Affect in mathematical problem posing: conceptualization, advances, and future directions for research
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Affect in mathematical problem posing: conceptualization, advances, and future directions for research Jinfa Cai 1 & Roza Leikin 2 Accepted: 27 October 2020/ # Springer Nature B.V. 2020
1 Introduction The importance of this special issue is rooted in the idea that the cognitive and affective fields are interrelated and support each other in the learning process. For example, Pellegrino and Hilton (2012) have pointed out the centrality of both cognitive and socio-emotional dimensions in necessary skills for the twenty-first century. They list complex problem solving and creativity among the basic twenty-first-century cognitive skills that determine intellectual development, career readiness, and adaptation to exponential environmental changes. At the same time, they highlight socio-emotional skills such as positive self-evaluation and collaborative skills, responsibility and commitment, openness and flexibility to a variety of points of view, interest, and curiosity; these are usually considered to be components of affective and social development. From a dialectical perspective, Rothstein (2004) suggested that noncognitive and cognitive abilities have the potential to mutually reinforce each other to maximize student learning, and Farrington et al. (2012) also maintained that cognitive and non-cognitive factors continually interact in essential ways to foster learning. Although the importance of affect has recently received increased attention (e.g., Cai et al., 2017; Duckworth & Seligman, 2005; Dweck, Chiu, & Hong, 1995; Farrington et al., 2012; Hannula et al., 2019; Moyer, Robison, & Cai, 2018; Steele & Aronson, 1995), students’ affect has been far less studied than their content knowledge and academic skills. Because problem posing is related to complex problem solving and creativity-directed activities (Cai et al., 2017; Leikin, 2018; Silver, 1997), it is a unique mathematical activity that provides multiple opportunities for the advancement of both cognitive and affective competencies as well as their integration. The importance of the integrative development of cognitive and non-cognitive competencies thus
* Jinfa Cai [email protected] Roza Leikin [email protected]
1
University of Delaware, Newark, DE, USA
2
University of Haifa, Haifa, Israel
Cai J., Leikin R.
motivates this special issue’s focal question: How is problem posing in teaching and learning mathematics interconnected with affective factors such as motivation, engagement, beliefs, attitudes, values, emotions, feelings, moods, and self-efficacy (Attard, 2014; McLeod, 1992)? Ultimately, the goal of this special issue is twofold. First, it aims to reflect and analyze the state of the art in research on affective factors associated with mathematical problem posing. Second, by drawing attention to a research gap in this area, the special issue attempts to stimulate researchers to fill the gap through systematic research that integrates advances in the research on mathematical problem posing and the research on the role of affect in mathematics
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