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This is the accepted version of a paper published in European Journal of Education. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.

Citation for the original published paper (version of record): Runesson Kempe, U. (2019)

Teachers and researchers in collaboration. A possibility to overcome the research-practice gap?

European Journal of Education, 54(2): 250-260 https://doi.org/10.1111/ejed.12336

Access to the published version may require subscription. N.B. When citing this work, cite the original published paper.

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Teachers and researchers in collaboration. A possibility to overcome the research – practice gap?

Abstract. Taking as its point of departure the discussion about the disconnection between research and practice, this article presents learning study as a research approach to overcoming this gap. Learning study has commonalities with design research and lesson study but is a teacher - researcher collaboration where the researcher and teachers have a common object of research. Thus, it is research with teachers, rather than on teachers and is focused on

constructing knowledge concerning objects of learning as well as teaching-learning

relationships. The focus of the research collaboration is professional problems related to the object of learning that teachers encounter in their everyday practice. The process is guided by a theory of learning and pedagogy—variation theory. The knowledge product of learning study is a theoretical description of what must be learned in order to develop a specific capability. Examples of knowledge contributions from learning study are given, and it is suggested that such knowledge can be considered to be public knowledge that can be shared, used and developed by other teachers in other contexts. Furthermore, it is suggested that there are specific features of learning study that make it a research approach that may strengthen connections between research and practice.

Keywords: design research, learning study, lesson study, linkage of research and practice, teacher-researcher collaboration, variation theory

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Teachers and researchers in collaboration. A possibility to overcome the research – practice gap? Ulla Runesson

Correspondence

Ulla Runesson, Jönköping University, Gjuterigatan 5, 55318 Jönköping, Sweden Email : ulla.runesson@ju.se

1. INTRODUCTION

The research-practice relationship is a frequently and persistently addressed issue in education. It has been described as the great divide (Berliner, 2009) or the theory -practice gap (Korthagen, 2007). On the one hand, theorists/researchers claim that results from educational research (i.e., theoretical concepts, models or proposals) have relevance for teachers and can inform practice. Teachers have, on the other hand, expressed that educational research is distanced from their everyday problems, too theoretical and not easy to access (Silver & Lunsford, 2017). The importance of bridging and overcoming this divide has been frequently highlighted and it has been argued that teachers must be key stakeholders, working with researchers as co-producers to generate

knowledge that can close the credibility gap (Kieren, Krainer, & Shaughnessy, 2013). In this article, I discuss some models for practitioner and researcher collaboration and in what ways such joint endeavours could benefit both practice and theory. I elaborate on learning study, which is a theory-informed version of the Japanese lesson study (Lewis, 2002; Stigler & Hiebert, 1999) and on how it (Marton & Pang, 2003)can be a research approach to studying the relationship between teaching and learning, how new insights into learning and teaching can be produced and how such knowledge can be shared with teachers who do not participate in the study. Furthermore, I argue that such knowledge can have both theoretical and practical significance.

2 OVERCOMING THE PRACTICE -RESEARCH DICHOTOMY

A recurring theme in research on teaching practice is the very limited influence of educational research on improving classroom teaching and learning. Two conditions have been suggested as necessary to overcome this limitation. One is acknowledging Dewey’s notion of teachers as both

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consumers and producers of knowledge. This implies viewing them as experts and competent partners in the research process and in the dissemination of the results (Kieran, Krainer, & Shaughnessy, 2013). A second is that teachers and researchers must have a shared and joint

research focus (Carlgren, 2012); thus, it is research with teachers, rather than on teachers. If the aim is to develop knowledge that is useful for improving teaching practice, the research questions must stem from teachers’ practical problems. This challenges traditional university-based research and the various forms of collaborative and interventionist approaches that have emerged in the last decades can be seen as a response to the deficiency of many traditional research approaches in overcoming the research-practice divide.

Researching the classroom in cooperation with teachers was first recognised by Stenhouse (1981) and has been taken up by several others (e.g., Cochran-Smith & Lytle, 1999; van den Akker, 1999) and there are different approaches to manifest these ideas. Three of these will be presented below.

