A componential view of children's difficulties in learning fractions

Abstract

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.

Developing Deaf Students Fraction Skills Requires Understanding Magnitude and Whole Number Division

“…Hiebert & LeFevre (1986) stressed that teachers should focus on conceptual and procedural mathematical skills especially when doing two-step problems or more. One recently study (Gabriel et al, 2013) showed primary school children mastered the part-whole and proportion categories, but struggled to see fractions as numbers, and noted that equivalent fractions are very difficult to understand. This leads to not understanding operational procedures for doing fractions.…”

The conceptual/procedural distinction belongs to strategies, not tasks: A comment on Gabriel et al. (2013)

“…The issue I wish to raise in this commentary is not with the conclusions of Gabriel et al (2013), but rather a general issue concerning the notion of conceptual and procedural tasks in mathematics. One of the difficulties is that a single task can reflect both types of knowledge.…”

“…In their recent article, Gabriel et al (2013) propose that the difficulty experienced by Belgian children in learning fractions stems from the fundamental dichotomy of procedural and conceptual knowledge of fractions. Indeed, the authors are not alone in this conclusion, as the procedural/conceptual knowledge divide has been a focus in several recent studies in numerical cognition (Hallett et al, 2010; Hecht and Vagi, 2012).…”

Involvement of Algebraic-Geometrical Duality in Shaping Fraction’s Meaning and Calculation Strategies with Fractions

“…Fractions have been used for centuries and are manipulated in a great variety of everyday life situations and in mathematics. Thus why is it so hard for pupils to learn and represent fractions (Gabriel et al, 2013)? Various models have been proposed in order to explain those difficulties (Behr et al 1983;Mamede et al, 2005;Grégorie, 2008).…”