Variation Theory and the Improvement of Teaching and Learning

Citation

Isak, G. and Posch, P. (2013), "Variation Theory and the Improvement of Teaching and Learning", International Journal for Lesson and Learning Studies, Vol. 2 No. 2, pp. 188-194. https://doi.org/10.1108/20468251311323414

“Learning studies improve students’ learning of particular objects of learning, enhance the professional development of teachers, improve teacher collaboration and help to promote a learning culture that facilitates the development of the school as a learning community” (Lo, 2012, p. 198). This is a strong claim. Let us have a look at each aspect of this statement. Our contribution has two parts. The first part is a summary of the main contents of the book. The second part is a discursive comment on selected aspects of the book.

Part 1: summary of the main messages of the book

“Learning study” is one of many examples of innovations which initially have been conceived in Europe and have been implemented and further developed in the Far East and slowly appear to come back to Europe. Its theoretical core (variation theory) was developed by Ference Marton who was Professor at Gothenburg University in Sweden. The educational implementation of this approach (learning study) was developed and tested by Marton, Mun Ling Lo and others at the University of Hong Kong. They adapted the procedures of Japanese Lesson Study and developed a conceptual framework based on variation theory and renamed it “Learning study”.

Here are some essential concepts of variation theory as elaborated in the book:

1. (1)

   A generic term in variation theory is “ways of seeing”. Learning is regarded as a change of seeing a phenomenon or an object of learning. “Teachers must help students to develop powerful ways of seeing if they want to improve the students’ capability to solve problems or deal with new issues […]” (p. 21).

2. (2)

   If teachers wish to help students to see the object of learning the same way as they do, they must first try to uncover students’ own “natural” ways of seeing the object and the differences between their views and those of the students (p. 21).

3. (3)

   Then they have to help students to develop a relationship to the object of learning because it influences the way a student responds to a learning situation. In the terminology of variation theory the teacher has to build a “relevance structure” between the students and the object of learning (p. 23).

4. (4)

   If teachers want students to see an object in exactly the way they do, then students must be able to focus on the same features of the object that they do (p. 65). As any object has many features students must focus on those features that are critical to a certain way of seeing. In the terminology of variation theory these are the “critical features” of an object of learning (p. 27). The critical features and their relationship to each other and to the whole of an object of learning are called the “internal horizon of learning”, whereas the context which provides meaning to an object of learning is termed “external horizon” (p. 24). Lo provides a number of methods to identify critical features of an object: literature review, sharing past experience of teaching the topic with other teachers, interviewing students, administering a diagnostic pre‐test and post‐test and analyzing the students’ responses, observing lessons taught by another teacher and listening to students during the lesson to find out how they see the object of learning (p. 70f). Teachers must have a deep understanding of basic concepts and the knowledge structure of the discipline they teach, including the relationships among the concepts (potentially critical features and aspects) (p. 71).

5. (5)

   An object of learning has two aspects: “a specific aspect which refers to the subject matter, knowledge or skill that we wish students to learn (short term goal or “direct” object of learning), and the general aspect, which refers to the capabilities that can be developed through learning of the specific aspect (long‐term goal or “indirect” object of learning)” (pp. 25, 52). The quality of learning outcome is heavily dependent on the teacher's choice of the indirect object of learning (p. 51).

6. (6)

   A central claim of variation theory is that the actual learning process is dependent on variation (p. 29). To discern an object from its context and distinguish it from other objects, we must experience variation of the object. If certain aspects of an object are varied and certain aspects are kept constant, new aspects of an object can be discerned and new meanings constructed. This hypothesis lies at the heart of variation theory and is supported by various empirical studies (p. 29). Teaching is the creation of patterns of variation that allow students to discern the critical features of an object of learning (p. 30f). This – it is claimed – is a necessary condition of learning (p. 83). The book is full of examples in different subject areas and levels of complexity.

7. (7)

   The following sequence of phases of a learning process is suggested in the book:

   • •

     Learning should start with the learner's encounter with the undivided whole of an object of learning and the teacher should first help students to separate the object from its context. Thereby a “relevance structure” can be created, a specific relationship between student and object (pp. 91, 97).

   • •

     Critical features of an object are discerned by experiencing the difference (variation) between two values as contrast. Contrast is produced by examples and non‐examples but also by experiencing variation between prior knowledge of students and seeing the same thing as intended by the teacher (p. 85f).

   • •

     When the learner becomes aware of a value by contrasting it with another value (e.g. male vs female), one can say metaphorically that the value is separated from the object, and a dimension of variation (e.g. gender) is opened up (p. 90).

   • •

     If a focused value (e.g. a triangle) is kept invariant while other aspects that are not critical (e.g. size and types of triangles) are systematically varied, the focused value is generalized (p. 93).

   • •

     Sometimes the understanding of an object depends on the simultaneous awareness of several critical aspects and how these aspects relate to each other and to the object as a whole. Fusion takes place if the dimensions of variation that correspond to the critical aspects are varied simultaneously (p. 96).

