argue that there are two critical aspects of noticing student mathematical thinking: noticing within an instance of student thinking and noticing among instances of student thinking. We use the noticing literature to illustrate these distinctions. We then discuss how the MOST Analytic Framework analysis provides structure and guidance for noticing both within and among instances, and illustrate the complex interaction of these two types of noticing through the analysis of an excerpt of classroom dialogue. We conclude by offering the perspective that studies of noticing must go beyond placing value on student mathematical thinking to discriminating among instances of student thinking based on their potential to be used to support students’ understanding of important mathematics.