## Abstract

In this article, we examine how a sequence of modeling activities supported the development of students’ interpretations and reasoning about phenomena with negative average rates of change in different physical phenomena. Research has shown that creating and interpreting models of changing physical phenomena is difficult, even for university level students. Furthermore, students’ reasoning about models of phenomena with negative rates of change has received little attention in the research literature. In this study, 35 students preparing to study engineering participated in a 6-week instructional unit on average rate of change that used a sequence of modeling activities. Using an analysis of the students’ work, our results show that the sequence of modeling activities was effective for nearly all students in reasoning about motion with negative rates along a straight path. Almost all students were successful in constructing graphs of changing phenomena and their associated rate graphs in the contexts of motion, light dispersion and a discharging capacitor. Some students encountered new difficulties in interpreting and reasoning with negative rates in the contexts of light dispersion, and new graphical representations emerged in students’ work in the context of the discharging capacitor with its underlying exponential structure. The results suggest that sequences of modeling activities offer a structured approach for the instruction of advanced mathematical content.

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Ärlebäck, J.B., Doerr, H.M. Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence.
*ZDM Mathematics Education* **50**, 187–200 (2018). https://doi.org/10.1007/s11858-017-0881-5

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DOI: https://doi.org/10.1007/s11858-017-0881-5