Elementary Mathematics

Patterns and Structure 4

de Eugene Douglas Nichols, Frances Flournoy, Robert Kalin, Leonard S. Simon

**Statement of Philosophy** Elementary Mathematics-Patterns and Structure is a series of eight textbooks designed for a basic eight-year course, plus a three-book accelerated sequence. The accelerated sequence can be used with selected pupils after the completion of the fourth book in the basic series. This series is contemporary. The content and spirit are in harmony with the latest developments in mathematics curriculum and with suggestions made by many influential groups. The name, patterns and structure, is a true reflection of one of the emphases found in this series. The pupils discover patterns and are made aware of important relationships between operations and number systems, from the counting numbers through the real numbers. At the same time the structural characteristics of these systems and of mathematics in general are explored. While emphasis s placed on these structural characteristics, a thorough preparation in arithmetic skills is provided. There are regular reviews and practice exercises throughout the series. In addition to the emphasis on structure and patterns in arithmetic, a consistent, intuitive development of basic geometric topics is provided. An introduction to coordinate geometry, which brings together ideas of arithmetic, algebra, and geometry, is developed in a simple and interesting way. No essential part of mathematics which serves as a background for the of high school mathematics is omitted. Thus, the series presents a balanced diet of essential parts of all pre-high school mathematics. The discovery approach is used. A great deal of responsibility for learning is placed on the learner, as he is constantly guided by sequences of carefully paced questions leading to discoveries of new concepts and relations. The pupil is placed in the role of an active participant in the learning process. For example, by studying patterns the learner discovers the principles underlying the algorithms stemming from the positional nature of our numeration system. While actively participating in the learning process, the pupil develops powers of logical thinking through skillfully designed series of questions carefully assessed as to their appropriateness for his maturity level. Written words, pictures, diagrams, and physical activities—all are exploited to the best advantage in developing the pupil's logical thinking ability. Thus, while learning to do mathematics well, he learns to understand it and to tell why he does what he does. He learns thereby to be self-reliant and to uncover his own errors. The accelerated sequence provides pupils who have demonstrated excellent performance with an opportunity to proceed at a more rapid pace, to investigate many concepts in greater depth, and to begin the first formal course in elementary algebra earlier. No essential topics of pre-algebra mathematics are sacrificed in the process. This three-book accelerated sequence was created to meet the needs of pupils who, at an early age, display a clear-cut aptitude for mathematics. Thus, they can learn more rapidly and do not require as much practice material as other students of mathematics. Thus, the main objectives of the series are: ■ to develop in pupils understanding of and appreciation for the structure and patterns found in arithmetic and geometry; ■ to develop and maintain arithmetic skills; ■ to provide pupils with a thorough foundation in all aspects of pre-high school mathematics; and ■ to enable pupils to understand the why, as well as the how, of basic mathematics.