Affective determinants of mathematical problem posing: the case of Chinese Miao students
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Affective determinants of mathematical problem posing: the case of Chinese Miao students Meng Guo 1 & Frederick K. S. Leung 1 & Xiang Hu 2
# Springer Nature B.V. 2020
Abstract
Students’ affective characteristics have been confirmed to shape their mathematics learning outcomes, including problem-solving performance and mathematics achievement. However, it remains unclear whether affect influences student mathematical problem posing - a process closely related to mathematical problem solving. Drawn from the expectancy-value theory (EVT), this study examined the relationship between students’ affective factors (self-concept, intrinsic value, and test anxiety) and their mathematical problem posing performance (complexity, quantity, and accuracy). Structural equation models were employed to analyze the data of 302 Chinese Miao students. The results showed that self-concept had a positive association with the complexity and accuracy of the problems posed. Intrinsic value was positively related to the complexity and quantity of the problems posed. Conversely, test anxiety negatively predicted the complexity of the problems. Our findings provide quantitative evidence of the significant influence of students’ affective characteristics on their problem posing performance and offer a better understanding of the problem-posing ability of Chinese minority students. Moreover, this study validates an instrument measuring student affect in mathematical problem posing based on EVT. Keywords Problem posing . Motivation . Affect . Minority students . Expectancy-value theory . Anxiety
1 Introduction Problem posing has been a topic of enduring interest in the mathematics education community, given its important role in advancing students’ mathematical thinking and understanding (English, 2019). Improving students’ mathematical problem-posing ability has been identified * Xiang Hu [email protected]
1
Faculty of Education, The University of Hong Kong, Pokfulam Road, Hong Kong, SAR, China
2
School of Education, Renmin University of China, Haidian District, Beijing, China
Guo M. et al.
as an essential learning outcome in many national mathematics standards, including China (Ministry of Education of the People’s Republic of China, 2012) and the USA (National Council of Teachers of Mathematics, 2000). Extant research has provided detailed information on the development of students’ problem-posing ability (Silver & Cai, 1996; Zakaria & Ngah, 2011), the cognitive determinants of problem posing (e.g., field dependence versus independent cognitive style in Nicolaou & Xistouri, 2011), the relationship between problem posing and problem solving (Cai & Hwang, 2002; Xie & Masingila, 2017) and between problem posing and creativity (Leikin & Elgrably, 2019) and students’ mathematical knowledge (Van Harpen & Presmeg, 2013), teaching mathematics via problem posing (Cai & Hwang, 2019), teacher education through problem posing (Cai et al., 2019; Chen & Cai, 2019; Crespo & Harper, 2019), and cross-national differences in problem posing (Van H
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