E d u c at i o n i nq u i ry Education Inquiry is an international on-line, peer-reviewed journal with free access in the field of Educational Sciences and Teacher Education. It publishes original empirical and theoretical studies from a wide variety of academic disciplines. As the name of the journal suggests, one of its aims is to challenge established conventions and taken-for-granted perceptions within these fields. Education Inquiry is looking for lucid and significant contributions to the understanding of contextual, social, organizational and individual factors affecting teaching and learning, the links between these aspects, the nature and processes of education and training as well as research in and on Teacher Education and Teacher Education policy. This includes research ranging from preschool education to higher education, and research on formal and informal settings. Education Inquiry welcomes crossdisciplinary contributions and innovative perspectives. Of particularly interest are studies that take as their starting point, education practice and subject teaching or didactics. Education Inquiry welcomes research from a variety of methodological and theoretical approaches, and invites studies that make the nature and use of educational research the subject of inquiry. Comparative and country-specific studies are also welcome. Education Inquiry readers include educators, researchers, teachers and policy makers in various cultural contexts. Every issue of Education Inquiry publishes peer-reviewed articles in one, two or three different sections. Open section: Articles sent in by authors as part of regular journal submissions and published after a blind review process. Thematic section: Articles reflecting the theme of a conference or workshop and published after a blind review process. Invited section: Articles by researchers invited by Education Inquiry to shed light on a specific theme or for a specific purpose and published after a review process. Education Inquiry is a continuation of the Journal of Research in Teacher Education, which is available in printed copies as well as electronic versions and free access at

Purpose – The purpose of this paper is to present a model for supporting and increasing teachers’ reflection process. Design/methodology/approach – The model is grounded in two concepts from variation theory: critical aspects and dimensions of variation. Those concepts are related to the concepts of reflection in-, on- and for-action. Analysis of data allows for determination of what kind of reflection is used in teachers’ professional development (PD) and the teachers’ perceptions of the relevance and usefulness of the PD. Findings – The results show that, using the concepts of critical aspects and dimensions of variation, teachers practiced reflection in-, on- and for-action in a non-dualistic way. Practical implications – The preliminary results confirm that the teachers change their behaviours, through reflection processes, if they have the opportunity to focus on the object of learning and to use research results found in mathematics education in order to open up dimensions of variation in the identified critical aspects. Social implications – The design of algebra modules, according to concepts from variation theory and the reflection process, is the main result of this study. The model used in creating the modules has the potential for supporting and increasing teachers’ reflection process. Originality/value – A conceptual model of work practice evolution is proposed. The model is conceived as an intermediary between models of reflection, action at work and models of organisational teaching in the classroom. It considers work practices as evolving through confrontations between critical aspects, action in context, reflections in-, on- and for-action. The author advocate that the use of the presented methodology is not only inevitable but also vital to improve teachers’ PD.

The research study this article is based on aims to implement research knowledge to teaching, that is, the concept of critical aspects and dimensions of variation used in the variation theory. To do this, the researchers worked with willing teachers to explore how to make mathematics teaching more effective. This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding of subtraction as well as their learning of it. The students' tests, examinations of students' mathematical work, the teachers' lessons plan and reports of the instructions for lessons form the data base for the article. The analysis indicates that one of the critical aspects in the process of implementation of the variation theory in the teachers' practice was to identify the critical aspects in students' learning. Another critical aspect in the implementation of the variation theory was to open up dimensions of variation in the identified critical aspects of the students. By giving teachers the possibility to develop the ability to identify critical aspects in students' learning, dimensions of variation are opened up in these aspects, and by applying this knowledge in the daily teaching, they have the possibility to improve students' learning. The findings suggest that developing an understanding of the students' critical aspects can be a productive basis in helping teachers make fundamental changes in their instructions and improve students' learning.

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The point of departure in this study is that differences in solving seconddegree equations result from differences in what is presented to the students in a learning situation. However, the specified aim is to describe what kind of differences seem to be crucial for learning, and what does seem fruitless.The study is carried out in an upper secondary school in Sweden. Data consist of video-recorded lessons and tests. Two teachers and 45 students participated in this study. The analysis has been made with the aid of variation theory. The results show that the teachers focused on different aspects of a second-degree equation, and that this implied different learning outcomes as some of the aspects were not critical to promoting learning while others were.