2.1 Design research

One approach to overcoming the gap is design research (Brown, 1992; Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003; Kelly, Lesh, & Baek, 2008;). Although building on different traditions, it aims to develop both theories and practice (Cobb, Jackson, & Dunlap, 2016). It is an interventionist approach which includes cycles of planning, enactment, analysis and revision. Design research strives to generate practical design principles together with contextualised theories of learning. Hence, having dual aims, it resonates with Stoke’s notion of Pasteur’s quadrant (Stoke, 1997). Stoke rejects the model of applied and basic research as two ends on a linear scale. Instead, he combines them as two dimensions in a two-by-two graph where the x-axis represents practical relevance and the y-axis theoretical relevance and contribution. Research that produces results that are high in both

dimensions generates practical as well as theoretical common public knowledge.

Whether design research does fulfil these double goals has, however, been debated (Anderson & Shattuk, 2012) and further assessment is needed to obtain a nuanced judgement of how well this double aim is fulfilled (McKenney & Reeves, 2013). Another critique has been raised

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from a systematic review by Ormel and colleagues (Ormel, Pareja-Robliin, McKenney, Voogt, & Pieters, 2012). They point to the lack of overlap in researcher-practitioner roles in some of the studies. They conclude that researchers are mostly accountable for research and teachers for teaching and that teachers’ practical knowledge is even sometimes omitted. Therefore, they defined some of the studies as cooperative rather than collaborative. Yet another problem raised by Cai, Morris, Hohensee, Hwang, Robison, and Hiebert (2017) is the implementation of results from design research studies. They point out that elements of implementation are seldom integrated in the research process. This could, they say, run the risk that even a research-based curriculum will fail to be fully realised (p. 343).

2.2 Lesson study

Whereas design research, in my view, is mainly university-driven (research from outside, see Carlgren, 2012), the Japanese lesson study, in its origin, is teacher-driven. Lesson study has been suggested to reinforce the theory-practice gap (Huang & Shimizu, 2016), but whereas in design research there is a theoretical foundation, in lesson study, an explicit theoretical grounding is seldom reported (Elliott, 2012; Stigler & Hiebert, 2016). Lesson study has received much attention since it was introduced to the West around the year 2000 (Lewis, 2002; Stigler & Hiebert, 1999; Yoshida & Fernandez, 2004) and there is extensive literature on its effects. What is mostly reported, however, is the improvement of teachers’ teaching skills and teachers’ learning (e.g., Lewis, Perry, & Hurd, 2009; Robinson & Leikin, 2011). If these are its only goals, in my view, lesson study will be restricted to a model for professional development and not used for generating knowledge that is relevant outside the local context (c.f. Stigler & Hiebert, 2016).

It has been proposed that there are elements of lesson study that generate new and relevant knowledge, making it a legitimate knowledge source for professionals. These elements include shared problems, small tests of small changes and taking advantage of different kinds of knowledge and expertise (Morris & Hiebert, 2011, p. 6). The lesson study, Morris and Hiebert argue, is ‘real research’ and a methodology that can generate knowledge to improve teaching. Its outcome —an instructional product—has the potential to ‘guide actions towards helping students to achieve

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the learning goals’ (Morris & Hiebert, 2011, p. 8). Such instructional products are exemplary lessons with a learning goal in mind, manifested as lesson plans with annotated instructional activities, a sequence of problems, annotated lesson plans or diagnostic tests that are detailed enough to affect classroom practice. Instructional products generated in lesson study have high ecological validity, Stigler and Hiebert (2016) argue, and the problem of implementation as a separate process will not be an issue, as it is integrated into the knowledge-generating process.

Whereas it has been reported (Enthoven & de Bruijn, 2010) that knowledge generated in various forms of professional learning communities seldom reaches outside the local context, and thus is not disseminated to other teachers, others (Morris & Hiebert, 2011; Stigler & Hiebert, 2016) point to the potential of lesson study to generate contributions that are informative for other teachers and other classrooms. Since lesson study addresses common teaching problems and challenges that teachers encounter, the knowledge gained is valid for contexts beyond the local classroom where the research is conducted. The instructional product is tentative, however, and open to being tested, refined and developed (Morris & Hiebert, 2011).

