Janine T. Remillard

Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula:

Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers’ interactions with curriculum materials.

Teachers' Orientations Toward Mathematics Curriculum Materials: Implications for Teacher Learning

This study was prompted by the current availability of newly designed mathematics curriculum materials for elementary teachers. Seeking to understand the role that reform-oriented curricula might play in supporting teacher learning, we studied the ways in which 8 teachers in the same school used one such curriculum, Investigations in Number, Data, and Space (TERC, 1998). Findings revealed that teachers had orientations toward using curriculum materials that influenced the way they used them regardless of whether they agree with the mathematical vision within the materials. As a result, different uses of the curriculum led to different opportunities for student and teacher learning. Inexperienced teachers were most likely to take a piloting stance toward the curriculum and engage all of its resources fully. Findings suggest that reform efforts might include assisting teachers in examining unfamiliar curriculum resources and developing new approaches to using these materials.

Curriculum Materials in Mathematics Education Reform: A Framework for Examining Teachers’ Curriculum Development

AbstractThis paper presents a model of teachers’ construction of mathematics curriculum in the classroom or their curriculum development activities. The model emerged through a qualitative study of two experienced, elementary teachers during their first year of using a commercially published, reform-oriented textbook that had been adopted by their district (Remillard 1996). The aim of the study was to examine teachers’ interactions with a new textbook in order to gain insight into the potential for curriculum materials to contribute to reform in mathematics teaching. The resulting model integrates research on teachers’ use of curriculum materials (cf. Stodolsky 1989) and studies of teachers’ construction of curriculum in their classrooms (cf. Doyle 1993). The model includes three arenas in which teachers engage in curriculum development: design, construction, and curriculum mapping. Each arena defines a particular realm of the curriculum development process about which teachers explicitly or implicitly ma...

Numeracy and Communication with Patients: They Are Counting on Us

Patient-centered interactive communication between physicians and patients is recommended to improve the quality of medical care. Numerical concepts are important components of such exchanges and include arithmetic and use of percentages, as well as higher level tasks like estimation, probability, problem-solving, and risk assessment - the basis of preventive medicine. Difficulty with numerical concepts may impede communication. The current evidence on prevalence, measurement, and outcomes related to numeracy is presented, along with a summary of best practices for communication of numerical information. This information is integrated into a hierarchical model of mathematical concepts and skills, which can guide clinicians toward numerical communication that is easier to use with patients.

Teaching Mathematics for Understanding: A Fifth-Grade Teacher's Interpretation of Policy

Jim Green is a committed, experienced fifth-grade teacher who has learned about the states efforts to change mathematics teaching indirectly through his districts newly adopted, state-approved textbook. Jim views application and critical thinking as the most prominent features of the changes called for in mathematics instruction, a view shaped by his perception of mathematics as something that must always be useful and necessary in ones life. It is important to Jim that students, particularly those from low-income, minority families (like those in his school), learn to appreciate mathematics for its relevance to their lives. These ideas about mathematics, his students, and learning guide his practice and have influenced his interpretation of the Framework. Consequently, Jims view of the states reform efforts consists of changes that he can make to his current curriculum and teaching strategies, which focus on applications, without making major changes in his pedagogical practices or beliefs about mathematics, teaching, and learning.

Modes of Engagement: Understanding Teachers’ Transactions with Mathematics Curriculum Resources

Drawing on research on elementary teachers in the United States, this chapter explores and theorizes the relationships that teachers develop with curriculum resources as they use them. The central argument is that teachers are positioned by and through their encounters with curriculum materials as particular kinds of users of them. The chapter examines modes of address in curriculum resources and modes of engagement taken up by teachers to illustrate how this positioning happens, including how teachers participate in it through their epistemological stances and orientations. Modes of address are experienced through various forms found in curriculum resource, including structure, look, voice, medium, and genre. Modes of engagement are seen in forms of teacher reading, including what the teacher reads for, which parts she reads, when she reads, and who she is as a reader. Four examples of teachers engaging with a curriculum resource designed to reflect the NCTM Standards are used to illustrate how modes and forms of address interact.

TEACHING FRACTIONS IN ELEMENTARY SCHOOL

This research analyzed how fractions are taught in the fourth grade of elementary school in Flanders. Analysis centered on the presence of five features of instruction recommended by research on teaching and learning fractions (i.e., multiple solution pathways, linking representations, estimation and justification of the solution, collaboration, embedment in a realistic context). Our sample consisted of 88 instructional episodes that were selected out of 24 videotaped lessons and the corresponding lessons in the teacher’s guide. Analysis related to instruction as described in the teacher’s guide, instruction during the whole group phase of teaching, and instruction during the individual practice phase of teaching. The study revealed (1) that the observed lessons reflected to a limited extend the recommended instructional features and (2) factors that contributed to a departure from these recommendations. This research is situated in the domain of teaching and learning fractions and within the broader domain of curriculum implementation.

Examining Teachers’ Interactions with Curriculum Resource to Uncover Pedagogical Design Capacity

This chapter considers how teachers interact with curriculum resources to design and enact mathematics instruction and the capacities involved in doing this work. It begins with a discussion of conceptual and empirical issues related to curriculum, resources as a genre of tools, and pedagogical design capacity (PDC). These concepts are then illustrated, using one elementary teacher’s interactions with an unfamiliar curriculum resource. Analysis of the teacher’s reading of the guide, an enacted lesson, and pre- and post-observation interviews, identified robust and underdeveloped aspects of the teacher’s PDC. Analysis of the teacher’s guide indicates a lack of transparency about key mathematical and pedagogical concepts, which shed light on these findings.

Mapping the Relationship Between Written and Enacted Curriculum: Examining Teachers’ Decision Making

I offer an approach to representing and examining the relationship between curriculum resources and the performance of teaching, for the purpose of analyzing teachers’ design work. The approach builds on the assumptions that teaching is a design activity, that curriculum resources are tools that convey complex instructional ideas, and that, in using these tools, teachers interact with them and selectively leverage resources to design and enact instruction. I introduce the instructional design arc as a unit of analysis, referring to an episode in a lesson, prompted by the teacher, and that require the teacher to make instructional design decisions in the moment. When compiled into a lesson map, these design arcs model the episodic and emerging contours of the enacted lesson, representing teachers’ planned and in-the-moment decisions. Using data from 3rd to 5th grade mathematics classrooms in the USA, I analyze instructional design arcs within mathematics lessons, focusing on teachers’ design work.

Examining Youth’s Mathematics Practices in an After-School Robotics Team

Sixteen-year-old Joseph and his teammate, Kim, were in the process of determining a diagonal length on the robot competition field. After consulting the competition manual and measuring several side lengths, Joseph realized that he might need to use some geometric principles to calculate the missing diagonal length. It was at this point that he called across the room to Ms. Miller, the team advisor, who was also a math teacher in the high school, indicating that, “We need geometry!”