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Within the realm of outdoor education, there are as many definitions of what it is or what it isn't as there are books. One definition is that outdoor education is teaching outside the classroom. It combines with and blends as part of the total curriculum. This handbook is designed as a manual to help train and support staff related to outdoor education programs. Although it is specifically oriented toward resident outdoor education programs, most of the material has been generalized and can easily be used by a school or resident center in developing an approach to outdoor education. The handbook includes: (1) discussions of sensory awareness, discovery learning, group dynamics and leadership, and the three-legged stool of group function styles of leadership; (2) lesson units for teaching creative arts, language arts, natural science, math, physical education and recreation, and social science; and (3) samples of forms, lists, and evaluations, i.e., letter to parents, equipment list, health form, permission slip form, a daily program schedule, camp rules and regulations, dining room procedure (family style feeding), school menu list, activity sign-up sheets, student instructors' responsibilities and camp contract, and parent on-site evaluation. A 20-item bibliography on theories and practices of outdoor education is included. (NQ)

Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed is the resource role of the mathematics specialist in diagnosing individual student needs and in planning a program to build sequential understandings and skills. Listed are mathematical facts and concepts (for sets and subsets, numbers and numeration, operations, mathematical sentences, measurement, graphs, and geometric figures) followed by suggested teaching activities such as using graph paper to diagram multiplication facts and using both a yardstick and a meter stick to measure student height. Suggested are games and experiences to help children discover and test mathematical generalizations. Recommended instructional approaches include using magic squares to develop computational skills, adapting the seminar teaching/learning style to encourage higher intellectual skills, and the discovery of alternate problem-solving methods to develop creativity. Noted is the relationship of mathematics to other subjects such as science, geography, and music and the need for coordination between mathematics specialists and teachers of gifted children at the elementary and junior high school levels. (LH)

This document is one of a series of eight Teacher Education Modules developed by Adams State College Teacher Corps Program. As a result of completion of this module, which is itself a cluster of nine mathematics learning modules, the elementary education student will: a) gain a knowledge and understanding of the concept of elementary school mathematics; b) have a deeper understanding of the specific topics than would be expected of an elementary student; c) realize and appreciate the logical development of material from precise definitions based on intuitive concepts to facts derived from these concepts; d) increase his confidence in his own mathematical ability; e) see mathematics as a body of interdependent knowledge; and f) realize that mathematics proficiency in the mechanical processes of mathematics is not sufficient for the present-day student. Each module contains a statement of the underlying rationale; a statement of the objectives of the module; enabling activities, which are generally taken from other reference works; and procedures for evaluation. The topics of the modules include a) logic; b) set concepts; c) whole numbers and counting; d) operations on sets; e) binary operations; f) addition, subtraction, and inequalities of whole numbers; g) multiplication and division and the distributive properties of operations on the set of whole numbers; h) fractions; and i) geometric concepts. (HMD)

This paper explores two kinds of graphs, isopathic graphs and air­ port graphs. A distance property of graphs in general is also examined. Isopathic graphs are graphs in which every maximal path has the same length. The major theorem of this section characterizes isopathic graphs as extended stars, bipartite or hamiltonian. There is then a discussion of the latter two classes of isopathic graphs. At the end of Section I, there is an introduction to isopathic di­graphs, a natural concern after an exposure to isopathic graphs. Airport graphs, more appropriately snob graphs, can be thought of in the following way. It might be advantageous in some milieu that before a person would become friends with another person, A, he would first de­velop friendships with all people who are stronger than A. If in a graph strength corresponds to degree, and friendship to adjacency, an airport graph is formed when all points have this property. The resulting graph has a special structure which is examined in Section II. The concept of the "distance of a graph" is presented in Section III. Here the degree of a point is seen to be of greater importance than is the condition of being a special point. (Special points correspond to the snobs of Section II.) Notation used in this paper is that given in Frank Harary's book, Graph Theory, unless it is explicitly defined as the need arises.

This paper explores two kinds of graphs, isopathic graphs and air­ port graphs. A distance property of graphs in general is also examined. Isopathic graphs are graphs in which every maximal path has the same length. The major theorem of this section characterizes isopathic graphs as extended stars, bipartite or hamiltonian. There is then a discussion of the latter two classes of isopathic graphs. At the end of Section I, there is an introduction to isopathic di­graphs, a natural concern after an exposure to isopathic graphs. Airport graphs, more appropriately snob graphs, can be thought of in the following way. It might be advantageous in some milieu that before a person would become friends with another person, A, he would first de­velop friendships with all people who are stronger than A. If in a graph strength corresponds to degree, and friendship to adjacency, an airport graph is formed when all points have this property. The resulting graph has a special structure which is examined in Section II. The concept of the "distance of a graph" is presented in Section III. Here the degree of a point is seen to be of greater importance than is the condition of being a special point. (Special points correspond to the snobs of Section II.) Notation used in this paper is that given in Frank Harary's book, Graph Theory, unless it is explicitly defined as the need arises.