Abstract
Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers’ professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions.
Highlights
Mathematical modeling has been a prominent research topic among the international mathematics education community for several decades and is widely accepted as an essential component of mathematical literacy (e.g., Niss, 2015; OECD, 2003)
Adapting frameworks developed in previous comparative studies, namely Mathematics Teaching in the 21st Century (MT21) and Teacher Education and Development Study in Mathematics (TEDS-M), the present study aims to compare pre-service teachers’ (PSTs)’ professional mathematical modeling competences in Germany, Mainland China, and Hong Kong
Regarding PSTs’ mathematical pedagogical content knowledge (MPCK) of mathematical modeling, first—for the two aspects related to the learning perspective—it appears that providing feedback on students’ answers is relatively more difficult or demanding than evaluating students’ answers, for PSTs from Germany and Mainland China
Summary
Mathematical modeling has been a prominent research topic among the international mathematics education community for several decades and is widely accepted as an essential component of mathematical literacy (e.g., Niss, 2015; OECD, 2003). Teachers’ professional mathematical modeling competencies have been widely accepted as the key factor that determines the successful implementation of mathematical modeling in mathematics teaching (Barquero et al, 2018; Greefrath & Vorhölter, 2016). Mathematical modeling teaching poses substantial challenges to the common instructional practices to which teachers are accustomed (Doerr, 2007; Ng, 2013). New forms of mathematical and extra-mathematical knowledge and pedagogical content knowledge are necessary to teach mathematical modeling (Blum, 2015; Doerr, 2007; Kaiser & Maaß, 2007). Pre-service mathematics teachers must develop such professional competencies to minimize the potential occurrence of barriers to mathematical modeling teaching (Winter & Venkat, 2013). In the field of mathematical modeling, few studies have investigated teachers’ professional modeling competencies, in particular, the two most relevant competence components—MCK and MPCK—simultaneously
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