A componential view of children's difficulties in learning fractions

Frontiers in Psychology

Florence Gabriel¹ 

关键词: fractions;    equivalence;    part-whole;    proportion;    arithmetic operations;    fraction subcontructs;   

DOI  :  10.3389/fpsyg.2013.00715

学科分类：心理学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY