Role of representations in the initial fraction learning by fifth-grade students
Fractions are an essential foundational skill for future mathematics success (NMAP, 2008). Fraction concepts are an intrigued area of number sense that many elementary and middle school students have been struggling with (Hiebert, 1985; NMAP, 2008). These students face tremendous challenge in developing an understanding of the concept and meaning of fractions. Using different representations in learning the concept of fraction (equivalence, comparison, or estimation) gives students various opportunities that they could see the concept and meaning of fractions before they engage in the standard algorithms of fraction computations (NMAP 2008; Cramer, K., Wyberg, T., Leavitt, S. 2008; Cramer, K., Behr, M., Post T., Lesh, R., 2009). These opportunities may help students to have a better sense of fraction concepts and computations when they encounter the fraction concepts in the higher grades. This action research project is aiming to investigate how various representations (using area, linear and set models) impact the initial fraction learning by the fifth-grade students, and what role the various representations play in the development of fraction comparison, fraction estimation, and fraction equivalence. The study is expected to provide data on how fifth-grade students think and reason on the initial fraction learning using various representations. This data will contribute in shaping future instructions on the teaching and learning of fractional number sense.