Icelandic 5th-grade girls’ developmental trajectories in proportional reasoning

Abstract

Understandhrg of rat io an d proport ion is critical t o t he development of higher level mathematical skills. Followhrg Carpenter, Gomez, et al.'s (1999) proposal of a four-level t rajectory hr t he development o f proportional reasonhrg, a 12-week hr vestigation was undertaken of t he developmental trajectory of pro portional reas onhrg of girls hr two 5t h-grade cl asses i n Iceland. Students hr these classes were accustomed to hrstructional practices that en couraged t hem to de vise an d explahr their own solution s to mathematical problems. Results of the study cmffirm the learnhrg trajectory with the addition of a further disthrct level of development between Levol 2 and Level 3. R esults sh owed that girls moved easily, with mhr imum scaffoldhrg, from Level i to 2 and from Level 2 to 3. The transition to Level 4, wh ich hr volves explicit awareness of 'wit hhr' an d' between' multiplicative r elationships, t ook great er time an d effort.Teacher awareness of the four-level learnhrg strategy, with the new emerghrg Level 3, assists hr th e design o f appropriate pro blems, cla ss structure, and teachhrg strategies. Building on Lamon's notions of un itizhrg and normhrg as by Carpenter et al.'s (1999) developmental model, this study contributes to our com prehension of s tudents' unders tandhrg of proportionality an d how it develops.

Developing equitable elementary mathematics classrooms through teachers learning about children's mathematical thinking: Cognitively Guided Instruction as an inclusive pedagogy

“…There has been some work with CGI in Iceland (Steinthorsdottir & Sriraman, 2009) and there is ongoing work with pre-service teachers in Israel (Steinberg, 2013). To date CGI has not been developed or researched within mainstream classrooms in the UK.…”

Inquiry pedagogy to promote emerging proportional reasoning in primary students

“…comparing ratios between situations such as in using scaled drawings or when comparing the ratio of dirt to water used by two children making different numbers of pies (Steinthorsdottir and Sriraman 2009). Such situations provide natural contexts for emphasising the critical component of proportional reasoning situations: "the multiplicative relationship that exists among the quantities that represent the situation" (Cramer et al 1993, p. 160).…”

6th Grade Students’ Solution Strategies on Proportional Reasoning Problems

“…A 'within' relationship is the multiplicative relationship between elements in the same ratio, whereas a 'between' relationship is the multiplicative relationship between the corresponding parts of different ratios ( Fig. 1) (Steinthorsdottir & Sriraman, 2009). Researchers have identified that the number structures of the problems have various effects on proportional reasoning ability.…”