Icelandic 5th grade girls developmental trajectories in proportional reasoning. Paper submitted for publication

• Main Authors: Olof B. Steinthorsdottir, Bharath Sriraman
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2007
• Subjects: Gomez; Iceland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.526.8120; http://www.merga.net.au/documents/MERJ_21_1_Steinthorsdottir.pdf

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