The DZLM approach

The DZLM (German Center for Mathematics Teacher Education) was launched in 2011 with the aim to support and pursue the existing programmes and structures for continuous professional development (CPD) nationwide, network all reforms in this field and develop new research-based exemplary courses. DZLM is a joint endeavour of different researchers from different universities, collaborating with representatives from school administration of all 16 federal states and teachers from school practice. DZLM follows a design-based research paradigm (van den Akker, Gravemeijer, McKenney & Nieveen, 2006) when designing and researching programmes for different target groups of teachers and topics. DZLM offers qualification of facilitators, in-service-teacher education and out- of-field teaching and acts as a network platform for information and exchange.

One important issue for the DZLM was to install a competence framework for PD courses as an important orientation for teachers and facilitators to address the different areas of relevant content (see Figure 10.1, cf. Lipowsky & Rzejak, 2015; Garet, Porter, Desimone, Birman & Yoon, 2001).

This framework was the framework of principles for content design that has to be selected from and concretized in each PD course (see course 2 as an example).

Beside the competence framework, DZLM has established design principles for the teaching and learning processes for all contents as guidelines for designing and analyzing CPD courses. This has been done in a cooperative process of all DZLM researchers reviewing the current state of research in the field. Based on this process, six design principles have been generated to provide criteria of efficient teachers’ professionalization. They were based in the research literature of effective PD (for further details, see Barzel & Selter, 2015). We have organized

166 Barbel Barzel & Rolf Biehler

DZLM competence framework for PD courses

FIGURE 10.1 DZLM competence framework for PD courses.

the research results into six keywords that can also be useful for communicating

design principles to facilitators:

  • Competence-orientation: crucial for effects and efficacy of professionalization is the clear focus on content to improve and deepen teachers’ knowledge, and performance in teaching
  • (Garet et at., 2001; Timperley, Wilson, Barrar & Fung, 2007)
  • Participant-orientation: centring on the heterogeneous and individual prerequisites of participants; moreover, participants get actively involved in the PD unit instead of pursuing a simple input-orientation
  • (Clarke, 1994; Krainer, 2003)
  • Stimulation of cooperation: motivating participants to work cooperatively, especially between and after the face-to-face phases; ideally sustainable professional learning communities are initiated
  • (Krainer, 2003; Bonsen & Hiibner, 2012)
  • Case-relatedness: using cases such as videos of teaching or students’ documentation, which are relevant for the school practice, to enable new perspectives and to realize further dimensions of teaching effects
  • (Borko, 2004; Timperley et at., 2007; Lipowsky & Rzejak, 2015)
  • Diverse instruction formats: during PD courses, it is important to realize a mixture of different formats (like lectures, individual and collaborative work); also, phases of attendance, self-study and e-learning should alternate
  • (Deci & Ryan, 2000; Lipowsky & Rzejak, 2015).
  • Fostering reflection: continuously encouraging participants to reflect on their conceptions, attitudes and practices
  • (Deci & Ryan, 2000; Putnam & Borko, 2000; Schoen, 1983)

Taking these principles seriously naturally yields to the necessity to realize CPD initiatives in long-term formats as well (Rosken-Winter, Schiiler, Stahnke & Blomeke, 2015; Fishman, Penuel, Allen, Cheng & Sabelli, 2013).

The DZLM provides an organizational and supporting structure to accompany the programmes with associated research. One main question is to focus on the effects of CPD programmes. There is a consensus in literature that the effects of CPD occur on different levels, and that just the number of levels varies: Whereas Guskey (2000) defines five levels of effects, Lipowsky and Rzejak (2015) distinguish four levels of effects: level 1, participant’s reactions; level 2, participant’s beliefs and professional knowledge; level 3, participant’s use of new knowledge and skill in the classroom; and level 4, student learning outcomes. Guskey’s (2000) additional level describes “Organization Support and Change” and is positioned between the second and third levels in the aforementioned hierarchy. Guskey’s extra level specifies whole school changes as a result of CPD. Since DZLM focuses less on whole schools but more on individual teachers, the orientation is on the four-level variant.

