The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…

The Education Technology Center (ETC) Fractions Group works to investigate well-documented difficulties that children have in understanding fractions. A central assumption underlying this group's inquiry is that students' difficulties in manipulating fractions arise from their lack of understanding about the nature of fractions. In order to learn…

Twin aims--to advance theory and to improve practice in science, mathematics, and computing education--guided the Educational Technology Center's (ETC) research from its inception in 1983. These aims led ETC to establish collaborative research groups in which people whose primary interest was classroom teaching and learning, and researchers…

This book which treats the central issues facing mathematics teaching today, provides both a picture of current practice and innovation and a state of the art review of research in mathematics education. The first section, "Innovations," provides an overview of new technologies, new forms of assessment, and new curriculum developments.…

This integrative study of student socioeconomic status (SES), race and gender focused on mathematics achievement and self-esteem in the school context. Data for the study were derived from the Pennsylvania Educational Quality Assessment Program for the years 1981 through 1984. Analyses were conducted at the fifth, eighth, and eleventh grade…

In spite of courses and workshops, beginning teachers are most likely to teach mathematics just as they were taught. Changes in certification requirements, such as expecting teachers to complete more coursework, or improvements in curriculum materials, such as programs that emphasize problem solving, have also been insufficient to alter the…

Some mathematics educators feel that too little geometry is taught in elementary schools. This may have serious effects as many students arrive in the traditional high school geometry course without essential backgrounds in informal geometry. The result of this lack of preparation is often lower scores on standardized tests. In this situation,…

This paper describes a middle school mathematics clinic in the District of Columbia Public Schools, which was designed to aid students in the transition from mathematics in the primary grades to high school mathematics courses. It is intended to provide the low achiever with effective diagnostic and corrective instruction by the best trained…

This study summarizes data collection activities associated with the first two years of a large scale project involving teachers of science and mathematics with computers. The innovation being implemented in the project is that of using computer based strategies directly in the teaching of science and mathematics in the classroom and laboratory.…

The translation of research findings into practical use has been a persistent problem in education. This paper describes a model that seeks to avoid some of the implementation and dissemination practices of the past--practices that produced disappointing results. The purpose of the study was to develop and test a model that brings together…

This document was developed as a resource for secondary mathematics educators. The supplemental guide is designed to help educators challenge their students and provide each student with learning experiences to help them achieve success. Chapters reflect the mathematics curriculum and within each subject, activities are listed in the common…

The focus of this workshop involving people from 13 countries in Asia and the Pacific Region was on using computers to assist learning in mathematics. The report contains the following sections: (1) Introduction; (2) The Mathematics Curriculum: Innovation and Change; (3) The Mathematics Classroom: New Ideas with Computers; (4) Software: Quality…

The project was designed to study factors within secondary schools that tend to affect young women's enrollment, perseverance, and achievement in extensive programs in mathematics, since mathematics is the "critical filter" to entrance and advancement in an increasing number of academic and professional fields. A sample of eight high…

This is a guide for use in semester-long courses in Elementary Functions and Analytic Geometry. A list of entry-level skills and a list of approved textbooks is provided. Each of the 18 units consists of: (1) overview, suggestions for teachers, and suggested time; (2) list of objectives; (3) cross-references guide to approved textbooks; (4) sample…

This booklet was designed to provide information on secondary school mathematics courses being developed or revised, reinforcing a National Council of Teachers of Mathematics recommendation calling for "a flexible curriculum with a greater range of options." A survey of mathematics supervisors led to the identification of over 450 persons who…