Abstract
The aim of this study is to investigate the types of teacher and peer interventions to test the validity of modelling along with the modelers’ reactions to these interventions. A teaching experiment was employed in the study. Forty-five pre-service secondary school mathematics teachers participated in the research. As a data collection tool, a worksheet was prepared by taking the monthly average temperature values of the last five years from the Meteorology Directorate of the province in which the study was conducted. At the end of the mathematical modelling process, teacher and peer interventions were carried out. The types of teacher and peer interventions were categorized. The reasons for intervening in the modelling process by both the teacher and peers were insufficient explanations and student error. In addition, the teacher intervened to advance the process. The teacher intervened for diagnosis, advice and feedback, and the peers intervened for diagnosis and feedback in this process. While teacher intervention occurred at the stage of mathematical model and results, peer intervention occurred at the stage of testing the real model and result. The participants returned to revise their real model, mathematical model and results. In the modeling process, while peer support may be sufficient to test the validity of the real model and real results, teacher support is required to test the validity of the mathematical model and its results.
Highlights
Mathematical modelling was formerly used in applied sciences such as physical chemistry or engineering
After this concept began to be used in mathematics education, it was included in the mathematics curricula of several countries such as the USA, Germany, and Turkey (Blomhøj & Kjeldsen, 2006; Blum & Borromeo Ferri, 2009; Common Core State Standards Initiative [CCSI], 2010; Lingefjärd, 2006; Ministry of National Education [MoNE], 2013)
The aim of this study is to investigate the types of teacher and peer interventions related to test models’ validity along with the modelers’ reactions to these interventions at the end of the mathematical modelling process
Summary
Mathematical modelling was formerly used in applied sciences such as physical chemistry or engineering. Mathematical modelling represents a cyclic process bridging between the real world and the mathematics world, defined as transporting a real-world situation or problem into the world of mathematics and making interpretations of potential realworld solutions (Blum & Borromeo Ferri, 2009; Czocher, 2017; Lesh & Doerr, 2003). This modelling process can iterate with new or different variables and assumptions to develop or change the models (CCSI, 2010). According to Borromeo Ferri (2010) and Durandt and Lautenbach (2020), this kind of cycle was chosen because it is sufficiently detailed, common in education studies, a suitable and helpful tool for analyzing modelling processes
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