There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N=435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

Understanding complex systems requires reasoning about causal relationships that behave or appear to behave probabilistically. Features such as distributed agency, large spatial scales, and time delays obscure co-variation relationships and complex interactions can result in non-deterministic relationships between causes and effects that are best…

Spatial discontinuity between causes and effects is a feature of many scientific concepts, particularly those in the environmental and ecological sciences. Causes can be spatially separated from their effects by great distances. Action at a distance, the idea that causes and effects can be separated in physical space, is a well-studied concept in…

The aims of this study were to investigate how upper-elementary-grade students compare the volume of rectangular prisms of equal volume (specifically, students' noticing and reasoning for invariance of volume and coordination of the three linear dimensions of rectangular prisms) and how students' levels of sophistication in volume measurement…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…