Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)

Suggests that a discussion-based approach focused on experiences of actual environmental issues, encountered problematically, should characterize environmental education activities. An ecology exercise dealing with organic pollution of a river provides a context for the educational principles and ecological concepts included the study. (24…

Describes the modern hot-air balloon and the physics of ballooning. Proposes that students construct their own hot-air balloon and presents an experiment calculating the time needed for a balloon to rise to the ceiling of a gymnasium. (MDH)

Discusses the rationale and use of problem fields which are sets of related and/or connected open-ended problem-solving tasks within mathematics instruction. Polygons with matchsticks and the number triangle are two examples of problem fields presented along with variations in conditions that promote other matchstick puzzles. (11 references) (JJK)

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Presents three stories from mathematics history that can be integrated into classroom teaching: (1) the account of how Eratosthenes measured the circumference of the earth to discuss the concept of units in measurement, (2) ideas from Archimedes, Vite, and Descartes to introduce pi, and (3) the discovery of the Cardanic formula as an example of…

Presents eight points to emphasize when teaching the concept of place value. Contends that converting numbers from one base to another helps students understand the concept of place value and the importance of context in establishing meaning. Provides a BASIC computer program to make conversions. (MDH)

Mathematical fiction writing as a learning tool is discussed utilizing an actual example of a student's fictional text related to the field of geometry. Commentary about this example and how it relates to other areas of mathematics can provide teachers with insight into students' schema for organization and internalization of mathematical…

This lesson plan demonstrates how to use common animals in your backyard or school grounds to study basic ecological principles with students. An example study uses squirrels for observational study. Includes background information, references, suggested equipment, activities, and observation techniques. (MCO)

Urges music educators and music therapists to cooperate in providing motivation for at-risk students through specially planned activities. Identifies means of meeting the risks of (1) lack of self-discipline and motivation; (2) not learning effectively; (3) alcohol and drug abuse; and (4) focus on rudimentary survival skills. (DK)

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)

A list of potential writing ideas and general guidelines to be used in integrating writing into the mathematics classroom are provided. Ideas under the headings of narrative, descriptive, and expository writing are included. (KR)

Presents a method of transforming 15 mathematics students' questions expressing confusion and frustration into activities that (1) engage the hidden meaning behind the question; (2) open the dialog with students, and (3) provide a chance to interact with students on crucial issues of what is at stake in learning mathematics. (MDH)

Describes how teachers can improve introductory soil science courses by applying concepts taught in the classroom to actual field situations. Presents a specific example of a field exercise designed to illustrate soil properties and processes with respect to their environmental settings. (11 references) (Author/MCO)

Proposes a novel method of introducing and promoting the topic of geometric sequences through the problem of calculating the number of games necessary to determine the winner of a single elimination tournament in which two, three, or more teams compete at a time. (MDH)