3 LESSON STUDY GUIDED BY THE VARIATION THEORY OF LEARNING

It has been suggested that lesson study can be improved by adopting an explicit theory in the process (Elliott, 2012; Huang, Gong, & Han, 2016; Marton & Pang, 2003; Runesson, 2016) and, as Nuthall (2004) points out, a theory is needed when examining how teachers’ actions affect student learning. One theory that can be used is the variation theory of learning (Marton & Booth, 1997; Marton, 2015). Inspired by Stigler and Hiebert’s seminal report on the Japanese culturally embedded teaching practice (Stiegler & Hiebert, 1999), a group of researchers in Hong Kong took up the lesson study concept around the year 2000. In several projects aiming to help teachers to plan lessons that would lead to better learning, they combined the lesson study approach with the variation theory. Because of its specific focus on learning—and not on the lesson—, the approach was named learning study. The results of these projects were very promising. General attainment tests demonstrated a reduction in the learning gap between high- and low-achievers among groups where the teachers

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had participated in learning studies (Cheng & Lo, 2013). Furthermore, it was demonstrated that when the variation theory was used as a theoretical tool in the lesson study process, learning gains were higher than in lesson studies conducted without variation theory (Marton & Pang, 2003). The lesson study using the variation theory was shown to be successful in enhancing learning of specific objects of learning. What then is the contribution of the variation theory to lesson study?

3.1 Object of learning in focus

The variation theory has its roots in phenomenography (Marton & Booth, 1997), a research approach for studying differences in individuals’ ways of experiencing something—a phenomenon, problem or situation. One central idea in phenomenography—and consequently in variation theory—is that learning always has an object. Hence, when the variation theory is applied in a learning study, the focus is on what the learners learn: the object of learning. Focusing on a particular object of learning and exploring its character are specific features of the variation theory-informed version of lesson study. But why does the object of learning need to be attended to?

In the contemporary worldwide educational reform towards an outcome-based curriculum, the notion of ‘learning objectives’ is central. I would argue, however, that learning objectives cannot be taken for granted and be directly applied in class. There is a gap that must be filled before the teacher makes decisions on teaching methods, arrangements and assessments. This gap concerns the object of learning.

An object of learning is specific to a certain group of learners, whereas learning objectives are general in character. The object of learning entails what must be learned to achieve the learning objective. An object of learning is the answer to the question ‘What is to be learned?’ Why educational objectives cannot be the same as the object of learning follows from the following set of arguments: every educational objective corresponds to a capability1; every capability consists of different components; at a certain point in time some students in an age group have already

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mastered some components, while others have mastered other components. Students must learn those component parts of the capability in question that they have not already mastered, hence, to a certain extent, different students have to learn different things. So, which aspects need to be discerned by the learners? The critical aspects cannot be fully known in advance or be identified from a predefined learning objective. Neither can they be found from subject matter knowledge only. In a learning study, critical aspects are identified in a transactional process that includes what is targeted, the learners and their learning. Identification of critical aspects happens in a process which resonates with Dewey and Bentley’s (1949) notion of the transaction of the known, the knower and the known. Therefore, in learning studies, students’ learning before and after the teaching session(s) must be carefully analysed, either by diagnostic tests and/or in interviews/written text.

3.2 Learning, discernment and variation

When differences are found in students ‘various ways of experiencing, for instance, a linear function, the variation theory can provide answers, not only to why there are differences, but also to the reasons of the differences and how to overcome them.

The variation theory states that learning implies seeing something in a new way by discerning aspects that have not previously been discerned. For example, when a child realises that when counting objects (‘one, two, three….five’), the ‘five’ does not just mean the last counted object2, but also the whole set of five; she or he discerns both the ordinal (the fifth) and the cardinal (i.e., the last uttered word indicates all five) aspects. From this, it follows that learning failures cannot be explained by deficiencies in the learner, but rather by limitations in discernment.

