Discussion

The results presented in the preceding sections were primarily aimed at developing a test on professional competence of pre-service teachers specifically for teaching mathematical modelling. In a first step, the theoretical foundations were laid and, based on this, the structure of professional competence used for teaching mathematical modelling was explained. Subsequently, the relevant constructs were operationalised and empirically checked. The results of the analyses presented regarding the test quality are summarised below and are classified in the current state of research to discuss possible explanations for the observed results on this basis. In order to further define the scope of the results, key limits of the test instrument in relation to the present study will be addressed. The book concludes with an outlook, in which possible implications are derived from this study for didactic research as well as for university teacher education.

Outlook

The presented test instrument opens up a wide range of approaches for further didactic research and valuable implications for university teacher education; it may not be considered in isolation from the findings of the above discussion or from the limits set out. Against this background, this chapter provides an outlook for further research.

Test Instrument

Key didactic aspects of mathematical modelling (see Sects. 1.1, 1.2 and 1.3), in particular the possibilities of characterising and acquiring modelling competence (see Sects. 1.1.3 and 1.4), were explained in previous sections.

Test Quality

General standards in the form of quality criteria can be used in order to assess the quality of an instrument and/or to construct a high-quality test. Three main indicators, the so-called “core quality criteria,” have emerged: objectivity, reliability and validity (e.g. Bühner, 2011; Ebel & Frisbie, 1991; Linn, 2011; Miller, Linn & Grolund, 2009; Rost, 2004). These primary and selected secondary quality criteria (fairness and usability) are examined in more detail in the following using a data set of 349 pre-service teachers for secondary education at several German universities.

Mathematical Modelling

The integration of applications and mathematical modelling into mathematics education plays an important role in many national curricula (Kaiser, 2020; Niss et al., 2007), and thus an increasing role in teacher training.

Professional Competence for Teaching Mathematical Modelling

Professional competence is a widely discussed topic (see, e.g. Cochran-Smith & Fries, 2001; Darling-Hammond & Bransford, 2005) and was measured globally in various large-scale studies (see, e.g. Blömeke et al., 2014; Kunter et al., 2013). The dimensions for the subject of mathematics range from knowledge to mathematical content to pedagogical and didactic knowledge of teachers with the aim of bringing them together.