Developing prospective teachers' covariational reasoning through a model development sequence

• Published in: Mathematical thinking and learning Vol. 21; no. 3; pp. 207 - 233
• Main Authors: Kertil, Mahmut, Erbas, Ayhan Kursat, Cetinkaya, Bulent
• Format: Journal Article
• Language: English
• Published: Philadelphia Routledge 03.07.2019; Taylor & Francis Ltd
• Subjects: Covariational reasoning; Elementary Education; Elementary School Mathematics; Mathematical Concepts; Mathematical Logic; mathematical modeling; Mathematical Models; Mathematics Education; Mathematics Teachers; Middle School Mathematics; Middle School Teachers; Preservice Teachers; prospective mathematics teachers; quantitative reasoning; rate of change; Reasoning; Student Attitudes; Thinking Skills
• ISSN: 1098-6065; 1532-7833
• DOI: 10.1080/10986065.2019.1576001

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.