Spontaneous focusing on quantitative relations as a predictor of the development of rational number conceptual knowledge

Abstract

<p> Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students’ spontaneous focusing on quantitative relations, in situations that are not explicitly mathematical. Even after controlling for a number of known predictors of rational number knowledge, spontaneous focusing on quantitative relations is found to have a strong impact on students’ learning of rational number conceptual knowledge. This finding opens new possibilities for developing pedagogical solutions to one of the most difficult challenges of mathematics education. The findings suggest that students’ own focusing tendency and self-initiated practice may have on important role in the long-term development of complex cognitive skills.</p>