The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)

The NCTM Standards present a picture of classroom instruction different from present practice in secondary schools. Presented are three instructional practices: (1) presenting open-ended problems, (2) communication of ideas, and (3) probing for diversity and recommendations for restructuring mathematics instruction based on the California…

Doing mathematics includes the activities of making observations, searching for patterns, formulating conclusions called conjectures, and verifying these conjectures. Presented is an activity that develops pattern discovery and measurement skills using a protractor, compass, and ruler by drawing various stars. Appropriate worksheets and directions…

Presented are three methods to enrich the mathematics classroom. The first introduces an activity allowing students to discover the law of sines. The second gives eight distance-rate-time problems of value for their counterintuitive or elegant solutions. The third poses multiple answer questions that promote student interaction and communication.…

Presented is a teacher's guide for a hands-on activity challenging students to develop problem-solving behaviors by exploring the construction of a right-cylinder of maximum volume from an m x n sheet of metal. Reproducible worksheets leading students through the activity are provided. (MDH)

From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)

The Summer Mathematics Enrichment for Minority Students program was piloted during 1990 by the Texas Academy of Mathematics and Science at the University of North Texas. The program provided 19 mathematically talented minority junior high students with rigorous academic instruction, role models, on-campus residence, and social/recreational…

Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

As educators it is crucial to cater to and meet all learning needs of students, including the needs of gifted and talented students. It is highly probable that each year in their classrooms teachers will have students that are advanced in mathematics and this will pose a challenge for them as teachers to meet their learning needs. Johnson (2000)…

This document is a collection of 77 shared teaching ideas from the "From the File" department that appears regularly in the "Arithmetic Teacher." The ideas are reproduced in file-card size and categorized for easy use and handling. This useful source of activities and problems is designed to help elementary and middle school…

This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed…

The foreknowledge that a given school mathematics problem might have no specific solution or no solution at all affords students the challenge of investing careful consideration in the explicit problem conditions, as well as in the problem's unstated assumptions. Hence, the implication is that mathematics teachers, rather than speaking to their…

Teachers of mathematics are leading a nationwide effort to bring about a complete redesign of both school and college mathematics programs by setting new and more demanding standards for what students must learn about mathematics, as well as for what teachers themselves must accomplish as professionals in the classroom. This brief document is…

This report examines the impact of the Chapter 1 Extended-School-Day On-Campus and Off-Campus programs on the academic achievement of students served during the 1988-89 school year in Houston (Texas). Both programs provided supplemental instruction in reading/language arts, mathematics, and English as a Second Language after the regular school…

Children have many natural opportunities to learn about the basic aspects of quantity. This booklet is addressed to parents who want to support their children's mathematical growth. The activities presented suggest many ways in which parents and children can use mathematics in their environment. The activities are organized around common…