The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling – An Intervention Study

Abstract

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities.The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.Keywords: teacher beliefs, teacher education, mathematical modeling, teacher training Theoretical Background IntroductionMathematical modeling means solving complex, realistic and open problems with the help of mathematics. Although mathematical modeling became part of the national German curriculum in 2004 and has been discussed among mathematics educators for decades, it is still rare in day-to-day teaching practice (Blum, 2002).In the present study, we wanted to know whether specially designed (written) curriculum materials for teachers support the development of students' modeling competences. We focused on the design of curriculum materials because materials -other than long-term teacher training -can reach many teachers easily and effectively. We designed mathematical modeling teaching materials for the target group of six grade students (age 11) because modeling is part of the curriculum for this grade. Teachers were asked to use these materials over a period of one school year. The effectiveness of the materials was evaluated in a pre-post control group design by means of a standardized test to assess student competences in mathematical modeling. We also assessed teacher beliefs before and after the intervention because it was expected that their beliefs play a mediating role in the effectiveness of the written materials.The main research questions of the study were:1. Does teacher use of curriculum materials directly influence student modeling competen...

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