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David Muñez; Josetxu Orrantia; Rosario Sanchez; Lieven Verschaffel; Laura Matilla – Journal of Cognition and Development, 2025
Previous research has demonstrated a link between children's ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved.…
Descriptors: Foreign Countries, Elementary School Mathematics, Elementary School Students, Elementary School Teachers
Hallett, Darcy; Nunes, Terezinha; Bryant, Peter – Journal of Educational Psychology, 2010
Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…
Descriptors: Mathematics Skills, Concept Formation, Foreign Countries, Arithmetic
Sarama, Julie; Clements, Douglas – Young Children, 2009
Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…
Descriptors: Concept Formation, Mathematics Instruction, Elementary School Mathematics, Developmental Stages
Kamii, Constance; Rummelsburg, Judith – Teaching Children Mathematics, 2008
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
Descriptors: Textbooks, Mental Computation, Number Concepts, Word Problems (Mathematics)
Baroody, Arthur J.; Brach, Catherine; Tai, Yu-chi – Cognition and Instruction, 2006
A schema based view of addition development is compared with Siegler's latest strategy-choice model, which includes an addition goal sketch (a basic understanding of "the goals and causal relations" of addition; Siegler & Crowley, 1994, p. 196). This metacognitive component in the latter model is presumed to develop as a child practices a basic…
Descriptors: Arithmetic, Mathematics Instruction, Models, Cognitive Development
Saxton, Matthew; Cakir, Kadir – Child Development, 2006
Factors affecting performance on base-10 tasks were investigated in a series of four studies with a total of 453 children aged 5-7 years. Training in counting-on was found to enhance child performance on base-10 tasks (Studies 2, 3, and 4), while prior knowledge of counting-on (Study 1), trading (Studies 1 and 3), and partitioning (Studies 1 and…
Descriptors: Prior Learning, Performance Factors, Child Development, Young Children
Moser, James M. – 1972
The arithmetic portion of the Developing Mathematical Processes (DMP) program, as it applies to children of ages 5 to 8, is described in some detail. The terminal objective of the number program of the primary segment of DMP is the ability of the child to correctly write, read and validate mathematical sentences of the form A = B plus or minus X.…
Descriptors: Arithmetic, Cognitive Development, Early Childhood Education, Elementary School Mathematics
Kamii, Constance – 1994
Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…
Descriptors: Arithmetic, Cognitive Development, Elementary School Mathematics, Fractions
Canobi, Katherine H. – Journal of Experimental Child Psychology, 2005
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…
Descriptors: Elementary School Students, Cognitive Development, Arithmetic, Individual Differences
Steffe, Leslie P.; Parr, Robert B. – 1968
Six tests were constructed, four on a pictorial level and two on a symbolic level, to measure the performance of fourth-, fifth-, and sixth-grade children, in three different ability groups, on problems concerning ratios or fractions. Two variables were of interest in the four tests on a pictorial level: (a) "equal" ratio situations vs.…
Descriptors: Arithmetic, Cognitive Development, Concept Formation, Elementary School Mathematics

Brown, Margaret; Kuchemann, Dietmar – Mathematics in School, 1977
Children between the ages of 10 and 13 were asked to write stories to accompany five computational problems. Stories were scored for suitability and it was found that students were most successful on subtraction and least successful on multiplication stories. Scores on this test correlated with mathematics achievement scores. (SD)
Descriptors: Arithmetic, Basic Skills, Cognitive Development, Educational Research
Okazaki, Masakazu – International Group for the Psychology of Mathematics Education, 2003
If we consider the gap between mathematics at elementary and secondary levels, and the logical nature of the higher level, it is important that aspects of children's logical development in the latter grades in elementary school be clarified. We focused on 5th graders' learning "division with decimals" as it is known to be difficult to…
Descriptors: Childhood Attitudes, Grade 5, Elementary School Mathematics, Arithmetic

Nesher, P.; And Others – Educational Studies in Mathematics, 1982
Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…
Descriptors: Addition, Arithmetic, Cognitive Development, Computation

Baroody, Arthur J.; Gatzke, Mary R. – Journal for Research in Mathematics Education, 1991
Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Elementary School Mathematics

Thornton, Carol A. – Educational Studies in Mathematics, 1990
In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Elementary Education