El conocimiento de las fracciones. Una revisión de su relación con factores cognitivos

Abstract

Learning fractions presents large difficulties for many children and adults. This is a serious problem, because different studies have shown that fraction knowledge predicts advanced mathematics, like algebra. Adult mathematic knowledge is related to employment opportunities, participation in high-skills occupations and economic and social well-being. Therefore, since fractions represent a backbone in mathematics achievement, understanding the factors that explain fractions learning is very important. Some theories of numerical cognition propose that general cognitive factors, like attention or working memory, contribute to learning mathematics. However, recent research has shown different and contradictory results about which cognitive factors are involved in fraction learning. Identifing the cognitive factors that explain fraction knowledge could lead to early identification of children with potential math learning difficulties and the development of interventions to improve their achievement. Therefore, the aim of this article is to perform a systematic literature review to analyze the relationship among some cognitive factors and fraction knowledge. A systematic literature search could define the state of the art on this topic, identify possible sources of controversy among studies, analyze those reasons to recognize points of agreement and discrepancy among studies and direct all this information towards future research lines. A systematic search of empirical articles was done on Education Research Complete, ERIC, MEDLINE Primary Search, PsycARTICLES, and PsycINFO databases. Search was carried out on September of 2017, with keywords in Spanish and their translation into English. Search terms were “fractions” (“fracciones”) and “cognitive ability” (“habilidad cognitiva”), “cognitive processes” (“procesos cognitivos”), “working memory” (“memoria de trabajo”), “attention” (“atencion”), “intelligence” (“inteligencia”), “speed of processing” (“velocidad de procesamiento”), “inhibition” (“inhibicion”) and “language” (“lenguaje”). Articles inclusion criteria were: (a) empirical studies, (b) with scholar age samples (6-18 years old), (c) published on peer review journals, (d) written in spanish or english. Thirteen publications were selected. They agree about attention predicting conceptual and procedural knowledge of fractions between fourth and sixth grade, (b) language and fluid intelligence explains conceptual knowledge of fractions in the initial stage of its systematic teaching, (c) central executive predicts fractions concepts in advanced levels of fraction instruction but not in the initial stages of learning, (d) central executive and fluid reasoning does not predict procedural fraction knowledge when other cognitive factors and mathematical abilities, like attention or whole number calculation skills, are included in the explanation models. In broad terms, these results are in line with some theoretical models of numerical cognition and suggested that cognitive processes and abilities are important to learn fractions. There are some practical implications to these results. Fraction learning could be improved by using pedagogical strategies and didactic materials which maximize cognitive performance. For example, employing novelty and ludic materials for teaching fractions could enable students to focus, maintain attention and improve their learning. Also, short instructions with low linguistic complexity would help students with attention, working memory or language difficulties to afford fractions activities and achieve a meaningful learning. On the other hand, working memory load to perform complex fraction activities would be reduced if basic fraction concept and procedures are consolidated in long term memory. Therefore, before advancing to more complex fractions activities in higher grades, the teacher should verify that the basic notions of fractions have been learnt and memorized by students. To develop theoretical cognitive models of mathematics learning, future research might analyze if cognitive factors contribute to fractions knowledge mainly through direct or indirect effects (that is, via their effects on others areas of math knowledge which affect fraction learning). On the other hand, the tasks used to measure cognitive factors are not always pure, that is, different cognitive operations are involved in their execution. Future studies might work with latent variables that allow the identification of the share variance between cognitive task, and consequently, the main cognitive factors involved in fractions learning.