Using App Inventor to Explore Low-Achieving Students' Understanding of Fractions

摘要

A student's understanding of fraction magnitude impacts his/her understanding of algebra (e.g., Booth & Newton, 2012; Siegler et al., 2012), which then influences his/her likelihood of graduating high school (Orihuela, 2006) or succeeding in higher education (Adelman & United States., 2006; Trusty & Niles, 2004). Literature suggests that students gain this understanding when they create and work with various representations of fractions (e.g., Ainsworth, Bibby, & Wood, 2002; Panaoura et al., 2009; Siegler, Fazio, Bailey, & Zhou, 2013), which can occur when students engage in constructivist activities such as developing games (Kafai, 1996, Apr). This study examines an intervention where low-achieving eighth-grade students develop games about fraction magnitude using App Inventor, a novice programming environment, to determine what representations students create in their games, how their understanding of fraction magnitude develops when making their games, and what challenges they experience other than challenges concerning fractions. It uses a holistic case study with embedded units to understand the major themes for each research question while considering the influences of individual backgrounds and the various kinds of games each developed. Kolb's (1984) experiential learning theory, which states that ideas are formed by experiences and which occurs when one programs or codes a computer (Robins, Rountree, & Rountree, 2003), grounds the data analysis.;The findings of this study indicate that students primarily use numeric representations and area models to represent fraction magnitude, which are also the most common representations found in textbooks (Zhang, 2012). They developed their understanding by working with area models, talking about area models, or by developing code to compare two fractions. The way they constructed and critiqued these representations map to the experiential learning cycle, showing that they engaged in concrete experiences with fractions, reflected on the experience, conceptualized their new learning, and experimented with that learning to develop their understanding of fraction magnitude. The challenges they experienced ranged from coding difficulties, such as decomposing their designs into components to code, to non-coding challenges, such as collaborating. Limitations of this study are discussed and implications for practice and future research are delineated.