Examining socio-mathematical norms related to problem posing: a case of a gifted and talented mathematics classroom
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Examining socio-mathematical norms related to problem posing: a case of a gifted and talented mathematics classroom Aslı Çakır 1
& Hatice Akkoç
2
# Springer Nature B.V. 2020
Abstract
In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a socio-mathematical norm: student and teacher. The findings revealed three sociomathematical norms (reformulations of problems, generating new problems, evaluation and correction based on the sufficiency of the information) that reflect the classroom’s micro-culture, which involves problem posing. In addition to these basic norms, normative understanding related to “posing more challenging problems” allowed for challenging mathematical situations in the classroom, which is of particular importance for gifted and talented students. We discuss the teacher’s and students’ roles in problem posing activities. We also explore possible reasons for not observing socio-mathematical norms regarding the assessment of posed problems on a criterion that could support students for posing more original, more complex, and more realistic problems. The study suggests practical implications for the dynamics of a classroom where students engage in problem posing activities and theoretical implications regarding the two dimensions of a norm. Keywords Socio-mathematical norms . Problem posing . Gifted students . Talented students
* Hatice Akkoç [email protected] Aslı Çakır [email protected]
1
Institute of Educational Sciences, Marmara University, Istanbul, Turkey
2
Department of Mathematics and Science Education, Ataturk Faculty of Education, Marmara University, Istanbul, Turkey
Çakır A., Akkoç H.
1 Introduction Problem posing (PP) is an essential intellectual activity in the process of scientific inquiry (Cai, Hwang, Jiang, & Silber, 2015). As it is also at the center of mathematical activity, the development of PP ability is an essential target for mathematics education (Chen, Van Dooren, & Verschaffel, 2015). Previous research on problem solving in mathematics education found that the development of PP ability is as important as problem solving ability (Bonotto & Santo, 2015). The literature emphasizes that more research is needed on how PP experiences influence students’ mathematics learning through affective aspects (Cai et al., 2015). Kang and Kim (2016) consider teacher belief as an affective factor in negotiating social interaction and mathematical meaning. Therefore, they emphasize that “the norms that could promote social interaction in mathematics classrooms both implicitly and explicitly were closely connected with a teacher’s belief about mathematics and its teaching and learning” (Kang & Kim, 2016, p. 2734). Social norms (SNs) refer to “regularities in the interaction patterns that
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