A brief overview of the language of mathematics is presented, with specific attention given to its structure and facility. It is felt that professional discretion has to be exercised as to which elements of the material are acceptable for student use. However, it is viewed as essential that teachers be exposed to the structure in order to deal…

The development and field testing of two instructional mathematics programs are discussed. The general instructional program evolved from earlier research, and was field tested with 40 teachers and over 1000 fourth-grade students. Data reflected that this program had strong, positive effects on students' achievement. The second program focused on…

This 10 unit manual introduces the concepts and components of mastery learning and helps instructors organize mastery learning courses of their own. Unit I introduces mastery learning as a process involving the development and presentation of objectives, homework, formative evaluation, corrective assignments, evaluation retakes, and summative…

This study used 152 grade eight students ranging in age from 12 to 14 years from a suburban middle school in central New Jersey. The investigations gave particular attention to the identification of variables that represent understanding of fundamental mathematical structures. The first year of the research took place during the 1978-1979 school…

In presenting a historical overview of trends in vocabulary research, this paper emphasizes the importance of word knowledge as a critical component in reading comprehension. It describes research examining current psychological and pedagogical models as they relate to vocabulary knowledge, and explores vocabulary research in the area of specific…

The concept that it is important for students to learn how to read the language of mathematics is promoted. Most mathematics teachers neither have the knowledge nor feel the responsibility to develop reading skills in their students. The materials in this document are viewed to be of sufficient variety and potential for making important…

Presented is the final report of a one-year project on the structure of high school mathematics knowledge sponsored by the National Institute of Education (NIE). The main body contains conclusions on a conceptual framework for representing high school mathematics. Results are presented through discussion of three domains from the secondary school…

Hierarchically organized knowledge about actions has been postulated to explain planning in problem solving. Perdix, a simulation of problem solving in geometry with schematic planning knowledge, is described. Perdix' planning knowledge enables it to augment the problem space it is given by constructing auxiliary lines. The planning system also…

Ten research reports related to mathematics education are abstracted and analyzed. Five of the reports deal with aspects of mathematics instructional practices, four with areas of learning theory, and one with student achievement. Research related to mathematics education which was reported in RIE and CIJE between July and September 1980 is…

The purpose of the study was to find out if and how the subject matter of a remedial high school classroom interacted with the social organization of that classroom and the differences it made. Two classrooms with different subject matter (mathematics and social studies) were observed over the course of a school year. The multiple awarenesses and…

This document highlights points made in papers presented in the two scheduled sessions devoted to issues in mathematics education affecting minority students at the 1980 National Council of Teachers of Mathematics (NCTM) conference. The first meeting was part of the official NCTM conference program. The second meeting was sponsored by the National…

Nineteen projects related to mathematics education issues among minorities, funded by the Learning and Development Unit at the National Institute of Education (NIE), are summarized. It is felt that minorities and mathematics education issues have been largely neglected in recent investigations. This neglect is seen to have the potential to render…

The uses of verbal rules in solving arithmetic problems are presented. Thirty-six problems were used in individual testing of five students who were enrolled in a remedial mathematics course at a community college. Two or three weeks prior to the individual exams, the students had been tested in their class on the material. The study indicated…

Presented are new principles and methods in the instruction of mathematics, with the primary focus at the elementary school level. The first half has the following sections: (1) The Influence of Environment on Child Behavior; (2) Pre-Mathematics; (3) The General and the Abstract; (4) The Passage from Pre-Math to Mathematics; (5) Building a…

Research indicates that the brain grows in spurts occurring every two years or so and alternating with plateau periods in which the gains due to growth are consolidated. While the number of brain cells no longer increases after the age of about 18 months, substantial increases in the complexity of neural networks occur generally between the ages…