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Schulz, Andreas – Mathematical Thinking and Learning: An International Journal, 2018
Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…
Descriptors: Computation, Mathematics Instruction, Multiplication, Arithmetic
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Batchelor, Sophie; Keeble, Sarah; Gilmore, Camilla – Mathematical Thinking and Learning: An International Journal, 2015
When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this…
Descriptors: Mathematics Skills, Preschool Children, Numeracy, Number Concepts
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Manfra, Louis; Dinehart, Laura H. B.; Sembiante, Sabrina F. – Journal of Research in Childhood Education, 2014
This study explores the effects of counting objects and reciting numbers in preschool on 1st-grade math performance. Data on 3,125 low-income preschoolers' (4-to 5-year-olds) counting abilities (orally reciting numerals in chronological order and counting blocks) were collected during a fall session (between September 15 and December 15) and were…
Descriptors: Preschool Children, Grade 1, Elementary School Students, Low Income Groups
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Obersteiner, Andreas; Reiss, Kristina; Ufer, Stefan; Luwel, Koen; Verschaffel, Lieven – Cognition and Instruction, 2014
External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…
Descriptors: Grade 1, Elementary School Students, Numbers, Number Concepts
Purpura, David J.; Ganley, Colleen M. – Grantee Submission, 2014
Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the…
Descriptors: Preschool Children, Kindergarten, Short Term Memory, Language Skills
Jordan, Nancy C.; Hansen, Nicole; Fuchs, Lynn S.; Siegler, Robert S.; Gersten, Russell; Micklos, Deborah – Grantee Submission, 2013
Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…
Descriptors: Elementary School Mathematics, Elementary School Students, Grade 4, Grade 3