This research was concerned with the clarification of the role that the external representation process (e.g. drawing) plays in children's solving of complex arithmetic problems. Fourteen children in the 10- to 12-year-old age range were asked to represent and solve five complex arithmetic problems (three with temporal organization of data, two…

A study of the relationships between Chinese dialects based on a quantitative measure of dialect affinity is summarized. First, tone values in all the dialect localities available in the early 1970s were used to calculate the dialectal differences in terms of tone height with respect to the "yin and yang" split. In the late 1970s, calculations of…

This module is the second in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include rounding off, precision of measurement, and the…

This document advances the premise that the scientific method to identify cause-effect relationships is undoubtedly the single most important factor in the geometric expansion of scientific advances evidenced thus far during the 20th century. To understand these advances and to make educated decisions concerning them, the citizenry must be…

This document, prepared for a seminar for education reporters, consists of a presentation followed by reactions from three other persons. The presentation first considers mathematics literacy from the perspective of future workforce needs. The requirements for many jobs are increasing due to the introduction of technology, while an informed…

The Student Merit Award Program was designed to motivate, stimulate and reward students for their study and achievement outside the mathematics classroom by providing enrichment material on a variety of mathematical topics. In general, these topics are either not found in the standard curriculum or represent a more in-depth study of standard…

This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

The "General Mathematics" series contains six modules intended to help students become more competent with basic mathematics. This module on fractions is designed to build or increase students' level of understanding and to help them develop those skills necessary to successfully understand and use basic fraction skills that are necessary for many…

This is a collection of Pascal programs that were developed for a 1986 National Science Foundation-sponsored high school teachers' summer workshop. The programs can be used as a means of extending or enriching textbook material in either high school mathematics or Pascal courses. Some suggested uses are: (1) teacher demonstrations in mathematics…

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

This guide was prepared to assist in determining the mathematics that should be included in drafting, electricity, electronics, and machine shop programs. Information for the guide was obtained by asking teachers from every postsecondary vocational school in Kentucky to respond to a questionnaire listing mathematics competencies for their…

This teaching guide accompanies the film series "Challenge of the Unknown," which focuses on problem solving in the real world. The guide is designed to bridge the gap between the concepts presented in the films and their classroom applications, by answering teachers' questions and needs and providing a variety of possible activities.…

Described is the mathematics achievement of 391 elementary education majors at the University of Arizona. Students were administered two subtests of the California Achievement Test: the Mathematics Computation Subtest and the Mathematics Concepts and Application Subtest. The CAT was administered in a non-standard manner. Students were allowed…

Data from the pilot use of a mathematical applications in science course for secondary-school pupils are presented. The course was offered in a variety of ways. Among these were: 1) as a one-semester elective course to sophomores who were planning to study chemistry; 2) as part of a physical science course for low achievers; 3) as part of a…