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Ratio and Proportion are essential topics in the middle-grades mathematics curriculum. The ability to reason proportionally is important in students' transition from elementary school mathematics to high school mathematics and science. The study of ratio and proportion lays a foundation for first-year algebra, and subsequent mathematics and science study assumes that students can reason proportionally. Many textbooks, however, limit the problems involving proportions to those that emphasize procedural competence rather than conceptual understanding. These problems usually require students to use ratios and set up equations. Students may solve such problems “correctly” using the traditional algorithm of cross-multiplying and dividing, but their solutions do not necessarily give us much information about their understanding of the multiplicative relationships involved in proportions.
Hannah Slovin (Fri,) studied this question.