Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator

Methuseli Moyo,France M Machaba

doi:10.4102/pythagoras.v42i1.602

Abstract

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners’ understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners’ transition from whole numbers to rational numbers enabled them to deal with the more complex concept of fractions. A qualitative case study approach was followed. A test was administered to 40 learners. Based on their written responses, eight learners were purposefully selected for an interview. The findings revealed that learners’ definitions of fraction were neither complete nor precise. Particularly pertinent were challenges related to the concept of equivalent fractions that include fraction elements, namely the numerator and denominator in the phase of rational number. These gaps in understanding may have originated in the early stages of schooling when learners first conceptualised fractions during the late concrete learning phase. For this reason, we suggest a developmental intervention using physical manipulatives to promote understanding of fractions before inductively guiding learners to construct algorithms and transition to the more abstract applications of fractions required in Grade 9.

Highlights

Transitioning from whole number concepts to rational numbers traditionally poses a considerable challenge to the mathematically developing mind and may become a stumbling block in the way of maturation in number conceptualisation (Durkin & Ritle-Johnson, 2014; Simon, Placa, Avitzur, & Kara, 2018).Experience with whole numbers makes the transition to rational numbers somewhat abstract (Simon et al, 2018). Bruce, Bennett and Flynn (2014) explain that fractions are multiple digits that represent one quantity, making different interpretations of fractions possible
They failed to understand that an object must be divided into identical pieces when defining and representing fractions
In the data collection process, all participants wrote a test and the researchers conducted a follow-up interview with 20% of the sample to establish how learners had reasoned while completing the test

Summary

Introduction

Transitioning from whole number concepts to rational numbers traditionally poses a considerable challenge to the mathematically developing mind and may become a stumbling block in the way of maturation in number conceptualisation (Durkin & Ritle-Johnson, 2014; Simon, Placa, Avitzur, & Kara, 2018).Experience with whole numbers makes the transition to rational numbers somewhat abstract (Simon et al, 2018). Bruce, Bennett and Flynn (2014) explain that fractions are multiple digits (numerator and denominator) that represent one quantity, making different interpretations of fractions possible. Conceptual understanding in the context of this article refers not to isolated facts, but to the ability of learners to make meaningful connections between fractional elements such as the numerator and the denominator. In their studies, Deringöl (2019) and Simon et al (2018) found that learners faced challenges in terms of viewing the numerator and the denominator as representing a whole together. In his study, Deringöl found that learners had difficulty comprehending the principle of identical pieces in the piece-whole relationship They failed to understand that an object must be divided into identical pieces when defining and representing fractions

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Conclusion