Examining students’ quantitative reasoning in a virtual ecosystem simulation of the water cycle

In this study, we designed and tested an instructional module to help students develop their quantitative reasoning while examining the scientific phenomenon of the water cycle. The results from a design experiment in a sixth-grade classroom showed that students exhibited reasoning that integrated science and mathematics and avoided the typical naïve conceptions about the water cycle. Specifically, students engaged in covariational and multivariational reasoning as they coordinated the simultaneous change of the quantities involved in the water cycle. They also exhibited transitive reasoning in terms of those quantities and relational reasoning connecting the water cycle to other science content. These forms of reasoning illustrate the power of mathematical reasoning for helping students construct an advanced understanding of the water cycle phenomenon. The findings also show that the context of science helped students to construct advanced forms of mathematical reasoning about quantities, illustrating the reciprocal relationship between math and science learning.