Based on the hypothesis that the construction of number is closely related to the development of logic, this book records a series of experiments investigating classes, relations, and numbers as cognitive domains. The author finds that number is organized, stage after stage, in close connection with the gradual elaboration of systems of inclusions…

The purpose of the study was to determine whether kindergarten children could perform successfully on Piagetian class inclusion tasks and whether their performance was a function of the types of conditions under which the task was presented. Children were asked to classify items based on a physical attribute not visually perceptible (painted…

Three studies were conducted to assess the abstraction processes involved in the development of the ability to associate numerals with sets of the appropriate size (numeration). Experiment 1 examined the sequence of the ability to discriminate relative numerical magnitude, numerical equivalence, Arabic numerals, absolute size of a set, and…

GRADES OR AGES; Kindergarten. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The guide has seven sections: 1) emphasis in mathematics; 2) three approaches--use of number in daily activities and content areas, manipulative materials and mathematically structured materials, and structuring special activities and/or problems; 3)…

This study traces the development of nondecimal numeration from the 16th century to the present. The first six chapters detail the contributions of mathematicians as well as people from other fields. Applications to computers are covered in one chapter, while another chapter discusses the coverage of numeration systems in college textbooks for…

The strategy of defining operations by generating two-dimensional number sequences is described. (MP)

Sixty kindergarten, first-grade, and second-grade children were required to construct numerically equivalent collections and to determine asymmetric-transitive relations among nonequivalent collections, using two strategies of cardinal number: correspondence and counting. A novel "collinear correspondence" task was also introduced and compared…

Described is the adaptation of the materials of the Kent Mathematics Project for use with mildly retarded students aged 11 to 16. (DB)

Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

Monsters are used as an example to illustrate that multiplication of the natural numbers is associative. (JT)

This article presents some alternative formulae for Chinese-Western conversion of dates. (CHK)

Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)