Semantic and Syntactic Fraction Understanding

Anass Bayaga,Michael J Bossé

doi:10.26822/iejee.2019248587

Abstract

This study begins by connecting semantic elaboration with conceptual understanding and syntactic elaboration with procedural understanding in the context of fractions. Through case studies and discourse analysis, the work and communication of students in fourth through sixth grade is analyzed to determine the extent of their semantic and syntactic elaboration regarding fractions and fraction operations. Findings are that, while some students emphasized one form of elaboration over the other, some students demonstrated use of both forms of elaboration. Indeed, it is wondered if semantic and syntactic elaboration should be seen as more complementary than adversarial.

Highlights

This study expanded upon the common notion of semantic and syntactic elaboration of fractions
Semantic elaborations of fractions include the subconstructs of ratio, operator, quotient, measure, and part-whole together with fraction equivalence and syntactic elaborations include whole number bias, incorrect fraction operation strategies, and errors associated with division of two fractions (Behr et al, 1983; Braithwaite et al, 2017; Bulgar, 2003; Charalambous & Pitta-Pantazi, 2007; Gabriel et al, 2013; Kieren, 1976; Siegler, Thompson, & Schneider, 2011; Tirosh, 2000; van Steenbrugge et al, 2014)
Consistent with Hallett, Nunes, and Bryant (2010), it was revealed that individual students tend to employ semantic elaboration to a greater or lesser extent than syntactic elaboration

Summary

Introduction

Literature ReviewWhile researchers continue to examine students’ learning of fractions (Kara & Incikabı, 2018; Hyde, Khanum, & Spelke, 2014; Inglis & Gilmore, 2013; Jacob & Nieder, 2009; Meert, Grégoire, & Noël, 2009; Murray, Olivier, & Human, 1996), students continue to possess limited understanding of fractions and often remain unable to adequately communicate ideas associated with fractions. Meert, Grégoire, and Noël (2009) and Murray, Olivier, and Human (1996) report specific challenges students encounter, including a lack of conceptual understanding of equality. Meert, Grégoire, and Noël (2009) and Murray, Olivier, and Human (1996) report specific challenges students encounter, including a lack of conceptual understanding of equality. These challenges lead to students incorrectly performing arithmetic operations on fraction and developing their own incorrect arithmetic heuristics. In the context of mathematics, with fractions, many have ascribed semantics with connecting mathematics to real-world scenarios (e.g., Leibovich & Ansari 2016; Opfer & DeVries, 2008) In this current investigation, we will extend upon this notion and define particular fractional arithmetic and understanding as either semantic or syntactic

Methods

Results

Conclusion