One fundament of the variation theory is that learning and seeing things in a new way stems from experiencing difference rather than sameness. Marton (2015) argues that the discernment of an aspect requires experiencing a difference between (at least) two things or parts of the same thing. For instance, in order to discern a new concept, one needs to experience contrast

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(variation) between the new concept and another concept and hence how it differs from the other concept.We can probably more easily become acquainted with specific features of the natural numbers if they are contrasted with negative numbers, for instance, –18 < 3, but 18 > 3. Furthermore, if an aspect is varied, or opened up as a dimension of variation against a stable background, it is likely to be discerned. From this, it follows that the critical aspect must be varied in order to be made possible to discern. So, in a learning study, the variation theory is not only applied when examining students’ learning and what they must learn (the critical aspects), but also when designing the lesson. When the research group has identified what are presumed to be the critical aspects, careful consideration is given to how patterns of variation and invariance can be created to make the critical aspects possible to discern. For example, in mathematics, principles of variation can be used when choosing examples by deliberately and systematically varying the numerals within and between examples (Kullberg, Runesson, & Mårtensson, 2014; Runesson, 2005; Watson & Mason, 2006), or when deciding the sequence of the lesson (Kullberg, Runesson, Marton, Vikström, Nilsson, Mårtensson, & Häggström, 2016).

From a variation theory perspective, learning and teaching are described in

commensurable terms, i.e., learning is seen as a change in the discernment of the object of learning and teaching can be described in terms of what aspects of the object of learning are afforded to discern. The cyclic process of learning study (See e.g., Cheng & Lo, 2013) allows one to analyse students’ learning (i.e., the learning outcomes from the post-test) in light of the enacted learning situation—the lesson. Students’ learning is analysed from the point of view of what is or is not discerned and the lesson(s) from the perspective of what is made possible to discern by means of variation in the midst of invariance. Hence, the critical aspects can be validated, refined, specified and rejected, and/or new aspects can be found and the lesson can be improved to make the critical aspects possible to discern.

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4 GENERATING KNOWLEDGE ABOUT TEACHING AND

LEARNING IN LEARNING STUDY

In the previous section, I argued that learning objectives could not be directly applied to the classroom. Still, this is what teachers are expected to do—to develop students’ knowing of something known, but usually without knowing the meaning of knowing (Carlgren, Ahlstrand, Björkholm, & Nyberg, 2015). They suggest that ‘Learning study is a way to study the meaning of knowing specific objects of learning’ (p. 144). For instance, one expected learning outcome in a syllabus can be ‘to be able to read between the lines’, thus, drawing conclusions about something that is not explicitly expressed in a text. What does it mean to be able to read between the lines? What must be learned to develop this capability? These questions must be answered if one wants to help someone to develop this specific capability. My experience is that teachers, even if they have many years of experience, cannot bring answers to these questions. What they can do, however, is to give examples of activities that they think can promote the development of the capability. In my view, activities can only be decided upon when there is an answer to the question ‘what must be learned?’

The first example comes from a learning study conducted in Sweden in Grades 4 and 5 (Rosenbaum, in progress, 2018). This example shows that one way to find the critical aspects is to take as the point of departure differences in students’ understanding in terms of differences in how a given task is solved. A group of teachers worked collaboratively with a researcher to explore an aspect of reading comprehension: to be able to draw conclusions about characteristics of a principal character in a story. Video recordings from the lessons and students’ written texts included the analysed data. After having read a story, the students had to describe the main character to an actor who had not read the text and who would perform this character in a film. By carefully examining differences between the students’ written texts, the research group identified some aspects that could be critical differences between the different ways the task was solved. This also provided key insights into what was necessary to learn and discern in the text in order to be able to find

characteristics of the protagonist. So, for instance, the researchers found that the students must learn that conclusions can be drawn by interpreting how the protagonist actsby seeing how other

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characters in the story react to the protagonist and/or comparing the protagonist with others in or outside the text. These conclusions were drawn from the pre-test and the lessons were designed accordingly.

