The attainment of proportional reasoning is considered a milestone in students' cognitive development. According to the NCTM's Curriculum and Evaluation Standards (1989), this ability is “of such great importance that it metits whatever time and effort must be expended to assure its careful development” (p. 82). As teachers and researchers know, students' understanding of proportionality develops slowly over a number of years. This article reports research findings regarding the learning and teaching of proportional reasoning that have potential for making contributions to classroom practice.
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Cramer et al. (1993) studied this question.