Preservice mathematics teachers' understandings of intensive quantities and functions involved in introductory mathematics models for global warming
Gonzalez Martinez, Dario Andres
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This dissertation examined preservice mathematics teachers’ (PSTs) understandings of intensive quantities and functions involved in introductory mathematical models for global warming. The study had two parts. The first part explored PSTs’ conceptions of three intensive quantities: concentration, energy density, and energy flux density. The second part examined PSTs’ covariational reasoning regarding three functions: the forcing by CO2 function F(C), the planetary energy imbalance function N(t), and the mean surface temperature function T(t). The study followed an exploratory, multiple-case research design. Three PSTs enrolled in a mathematics education program at a large Southeastern university participated in the study, each completing six mathematical tasks designed for the study during four individual, task-based interviews. The study’s first part revealed that PSTs’ conceptions of the intensive quantities were shaped by their understandings of a quantity’s: (a) measurable attribute (what is being measured) and (b) measurement process (how the attribute is being measured). To identify a measurable attribute, PSTs needed to conceptualize each quantity as a constant multiplicative relationship between quantities that can vary. Depending on the quantity, PSTs used division differently to measure such attribute (measurement process): measurement division for concentration (Type 1) and partitive division for energy density and energy flux density (Type 2). The latter two quantities were challenging for PSTs because they conceived temperature and energy as equivalent quantities. The study’s second part revealed that PSTs did not reason about co-variation in terms of the rate of change when making sense of the functions. Two PSTs were often unable to reason beyond the direction in which change was occurring. The other consistently reasoned in terms of amounts of change in y for changes in x. Additionally, PSTs’ conceptions of intensive quantities and ability to reason about co-variation impacted their understanding of two central concepts regarding global warming: the Earth’s energy budget and the radiative equilibrium. Also, there was an unexpected finding regarding PSTs’ ability to conceive what I termed monotonically asymptotic variation, which appeared central to make sense of all three functions. I concluded with a discussion of the study’s implications and suggestions for future research.