Relationships Between Research and the NCTM Standards
The current debates
about the future of mathematics education often lead to confusion about the
role that research should play in settling disputes. On the one hand,
researchers are called upon to resolve issues that really are about values
and priorities, and, on the other hand, research is ignored when empirical
evidence is essential. When research is appropriately solicited, expectations
often overestimate, or underestimate, what research can provide. In this
article, by distinguishing between values and research problems and by
calibrating appropriate expectations for research, I address the role that
research can and should play in shaping standards. Research contributions to
the current debates are illustrated with brief summaries of some findings
that are relevant to the standards set by the NCTM.
Gender Differences in First-Grade Mathematics Strategy Use: Parent and Teacher Contributions
Martha Carr, Donna L. Jessup, Diana Fuller
In this study we examined how parents and teachers influence the development of gender differences in mathematics strategy use in the 1st grade. Children were interviewed about their strategy use, their metacognitive knowledge about specific strategies, and their perceptions of parents' and teachers' attitudes toward various strategies. Parents and teachers completed questionnaires about the types of strategy and metacognitive instruction they provided. Previous results (Carr & Jessup, 1997) were replicated with boys correctly using retrieval during the 1st grade more than girls and girls correctly using overt strategies more than boys. Boys were influenced by the belief that adults like strategies indicating ability and by teacher instruction on retrieval strategies. Girls' strategy use was not related to perceived adult beliefs or actions.
The Dilemma of Transparency: Seeing and Seeing Through Talk in the Mathematics Classroom
In this article talk is understood to be a resource for mathematical learning in school. As a resource it needs to be both seen (be visible) to be used and seen through (be invisible) to provide access to mathematical learning. Lave and Wenger's (1991) concept of transparency captures this dual function of talk as a learning resource in the practice of school mathematics. I argue that the dual functions, visibility and invisibility, of talk in mathematics classrooms create dilemmas for teachers. An analytic narrative vignette drawn from a secondary mathematics classroom in South Africa illustrates the dilemma of transparency that mathematics teachers can face, particularly if they are teaching multilingual classes.
Motivation for Achievement in Mathematics: Findings, Generalizations, and Criticisms of the Research
James A. Middleton, Photini A. Spanias
In this review we examine recent research in the area of motivation in mathematics education and discuss findings from research perspectives in this domain. We note consistencies across research perspectives that suggest a set of generalizable conclusions about the contextual factors, cognitive processes, and benefits of interventions that affect students' and teachers' motivational attitudes. Criticisms are leveled concerning the lack of theoretical guidance driving the conduct and interpretation of the majority of studies in the field. Few researchers have attempted to extend current theories of motivation in ways that are consistent with the current research on learning and classroom discourse. In particular, researchers interested in studying motivation in the content domain of school mathematics need to examine the relationship that exists between mathematics as a socially constructed field and students' desire to achieve.
Elementary Preservice Teachers' Changing Beliefs and Instructional Use of Children's Mathematical Thinking
Nancy Nesbitt Vacc, George W. Bright
In this research, we examined changes in preservice elementary school teachers' beliefs about teaching and learning mathematics and their abilities to provide mathematics instruction that was based on children's thinking. The 34 participants in this study were introduced to Cognitively Guided Instruction (CGI) as part of a mathematics methods course. Belief-scale scores indicated that significant changes in their beliefs and perceptions about mathematics instruction occurred across the 2-year sequence of professional course work and student teaching during their undergraduate program but that their use of knowledge of children's mathematical thinking during instructional planning and teaching was limited. Preservice teachers may acknowledge the tenets of CGI and yet be unable to use them in their teaching. The results raise several questions about factors that may influence success in planning instruction on the basis of children's thinking.