Spontaneous focusing on multiplicative relations and fraction magnitude knowledge

ABSTRACT

To test the hypothesis that a higher tendency to spontaneously focus on multiplicative relations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional quantities, we presented sixth graders (n = 112) with fraction number line estimations and a novel task in which numerical information embedded in narratives could be estimated as fractions. Consistent with our main hypothesis, we found that SFOR tendency predicted both forms of fraction estimation. However, the relation between SFOR and fraction magnitude comparisons was mediated by fraction estimation, both on the number line and on whole number relations embedded in narrative vignettes. Thus, a higher tendency to recognize multiplicative relations in non-explicitly mathematical situations may contribute to increases in the precision with which students encode fractional relations in everyday contexts, both as spatial and numerical relations.

KEYWORDS:

• Fractions
• spontaneous mathematical focusing tendencies
• individual differences
• fraction estimation
• mathematical cognition
• spontaneous focusing on quantitative relations

Acknowledgments

We would like to thank Cassie Griger and Elena Lieb, all the participants and teachers without whom this research could not have been carried out.

Additional information

Funding

This research was funded by Academy of Finland Grant 311080 awarded to the first author and by US Department of Education, Institute of Educational Sciences Grant R305B100001 awarded to the last author.

Notes on contributors

Jake McMullen

Jake McMullen is a post-doctoral researcher and adjunct professor (Docent) at the Department of Teacher Education, University of Turku, Finland. His main research interests are mathematical learning and instruction, especially examining the development of adaptive expertise in mathematics.

Robert S. Siegler

Robert S. Siegler is Professor of Psychology and Education at Columbia University. He is a recipient of the American Psychological Association's Distinguished Scientific Contribution Award, as well as having been chosen to be a member of the National Academy of Education and of the Society of Experimental Psychologists. His current research focuses on the development of mathematical thinking, particularly their understanding of rational numbers; ways of improving children’s mathematical thinking; and educational applications of cognitive-developmental theory.