This document outlines the Mathematics Curriculum Framework Project and provides details on the mathematics strands, standards, and benchmarks in the state of Michigan. Many activities related to the strands, standards, and benchmarks are presented for elementary, middle, and high school levels. A CD-ROM, a list of additional publications, and…

This paper presents learning tasks of a new type that are made possible by dynamic geometry software and discusses reasons why it takes time for teachers to design and use such tasks. The paper is divided into four sections: (1) The Spatial and the Theoretical; (2) Tasks in Dynamic Geometry Software Fostering the Learning of Geometry; (3) The…

In professional development, attention to both collaboration and critical thinking in the various interactive socialization processes of teaching practices should be essential strategic elements in a formative environment. This study presents contributions from the teleinteractive dynamic established in a virtual environment for the critical…

A case study is presented on what is learned by a very advanced Math student in a ninth grade class (fifteen years old, approximately). This case was obtained from an exploratory study carried out in a classroom of eighteen students when the employment of certain cultural artifacts was introduced to approach the theme of basic geometrical…

In this research work we explored the nature of 9-12 year old pupils' responses to probabilistic problems with tree diagrams. It was found that a large percentage of pupils failed to respond correctly even to very simple problems that demanded the identification of "possible routes/paths" in figures with tree diagrams/mazes. The results…

The study was designed to enhance teachers' understating of students' learning by using assessment tasks. Four third-grade teachers and the researcher collaboratively set up a school-based assessment team in the two-year Assessment Practices in Mathematics Classroom project that assisted teachers in implementing assessment as integral part of…

The ability to recognize equivalent algebraic expressions quickly and confidently is important for doing mathematics in an intelligent partnership with computer algebra. It is also a key aspect of algebraic expectation, the algebraic skill that parallels numeric estimation. The progress in this ability of 50 students learning mathematics with CAS…

For the past three years, we have been investigating the implications of testing on students in elementary mathematics classrooms throughout the state of NJ. Our research, and the work of others, indicates that the impact of testing depends on many factors, not the least of which involves how teachers prepare their students for the test. In this…

In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (1) the learners' mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present; and (2) the kinds of knowledge that learners may be building (including…

Many theoretical explanations for knowledge transfer or generalization assume that such processes are rooted in the acquisition of abstract rules, principles, or schemata applicable in context-independent ways. This case study is part of a larger research program examining how what often appears to be generalized knowledge or performance is, in…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Here, we report on our empirical findings from the initial semi-structured interviews. We analyse the responses of three pairs of 12-year-old pupils to a range of algebra questions. In…

This paper explores the nature and status of the mathematics reform movement (focusing on California's initiatives) in America's public schools, the connection between the reform movement and constructivist epistemology, the development of an assessment tool for measuring the degree of reform present in a secondary mathematics classroom, and the…

This paper describes a program for minimizing students' inability to relate present day school mathematics to real-world experiences, including the high-tech communities around them. The targeted population consisted of second grade elementary students in a growing middle class community located in a suburb of a large metropolitan area in the…

Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

The objective of this intervention guide is to prepare each student to be mathematically literate to survive in a world that is changing and growing as technological advances are creating new applications of geometry, measurement, statistics, and counting procedures. It accomplishes this goal by providing an intervention setting that includes…