Another example which illustrates that finding the critical aspects is an emerging process comes from a learning study of decimal numbers in Grade 6. The object of learning was to understand that decimal numbers are dense (Kullberg, 2012). One task given as a pre- and post-test was the following: ‘John says there are no numbers between 0.97 and 0.98. Is that correct or not? Please, explain your ways of reasoning.’ Very few students answered correctly on the pre-test. From this, the teachers assumed that they had to learn that between any two decimal numbers there are infinite numbers of other decimal numbers. To help the students to learn this, in lesson 1 (the first cycle) the focus was on what were the possible numbers between two numbers, for instance, 0.65 and 0.66, or 0.651 and 0.652. The numbers were only represented numerically as decimal numbers (e.g., 0.65) and verbally, as ‘six point sixty-five’. A number line was used and the different decimal numbers were marked as points on it. The results on the post-test after lesson 1 were very depressing; almost none of the students answered correctly. So, the research group had to

reconsider what was critical and what the students had to learn. When carefully analysing the data, they realised that seeing the rational number, for example, 0.65, only as a point on the number line and represented as a decimal number was not sufficient to understand that the number was dense. Hence, the critical aspects were revised and the next lessons in the cycle were different in terms of what aspects were made possible to discern by means of variation and invariance (Table 1).

[INSERT TABLE I ABOUT HERE]

From Table 1, it can be seen that three aspects were identified as critical: 1) ‘interchangeable representation’; 2) ‘numbers as a part of a whole’ and 3) ‘the divisibility of parts’ (Kullberg, 2010). All these aspects were made possible to discern in lessons 2 and 3 by means of patterns of variation and invariance. In these two lessons, critical aspect 1 (the interchangeable representation) was varied by using different numerical representations. So, for example, numbers such as 0.65 were represented

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as fractions ( 10065 ) and as percentages (65%). Furthermore, it became possible to discern that a rational number was related to a part-whole relation (critical aspect 2) when it was demonstrated that the size of the parts co-varied with the size of the whole (e.g., absolutely, the size of a quarter of one metre is bigger than the size of one centimetre, although the relative size of a quarter is the same). Finally, the divisibility of the parts (critical aspect 3) was made possible to discern when an interval between whole numbers on the number line (e.g., 2 and 3) was successively partitioned into smaller ‘parts’, i.e., tenths, hundredths, thousandths, and so on.

The research group determined that these aspects were critical, based on 1) The progress in learning outcomes on the lesson in the second cycle (in the post-test, almost all students gave a correct answer to the task, vs. after lesson 1, where only a couple could answer correctly); 2) The theoretical conjecture of the variation theory: that which is varied against an invariant

background is made possible to discern. Thus, the pattern of variation afforded specific learning possibilities (Table 1); and 3). The three aspects were similarly opened up as dimensions of variation in two of the (successful) lessons, and this was associated with an almost identical learning

improvement. Thus, the assumed critical aspects were validated in the third cycle.

What these examples illustrate is that applying the variation theory to the process means going into great detail of a specific capability and to specify the object of learning in terms of what is critical for learning. From this, certain understandings can be gained about the nature of the knowing in the reading comprehension and decimal numbers examples above. Such knowledge, I would suggest, is the very core of teachers’ professional knowledge.

The results of exploring such features of the lesson design can challenge and change beliefs about best practices or teaching traditions and praxis. Lindström (2017) reports results from a learning study in English in a Swedish school (Grade 6) which aimed to enhance students’

understanding of and ability to correctly use the progressive aspect. The research group started by exploring the students’ understanding of what the progressive aspect meant. Different ways in which this was experienced were found in the pre-assessment interviews. Many students thought, for instance, that saying ‘he lives’ or ‘he is living’ is a matter of formality, or that adults use the latter.

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Other students experienced no difference at all, which could be a reasonable way of thinking, since, in Swedish, the progressive aspect does not exist. There is no distinction made, for example, between ‘he is living’ and ‘he lives’. Traditionally, in Swedish schools, the progressive aspect is introduced in the present tense (e.g., ‘she is playing ice hockey’, ‘they are going to school’). In the learning study, it was found that the use of the present tense was insufficient. When only sentences in the present tense were used in the lesson, almost no learning progress was made. Therefore, the team had to consider how to change the teaching to help the students to understand the ‘ongoing-ness’ of the progressive aspect. They decided to reverse the conventional order and to start with examples in the past tense. This implied changing the existing praxis, but, to their surprise, they found that it helped the students to generalise the meaning of the progressive aspect. Starting with the progressive aspect in the past tense made it possible for them to experience the progressive aspect as conveying a specific aspectual meaning, separated from tense: the ‘ongoing-ness’ is not related only to the present tense. The research group drew the conclusion that ‘to differentiate between tense and aspect’ and ‘to differentiate between simple aspect and progressive aspects’ were critical for learning.

