Prospective Teachers Understanding Fraction Division Using Rectangle Representation

Abstract

Fraction division is one of the most difficult subjects in elementary school. Not only elementary students but many prospective teachers don’t understand the fraction division concept yet—most of them using a keep-change-flip algorithm to solve fraction division problems. A study using rectangle representation was conducted by us to prospective teachers. This study aims to see whether this rectangle representation will make prospective teachers understand or not. To do so, we made a mixed-method study with 80 prospective teachers as participants. The results show that 53,75% of prospective teachers use the keep-change-flip algorithm without understanding the concept of fraction division, and just 15% of prospective teachers understand fraction division. We assume that most prospective teachers still can’t imagine how fraction division works in a real-life context. They remember what they used to do to finish the fraction division problem that their teacher has introduced in primary school. Based on the results, we conclude that the study with rectangle representation still needs an improvement, whether the teacher’s explanation or the rectangle media.

Special Education Teachers’ Knowledge of Fraction Division.

“…Rational number arithmetic, such as fractions, is crucial for later mathematics achievement, developing abstract thinking as well as succeeding in many occupations. However, fractions, particularly fraction division, is a difficult topic in school mathematics, which applies to students and both inservice and prospective teachers (PTs) (Ma, 2010;Olanoff et al, 2014;Ristiana et al, 2021;Stohlmann et al, 2019). It is because it is the most complicated operation with complex numbers in the algorithm (Ma, 2010).…”

“…Olanoff et al's (2014) extensive review of the literature from the 90s to 2013 on elementary PTs' content knowledge of fractions indicates that these PTs possess the procedural skills to calculate fraction algorithms, but lack fraction number sense and knowledge to understand the meanings behind the procedures or why procedures work. Unfortunately, more recent studies of PTs show that this gloomy picture has not changed much (Adu-Gyamfi et al, 2019;Alenazi, 2016;Hohensee & Jansen, 2017;Ristiana et al, 2021;2014;Stohlmann et al, 2019;Van Steenbrugge et al, Whitehead & Walkowiak, 2017). Many PTs still make mistakes in fraction algorithms and have great difficulties in explaining why the procedures work, particularly for the 'flip and multiply' strategy for fraction division.…”

“…Although this topic has been widely studied in the past three decades in the context of teacher education and development. The results indicate that many teachers still lack a strong conceptual understanding of fraction division (Adu-Gyamfi et al, 2019;Ball, 1990;Lin et al, 2013;Lo & Luo, 2012;Ma, 2010;Ristiana et al, 2021;Stohlmann et al, 2019;Tobias, 2013;Wu & An, 2008). It is expected that teachers must know the subject they teach.…”