NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ1136680
Record Type: Journal
Publication Date: 2017
Pages: 20
Abstractor: As Provided
ISSN: ISSN-1098-6065
Between Counting and Multiplication: Low-Attaining Students' Spatial Structuring, Enumeration and Errors in Concretely-Presented 3D Array Tasks
Finesilver, Carla
Mathematical Thinking and Learning: An International Journal, v19 n2 p95-114 2017
The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D (rectangular) arrays, and when focusing on 3D (cuboid) arrays still frequently uses 2D representations. This article documents low-attaining children's partially developed multiplicative thinking as they work on concretely presented 3D array tasks; it also presents a framework for microanalysis of learners' early multiplicative thinking in array tasks. Data derives from a small but cognitively diverse set of participants, all arithmetically low-attaining and relying heavily on counting: this enabled detailed analysis of small but significant differences in their arithmetical engagement with arrays. The analytical framework combines and builds on previous structural and enumerative categorizations, and may be used with a variety of array representations.
Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: United Kingdom (London)
Grant or Contract Numbers: N/A