This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The Van Hiele level theory offers an explanation and a remedy for student difficulty with higher-order cognitive processes required for success in secondary school geometry. This document reports results of a study which involved about 2700 students in 13 high schools, selected to provide broad representation of community socio-economics in the…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

The following questions are addressed: (1) Are there sex differences in achievement, either in entering knowledge of geometry in the fall, or in achievement in acquiring standard geometry content by year's end? (2) Are there sex differences in the performance of students on the van Hiele test, either at the beginning or end of the year? and (3)…

This document focuses on a series of studies that viewed aspects of conditional reasoning. The investigations were concerned with the processes children use to acquire patterns of deductive inference and logical relationships pertaining to propositional reasoning. The first experiment, involving 96 children each in grades 2 and 5, investigated the…

Presented is a review of findings from research of teaching in the 1970's. It is noted most research was directed toward identifying effective instructional strategies for low achievers, and may not generalize to high achievers. Information is related to student time on task, length of school day, academic time, allocation of time to specific…

Presented are abstracts of 14 research reports. Topics covered include: (1) the effects of games on mathematics skills and concepts; (2) the use of problem-solving heuristics in the playing of games involving mathematics; (3) sex differences in electing mathematics; (4) the origins of sex differences in high school mathematics achievement and…

In this document, detailed objectives for each grade level are listed according to the following categories: for grades K-9, numeration, basic operations, fractions, money and time, and measurement and geometry; for grades 10-12, numeration, basic operations, fractions, and practical applications. Each objective is keyed to an expected level of…

The study of the non-Euclidean geometries resulting from changes in the Euclidean parallel postulate often strengthens an individual's awareness and understanding of the deductive systems of mathematics in general. Students at both the high school and college levels are frequently fascinated by the study of deductive systems such as the two…

Several highly motivating lessons particularly pertinent to the study of mathematics in high schools and the first years of college are presented. These lessons fall into four categories: (1) problems that present a challenge and which are interesting for their own sake; (2) problems based on real situations that can be understood by the student;…

This module utilizes hole punching with a pencil, paper folding, rubber band stretching, and unique board models to "picture" key geometric concepts in an intuitive manner. The module is virtually self-contained, except for common classroom items which are scissors and a protractor. The introductory lesson allows for a variety of approaches for…

The inservice learning module described focuses on teaching mathematical concepts at the elementary grade level. Specifically covered in the module are discovery learning, drill activities, understanding number concepts, and introduction to geometry. Information is provided in this descriptive report on the scope and sequencing of topics and the…

This SMSG study guide is designed to provide assistance to teachers who wish to improve their professional competence by self-study or by group study. The main purpose of the guide is to list and organize suitable references. Topics covered include: (1) algebra; (2) geometry; (3) number theory; (4) probability; and (5) statistics. (MP)

This is part one of a two-part manual for teachers using SMSG junior high school text materials. For each chapter, a brief overview is given and sample test questions are listed. Each section contains a discussion of the topic at hand and answers to all the exercises. Chapter topics include: (1) what is mathematics; (2) numeration; (3) whole…

This curriculum bulletin is one of a planned series of bulletins designed to meet the needs of teachers and supervisors who are working to improve the achievement level of mathematics. The material has been planned to help teachers meet the diverse mathematical needs of the children in fifth-grade classes. In addition to the emphasis that is…