# Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded in the Context of the Greenhouse Effect

8-2019

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## College/School

College of Science and Mathematics

## Department/Program

Mathematical Sciences

Nicole Panorkou

## Committee Member

Steven Greenstein

Eileen Murray

## Abstract

The greenhouse effect is one of the most pressing environmental as well as social issues of the present age. In news media and weather reports, most of the essential information about the phenomenon is expressed in forms of graphs and pictures. However, the interpretation of such graphs is challenging for students; they often focus on the shape of the graphs, overlooking the covariational relationships between the concerned quantities. Building on the framework of critical mathematics literacy and social justice mathematics, in this study I aimed to explore the power of dynamic mathematical modeling activities for engaging students in covariational reasoning and developing their understanding about the greenhouse effect. More specifically, this study aimed to explore a) the extent to which students’ understanding of the greenhouse effect and covariational reasoning changed as a result of their engagement with the mathematical modeling activities, and b) the ways in which students may reason covariationally as they engage with mathematical modeling activities in the context of the greenhouse effect.

To engage students in covariational reasoning in the context of the greenhouse effect, three NetLogo dynamic simulations and accompanied activities were developed and implemented in two sixth-grade classrooms in the form of a whole class design experiment. Both quantitative and qualitative data were collected in the form of pre- and post-assessments and video recordings of whole class discussions and small group interactions. The analysis of the quantitative data shows a significant improvement in post-assessment scores of the treatment group students compared to their peers in a control group. The qualitative analysis that followed helped me understand the meaning of the improved post-assessment scores by studying students’ reasoning as they interacted with the simulations. The analysis of the qualitative data indicates that the design of the three simulations and activities as well as the targeted questioning provided a productive space for students to engage in different levels of covariational reasoning according to Carlson et al.’s mental action framework and helped them identify the causes and the consequences of the greenhouse effect.

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