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.

This paper discusses our work in progress aiming to explore how computer simulations can be integrated into the K-12 curriculum of Earth and Environmental science. Several interactive simulations using Netlogo, a multi-agent modeling environment, and Scratch, a visual programming software are being developed with steerable parameters and the corresponding output plots for students to manipulate and interpret the results, respectively. Here, we present two simulations we designed on water cycle and discuss how these may help students learn about the distribution of water and its continuous move in the ecosystem.

This research study was designed to evaluate the extent to which professional development (PD) designed around a learning trajectory (LT) on geometric measurement of area was successful in helping teachers use the LT to conduct formative assessment. Six 3rd-grade teachers from the Midwest participated in 20 hours of PD centered on the LT. Data to evaluate the PD were obtained from a set of questionnaire prompts administered before and after teachers' participation in the PD. The results suggest that teachers increased their ability to elicit and interpret student thinking and use assessment results to make instructional decisions. We consider the design and evaluation of this PD to be valuable for future efforts aiming to use LTs to support teachers in their formative assessment practices.

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

Develop fifth-grade students' early expression of pattern relationships through instructional tasks.