COMBINING COVARIATIONAL REASONING AND CAUSALITY TO CONCEPTUALIZE FEEDBACK LOOPS.

This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the preservice teachers' reasoning about feedback loop between quantities involved the ability to conceive closed-loop covariation, which in this study was characterized by two cognitive realizations: (i) the conception of simultaneous change and (ii) the recognition of circular causality. These realizations, at least for the participants, appeared to be independent from one another. The theoretical distinction between open- and closed-loop covariation could inform instructional strategies to develop students' ability to think about and model feedback loops. [ABSTRACT FROM AUTHOR]