Introducing and fostering the teaching of mathematical modelling and applications is a long-standing concern in mathematics education. Already in the days of the New Math reform, applications and modelling were an international concern. For instance, the first issue of Educational Studies in Mathematics in 1968 was devoted to this topic collecting contributions of a conference with the title “Teaching mathematics so as to be useful” (Freudenthal 1968). The paper of Pollak (1979) that he presented at ICME 3 in Karlsruhe 1976 was a landmark, often quoted until today. In the German speaking countries, the 1976 conference in Klagenfurt on “Anwendungsorientierte Mathematik” (Dörfler and Fischer 1976) was an early supporting event. The creation of the ICTMA community dates back to 1983 and is another land mark in this development with its biannual conferences.
More recent, the ICMI Study 14 (Blum et al. 2007) provides an excellent overview of the international state of the art. Many contributions in these conferences and studies are constructive in nature: They develop courses, examples, assessment schemes and so on. The number of empirical research papers however is also growing. The study document of the ICMI study summarises the still needed research by means of detailed research questions in the following nine domains. We are quoting some specific and some general research questions (see Blum et al. 2002, p. 155–167, for more details):

(1)

Epistemology (e.g. “What are the process components of modelling? What is meant by or involved in each?”; loc.cit, p. 159)

(2)

Application problems (“What does research have to tell us about the significance of authenticity to students’ acquisition and development of modelling competency?”; p. 160)

(3)

Modelling abilities and competencies (e.g. “Can specific subskills and subcompetencies of ”modelling competency” be identified?”; p.160)

(4)

Beliefs, attitudes and emotions (e.g. “Can modelling effectively contribute towards promoting views of mathematics that extend beyond transmissive techniques to its role as a tool for structuring other areas of knowledge?”; p. 162)

(5)

Curriculum and goals (“What would be an appropriate balance—in terms of attention, time and effort between applications and modelling activities and other mathematical activities in mathematics classrooms at different educational levels?”; p. 162)

(6)

Modelling pedagogy (e.g. “What are the areas of greatest need in supporting the design and implementation of courses with an modelling focus?”; p. 164)

(7)

Sustained implementation (e.g. “What are the requirements for developing a mathematical modelling environment in traditional courses at school or university?”; p. 165)

(8)

Assessment and evaluation (e.g. “What are the possibilities or obstacles when assessing mathematical modelling as a process (instead of a product)?”; p. 166)

(9)

Technological impacts (e.g. “What important aspects of modelling are touched upon by the technological environment?”; p. 167)


Partly influenced by research results from these domains the implementation in curricula and everyday classroom practice has been varying over time and across countries. Without doubt, the international PISA study has supported a more extensive implementation of mathematical modelling in schools, as modelling is considered as one of the most important components of mathematical literacy (OECD 2003). As a result, in some countries, including Germany (cf. Klieme et al. 2003), national standards have taken up this concern and consider mathematical modelling as one of the central mathematical competencies to be developed at school level (cf. Niss 2003; Blomhøj and Jensen 2007).

Parallel to these societal and curricular developments, a growing body of empirical research on mathematical modelling is emerging. In Germany, several research projects have been created that focus on studying how students solve mathematical modelling problems and on the instructional strategies for fostering mathematical modelling. This research picks up the question what we understand by “mathematical modelling competency”, how this competence can be assessed under classroom conditions, and how this competence can be conceptualised and measured paying attention to standards in cognitive psychology and psychometrics.

The current special issue of the Journal für Mathematikdidaktik (JMD) was motivated by the intention to make research approaches and research results of projects based in Germany better known internationally. The issue editors invited contributions from Germany and contributions from projects in neighbouring countries, such as from the research group of Lieven Verschaffel in Belgium and of Kurt Reusser in Switzerland, who have done internationally influential interdisciplinary research on modelling and word problems combining perspectives from mathematics education and educational psychology. Due to limitations of space and time, some contributions that were originally invited for this issue will be published in future issues of this journal.

The seven contributions of this issue can be grouped into 3 categories.