Examining US elementary students’ strategies for comparing fractions after the adoption of the common core state standards for mathematics

Abstract

Choosing appropriate strategies and implementing them correctly to solve problems are essential parts of mathematical reasoning. In this study, we examined 214 US fourth graders’ strategy choice and implementation when solving a fraction ordering task amenable to multiple strategies. The students used 12 distinct fraction comparison strategies. Of these, the rectangle model, butterfly, circle model, and common denominator strategies were used most frequently. Overall, visual strategies were more common than symbolic or verbal strategies, perhaps reflecting the emphasis on visual models in the US Common Core State Standards for Mathematics and textbooks. Students experienced a range of difficulties in implementing their chosen strategies. Only 28 % solved the focal problem correctly, and only 22 % provided both correct fraction order and correct justifications. The implications of students’ strategy choice and implementation for teachers, teacher educators, and researchers are discussed.