Using Ordering Tasks to Determine Fraction Magnitudes

Parimalarani A/P Sivasubramaniam ,Nurzatulshima Kamarudin

doi:10.13189/ujer.2020.081319

Parimalarani A/P Sivasubramaniam , Nurzatulshima Kamarudin

Open Access

https://doi.org/10.13189/ujer.2020.081319

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Abstract

The focus of this study was to investigate the students' ability in ordering four types of proper fractions. Type I: same numerators; Type II: same denominators; Type III: different numerators and different compatible denominators; Type IV: different numerators and different incompatible denominators. The researchers used library search and survey methodology through document search and questionnaire methods. The respondents of this study were 100 fourteen-year old students in two secondary schools from two districts. The results revealed that (i) students could easily order Type I and Type II proper fractions; (ii) students had less difficulty ordering Type II proper fractions compared with Type I proper fractions; (iii) students had difficulty ordering Type III and Type IV proper fractions; and (iv) when presented with tasks on ordering of Type III and Type IV proper fractions, students had most difficulty when ordering Type IV fractions. This showed that students still struggle with determining magnitudes of Type III and Type IV proper fractions. The findings of this study revealed that an appropriate method of instruction should be developed to teach students to order fractions of Type III and IV because the skill of ordering proper fractions is necessary for the development of fraction sense and overall mathematical development.

Highlights

Fractions are difficult for children to master and many children struggle learning fractions (Gabriel, Szucs & Content, 2013; Brown, 2015)
A large percentage of respondents in this study did not have the ability to solve ordering of proper fractions, especially of Type III tasks which consisted of fractions with different numerators and different but compatible denominators and Type IV tasks, which consisted of fractions with different numerators and different and incompatible denominators
The method used in schools to teach ordering of fractions clearly has to be improved so that students have a quantitative and conceptual understanding of fraction magnitudes

Summary

Introduction

Fractions are difficult for children to master and many children struggle learning fractions (Gabriel, Szucs & Content, 2013; Brown, 2015). Competency with fractions are necessary for daily activities, such as dealing with measurements for recipes and financial management but, knowledge of fractions is used in daily life, including budgeting, and understanding mortgage rates to carrying out home repairs (Hansen, 2015). Many educators indicate that understanding fraction magnitudes provides the foundation for acquiring knowledge of fraction operations. Knowledge of fraction magnitude affects how well children perform in fraction arithmetic and their overall performance in mathematics (Siegler, Thompson, & Schneider, 2011). Fraction magnitude is an important skill that need to be mastered by all students if they want to carry out fraction operations successfully and succeed in mathematics in general

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