This study describes a teacher preparation program in mathematics and science and explores what impact the reformed curricula and teaching methods instituted in the program have on prospective teachers' understanding of rational numbers and integers. The study pursues obtaining in-depth insights regarding prospective teachers' concept development.…

More work with fractions needs to be done in the elementary school, with emphasis on concepts rather than computational algorithms. (MP)

Demonstrates the consequences of teaching rules without understanding using examples from two 3rd grade children. Suggests alternative instructional strategies. (KHR)

Attempted to verify knowledge regarding decimal and rational numbers in children ages 10-14. Discusses how pupils can receive and assimilate extensions of the number system from natural numbers to decimals and fractions and later can integrate this extension into a single and coherent numerical structure. (Author/MKR)

This is a reprint of an address given at the Christmas National Council of Teachers of Mathematics (NCTM) meeting in 1958. It provides a critique of elementary instruction and discusses the changes necessary. It calls for fundamental change in the concept of mathematics teaching. (PDD)

Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those…

In 4 experiments, the authors investigated the reversal of spatial congruency effects when participants concurrently practiced incompatible mapping rules (J. G. Marble & R. W. Proctor, 2000). The authors observed an effect of an explicit spatially incompatible mapping rule on the way numerical information was associated with spatial responses. The…

This paper aims to explore some properties of certain third-order linear sequences which have some properties analogous to the better known second-order sequences of Fibonacci and Lucas. Historical background issues are outlined. These, together with the number and combinatorial theoretical results, provide plenty of pedagogical opportunities for…

A critical examination of two key aspects of Piaget's account of how small children come to understand basic number concepts. (Author/CS)

THE MORPHOLOGICAL CHARACTERISTICS OF CZECH NOMINALS, WHICH CONSIST OF NOUNS, ADJECTIVE, NUMERALS AND PRONOUNS, ARE DESCRIBED IN THIS PREPRINT. THE PAPER DISCUSSED EACH CATEGORY SEPARATELY, DIVIDING IT INTO SUBCLASSES, AND PROVIDES ILLUSTRATIONS IN CZECH. IN THE PARADIGMS, SEPARATE FORMS FOR THE VOCATIVE ARE GIVEN FOR MASCULINE AND FEMININE NOUNS…

Based on a theory of rational numbers which sees the rational numbers construct of a person as potentially built on a number of subconstructs, this study explored the view of rational numbers as operators. Significant changes in performance level and quality appeared between ages 11 and 12 and 12 and 13. (JC)

Two experiments examined the ability of preschool children to reason about the numerical relations greater than and less than. Results showed that children as young as 21/2 years of age could make number-based relational judgments and compare two number pairs on the basis of a common ordering relation. (Author/JMB)