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(Ed.)
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 provided a constructive space for students’ forms of covariational reasoning in the context of gravity. This design can be used to
develop other STEM modules that integrate scientific phenomena with
covariational reasoning through technology.
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