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เนื้อหาย่อ : Current thinking concerning a modernized mathematics curriculum has made it abundantly clear that basic mathematical concepts must be intro- duced as early as possible. This text is written with the objective of giving the student a sound intuitive foundation for the continued study of algebra and geometry. Regardless of the level of student attainment, in the future more attention must be given to mathematical ideas than has been the case in the past. Correspondingly, less emphasis must be placed upon rote learn- ing and manipulative skills. The natural place to begin such a program is in the junior high school, for many good students have an excellent under- standing of rational arithmetic by the end of grade six. This book may be used whenever the arithmetic skills of the students are judged to be adequate. Our aim is to present topics in arithmetic, algebra, and geometry in such a way that the student will be stimulated by the ideas. It is our experience that even very young students, both strong and weak, are attracted to and fascinated by relations between numbers. There is a strong natural tendency to be interested in abstract relationships for the sake of the patterns that present themselves. We try to use this facet of human nature to generate good habits of mathematical thought while at the same time developing the necessary skills. Accordingly, we have given considerable space to an examination of the ideas underlying the familiar operations of arithmetic. We have used applications of arithmetic mainly as a motivating and test- ing device for the general concepts. Far from deleting essential material, we have instead added much that is new. What is missing is emphasis on special skills with little or no mathematical content. The presentation is informal and intuitive, not deductive, yet due attention is paid to principles. For example, the role of the commutative, associative, and distributive laws in determining calculation rules receives considerable attention. In the same way, the treatment of geometry is based on a few basic concepts. Some features of the book which have proved stimulating to both students and teachers are the following. The chapter on the history of methods of numeration calls attention to the need to make a careful distinction be- tween the idea of a number and the symbols used to represent numbers. Along these lines, attention is given to enumeration with bases other than ten. It is our experience that students at all levels enjoy and benefit from a study of other bases. The treatment of algebra begins with the use of vari-