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Yoshida, Hajime; Kuriyama, Kazuhiro – Journal of Experimental Child Psychology, 1986
Proposes the hypothesis that preschoolers have number concepts based on the numbers 1-5 rather than on the decimal structure. Results suggest that children understand numbers to 5 as a privileged anchor. Proposes a new model for a representational system of numbers. (Author/DR)
Descriptors: Computation, Concept Formation, Foreign Countries, Kindergarten Children

Hatano, Giyoo; And Others – Developmental Psychology, 1987
Examined whether representational changes in digit memory are functions of children's expertise in mental abacus operation when abacus operators reproduced series of digits forward or backward. Found skilled operators equally facile with forward and backward reproduction, but novices slower going backward. Suggests advanced operators apply their…
Descriptors: Cognitive Development, Computation, Concept Formation, Mathematical Concepts
Ohlsson, Stellan; Rees, Ernest – 1988
Children learn arithmetic procedures by rote, rather than by constructing them with an understanding of numbers. Rote learning produces lack of flexibility, nonsensical errors, and other difficulties. Proposed is a theory of conceptual understanding and its role in learning and executing arithmetic procedures. The basic hypothesis is that…
Descriptors: Computation, Computer Simulation, Concept Formation, Educational Research

Schonfeld, Irvin Sam – Developmental Psychology, 1986
Compares the Genevan and Cattell-Horn theories of intelligence and describes both similarities and differences. Describes a study investigating the relation of the Piagetian operative level to the child's ability to use crystallized solution procedures (aids) in making elementary numerical comparisons. (HOD)
Descriptors: Cognitive Development, Comparative Analysis, Computation, Concept Formation

Hart, Kathleen – Mathematics in School, 1987
Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)
Descriptors: Algorithms, Computation, Concept Formation, Elementary Education

Cowan, Richard – Journal of Experimental Child Psychology, 1984
Studies five-year-olds' relative number judgements of small and large number displays with and without perceptual aids. Children were found to respond to local rather than global density differences and to benefit from the provision of perceptual aids on both small and large number displays. (Author/AS)
Descriptors: Computation, Concept Formation, Conservation (Concept), Cues

Graeber, Anna O.; And Others – Journal for Research in Mathematics Education, 1989
Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)
Descriptors: Cognitive Structures, College Students, Computation, Concept Formation

Thornton, Carol A.; Smith, Paula J. – Arithmetic Teacher, 1988
This article describes the instructional efforts and success of two first grade teachers who cooperated in a year-long subtraction study with a university research team. Performance profiles of students in the experimental and control groups are presented, and implications for teaching are discussed. (PK)
Descriptors: Basic Skills, College School Cooperation, Computation, Concept Formation
Madsen-Nason, Anne; Lanier, Perry E. – 1986
This case study presents a descriptive portrait of how one general mathematics teacher transformed her classes from a computational to a conceptual orientation. The outcomes of the transformation for student learning and instruction are discussed. The findings suggest student gains in computational competence, mathematical effort, and attitude via…
Descriptors: Case Studies, Computation, Concept Formation, Educational Research

Lappan, Glenda, Ed. – Arithmetic Teacher, 1988
Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)
Descriptors: Computation, Concept Formation, Early Childhood Education, Elementary Education
Bernard, Y. F. – 1986
This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…
Descriptors: Computation, Computer Assisted Instruction, Concept Formation, Educational Research
Hiebert, James, Ed.; Behr, Merlyn, Ed. – 1988
This book contains revised versions of the major papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three major sections, along with an introductory chapter and two brief summaries. Part I includes chapters that deal primarily with analyses of subject matter. The four chapters…
Descriptors: Arithmetic, Computation, Concept Formation, Elementary Education
Bednarz, Nadine; Janvier, Bernadette – 1987
In mathematics, situations calling for reconstruction of a transformation are frequent. In such situations, children aged 6 to 7 concentrate on the states, combining them in different ways. The present research aims to illustrate that difficulties and strategies observed with children 6-7 years old are not specific to this age level, but are also…
Descriptors: Cognitive Processes, Computation, Concept Formation, Developmental Stages
Usnick, Virginia E. – Focus on Learning Problems in Mathematics, 1992
This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…
Descriptors: Addition, Cognitive Development, Cognitive Processes, Computation
Kaplan, Rochelle G. – 1990
This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…
Descriptors: Computation, Concept Formation, Curriculum Development, Elementary School Mathematics