The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

Children's understanding of mathematical concepts, written symbolization of these concepts, and a specifically defined readiness factor were investigated. Thirty-eight first graders were classified as ready or not ready according to scores on a readiness test. Students were paired, with 11 pairs of not-ready and 8 pairs of ready students; one…

A guide for using an abacus is accompanied by a heavy-duty paper abacus. The guide includes instruction in how to represent numbers on an abacus as well as in place value, addition, carrying, subtraction, and borrowing. Diagrams are used throughout the guide and a brief English-Spanish vocabulary list specific to the use of the abacus is included.…

Discovering 3 by 3 magic squares, using numbers 1 through 9, is presented as a learning activity on three different levels. (MP)

Presented is a paradigm for teaching basic and semibasic arithmetic facts to children with arithmetic difficulties, in which the student progresses from the use of concrete materials such as blocks, to the use of diagrams such as tally marks, to a reasoning process, to responding in an automatic manner. (DLS)

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)

The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)

Two studies examine preschool children's knowledge of the effects of the physical processes of addition and subtraction on the relative amounts of two sets. Results indicate that most preschool children discover the nature of addition and subtraction outside of their formal education and rather than having to teach these ideas, teachers can use…

Suggestions for improving problem-solving skills of first-grade students are made after the results of five studies of addition and subtraction story problems are presented. (JT)

An approach is illustrated that introduces selected models of addition and subtraction to students who have previously learned a model for either operation. (JT)

Issues include consistent individual differences in children's strategy choices, interpretation of differences within a framework, and the relation of differences to standardized test performance. (RJC)

Presents a method using weighted averages to approximate partial sums of alternating series. Examples are included. (PK)