We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

Teachers' mathematical content knowledge has been under scrutiny for some time. This development is in the wake of learners' unsatisfactory performance in national examinations and international achievement tests. A widely held belief is that one, if not the most important, of the efforts to improve and enhance the performance and…

Responding to students' questions is a critical part of teaching mathematics. A particular response may either stifle a student's inquiry or, ideally, stimulate his or her interest in mathematics. Although formulating responses that have the potential to engage students in developing new mathematical insights is challenging, the authors believe…

The past five decades have produced a tremendous archive of important and interesting strategies, frameworks and practices aimed at improvement in public education. Yet despite the vast set of knowledge generated by this work, gains have not been significant enough nor sustained. Young people still arrive at postsecondary institutions ill-prepared…

There often seems to be confusion as to when young children should be ready to learn basic math concepts. The truth is, children are born ready to do mathematics. They show amazing competencies very early in life. For example, one can show an infant two objects as one moves them behind a screen. Then one more object is added. When the screen is…

This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…

These three colloqium papers focus on math readiness and the young child, the use of games in teaching basic math skills, and the teaching of math concepts through informal day care activities. The first paper discusses notions about math readiness. It points out that mental age has little to do with readiness to learn basic concept skills and…

Discussed are the problems of teaching and learning fractions in the upper primary and lower secondary schools. Recommendations for teaching fractions are made and defects in various methods of fraction instruction are identified. It is suggested that fractions not be taught in upper primary and lower secondary schools. (Author/DS)

This book synthesizes the implications of research done by the National Center for Research in Mathematical Sciences (NCRMS) by integrating two bodies of research: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues in education such as equity and assessment of…

Descriptions of ten reading, mathematics and readiness programs chosen for statewide dissemination in South Carolina are presented in this document. The programs were selected following a study funded by Title I and conducted to serve 127,702 children in local South Carolina school districts. Each was found to provide solutions to critical…

Examines the varying opinions on school readiness within a broad context and, more specifically, in relation to mathematics learning. Focuses on the kinds of mathematical experiences children should have before entering formal schooling and suggestions for parents of young children. Specific areas examined include: (1) national standards as a road…

This paper focuses on a lesson plan in fractional number concepts that illustrates how research and practice have been brought together through the use of integrated media. A teacher applied the findings from her master's thesis by collaborating with an instructor of elementary mathematics methods courses and an experienced teacher on a lesson…

This report presents a summary of the State of South Carolina's utilization of Elementary and Secondary Education Act Title I and Education Consolidation and Improvement Act Chapter 1 funds as a resource for educationally disadvantaged students during the past 5 years, and identifies those projects exhibiting the greatest gains in terms of student…