This guide for a mathematics curriculum for grades 1-4 presents topics in sequential order for the entire four-year program. Grade level was not used for separating units; instead, an integrated sequencing of concepts was used in preparing this guide. The relationship between units is specified for the teacher as an explicit mapping of how a…

The first part of this volume reports on the 1959 Royaumont Seminar on secondary school mathematics, an important factor in the spread of "New Mathematics" at the beginning of the last decade. Key addresses on Reform in School Mathematics (Stone) and New Thinking in School Mathematics (Dieudonne) are reported in full, and there are summaries of…

Mathematics items developed to measure concept attainment for the topics of set theory, division, and expressing relationships were studied. A completely crossed design with 30 concepts and 12 tasks was used. The items were administered to 196 girls who had just completed the fifth grade and to 195 boys who had just begun the sixth grade.…

This guide for parents explains the objectives of the modern mathematics being taught in the schools and discusses the teaching methods being used. A few of the elementary concepts of modern mathematics (number lines, searching for patterns, different ways of analyzing problems, number bases, and sets) are briefly explained and justifications are…

The effectiveness of an advanced organizer based on examples is compared with that of one based on counter examples. The counter examples strategy was found to be more effective for the unit on finite groups. (SD)

An analysis of the conceptual development of children between the ages of five and six. The interrelationship of such concepts a big, long, small, and short is discussed. (JLH)

Children learned two linear function rules under varying conditions: presence vs. absence of pointing; visual cues (context vs. weight vs. both pictured); and a verbal-only baseline condition. A complex rule was learned as a transfer task. Visual cues aided both learning and transfer; pointing helped initial learning, but retarded transfer.…

The author emphasizes the importance of concepts and mathematical form in a discussion of understanding mathematics. (MN)

The aim of this article is to identify the natural relationships that exist between using computer programming in BASIC, and some particular mathematical concepts. Specific examples are given for use by the mathematics teacher who has the necessary facilities available. (MN)

Results of the 1974 mathematics section of the London board's Ordinary level examination are presented in the context of item-correctness differences between boys and girls. Implications are made that insecurity with concepts such as fractions and proportionality may explain why girls seem to have trouble with quantification and spatial…

Children aged four through eight performed a series of tasks involving two-dimensional isometrics to determine the amount of compatability between a mathematically-based organization of Euclidean transformation concepts and the existing cognitive structures of the children. Results confirmed that mathematical and cognitive structures are not…

The author proposes that computer programs which are designed to make algorithmic structures accessible and comprehensible be employed as advance organizers in mathematics instruction. These programs would bring clarity and structural integration to mathematical, instructional, and cognitive structures important to the mastery of mathematical…

The author argues that undergraduates, and especially those not planning to pursue mathematics, are not ready for a definitional approach to mathematics. He interprets data on student attribution of five terms (theorem, law, fact about numbers, definition, axiom) to definitions in support of his argument. (SD)

Reports that many creative leading mathematicians have introduced the concept of baby research, signifying a playful investigation that takes place at a childs' initiative and is carried out with freedom without specific knowledge or pre-conceived ideas of where it leads. (Author/AM)

Discusses the relationship between geometrical and numerical concepts in the mathematical development of young children. Based upon a longitudinal field study of 224 children, findings suggest that memorization ability facilitates understanding of numerical concepts but that subsequent mathematical development is restricted until basic geometry is…