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Finesilver, Carla – Educational Studies in Mathematics, 2022
Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…
Descriptors: Spatial Ability, Mathematics Education, Learning Strategies, Multiplication
Izsák, Andrew; Beckmann, Sybilla – Educational Studies in Mathematics, 2019
We examine opportunities and challenges of applying a single, explicit definition of multiplication when modeling situations across an important swathe of school mathematics. In so doing, we review two interrelated conversations within multiplication research. The first has to do with identifying and classifying situations that can be modeled by…
Descriptors: Multiplication, Mathematics Instruction, Measurement, Numbers

Vest, Floyd R. – Educational Studies in Mathematics, 1971
Descriptors: Arithmetic, Audiovisual Aids, Division, Instruction

Schmidt, Siegbert; Weiser, Werner – Educational Studies in Mathematics, 1995
Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…
Descriptors: Addition, Classification, Division, Elementary Education

Bell, Alan; And Others – Educational Studies in Mathematics, 1984
Determined effects of two task types on 12- and 13-year-olds' understanding of applications of multiplying and dividing positive numbers. Results indicate the persuasive nature of certain misconceptions and specific effects of context attributable to such aspects as relative familiarity. Implications of these and other results are discussed.…
Descriptors: Arithmetic, Division, Elementary Education, Elementary School Mathematics

Ricco, Graciela – Educational Studies in Mathematics, 1982
This study, written in French, presents the hierarchy of strategies used by children in solving multiplication and division problems, as they acquire the linear function concept. It is based on analysis of the different classes of problems, of specific tasks, and of strategies actually used in solutions. (MP)
Descriptors: Cognitive Processes, Division, Educational Research, Elementary Secondary Education

Foxman, Derek; Beishuizen, Meindert – Educational Studies in Mathematics, 2002
Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…
Descriptors: Addition, Arithmetic, Basic Skills, Division

Treffers, A. – Educational Studies in Mathematics, 1987
Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Division

Levain, Jean-Pierre – Educational Studies in Mathematics, 1992
Discusses how students at the end of the French primary school-cycle (10- to 11-year-old pupils) resolve multiplication and related division problems within an assessment perspective taking into account the 3 factors of the problem's representational structure, the numerical values used, and the context of the problem statement. (25 references)…
Descriptors: Arithmetic, Context Effect, Division, Elementary Education

Tirosh, Dina; Graeber, Anna O. – Educational Studies in Mathematics, 1989
Assessed are the extent to which the beliefs, "multiplication always makes bigger" and "division always makes smaller," are explicitly held by preservice elementary teachers. Insight into the sources of preservice teachers' beliefs and into the relationship among preservice teachers' beliefs, computational skills, and performance on word problems…
Descriptors: Arithmetic, Beliefs, Division, Elementary School Mathematics

Nesher, Pearla; Hershkovitz, Sara – Educational Studies in Mathematics, 1994
Studied schemes involved in solving two-step arithmetic word problems in (n=1824) elementary schoolchildren in Israel. Compound schemes and combinations of operations were found to affect the difficulty level of the problems. Appendix includes two versions of the test instrument. (Contains 17 references.) (MKR)
Descriptors: Addition, Arithmetic, Division, Elementary Education