Fourth to Sixth Grade Teachers’ Invented Real World Problems and Pictorial Representations for Fraction Division

Abstract

Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their own understanding as well as how to incorporate multiple representations in their instruction. This naturalistic inquiry study investigated fourth to sixth grade teachers' invented real-world problems and pictorial representations for fraction division. The teachers completed a written assessment focused on conceptual understanding of fraction operations through multiple representations at the beginning and conclusion of a weeklong professional development experience. The questions on the assessment were taken or modified from prior research studies. The results in this paper focus specifically on a task in which the teachers had to develop a real world story problem for 2 1 2 ÷ 3 4 and solve the problem by drawing a pictorial representation. The teachers showed statistically significant improvement on developing appropriate real-world problems and using pictorial representations to solve their problems. Implications for teachers' usage of multiple representations are discussed along with needed structures for professional development targeted on fractions.

Pengembangan worksheets interaktif berbasis web dengan video pada materi pecahan

“…(Roesslein & Codding, 2019) juga berpendapat proses memahami pecahan menjadi keterampilan yang sangat sulit bagi peserta didik, namun sangat penting bagi keberhasilan dalam keterampilan matematika di tingkat sekolah selanjutnya. Oleh karena itu, pembelajaran operasi pecahan ini membutuhkan pemikiran konseptual yang menantang guru agar dapat memberikan pemahaman dan pengalaman yang berkesan bagi peserta didik (Stohlmann et al, 2019).…”

Prospective Teachers Understanding Fraction Division Using Rectangle Representation

“…As a teacher, we should be aware of the students answer about fraction division. So, a teacher must understand about the fraction division concept for reducing misconception about that topic (Stohlmann et al, 2020). A teacher should introduce representation form that can be usefull for students, ask students to draw some fraction concept and proof that, and teacher should design how they do an assessment for students to see their understanding about fraction division.…”

“…Fraction division also have the different meaning, so students still not properly understand the meaning of fraction division. Fraction division known as measurement concept usually done with repeated substraction until the number that are divided become zero (Purnomo et al, 2019;Stohlmann et al, 2020;Widada et al, 2020). Furthermore, fraction division also known as equal share, for instance there is a half of cake that will be divided into a quarter of cake, how many person that will get that cake (Purnomo et al, 2019;Stohlmann et al, 2020).…”

Special Education Teachers’ Knowledge of 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.…”