Juliet A. Baxter

Subject-Matter Knowledge and Elementary Instruction: A Case from Functions and Graphing:

The purpose of the present investigation was to describe the relationship between teachers’ knowledge of mathematics and their instructional practice. An experienced fifth grade teacher was videotaped as he taught a lesson sequence on functions and graphing. In addition, a subject matter knowledge interview and card sort task were conducted with the teacher and a mathematics educator. The results suggest that the teacher’s knowledge of functions and graphing was missing several key mathematical ideas and that it was not organized in a manner to provide easily accessible, cross representational understanding of the domain. These limitations were found to relate to a narrowing of his instruction in three ways: the lack of provision of groundwork for future learning in this area, overemphasis of limited truths, and missed opportunities for fostering meaningful connections between key concepts and representations.

Effects of Reform-based Mathematics Instruction on Low Achievers in Five Third-Grade Classrooms.

In this study we examined the responses of 16 low-achieving students to reform-based mathematics instruction in 5 elementary classrooms for 1 year. We used qualitative methods at 2 schools to identify the needs of low achievers in these classrooms, which were using an innovative curriculum. Through classroom observations and interviews with teachers, we studied the involvement of low achievers in whole-class discussions and pair work. Results suggested that both the organization and task demands of the reform classrooms presented verbal and social challenges to low achievers that need to be addressed if these students are to benefit from reform-based mathematics instruction.

The Effects of an Innovative Approach to Mathematics on Academically Low-Achieving Students in Inclusive Settings:

This article presents results from a year-long study of an innovative approach to mathematics and its impact on students with learning disabilities as well as those at risk for special education. There is a considerable interest in the field regarding current mathematics reform, particularly as it reflects the simultaneous and conflicting movements toward national standards and inclusion. Results suggest that innovative methods in mathematics are viable for students with average and above average academic abilities and that students with learning disabilities or those at risk for special education need much greater assistance if they are to be included in general education classrooms. The success of the majority of students in this study raises questions about commonly advocated instructional methods in special education.

Dilemmas of Discourse-Oriented Teaching in One Middle School Mathematics Classroom

In this article we focus on the middle school mathematics lessons of 1 teacher who has been relatively successful at instituting discourse-oriented teaching in her mathematics classes over a 3-year period. Data include transcripts of videotaped lessons, field notes from observations of those lessons, and interviews with the teacher, all collected as part of documentation efforts for the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) project. We describe how the teacher provided both analytic scaffolding (help in structuring mathematical ideas) and social scaffolding (help in establishing norms for social behaviors) for 3 classes of roughly 30 at-risk students. We demonstrate how the teacher provided less analytic scaffolding for her students because of a well-intended focus on social scaffolding. We note occasions on which the classroom returned to a more traditional orientation, in contrast to the reform orientation the teacher worked to develop. We also discuss ways in which this result highlights parallels between current reform efforts and past studies of discovery learning. We hope to contribute to the theoretical discussion of reform and to suggest ways in which implementation efforts might benefit from midcourse adjustments.

We Talk About It, But Do They Get It?

This article reports on the last of a series of iterative research studies involving students with learning disabilities in reform mathematics classrooms at the intermediate grade levels. This study reports the findings from a larger, year-long case study that focused on ways to include students with learning disabilities and other students who are at risk for special education services in classwide discussions of problem solving. The data reported in this article detail the changes in teacher and student discourse over a nine-week period in one classroom. Sources of data for this study included videotapes, audiotapes, and informal interviews with the teacher, a paraprofessional, and students. A quantitative analysis of the results indicates clear patterns of change in teacher and student discourse. Nonetheless, intentional efforts to include target students in the whole-class discussions yielded instructional dilemmas that are underdescribed in the mathematics reform literature. Findings from this study have implications for special educators interested in mathematical problem solving, as well as math reformers who value the role of classroom discourse in daily instruction.

Enhancing Student Achievement on Performance Assessments in Mathematics

This article is part of a program of iterative research involving students with learning disabilities in reform mathematics classrooms at the intermediate grade levels. The study reports the findings from a larger, yearlong case study focusing on ways to improve problem solving through classwide performance assessment tasks and ad hoc tutoring for students with learning disabilities. The purpose of these interventions was to enhance a students deeper understanding of mathematics and to develop the kind of strategic knowledge needed to solve complex problems. A quantitative analysis of the results indicate that these two interventions led to demonstrable differences over time and when compared to a limited number of students with learning disabilities who did not receive this kind of instruction. Qualitative analyses of student performance show two distinct trends in the improvement of the students in the intervention group. Findings from this study have implications for special educators interested in mathematical problem-solving instruction, as well as policymakers who are interested in performance assessment.