A Comparison of Textbooks' Presentation of Fractions

Abstract

In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that teaching and learning of fractions is a complex process, and that fraction understanding is the foundation for later topics such as proportionality, algebra, and probability, makes it important to examine the variation in presentation of fraction concepts in U.S. textbooks, especially the difference between traditional and standards‐based curricula. The purpose of this study is to determine if differences exist in the presentation of fractions in conventional and standards‐based textbooks and how these differences align with the recommendations of National Council of Teachers of Mathematics, Common Core State Standards, and the research on the teaching and learning of fractions.

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

“…The implications of this study suggest that experiences for students at all levels need to move past a part‐whole interpretation and particularly past an area model for understanding fractions. These concerns are complicated by the fact that research on textbook content shows that textbooks lack coherence in their representation and presentation of fraction concepts (Cady, Hodges, & Collins, ) and that textbook content focuses predominantly on part‐whole interpretations (Lamon, ). Given the fact that teachers who are often uncomfortable with the content they are teaching depend heavily on guidance for examples and direction from textbooks, elementary teachers are not likely to encounter much in their teaching to challenge and expand their understanding of fractions, which will continue the cycle of students not developing a deep understanding of fractions.…”

Understanding development requires assessing the relevant environment: Examples from mathematics learning

“…Problems that had these characteristics constituted most of the problems in all textbooks that Braithwaite et al (2017) analyzed, as well as in three other textbook series analyzed by Cady, Hodges, and Collins (2015). The analyses of all three textbook series revealed strong associations between arithmetic operations and the types of operands (numbers) in the problems (Table 1).…”

“…Problems that had these characteristics constituted most of the problems in all textbooks that Braithwaite et al. (2017) analyzed, as well as in three other textbook series analyzed by Cady, Hodges, and Collins (2015).…”

Comparing the frequency and variation of additive word problems in United States first‐grade textbooks in the 1980s and the Common Core era

“…Cady et al. (2015) compared traditional with standards‐based curricula in light of relevant research literature, standards, and recommendations. They found significant differences related to features such as frequency of presentation of representations and use of real‐world contexts—thus, different degrees of (mis)alignment with research‐based recommendations.…”