GIRLS JOURNEY TOWARDS PROPORTIONAL REASONING

This study focused on 26 girls’ development of proportional reasoning in two fifthgrade classrooms in Iceland. The students were used to instructional practices that encouraged them to devise their own solutions to mathematical problems. The results supported four levels of proportional reasoning. Level 1, girls showed limited ratio knowledge. Level 2, they perceived the given ratio as an indivisible unit. Level 3, students conceived of the given ratio as a reducible unit. And at Level 4 students no longer thought of ratios exclusively as unit quantities, but understood the proportion in terms of multiplicative relations. The results suggest that students can reach level 3 reasoning with less struggle than it takes to achieve level 4, which suggests that the knowledge needed to operate on level 3 was within their reach. OBJECTIVES