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One important contribution of variation theory to learning study is that it brings the focus of the learning study sharply on the object of learning and provides a theoretical grounding to understand some of the necessary conditions of learning. The purpose of this paper is to argue that variation theory can serve as a guiding principle of pedagogical design.

Data from two case studies are used to support the argument.

This paper shows that variation theory is indeed a guiding principle; what the teacher is supposed to do in the classroom does not follow mechanically, as exemplified by two learning study cases. The first example shows that the principles of variation theory imply what features of the object of learning has to be invariant and what should vary in the students' experience. However, this is a necessary but not sufficient condition for learning. The second example shows also that even if one is aware of the pattern of variation and invariance needed, still it might take quite a bit of ingenuity to bring it about.

Teachers need a sound theory to help them make wise decisions about teaching. Variation theory provides a theoretical grounding to understand some of the necessary conditions of learning, so that wise pedagogical decisions can be made. This paper contributes to a deeper understanding of variation theory and its application in practice. Furthermore, the paper also shows that while a learning theory enhances the quality of a lesson study, a lesson study can also provide a platform for the testing and application of a learning theory.

The purpose of this paper is to collect new evidence about the efficacy of the pedagogical principles derived from our earlier study on boosting students’ financial literacy, with the aim of providing a theoretically and practically powerful account of how generative learning in the domain of financial literacy can be enhanced.

This is an example of learning study consisting of a design experiment, which aims to test the conjectures of the variation theory of learning. A total of 156 students who were aged from 14 to 16 years were taught under the three learning conditions which embedded the test criteria, and a total of seven lessons were used by the two participating teachers for each of the classes. To assess students’ appropriation of the object of learning, four tests were conducted, i.e. a pre-test, post-test immediately after the lessons, delayed post-test after six weeks and second delayed post-test after six months.

This study shows that a systematic use of the pattern of “contrast-fusion-generalization” to deal with the individual core economic concepts identified can help students lay a solid conceptual foundation for developing financial literacy. Furthermore, with the use of the meta-level pattern of “contrast-fusion-generalization” through complex everyday financial problems or situations which transcend the specific concepts, students can make effective use of the core economic concepts learned and transform them organically into one’s analytical framework. This enables students to discern and focus upon the critical aspects of novel financial situations and have a greater likelihood of making well-reasoned and sound financial decisions.

This paper sheds light on the ways in which students’ generative learning in the domain of financial literacy can be enhanced through the conceptual approach grounded in the variation theory of learning.

There have been ideological variations in the understanding of student-centered learning (SCL), culminating in varied practices of SCL across the world. The purpose of this paper is to explore the impact of learning study on teachers’ appropriation of the conditions for learning in SCL lessons.

Three secondary school mathematics teachers in Tanzania formed a learning study group, guided by the theory of variation, to share their experience of how to engage learners in experiencing critical aspects of the object of learning. In-depth interviews, records of teachers’ lesson preparation meetings, and students’ tests were tools used to collect data. All of the qualitative data were analyzed using a phenomenographic variation framework and coding strategies. Moreover, a paired sample t-test was used to analyze the students’ pre- and post-test results.

The results show that teachers were able to identify critical aspects of two objects of learning for mathematics and create conditions for engaging learners in experiencing those aspects sequentially and simultaneously. There was strong evidence that the theory of variation as a framework helps teachers to learn effective ways of creating conditions for students to appropriate features of the objects of learning for mathematics as well as developing a new SCL pedagogical framework.

This study suggests that using learning study guided by the theory of variation supports teachers’ appropriation of the conditions for student learning within an SCL framework.

The purpose of this chapter is to investigate students’ qualitatively different ways of understanding the learning object in three undergraduate courses in the discipline of accounting. The theoretical framework of variation theory, a general learning theory, is applied. The lecturers chose a learning object which is investigated under two different teaching conditions – the conventional lecture model and the variational method. Two student groups were identified as a comparison group and a target group, comparable in various relevant parameters. All students took three required accounting courses. In the comparison group, the lecturers used the conventional lecture model and in the target group the variational model. The results indicated significant differences between the two groups’ examination results in the three courses, with students in the target group performing much better. The educational implications and limitations of the study, and areas for further research, are discussed.

The purpose of this paper is to report on a study of teacher learning through participation in sustained collaborative subject-based professional development groups supported by a facilitator, using a model of teachers’ conceptions of teaching developed from phenomenography to identify what are the critical features of teaching that must be present if teachers are to learn, and using a variation theory of learning to explain how they learn.

The groups engaged in cycles of lesson study action research to improve the learning outcomes of their students. The authors intended to engage the teachers in an exploration of their own and their students’ experiences to understand the relationship between the enactment of the research lesson(s) and the educational outcome. The authors collected over 157 hours of video recorded teachers’ meetings involving 15 groups, 47 hours of follow-up interviews and 97 hours of lessons. In this paper the authors report on the progress of one of those groups. The authors analysed the transcripts to see what, if any, dimensions of variation were opened in discussion, affording the opportunity for learning. The authors sought the simultaneous juxtaposition, the bringing together, of threads that have entered the discussion that have the potential to open dimensions of variation – to add critical features to the “what” and “how” dimensions of teaching.

