This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

This book provides regular classroom and special education teachers with alternative, individualized methods of teaching math computation skills. Learning activities are designed to appeal to auditory, visual, and kinesthetic learning modalities. Six mathematics topics addressed include modeling addition and subtraction, basic facts for addition…

The performance of 13 and 17-year-olds on National Assessment items involving computation with fractions is reviewed, together with findings from related research. Recommendations for improving instruction are offered. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

This cross-sectional study investigated the problem-solving strategies used by schooled and unschooled Nigerian children to solve simple addition and subtraction problems. The purpose of the study was to: (1) verify with Nigerian children, models of the knowledge and strategies underlying children's solutions to simple word problems; (2) test the…

This study empirically examined the proposition that different item selection procedures contribute to the development of achievement tests that optimally serve different purposes. A test of 110 addition and subtraction problems was given to a sample of 371 first-grade students. Three subsets of 30 items were selected from this 110-item test. The…

This study investigates the influence of changes in the wording of simple addition and subtraction problems without affecting their semantic structure on the level of difficulty of those problems for first and second graders and on the nature of their errors. The objective is to contribute to a better understanding of the process of constructing a…

Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt…

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

The purpose of the study was to survey self-regulation while responding to the addition facts. First graders' performance on microcomputer practice exercises was observed and recorded. Subjects could choose an analytic mode of operation using a symbolic or a finger strategy; or, they could choose a geometric mode of operation using a pictorial or…

The document presents the final report of the Initial Learning in Mainstreaming Project, which developed and tested instructional techniques in 14 specific mathematics skill areas with 429 handicapped and normal elementary school students in Grace and Soda Springs, Idaho. Skill areas included addition facts; subtraction facts; carrying…

The effect of a self-instructional (SI) training paradigm on the arithmetic deficits of orthopedically handicapped children and the degree to which training effects generalize to the classroom and to another arithmetic function were studied. The study consisted of two experiments, each conducted with three orthopedically handicapped students with…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) systems of numeration from an historical point of view, (2) a…

Excerpts from interviews with pupils in grades 1, 2, 3, and 6 to ascertain their interpretations of mathematical sentences and symbols are presented. Children were found to consider the equal sign as an operator symbol ("do something") and not as a relational symbol. Implications for teaching are briefly discussed. (MS)

Material included in this bulletin provides an overview of research studies which pertain to teaching addition and subtraction of whole numbers in the primary grades. The studies mentioned relate directly to the following questions: (1) What foundation for addition and subtraction do children have upon entering school? (2) What is the relative…