This paper characterizes the views on mathematical learning of five high school students based on the students' reflections on their mathematical experiences in a longitudinal study that focused on the development of mathematical ideas and reasoning in particular research conditions. The students' views are presented according to five themes about…

This paper describes a limited longitudinal study of young children's early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT…

Math can help children understand and think about the many aspects of their world through its connections to them. Teachers who see, and help children see, those connections enrich children's learning and development. Teachers know that building children's vocabularies helps them understand stories they hear and later will read. But by taking a…

The purpose of this study was to explore how parents and their young children attended to mathematical concepts as they engaged in shared book reading. Thirty-nine parents and their 4-year-old children from a culturally diverse metropolitan area were videotaped as they read "Mr. McMouse" (Lionni, 1992) and "Swimmy" (Lionni, 1963). Shared reading…

This paper argues that operations with negative numbers should be taught using a curriculum that is grounded in algebraic geometry. This position is supported by the results from a study that compared the conceptual understanding of grade 9 students who received the Algebra Project transition curriculum to a control group of grade 6 gifted…

This report describes the results of a three-year study, the Informed Instruction Project, that investigated different approaches to mathematics instruction for students with learning disabilities and at-risk for special education services. The project focused on two strands of inquiry: (1) the effects of a computer-based diagnostic assessment…

A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…

Students who study algebra are more likely to attend college than those who don't. A major hurdle for students in studying algebra is the transition from arithmetic to algebra. In response to overcoming this hurdle, the College Board and Educational Testing Service has developed "Algebridge," a teaching supplement that integrates…

Educators can learn to use the unique cultural aspects of their students to create a learning environment that fosters the acquisition of mathematics concepts and principles. When teaching students in a multicultural setting, it is important to build on the student's intuition of the subject matter, to base instruction on situational story…

The materials provided in this package include a 24-minute video and a professional development guide. The video portrays several different approaches to teaching mathematics in ways that are consistent with the National Council of Teachers of Mathematics (NCTM) Standards. The methods employed differ from conventional mathematics teaching in…

This manual provides a relevant resource for mathematics teachers who wish to take advantage of the extensive library of computer software materials available to expand and strengthen classroom instruction. Classroom management procedures, software duplication guidelines, procedures for copying diskettes for MS DOS and Apple II computers, and…

This manual provides a resource for mathematics teachers who wish to take advantage of the extensive library of computer software materials available to expand and strengthen classroom instruction. Classroom management procedures, software duplication guidelines, copying procedures of diskettes for MS DOS and Apple II computers, and methods for…

This material was produced by a task force of the National Council of Teachers of Mathematics to provide independent study projects for use in grades four through six. The major goals are as follows: (1) to encourage student research, investigation, and communication of mathematics through reporting and writing; (2) to provide activities that are…

As momentum for change in U.S. education continues to grow, questions about the nature and goals of mathematics education take on increasing urgency. This report proposes a framework for reform of school mathematics mainly through reshaping of the mathematics curriculum. Chapters included are: (1) "A Rationale for Change," describing changing…