Developing prospective teachers’ covariational reasoning through a model development sequence

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented with 20 participants in a mathematical modeling course offered to prospective teachers. The participants' developing abilities of covariational reasoning were documented under three categories: (i) identifying the variables, (ii) ways of coordinating the variables, and (iii) ways of quantifying the rate of change. The results revealed significant improvement in the prospective teachers' ways of identifying and coordinating the variables, and in quantifying the rate of change. Moreover, the results indicated that preference for a particular way of thinking in identifying and coordinating the variables determined the prospective teachers' way of quantifying the rate of change and thereby their level of covariational reasoning.
Mathematical Thinking and Learning


Prospective Middle School Mathematics Teachers' Covariational Reasoning for Interpreting Dynamic Events During Peer Interactions
Yemen-Karpuzcu, Secil; Ulusoy, Fadime; Işıksal Bostan, Mine (2017-01-01)
This study investigated the covariational reasoning abilities of prospective middle school mathematics teachers in a task about dynamic functional events involving two simultaneously changing quantities in an individual process and also in a peer interaction process. The focus was the ways in which prospective teachers' covariational reasoning abilities re-emerge in the peer interaction process in excess of their covariational reasoning. The data sources were taken from the individual written responses of p...
Pre-service Mathematics Teachers’ Understanding of Rate of Change Throughout a Model Development Sequence
KERTİL, MAHMUT; Erbaş, Ayhan Kürşat; Çetinkaya, Bülent (2022-01-01)
© 2022, National Science and Technology Council, Taiwan.This study examined a cohort of middle school pre-service mathematics teachers’ understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling course for pre-service teachers. The data were collected from twenty senior year middle school pre-service math...
Developing eighth grade students’ mathematical practices in solids through argumentation: a design-based study
Şahin Doğruer, Şule; Akyüz, Didem; Department of Elementary Education (2018)
The purpose of this study was to obtain classroom mathematical practices of eighth graders’ during the concept of solids and to test the effectiveness of this content in an eighth-grade mathematics classroom. In this respect, an instructional sequence was used with guidance of a hypothetical learning trajectory. The context was basic elements of prisms, their surface area, basic elements of cylinder, its surface area and its volume. The process continued through four and half weeks. Argumentations, dynamic ...
Işıksal Bostan, Mine (2011-07-06)
In this study we aimed to examine prospective elementary mathematics teachers' mathematical knowledge for teaching. More specifically, our aim was to understand whether the Teaching Method Course had an effect on prospective mathematics teachers' mathematical knowledge. The study was conducted with 31 prospective elementary mathematics teachers in a large public university in Ankara, Turkey in 2010-2011 fall semester. To collect data, a survey instrument including 5 open-ended questions was developed by the...
Exploring secondary mathematics teachers’ conceptions of mathematical literacy
Genç, Murat; Erbaş, Ayhan Kürşat; Department of Secondary Science and Mathematics Education (2017)
The purpose of this research study was to investigate secondary mathematics teachers’ conceptions of mathematical literacy. In doing so, the following three crucial interrelated issues were addressed: (i) teachers’ conceptions of what the notion of mathematical literacy means, (ii) teachers’ conceptions of how the development of mathematical literacy could be facilitated, and (iii) teachers’ conceptions of what a mathematics curriculum emphasizing mathematical literacy should look like. The data gathered fo...
Citation Formats
M. Kertil, A. K. Erbaş, and B. Çetinkaya, “Developing prospective teachers’ covariational reasoning through a model development sequence,” Mathematical Thinking and Learning, pp. 207–233, 2019, Accessed: 00, 2020. [Online]. Available: