Beyond Elementary: Examining Conceptual Demands of Division of Fractions in Current US Curricula

Leanna R. Carollo


The Common Core State Standards of Mathematics (CCSSM), a set of US educational standards which has recently been adopted by 45 states, creates a more rigorous and coherent set of standards for American students, making elementary math anything but elementary. The adoption of these new standards formulates the research questions for this study: How well do current curricula match the CCSSM and how well do current curricula support teacher knowledge to implement the standards? In this study, three diverse curricula used in the United States, Prentice Hall, Singapore Math, and CK-12, are examined with three evaluation tools. These tools measure (a) the cognitive demands of the mathematical tasks in each curricula, (b) the mathematical coherency of an instructional unit, and (c) the resources in each curricula that support teachers’ understanding of mathematics. Division of fractions is the topic of analysis because of its frequent occurrence in algebra which is the foundation for higher-level math. I find that Singapore Math’s problems reach higher-level cognitive demands more often than Prentice Hall and CK-12. Prentice Hall and CK-12’s reliance on using the standard division algorithm inhibits conceptual thinking for both students and teachers. From a Curriculum Review Tool, which focuses on teacher knowledge, I find that Singapore Math is the closest to reach the division of fraction CCSSM when compared to Prentice Hall and CK-12. Resource tools for teachers can be developed that better support students’ learning by combining characteristics from each curriculum such as word problems, manipulatives/pictures, and samples of students’ work.


Conceptual Understanding; Division of Fractions; Elementary Math; Common Core State Standards; Singapore Math; CK-12; Prentice Hall; Curriculum

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