In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that…

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…