Summarized is the research focused on the relationship between children's increasing capacity to process information and the levels at which they should be capable of recognizing mathematical concepts. Implications for mathematics curricula and teachers are discussed. Lists three references. (YP)

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

The authors argue that mathematics curricula and teachers should set as objectives the development of logical processes, concepts, and language. The teaching materials described in this article have been used to help second, fourth, and seventh graders become skillful in the use of logic. (PK)

Offers recommendations for curriculum renewal, indicating the major ways each of the four major disciplines (secondary English, social studies, mathematics, and science) can improve by the year 2000, and presenting an incremental strategy for achieving such gains. (SR)

Suggests what the mathematics curriculum in middle and secondary schools will be like in the year 2000. Looks at the preservice college or university preparation of mathematics teachers, and their role in the public schools. (SR)

Examines four major elements of a strong mathematics program (tracking, curriculum, student needs, and articulation), interpreting them as they pertain to community colleges. Discusses the role of two-year colleges in the mathematical preparation of future elementary school teachers and provides sample workplace-oriented math problems. (MAB)

Presents one model for a liberal arts mathematics course that combines probability and calculus. Describes activities utilized in the course to heighten students' interest and encourage student involvement. Activities include use of visualization, take-home tests, group problem solving, research papers, and computer usage with DERIVE computer…

Addresses the national goal for U.S. students to be first in the world in mathematics and science achievement by the year 2000. Proposes an eight-point action agenda for mathematics reform for rural and small schools. Actions involve (1) educating teachers and administrators; (2) keeping parents and community informed; (3) adopting new text and…

Ten research-supported instructional components are presented for promoting mathematics achievement in students with learning problems. A curriculum (Strategic Math Series) found to be effective in teaching students with learning problems to acquire and understand basic facts and apply them in problem-solving activities is described. (Author/JDD)

Describes the mechanics of group work in the college mathematics classroom specifically group formation, preliminary class work, class and group discourse, individual and group assignments, and impact on test taking. Includes examples from a first-semester calculus course. (JJK)

Presents a method for demonstrating addition and subtraction of integers on the number line in a way that distinguishes between subtraction and negative numbers. The model depicts the sign of the number by forward or backward movement on the number line. Subtraction is illustrated by a turning around movement. (MDH)

Describes new approaches to mathematics education outlined in standards published by the National Council for Teachers of Mathematics. Highlights a new emphasis on interactive learning and real world applications in favor of rote memorization and drilling. Discusses the role of standards in educational reform efforts and suggests steps for change.…

Shortcomings of mathematics curricula are described and research on the use of sameness analysis with learning-disabled and at-risk students is outlined. The paper then illustrates how to teach addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics.…

Five Connecticut school districts formed math research teams to participate in a three-year project involving intensive curriculum evaluation and development. Training and long-term technical assistance provided skills and support for evaluating and revising their math curriculum. Professional development was tied closely to teachers' interest in…