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Many studies use instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) to support students’ development of reasoning about covarying quantities. While students’ forms of covariational reasoning and the designs are often the focus of these studies, the way students’ interactions and transitions between artifacts shape their actions and thinking is often neglected. By examining the transitions that students make between artifacts as they construct and reorganize their reasoning, our study aimed to justify claims made by various studies about the nature of the synergy of artifacts. In this paper, we present data from a design experiment with a pair of sixth-grade students to discuss how their transitions between artifacts provided a constructive space for them to reason about covarying quantities in graphs. 

In this paper we present an integrated design approach for bridging content between science, technology, engineering, math, and computational thinking (STEM+C). We present data from a design experiment to show examples of the kinds of integrated reasoning that students exhibited while engaging with our design. We argue that covariational reasoning can provide strong scaffolding in making integrated connections between the STEM+C content areas. 

The phenomenon of the sea level rise is a pressing environmental and social issue of the present age. Starting with the assumption that mathematics can be utilized to help students explore this phenomenon, we designed a simulation in NetLogo, in which students investigated the relationships between the quantities of temperature rise, height of future sea level, and total land area. In this paper, we present the analysis of a whole-class design experiment in a sixth-grade classroom and discuss how our design helped students to examine sea level rise as both an environmental and a social issue. 

In this report, we discuss five forms of reasoning about multiple quantities that sixth-grade students exhibited as they examined mathematical relationships within the context of science. Specifically, students exhibited forms of sequential, transitive, dependent, and independent multivariational reasoning as well as relational reasoning. We use data from whole-class design experiments with students to illustrate examples of each of these forms of reasoning. 

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.