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ERIC Number: EJ883862
Record Type: Journal
Publication Date: 2009
Pages: 25
Abstractor: As Provided
Reference Count: 23
ISSN: ISSN-1033-2170
Icelandic 5th-Grade Girls' Developmental Trajectories in Proportional Reasoning
Steinthorsdottir, Olof B.; Sriraman, Bharath
Mathematics Education Research Journal, v21 n1 p6-30 2009
Understanding of ratio and proportion is critical to the development of higher level mathematical skills. Following Carpenter, Gomez, et al.'s (1999) proposal of a four-level trajectory in the development of proportional reasoning, a 12-week investigation was undertaken of the developmental trajectory of proportional reasoning of girls in two 5th-grade classes in Iceland. Students in these classes were accustomed to instructional practices that encouraged them to devise and explain their own solutions to mathematical problems. Results of the study confirm the learning trajectory with the addition of a further distinct level of development between Level 2 and Level 3. Results showed that girls moved easily, with minimum scaffolding, from Level 1 to 2 and from Level 2 to 3. The transition to Level 4, which involves explicit awareness of "within" and "between" multiplicative relationships, took greater time and effort. Teacher awareness of the four-level learning strategy, with the new emerging Level 3, assists in the design of appropriate problems, class structure, and teaching strategies. Building on Lamon's notions of unitizing and norming as by Carpenter et al.'s (1999) developmental model, this study contributes to our comprehension of students' understanding of proportionality and how it develops. (Contains 10 figures and 1 table.)
Mathematics Education Research Group of Australasia. GPO Box 2747, Adelaide SA 5001, Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Grade 5
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Iceland