Pre-service elementary mathematics teachers’ ways of thinking about rate of change in the context of a modeling activity

As a part of a larger study aiming at developing pre-service teachers’ pedagogical knowledge about mathematical modeling, this study investigates pre-service elementary mathematics teachers’ ways of thinking regarding rate of change in the context of a modeling task on population growth. The participants of the study were 9 prospective middle school mathematics teachers in their senior year attending a public university. The study was conducted as a part of an undergraduate course on mathematical modeling for prospective teachers. Data were collected through the prospective teachers’ written group work and reports regarding their solution to the modeling activity, individual reflection papers, and researchers’ field-notes. The results showed that participants demonstrated two different ways of thinking about the expression “rate of change in population with respect to time”: (i) percentage of change in population, and (ii) per year change in population (slope). Even though “percentage” interpretation was dominant, some of the participants were directed to “per year change in population” interpretation as the year intervals in the problem context were not given with equal intervals. The results revealed about prospective teachers’ difficulties in conceiving the difference and the mathematical relationship between “percentage” and “slope” interpretations. The results also revealed about the problematic aspect of expressing the term/concept “rate of change” in Turkish. As possible sources of these difficulties, the results are discussed in light of the distinction between rate and ratio.