Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Investigates English students' strategies for addition and subtraction problems. Suggests some teaching methods for the results. (YP)

Use of several measurement models to analyze data from learning hierarchies, and a study--using over 300 Australian third- through fifth-graders--of the application of an item response theory model to a learning hierarchy in subtraction are discussed. The model's usefulness in explicating patterns of empirical results from the hierarchy is…

Examines the hypothesis that problem comprehension and computational processes interact during the solving of arithmetic word problems. Results suggest the absence of any interaction between the two processes. Questions the notion that automatized retrieval facilitates problem solving, as well as assertions suggesting that increasing computational…

Presented are the results of two pilot studies about multidigit addition and subtraction. The results are discussed in relation to possible alternative sequences in the teaching of addition and subtraction and the relationship between basic fact mastery and numeration concept attainment. (CW)

Examined Korean second and third graders' understanding of multidigit addition and subtraction. Korean children showed exceptional competence in multidigit addition and subtraction, and their solutions were based on quantitative understanding of multidigit numbers. Results are compared to the literature on the performance and conceptual structures…

Based on the cognitive psychological theories of Vygotsky and Davydov, discusses the establishment of connections between mathematical elements, and the algorithmic rules that govern them, and children's spontaneous mathematical concepts. Presents examples that establish connections involving addition and subtraction, comparing numerical…

Two studies pursued theory that knowledge of addition combinations facilitates learning of subtraction combinations. Study 1 involved 25 kindergartners and 15 first graders in a gifted program; study 2 involved 21 first graders in a regular program. Participants responded to two pairs of problems. Findings revealed that the complementary…

The current research explored children's ability to recognize and explain different concepts both with and without reference to physical objects so as to provide insight into the development of children's addition and subtraction understanding. In Study 1, 72 7- to 9-year-olds judged and explained a puppet's activities involving three conceptual…

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…

Results of the National Assessment of Education Progress (NAEP) related to subtraction are summarized and interpreted. Implications for instruction are discussed. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Hypothesizing that subtraction of (negative) integers requires formal operations, the author describes a study of children's understanding of related concepts. The study involves the use of apparatus embodying properties of the number line. (SD)

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 report presents results of several extensive empirical studies. Prior to these studies it was believed that errors in procedural skills such as multi-digit subtraction could be accurately modelled with two mechanisms: bugs ("competence" phenomena reflecting mistaken beliefs about subtraction which are stable over time) and slips…