The authors identified necessary conditions for teacher learning through collaborative subject-based professional development groups. Any member of the group might bring this about. The facilitator or coach might be expected to perform this role in the group, and to sustain the group’s attention on the critical features of the object of learning.

The paper provides valuable insights into strategies to change teacher perspectives from a transmission oriented to a construction oriented view of teaching in the face of new and challenging curriculum demands.

In the work reported here the authors have used variation theory to design lesson study. This is rather different from a learning study where the teachers engaged in the study use variation theory to design their research lesson(s). It is a learning study of teachers’ professional development.

The purpose of this paper is threefold. First, the authors set out to advance the thesis that lesson study should be considered as the signature pedagogy of teachers. Second, the authors want to argue that combining the core attributes of Chinese lesson study and Learning study will improve the practice of lesson study. Third, the authors attempt to demonstrate how teachers discover necessary aspects of the object of learning (here called “keys to learning”) through their engagement in Learning studies.

The paper conducted a contrastive analysis of two varieties of lesson studies: the Chinese lesson study and the Learning study.

Lesson studies form a field of varieties, but the commonality among them (i.e. the focus on the lesson) makes the lesson study a strong candidate for being “the signature pedagogy” of teachers. The most important attribute of the Chinese lesson study is its close connection to the daily work of teachers through its embeddedness in teacher research group (arguably the core organisational principle of the Chinese educational system). The most important attribute of the Learning study is its theoretical grounding which helps teachers create an environment for the students to discern and appropriate necessary aspects of the object of learning.

Different varieties may be enriched by including the two core attributes found in the Chinese lesson study and the Learning study.

Two empirical studies are used to exemplify how teacher might discover previously unknown necessary aspects of the object of learning (here called “keys to leaning”).

The purpose of this paper is to examine what are necessary conditions for learning the concept ABA form, a concept for analysing and composing music, and to discuss how the use of variation theory can contribute to the field of music education research.

The method used is a form of lesson study, but with only one participating teacher. Three cycles are conducted with three small groups of children, aged eight to nine years old.

The main findings are that the learning of ABA form requires first, awareness of the sequential form of the music, second, that the attitude to differences that appear between sequential parts of the music is consciously being re-direct from seen as “failures” to being interesting musical contrasts and third, that attention is being paid to different features within one musical aspect, that sounds (not only looks) different. It is found that a main contribution of applying variation theory to studies in the domain of music is the consideration of a part-whole relationship. When the teacher helps the children to create contrast and at the same time keeps focus on how it sounds, the children succeed in coming up with a composition in ABA form. To address the simultaneous relationship between acting and seeing, that is musical impressions and expressions, is crucial for learning.

This study is pioneering since music teaching is studied with the point of departure in an intended object of learning.

It has been proposed that lesson study creates joint and sharable knowledge products in terms of lesson plans that could be used and developed by other teachers in other school contexts (Morris and Hiebert). The purpose of this paper is to report on a study with the aim of examining how such a knowledge product produced in a Hong Kong school could be communicated and appropriated by a group of Swedish teachers.

A report from a successful Learning Study – a revised version of lesson study, based on a theoretical framework of learning – was brought to a group of three teachers. On the basis of this report, they planned and conducted two lessons in their own classes. The analysis draws on data from three of six video recorded lessons and was framed within a variation theory perspective. The focus of the analysis was on the object of learning.

It was found that the Swedish teachers used the documented Hong Kong lessons as a resource. They adapted the insights gained by the Hong Kong teachers to the specific group of learners and other conditions in the Swedish context.

The article is a contribution to the discussion about teachers as knowledge producers (c.f. Stenhouse).

The purpose of this paper is to present how experiences gained from a theory-informed lesson study – learning study (LrS) – in regard to a specific learning goal can be shared and used by other teachers in new contexts.

A group of teachers worked together in a cyclic, iterative process of planning, evaluating and revising teaching. The aim was to provide possibilities for grade 2 and 3 students to become familiar with negative numbers. The teacher group came to the conclusion that the students needed to be able to differentiate some aspects of negative numbers. The conjecture was put to the test in a follow-up study (FS) with five new teachers and eight classes. One lesson was taught based on the empirical findings in the LrS.

The results suggest that teachers’ collaborative work has possibilities to produce knowledge about critical aspects of learning that can be communicated and adopted in new contexts. The teachers in the FS were able to make sense of the results from LrS and incorporate the critical aspects in their teaching in a way that enhanced students’ learning.

It is demonstrated that teacher collaboration in LrS can create knowledge that goes beyond the border of the local context.

The purpose of this study is to explore whether the insights gained by teachers in a learning study can be shared by others and used to enhance other students’ learning.

An exploratory study analysed how four Mathematics teachers implemented the knowledge gained about student learning from a learning study about decimal numbers in their teaching. The teachers enacted two lessons with different conditions in terms of the knowledge identified about student learning in a total of eight classes in the fifth and sixth grades.

The findings indicate that, when the teachers enacted the knowledge in their lessons, students’ learning improved significantly as compared to when only some parts of this knowledge were enacted.

This suggests that teachers can produce knowledge that is also usable for other teachers and that enables better possibilities for student learning.

The study provides insights as to what extent findings from learning studies can be valuable for others.