This article describes how children learn the basic addition and subtraction facts, why many have difficulty mastering these basic skills, and what teachers can do to prevent or overcome these learning difficulties.

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…

This book contains activities using a technique that allows students to practice routine arithmetical operations without getting bored. Math Loops is a game in which each student receives a card containing answers to a mathematics question or problem and must listen for another student to call out the question. As the game progresses around the…

Six- to eight-year-old children (N=42) who were identified by their teachers as within the average range of ability in mathematics were individually tested on three different mathematics tasks. On the flashcard task and the nonverbal task where children replicated the number of buttons placed under a box, the same 14 addition problems with sums up…

There are numerous teaching suggestions to offer in guiding pupils to greater achievement in mathematics. This paper suggests that the instructor should begin where the pupil is presently and observe what interests the pupil in learning. Different methods for teaching mathematics such as using blocks, beads, films, filmstrips or slides, a…

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)