The sample assessment items in this volume are sorted according to the strands of number and operations, algebra, geometry, measurement, and data analysis and probability. Because one goal of assessment is to determine students' abilities to communicate mathematically, the writing team suggests ways to extend or modify multiple-choice and…

This in-depth case study explored the successes and struggles of elementary teachers as they implemented "Investigations in Number, Data, and Space," a K-5 research-based mathematics curriculum that offered students connected and meaningful mathematical problems and in-depth thinking. Data collection and analysis were based on the Zone…

We describe a large-scale urban school initiative aimed at teachers' professional development with the goal of increasing teachers' mathematics content knowledge and helping them improve their practice. Believing that the formation of professional communities of teachers is crucial in supporting teachers trying to implement changes in their…

Student learning depends on the teacher's actions, which are, in turn, dependent on the teacher's knowledge base--defined here by three components: knowledge of mathematics content, knowledge of student epistemology, and knowledge of pedagogy. The purpose of this study is to construct models for teachers' knowledge base and for their development…

In this paper we document the importance of institutional context in both constraining and enabling the work of mathematics teachers. We build from our current and ongoing collaborative efforts with middle-grades mathematics teachers to provide an analytic approach and resulting analysis that clarifies the critical role of institutional context in…

The object of this paper is to present and analyze some observations of the language children in 1st grade (6-7 years old) use when they talk about geometrical objects. The observations are made during a number of encounters with the pupils during one year. The work is part of an ongoing collaboration project between a university college and a…

This study investigated the fluency with which first-graders with strong, moderate, or weak mathematical abilities apply the decomposition-to-10 and tie strategy on almost-tie sums with bridge over 10. It also assessed children's memorized knowledge of additions up to 20. Children's strategies were analysed in terms of Lemaire and Siegler's model…

In contrast to the traditional top-down approach, a bottom-up approach is proposed by current reform in mathematics education. According to this alternative proposal, algorithmizing is the activity in which students should be involved. What can we do when we want to enact such an algorithmizing approach in a classroom and our students have already…

Equity and computer use for secondary mathematics learning was the focus of a three year study. In 2003, a survey was administered to a large sample of grade 7-10 students. Some of the survey items were aimed at determining home access to and ownership of computers, and students' attitudes to mathematics, computers, and computer use for…

This book is intended to provide practical guidance to elementary grade teachers in inclusive classrooms with students having difficulties in learning mathematics. Following an introductory chapter, chapter 1 provides an overview through the use of case studies of three students that note research on learning difficulties in mathematics, and on…

This paper presents information on a course entitled "Mathematics and Technology" which was created at the University of Montreal and was taught once during the winter term of 2001. The students in the course were for the most part future high school teachers. Several applications of mathematics in technology are introduced and students…

This book contains a collection of fraction lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to: (1) name fractional parts of wholes and sets; (2) represent fractional parts using the standard notation including proper fractions, improper fractions, and mixed numbers, and…

Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

We examine the long term history of the development of fundamental representational infrastructures such as writing and algebra, and how they were physically implemented via such devices as the printing press and computers, in order to (1) gain insight into what is occurring today both in terms of representational infrastructure change and in…

This report presents the results of survey research that collected responses of graduates (N=113, Fall 1999 through Fall 2001) from a reform-based mathematics and science teacher preparation program. All graduates' responses were compared to smaller subsamples of employed new elementary and middle school teachers with responses of a larger sample…