Presented are suggestions for increasing the efficient use of the transition board while reducing its overall size. Discussed are the construction and preparation of the boards. Teaching addition and subtraction using these materials is described. (CW)

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Presents two seasonally related investigations involving arithmetic series to develop critical thinking: (1) the number of candles needed for the eight nights of Hanukkah, and (2) the number of presents given during "The Twelve Days of Christmas." Students also calculated the amount of money needed to buy all the presents. (MDH)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

Activities and games which use dominoes to reinforce basic arithmetic skills are presented. Instructions and materials are provided for the activities and games, most of which involve addition and subtraction. Other skill areas which are covered include recognition and matching of domino patterns, multiplication, and division. A seven-item list of…

The purpose of this manual is to present a series of lessons on solving word problems, each focusing on a specific concept. The solving of story problems should be incorporated into the daily mathematics lesson so that children can maintain and increase their skills. The lessons are sequenced according to their complexity. Lessons one through…

This study used knowledge derived from classroom-based research on teaching and laboratory-based research on children's learning to improve teachers' classroom instruction and students' achievement. Twenty first-grade teachers, assigned randomly to an experimental treatment, participated in a month-long workshop in which they studied findings on…

This article examines the level of understanding by children (six- to seven-year-olds) of the addition and equality symbols. The article reports that about half of the subjects were unable to write the mathematical expression of simple addition while they were able to do it verbally. (YP)

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Learning the techniques of critical thinking and problem solving can be easy for children when presented problems involving fun topics. Problem sets which range from easy to hard written by elementary school students and educational consultants are included. Topics include addition, subtraction, multiplication, division, and fractions. Each topic…

This book provides practical ideas and information for volunteer tutors and teachers about teaching numeracy, as well as a reference section that concentrates on specific content areas. The first part of the book considers teaching techniques, the planning and presentation of numeracy material, evaluation of progress, reinforcement of newly…

In the foreword to this book, Inhelder states that its essential contribution is that "it transposed to actual reality Piaget's central epistemological thesis according to which mathematical thought is, from its most elementary manifestations, the product of the subject's activity that he characterized by the term 'reflective…

The study investigated which addition facts children and preservice teachers view as being difficult, whether it is possible to determine facts which are difficult for all children, and whether children and adults agree on which facts are difficult. Results indicated that children and adults disagree about the difficulty of facts. (PK)