Furthermore, to discern the concept of the ‘ongoing-ness’ of the progressive aspect and thus, that something is not necessarily happening right now, certain examples were found to be powerful. Examples like ‘she is living in London’ or ‘they are playing basketball in the schoolyard’ may not bring out the incomplete meaning of the progressive aspect. The research group assumed that examples that underscored a clear difference in meaning between something completed and something that was not (yet) completed were needed. Their assumption was verified. The

temporary and open-ended meaning of the progressive aspect was discerned when the two examples ‘he was drowning in the pool’ and ‘he drowned in the pool’ were juxtaposed and compared. The students realised that in the latter sentence there was no hope (‘he drowned’), whereas in the former (‘he is drowning’), there was still a possibility to be rescued.

One can conclude that identifying the critical aspects for learning is closely related to the improvement of teaching and finding how the lesson can be designed to afford learning of the

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critical aspects. By lesson design, I do not mean the organisation or the arrangement of the lesson, but how the content should be sequenced, what must be juxtaposed and what must be varied in the midst of invariance to bring the critical aspects to the fore of students’ attention.

5 THE KNOWLEDGE CONTRIBUTION OF THE LEARNING STUDY

It has been reported how lesson study could impact and change practice (Lewis, Perry, & Murata, 2006). This can also be said about learning study. However, as has been shown in the examples above, it can be concluded that, in comparison with lesson study (as it is commonly reported), learning study focuses on constructing knowledge about objects of learning and teaching-learning relationships. This aim, together with the theoretical grounding of learning study, is a feature it has in common with design research. However, the knowledge product of learning study is not teaching materials or lesson designs, but rather a theoretical description of what must be learned in order to develop a specific capability. The knowledge product of learning study is a contribution to theorising the meaning of objects of learning. The specification of the object of learning in terms of its critical aspects is also a specification of pedagogical actions (Carlgren et al., 2015).

But can such knowledge be claimed as public and general knowledge relevant outside the local context? I would argue that the knowledge generated in the studies referred to above is an example of what Morris and Hiebert (2011) and Hiebert and Stigler (2016) are calling for:

instructional products that can be shared, tested and improved. Shavelson, Phillips, Towne and Feuer (2003) have questioned the knowledge claims of design research (that is also relevant for learning study). They ask: ‘With so many confounding variables in a design study, can the knowledge claims be warranted? (p. 27). They also question what generalisability these knowledge products have. It can also be questioned if using one or a few lessons as a unit of analysis is enough to reach valid results. Stigler and Hiebert’s (2016) argument that the lesson ‘is small enough to represent key components of the system of classrooms, yet large enough to represent key components of

classroom teaching and learning’ (p. 584), together with the very close analysis of teaching and the very specific focus substantiate the validity of learning study in my view. Teachers in different contexts share the same problems, so it can be assumed that they could recognise and make sense

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of research that aims to guide their practice and shed light on these problems. In that sense, the ecological validity would be maintained.

5.1

Putting the results of learning study to the test

That theories about objects of learning can be communicated and used as resources by other teachers in other contexts has been shown in several studies. In one of them (Runesson &

Gustafsson, 2012), results from a learning study in Hong Kong were documented and communicated to a group of Swedish teachers. In order to study how results from a learning study could be

communicated to teachers in a different school context and how these could be used in the classroom, Runesson and Gustafsson (2012) studied three lessons conducted by three teachers in different classes. It was found that the theoretical descriptions of the object of learning identified in Hong Kong communicated well to the Swedish teachers, but that these adapted the insights gained by the Hong Kong teachers to the specific group of learners and other conditions in the Swedish context.

