title: Making Space for Spatial Proportions.
abstract: The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or magnitudes may be especially important for building robust fractions knowledge. In this commentary, we first reflect upon where these findings stand in a larger theoretical context, largely borrowed from mathematics education research. Next, we emphasize parallels between this work and emerging work suggesting that nonsymbolic proportional reasoning may provide an intuitive foundation for understanding fraction magnitudes. Finally, we end by exploring some open questions that suggest specific future directions in this burgeoning area.
authors.affiliation: 1 University of Wisconsin-Madison, USA.
authors.forename: Percival G
authors.initials: PG
authors.lastname: Matthews
authors.affiliation: 1 University of Wisconsin-Madison, USA.
authors.forename: Edward M
authors.initials: EM
authors.lastname: Hubbard
mesh_terms: D006801:Humans; D007858:Learning; D055641:Mathematical Concepts; D008433:Mathematics / Q000193:education*
keywords: fraction learning; fraction magnitude; mathematics