ERIC Number: EJ748167
Record Type: Journal
Publication Date: 2006-Sep
Pages: 28
Abstractor: Author
ISBN: N/A
ISSN: ISSN-0013-1954
EISSN: N/A
Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking
Empson, Susan B.; Junk, Debra; Dominguez, Higinio; Turner, Erin
Educational Studies in Mathematics, v63 n1 p1-28 Sep 2006
Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared) in their solutions to equal sharing problems and to see to what extent this coordination was multiplicative. A secondary goal was to document children's solutions for equal sharing problems in which the quantities had a common factor (other than 1). Data consisted of problem-solving interviews with students in 1st, 3rd, 4th, and 5th grades (n=112). We found two major categories of strategies: (a) Parts Quantities strategies and (b) Ratio Quantities strategies. Parts quantities involved children's partitions of continuous units expressed in terms of the number of pieces that would be created. Ratio quantities involved children's creation of associated sets of discrete quantities. Within these strategies, children drew upon a range of relationships among fractions, ratio, multiplication, and division to mentally or physically manipulate quantities of sharers and things to produce exhaustive and equal partitions of the items. Additionally, we observed that problems that included number combinations with common factors elicited a wider range of whole-number knowledge and operations in children's strategies and therefore appeared to support richer interconnections than problems with relatively prime or more basic number combinations.
Descriptors: Mathematics, Problem Solving, Elementary School Students, Numbers, Multiplication, Case Studies, Children, Thinking Skills, Interviews, Mathematical Concepts, Cognitive Processes
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: Elementary Education; Grade 1; Grade 3; Grade 4; Grade 5
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A