The same finding that specification of the object of learning in terms of its critical aspects had relevance outside the context where they were generated was demonstrated by Kullberg (2010; 2012). In a quasi-experimental study, she tested the validity of aspects identified in a learning study as critical for understanding that decimal numbers are dense (see above). Four teachers taught two lessons to two groups of students. One was taught on the basis of all the identified critical aspects (See Table 1). The other was designed without these critical aspects and was more in line with the first lesson in the learning study cycle. The learning outcomes in the follow-up study reflected the learning outcomes in the original learning study. Just like in the learning study, in the follow-up study, the greatest learning gains were found when the identified critical aspects were enacted as patterns of variation in the lesson. Kullberg (2012) notes, however, that, although the same critical aspects were bought to the fore of students’ attention by means of patterns of variation, the lessons were different in many other respects (e.g., organisation and representations used). Kullberg’s study suggests that the identified critical aspects are critical to develop a capability and specific knowing, thus they are features of the object of learning. The same

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is indicated by Runesson, Lövström and Hellquist (2018). They tested critical aspects for ‘realizing the existence of negative numbers’ identified in a learning study in Grade 2 in eight classes. The teachers were initially informed about the critical aspects in a meeting with the researchers. Short video clips from the lesson showing how the critical aspects were enacted as patterns of variation built into the examples given to the students were presented. The teachers were instructed to feel free to arrange the lesson as they liked, as long as the critical aspects were embedded as patterns of variation in the design of examples. When the results from the pre- and post-assignments were analysed, it was found that the improvement of students’ performance in the ’replication lesson’ reflected the improvement in the learning study lesson. Runesson, Lövström, and Hellquist (2018) suggest not only that the identification of critical aspects and embedding them as patterns of variation affect students’ learning, but also that these are relevant beyond the local context.

6 FINAL COMMENTS

Using learning study as an example, in this article, I suggested how research could address the problems of the disconnection between research and practice. One suggestion is to make problems that teachers face in their everyday practice the object of research. Without addressing teachers’ professional challenges, research is unlikely to ‘speak’ to practice. One defining feature of learning study is exactly this: the very point of departure is something the students find difficult to learn and teachers difficult to teach. The aim is to solve these problems. The results of learning study suggest a specification of the objects of learning in terms of what to teach—the critical aspects— and

pedagogical actions (how to open these aspects as dimensions of variation) to overcome such problems. As such, the contribution is both theoretical and practical.

Another possibility suggested to close the research - practice gap is to actively involve teachers in the research process, not only in executing and implementing ideas coming from the researchers (Adamson & Walker, 2011), but also in a genuine process of collaboration where the researcher and the teachers have a shared and common object of research. To generate knowledge that is relevant for their professional tasks, teachers must be included as interpretative professionals

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making professional sense of particular educational events in the research (Carlgren, 2012). In learning study, teachers are involved in the collaboration in this way; their experience and tacit knowledge are considered to be necessary and to contribute to the research process and subsequently to the results as well (Thorsten, 2017).

In learning study, theory has a specific role. It serves as a guiding principle for analysing learning and is used for analysing and designing teaching. The variation theory is a general theory for learning. However, it asserts some necessary conditions for learning. It does not say anything about how to learn and teach a particular object of learning. Therefore, in learning study, it must be applied to every specific content and group of learners. The variation theory is used as an analytical tool in the process and thus must become a ‘lived theory’ among the teachers. The theory provides them with a language, the jargon of the variation theory, to talk about teaching and learning in theoretical terms. When teachers in this way make the theory their own, it is most likely that the theory -practice gap will be closed.

NOTES

1 With ‘capability’ I do not refer to general capabilities, but to content-specific skills or ways of knowing.

2 For example, a child can show six fingers (one hand and the thumb) and when asked “What is six?” the

child points to the thumb (the sixth finger), This is interpreted as experiencing number words describing “the nth” object, thus without cardinal meaning (Björklund, Kullberg, & Runesson, 2018).

REFERENCES

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Björklund, C., Kullberg, A., & Runesson Kempe, U. (2018). Structuring versus counting - Critical ways of using fingers in in subtraction. ZDM Mathematics Education doi: 10.1007/s11858-018-0962-0 Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2, 141-178. Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017). Making classroom implementation an integral part of research. Journal for Research in Mathematics Education, 48, 342-347. doi: 10.5951/jresematheduc.48.4.0342

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TABLE 1. The identified critical aspects and the pattern of variation enacted in cycles 2 and 3 in the learning study (Kullberg, 2010; 2012).

Critical aspect Vary Invariant

The interchangeable

representation Numerical representation (fraction, decimals, percentage)

Number, e.g., 0.65

The number as a part of a

whole The whole Number

References

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