Abstract
Developing textbooks of optimal quality is crucial for enriching the students’ learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics (KM) textbooks revised in 2015 and developed an analytic framework encompassing horizontal and vertical dimensions to examine the learning opportunities presented to students by the textbooks. We assessed their topic sequence and frequency of fraction addition and subtraction contents with regard to the former and examined their contextual features, cognitive demands, and mathematical activities with regard to the latter. We observed that EM provided inadequate learning opportunities for fraction subtraction problems, representation problems, and high-order cognitive abilities. However, KM provided more even learning opportunities for fraction addition and subtraction problems, various contextual features, and high and low thinking skills. Moreover, we found that EM emphasized understanding and resolving activities, whereas KM underscored exploring and explaining activities. The findings of this study suggested updating fraction addition and subtraction contents in the U.S., South Korea, and other countries by considering horizontal and vertical dimensions.
Highlights
The curriculum is designed to achieve educational goals, and textbooks are the most prominent source of its dissemination (Alajmi, 2012; Charalambous et al, 2010; Tan et al, 2018; Yazıcıoğlu & Pektaş, 2019)
Among a multitude of mathematical topics, the current study examined fraction addition and subtraction problems in mathematics textbooks
The number of lessons for like denominator (LD) and unlike denominator (UD) was similar for Everyday Mathematics (EM) and Korean mathematics (KM)
Summary
The curriculum is designed to achieve educational goals, and textbooks are the most prominent source of its dissemination (Alajmi, 2012; Charalambous et al, 2010; Tan et al, 2018; Yazıcıoğlu & Pektaş, 2019). A mathematics textbook elucidates mathematical content, problems, pedagogy, and teaching strategies. Teachers are likely to use textbooks than curriculum for their instruction. According to the Trends in International Mathematics and Science Study (TIMSS), for instance, about 75% of fourth-grade mathematics teachers use textbooks as their chief teaching resources (Mullis et al, 2012). In this context, researchers conceptualize curriculum, textbooks, teacher’s instructions, and student outcome as the intended curriculum, potentially implemented curriculum, implemented curriculum, and attained curriculum, respectively (Valverde et al, 2002)
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