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    Developing teachers' models for assessing students' competence in mathematical modelling through lesson study
    (Taylor & Francis Ltd, 2017) Yenmez, Arzu Aydogan; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent
    Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.
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    Evolution of Mathematics Teachers' Pedagogical Knowledge when They are Teaching through Modeling
    (Necmettin Erbakan Univ, 2017) Yenmez, Arzu Aydogan; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent
    Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students. mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers. knowledge to use modeling in mathematics education and how this knowledge evolves. The aim of this study is to investigate how teachers. pedagogical knowledge to use modeling in the classroom is formed and modified through professional development activities based on lesson study cycle from modeling perspective. The professional development program reported in this study included five monthly cycles consisted of meeting before the implementation, implementation of the activity and a follow up meeting. The participants were four in-service mathematics teachers. Results showed that the program provided opportunities for teachers to test, revise, and refine their knowledge. More specifically, teachers generated effective strategies for proper implementation of the modeling activities in the classroom.
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    Facilitating a Sustainable Transformation of Sociomathematical Norms Through Mathematical Modeling Activities
    (Springer, 2023) Yenmez, Arzu Aydogan; Erbas, Ayhan Kursat
    We investigated and compared sociomathematical norms in secondary mathematics teachers' classrooms before and after using mathematical modeling activities. Participants were four secondary mathematics teachers. The data included 104 h of videotaped classroom observations and teacher interviews. The data analysis revealed notable changes in sociomathematical norms in teachers' lectures not utilizing modeling activities beyond those utilizing modeling activities. The results implied that teachers and students were convinced by and adopted what was done in the modeling environment. We discussed that modeling activities could be a powerful tool for mathematics teachers and students in challenging and transforming traditionally oriented classroom norms to those aligned with reform-oriented mathematical classrooms and their sustainability.
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    Mathematics teachers' knowledge and skills about questioning in the context of modeling activities
    (Routledge Journals, Taylor & Francis Ltd, 2018) Yenmez, Arzu Aydogan; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Cetinkaya, Bulent; Alacaci, Cengiz
    Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students' higher-level thinking through effective questions. However, teachers' utilization of effective and higher-level questions is usually limited in traditional settings. The goal of this study is to investigate how secondary mathematics teachers' knowledge and skills of questioning change when they are engaged in professional development activities based on the modeling perspective. The program included five cycles each of which lasted a month. Each cycle consisted of meetings before and after the implementation of a model-eliciting activity and its implementation. The results showed that the professional development program had a positive effect on teachers' ability to ask qualitatively different questions in order to move students' thinking forward.
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    Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study
    (EURASIA, 2015) Sahin, Zulal; Yenmez, Arzu Aydogan; Erbas, Ayhan Kursat
    The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up, model-eliciting, and model-exploration activities were used to stimulate participants to reflect and construct ideas about the concept of change. The data indicated that the participants' understanding of derivative was rather instrumental. Their explanations couldn't reveal the role of the big ideas regarding the concept of derivative with respect to what they mean, why and how they are related to the derivative and to each other. The results highlighted the fact that even if one of big ideas is ignored, the concept of derivative may not be fully understood relationally due to the compartmentalization of these big ideas in students' conceptual systems. If this happens to be the case, even though students can solve differentiation tasks/problems correctly, which implies procedural understanding, they may not be actually making sense of what the concept of derivative conceptually means.
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    The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students' achievements in polygons
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Erbas, Ayhan Kursat; Yenmez, Arzu Aydogan
    The purpose of this study was to investigate the effects of using a dynamic geometry environment (DGE) together with inquiry-based explorations on the sixth grade students' achievements in polygons and congruency and similarity of polygons. Two groups of sixth grade students were selected for this study: an experimental group composed of 66 students (34 boys and 32 girls); and a control group composed of 68 students (35 boys and 33 girls). The students in the experimental group taught with a DGE, while the students in the control group received textbook-based direct instruction. An achievement test was administered as pre-test, post-test, and delayed post-test in both groups. Qualitative data were collected through videotaped classroom observations. The results showed that the DGE together with open-ended explorations significantly improved students' performances in polygons and congruency and similarity of polygons. Furthermore, students in the experimental group showed greater interest and motivation toward learning geometry compared to those in the control group whom often showed lack of interest and curiosity. Also, students' comments and interpretations during lessons and tests were more accurate and advanced in the experimental group as they engage more in the DGE. Moreover, qualitative data suggested that boys showed greater interest in the computer-based learning environment than girls in the experimental groups although no significant gender effect on achievement was found. (C) 2011 Elsevier Ltd. All rights reserved.