German and Taiwanese secondary students’ mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance

Based on expectancy-value theory, this study adopted a person-centred approach to explore the heterogeneous profiles of secondary German and Taiwanese students’ mathematical modelling task values, and examined the differences in their mathematical modelling performance, controlling for the variable of intra-mathematical knowledge among the heterogeneous profiles. Authors conducted a survey study of 452 ninth graders (201 German students and 251 Taiwanese students). The results showed that German and Taiwanese students respectively displayed three profiles of mathematical modelling task values: a) moderate utility and moderate interest/attainment, b) high utility but low interest/attainment, and c) low utility but high interest/attainment. Furthermore, different profiles of mathematical modelling task values showed significant differences in mathematical modelling performance for Taiwanese students but not for German students, even after removing the variable of intra-mathematical knowledge. This study advances the understanding of students’ mathematical modelling task values and its relation with their mathematical modelling performance by the expectancy-value model of achievement motivation and person-centred analyses, and sheds light on the learning and teaching of mathematical modelling.