The relationship between domain- and task-specific self-efficacy and mathematical problem posing: a large-scale study of
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The relationship between domain- and task-specific self-efficacy and mathematical problem posing: a large-scale study of eighth-grade students in China Qimeng Liu 1
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& Jian Liu & Jinfa Cai & Zhikun Zhang
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# Springer Nature B.V. 2020
Abstract
This study explored 1634 Chinese eighth-grade students’ domain- and task-specific self-efficacy and its relationship to their problem-posing performance. In particular, the linear regression model, generalized additive model (GAM), and piecewise regression model (PRM) were used to detail the linear and non-linear relationships between these variables. The findings indicate that most (92.5%) of the students could pose mathematical problems in all tasks, but the effect of their domain-specific self-efficacy on their problem-posing performance was lower than the effect of their task-specific self-efficacy. Students’ problem-posing performance and their task-specific self-efficacy were not always matched when the requirements of the problem they posed varied in difficulty. As the level of difficulty increased, the correlation coefficient between task-specific self-efficacy and problem posing declined from 0.22 to 0.06. Furthermore, PRM confirmed that there were significant changes of the slope around the cut-point of the relationship between task-specific self-efficacy and students’ problem-posing performance. Moreover, the relationship between task-specific self-efficacy and posing performance was different for easy and difficult problems, as the cut-point and slopes before and after the point varied. The findings of this study contribute both to understanding self-efficacy as well as advancing understanding about the characteristics of problem posing from a non-cognitive perspective. Keywords Chinese students . Generalized additive model . Piecewise regression model . Problem posing . Self-efficacy
* Jian Liu [email protected] * Jinfa Cai [email protected] Extended author information available on the last page of the article
Liu Q. et al.
Among the various theories aiming to interpret and predict the processes driving behaviour and outcomes, social cognitive theory (Bandura, 1977) is one of the most prominent (Honicke & Broadbent, 2016). According to this theory, how people behave can be predicted by what they believe about their capabilities (namely, self-efficacy; Schunk & Pajares, 2002). Indeed, self-efficacy can influence peoples’ attempts to improve their behaviour in several ways, such as by determining the choices they make, the effort with which they engage, and their perseverance and anxiety (Bandura, 1986). Thus, researchers across many fields have explored the relationship between self-efficacy and other capabilities and psychological traits (e.g., Grigg, Perera, McIlveen, & Svetleff, 2018; Hoffman & Schraw, 2009; Jansen, Scherer, & Schroeders, 2015). Self-efficacy has received adequate attention in the vast majority of mathematics education research (Pajares & Urdan, 2006), but less in the area of problem posing. From Zimmerman’s (2000) point of view, self-eff
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