This study tested 148 preschoolers between the ages of 48 and 72 months on a Piagetian number conservation task. Children's judgment accuracy, estimation, and response latency were measured. Children were also questioned about the number conservation principle. A four-step developmental sequence was hypothesized: (1) nonconservation; (2) correct…

The described game provides children with practice in multiplying by three and in comparing the values of sets of coins. (SD)

The converse of a familiar construction problem is explored, and a partial solution presented. The general problem is "Given a segment with length whose square is x, construct a segment with length 1." (SD)

The authors recommend introducing complex numbers by first studying the integers modulo seven. (SD)

Procedures for using a calculator to check addition and subtraction problems in bases less than 10 are described. (SD)

The author states two "Birdcage Axioms" (often called the Pigeonhole principles) and shows how students can prove a variety of theorems from them. (SD)

Rules for determining the number of initial zeros and the period of a repeating decimal are stated and proved. (SD)

This article describes a series of activities and worksheets to provide students with experience in graphing number pairs. Students at different lev els can use the activities to relate basic arithmetical operations to graphs. (Worksheets are included.) (SD)

The author reviews the history of the Fibonacci sequence and its relation to Pascal's triangle. (SD)

The Chinese numerical system and its contrastive aspects with the English system are discussed, as well as some implications of the numerical system in the spoken language. (RM)

To introduce a third-grade class to division, a teacher prepared cards showing rectangular arrays from which some dots were missing; students used the remaining information to remake the cards. Related cards were used later in other activities to develop the repeated subtraction algorithm for division. (SD)

Children at many levels enjoy using spinners to explore probabilities and practice predicting, tabulating and graphing outcomes, and observing results. Directions for making spinners, descriptions of several activities, and sample worksheets are provided. (SD)

This book contains 15 essays written between 1969 through 1983. The essays included are: (1) "Semantic Analysis of Verbs in Terms of Conceptual Situations"; (2) "'Because' and the Concepts of Causation"; (3) "The Development of Language as Purposive Behavior"; (4) "Adaptation and Viability"; (5) "On the…