Competence approach is one of the major innovations in the latest school curriculum reform in Sweden that has been gradually introduced since 2011. This reflects broader international trend of Competence Based Education around the world during the past decade (Biemans, et.al, 2009, Niss and Højgaard, 2011). In order to familiarise teachers with latest curriculum innovations and to raise their general didactical competence of mathematics the Swedish National Agency for Education is implementing a project called Matematiklyftet. The project uses a praxis-based collegial learning approach supported by facilitators and presented in the project web portal https://matematiklyftet.skolverket.se/. The teachers’ activities are framed by study modules which material are freely available on the web. The teachers work with one module per term. Over twelve thousand teachers from about three hundreds schools take part in these activities yearly.

The authors of this paper were in charge of the material development for the high school module “Competence based mathematics teaching”. The module consists of eight parts:

1. Working with mathematical competencies

2. Problem-solving competency

3. Conceptual and procedural competencies

4. Modelling competency

5. Reasoning competency

6. Communicating competency

7. Development of competencies

8. Experiences and challenges

In each part participants carry out activities in four steps with the following allocation of time: individual preparation (45 – 60 min), collegial discussions (90 – 120 min), practical activities/lessons (one lesson), and common follow up and reflections (45 – 60 min).

The sources of inspiration for the project have been: Japanese “lesson study” model consisting of lesson preparation, auscultation and collegial reflections about the implemented lesson; and the SINUS project (Germany), in particular a scaling up form of using study modules, facilitators, and Internet based platform (Ostermeier, Prenzel, Duit, 2010).

However, the authors learned during the introduction to the module  development task that it is not possible to ask the teachers to do auscultations of each other’s lessons and to provide material that demands more than sixty minutes time to prepare for the first group discussion meeting. Thus, the idea of “lesson study” has to be implemented without teachers attending colleagues’ lessons and became a debilitated version of the Japanese model. Lesson without peer auscultation is a half-blind activity. To compensate for the absence of a colleague’s feedback the teachers had to rely on personal reflection and self-monitoring, which was a particularly demanding activity that needed special development. An attempt to substitute “auscultation of a colleague’s lessons” by the practice of “noticing” (Mason, 2002) was centrally promoted but not eagerly accepted by practicing teachers. The teachers had difficulty in impartially sketching notes of the events attracting their attention during the teaching for further reflection afterwards.

This paper provides the authors reflections about the process of the module development and some results from the teachers’ evaluations. The paper attempts to highlight two questions:

• What lessons could be learned from the process of material production for the professional development of mathematics teachers in Sweden?

• What feedback provided teachers aiming to improve the module material?

The Activity Theory (AT) has been used to provide theoretical ground for reflection on our developmental work (Cole and Engeström, 2007). This theory was also used to reflect on different aspects of learning activity (Davydov, 1999) and the effects of proactively introducing competencies in order to transform classroom practice (Cole and Engeström, 2007). According to Kinard, Kozulin (2008, p. 25), “the learning activity includes orientation in the presented material, transformation of the presented material into a problem, planning the problem-solving process, reflection on chosen strategy and problem-solving means, as well as self-evaluation”. These concepts were important for the design and evaluation of our “module work”.

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