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 prompted them to reason covariationally about the quantities involved in the phenomenon of the gravitational force. The results of a whole-class design experiment with sixth-grade students showed that covariational reasoning supported students’ understanding of the phenomenon of gravity. Also, the examination of the phenomenon of gravity provided a constructive space for students to construct meanings about co-varying quantities. Specifically, students reasoned about the change in the magnitudes and values of mass, distance, and gravity as those changed simultaneously as well as the multiplicative change of these quantities as they changed in relation to each other. They also reasoned multivariationally illustrating that they coordinated mass and distance working together to define the gravitational force. Their interactions with the design, which included the tool, tasks, representations, and questioning, showed to be a structuring factor in the formation and reorganization of meanings that students exhibited. Thus, this study illustrates the type of design activity that providedmore »
Integrating Covariational Reasoning and Technology into the Teaching and Learning of the Greenhouse Effect
This research study was designed to evaluate the extent and the ways in which sixth-grade students developed their reasoning about the greenhouse effect and covariation as a result of their engagement with an instructional module that seamlessly integrates environmental science, mathematics, and technology. Quantitative and qualitative data were obtained from a design experiment in two sixth-grade classrooms and were compared to the data from a control group of students in a third sixth-grade classroom. The results from the quantitative analysis indicated that students in the treatment group demonstrated a greater development than the control group. The findings from the qualitative analysis illustrated that students developed sophisticated forms of reasoning about the greenhouse effect and covariation through their engagement with dynamic simulations and careful task design that prompted students to explore the covariational relationships underlying the science of the greenhouse effect. We consider the design of this instructional module to be valuable for future efforts to develop integrated science, technology, engineering, and mathematics (STEM) modules.
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- Journal Name:
- Journal of Mathematics Education
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- Sponsoring Org:
- National Science Foundation
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