Context of the two PD courses

The following two examples of PD courses illustrate the work of the DZLM. Both examples are from North Rhine-Westphalia (NRW). It is the biggest federal state in Germany in terms of numbers of inhabitants (18 million of 82 million in the whole of Germany). The federal states are responsible for any educational issues. The nationwide standards in mathematics (KMK, 2012) serve as a recommendation, but most of the curricula in the federal states follow these standards. In previous years, two main innovations for upper secondary level and the final centralized examination (Abitur) have been brought up in NRW. It is, on the one hand, the introduction of graphic calculators (GC) as compulsory tools (by decree in 2012) in classrooms and examinations. On the other hand, the new state curricula in NRW (2014) fixed stochastics (probability and statistics) as an obligatory topic for all students (6 months’ teaching of stochastics in all mathematics classrooms). The main argument for the introduction of the GC was to support a deeper understanding of mathematics by interactive visualization, relief from routine calculations and routine analyses of data and support of modelling with more realistic examples. Regarding stochastics, in particular, the use of the GC for simulations is suggested.

For both topics - an introduction on using and teaching with GCs and on teaching stochastics - the DZLM has collaborated strongly with the educational administration in NRW and realized two PD courses: “GC compact” and “Stochastics Compact”. In the following, we present both courses to illustrate the work of the DZLM.

Teacher professional development is essential to further develop mathematics teaching and is still a current issue (Borko, 2004; Sztajn, Borko & Smith, 2017). In recent years, a shift can be stated in better conceptualizing and grounding professional development by means of research. It is no more aimed at eliminating shortcomings, but the development goes more into the direction of a continuous process of professionalization (Rosken-Winter & Szczesny, 2017). That is why the duration and formats of professional development should change from single short courses to courses consisting a mixture of several face-to-face meetings, as well as blended learning phases for supporting teachers (Fishman et al., 2013).

Common design aspects related to digital tools

Intensive professional development is especially needed to support teachers to involve digital tools in their teaching, as this is a big challenge requiring a rethinking of task formats as well of teaching routines within the orchestration of the classroom. We use the term “digital tools” to describe mathematical software such as spreadsheets, computer algebra systems (CAS), or statistical tools. These tools can be available on various platforms such as desktop computers, tablets, or handheld calculators. Pierce and Stacey (2010) have used the umbrella term “Mathematics Analysis Software” (MAS) to describe this kind of software, housed in a computer or a calculator, which they declare as cognitive tools, “in that they facilitate the technical dimension of mathematical activity and allow the user to take action on mathematical objects or representations of those objects” (Pierce & Stacey, 2010, p. 1). Considerable research over the past few decades, including reviews, has pointed out that MAS in mathematics education can be used to enrich teaching and learning (e.g. Blume & Heid, 2008; Heid & Blume, 2008; Barzel, 2012; Biehler, Ben-Zvi, Bakker & Makar, 2013; Drijvers et al., 2016). For example, these tools can facilitate constructivist teaching approaches like discovery learning by offering the opportunity to explore mathematical connections. In addition, digital tools can enhance conceptual understanding of specific content by providing easy access to multiple, linked and dynamic representations (Penglase & Arnold, 1996; Burrill et al., 2002).

Despite these results and recommendations by researchers, there is a “widely perceived quantitative gap and qualitative gap between the reality of teachers’ use of ICT and the potential for ICT suggested by research and policy” (Bretscher, 2014, p. 43). Factors which are discussed as reasons for the reluctance of using MAS by teachers are external factors like time constraints, resources and school culture, but much more important is the teacher him- or herself not changing teaching routines to integrate MAS.

For Germany, a current representative survey of more than 1000 teachers confirmed this fact by stating that STEM teachers do not assume their pioneering role to include technology in teaching, although literature offers a plethora of relevant teaching examples (Lorenz et al., 2017). The point that technology is nearly not used to enhance content- and process-related activities is even more crucial

(Lorenz et al., 2017). This is one important reason why DZLM offers a two-folded programme to support secondary teachers to integrate MAS in their teaching.

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