Since 1990 several hundred learning studies have been implemented and evaluated in the context of large research projects. Evaluation of the VITAL project, e.g. showed that only two of over hundred Learning Studies were unsuccessful and could not be completed – mainly due to a lack of support among school leaders, no consideration being given to reducing teachers’ workload or the Learning Study being led by inexperienced researchers or academics (p. 29). We were intrigued by the high impact of the projects on students’ learning and on the professional development of the participating teachers. The most remarkable finding for us was that low score pupils showed significantly more progress than high score pupils. This means that the gap between high performers and low performers narrowed. For Lo this finding was not particularly surprising, because it was part of the idea of a Learning Study to identify what caused students’ difficulties in learning a particular object of learning and its critical aspects so ways could be found to help students to overcome these difficulties (p. 34).

Part 2: comment on selected issues of the book

The following comments refer to some of the central elements of the concept of learning studies as exemplified in Lo's book. We organize them as a kind of dialogue between the two authors of the review: Gabi Isak, who is a teacher at a secondary school and presently seconded to the Institute of Instructional Research and School Development (IUS) of the School of Education of the Alpen‐Adria‐University Klagenfurt, and Peter Posch, who is retired Professor of Education and associate member of IUS.

Peter: Feedback from students to teachers is an important general principle of variation theory. “Teaching must […] begin with finding out students’ prior understanding of the object of learning […] We must know how students understand the object if we are to change their ways of seeing or understanding that object or phenomenon” (p. 105). This view corresponds to a surprisingly high degree to the findings of the largest meta‐analysis of educational research: the synthesis of over 800 meta‐analyses relating to achievement by John Hattie (2009, p. 173): formative feedback was found to be the most effective instructional intervention. “Feedback to teachers makes learning visible […] When teachers seek or are at least open to, feedback from students as to what students know, what they understand, where they make errors, when they have misconceptions, when they are not engaged – the teaching and learning can be synchronized and powerful”. It seems however, that formative feedback is difficult to introduce into the professional culture of teachers. Why is it so difficult? Is the refusal of feedback from students a psycho‐hygienic aid to forget about the huge gap between intended and real effects of teaching?

Gabi: It is true that many teachers do not even think of using student feedback to develop their own teaching or evaluate the students’ learning process. In my opinion, the reasons for that are lack of time and other factors which reduce actual teaching time such as administrative and organizational duties. But times are changing: Feedback culture is becoming more and more important even in German‐speaking countries. A new German publication “Warum fragt ihr nicht einfach uns?” (Why don’t you just ask us? by Berger et al., 2013) is typical for this trend. In our own teacher training courses feedback is one of the main tools used by the participating teachers to professionalize their teaching practice.

Peter: Most complex examples which Lo presents (e.g. the “electrochemical series”, p. 134ff, or the “cause of seasons”, p. 144ff) show that critical features can hardly be identified without a diagnosis of learning difficulties of students. “Critical features are critical precisely because learners have problems with them. The critical features of an object of learning must thus always be empirically determined.” On the other hand, she writes: “Through an in‐depth study of the object of learning, the sharing of teaching experience among teachers, discussions and literature reviews, most of the critical features of an object of learning can be found” (p. 71). This implies that critical features can be identified also per se apart from the concrete interaction with students which is illustrated by many examples in the book. It seems that the study of the critical features of learning objects could be a promising focus of initial teacher education.

Gabi: I think the study of critical features might even be an important aspect in subject‐related educational research, but as far as I know, this has not been done yet. It might improve content knowledge in initial teacher education, but also in in‐service teacher education. It would need more investment in subject‐related educational research, which is still a very young academic discipline in Austria. Variation theory offers valuable support for the further development of this discipline.

Peter: Lo claims that critical features of a learning object cannot be discerned without detailed knowledge of subject matter. “Teachers must teach subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge” (p. 107). “Teacher clarity” (e.g. the quality of explanations and examples) is another highly effective teaching quality that John Hattie (2009, p.125f) has identified. This finding supports to a high degree the hypothesis of learning studies that a prime task of teachers is the identification and teaching of critical features of a learning object. The substantial role of teachers’ content knowledge (CK) together with pedagogical content knowledge is also confirmed by Baumert et al. (2010, p. 168). They report findings from a one‐year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Their theoretical assumption was that pedagogical content knowledge (PCK) is inconceivable without a substantial level of CK but that CK alone is not a sufficient basis for teachers to deliver cognitively activating instruction that, at the same time, provides individual support for students’ learning. Findings have substantiated this assumption. Limited mathematical understanding of the content had detrimental effects on PCK and consequently negative effects on instructional quality and student progress. Such findings are a challenge for teacher education. Some experiences have already been documented (e.g. Lai and Lo‐Fu, 2013). Can learning studies act as an integrating factor for the design of teacher education?

Gabi: Lo explains quite convincingly that only teachers with a high degree of content knowledge will be able to discern critical features of an object of learning and will then be able to offer variation. Our university courses for in‐service teachers (Altrichter and Posch, 2009) are focused on Action Research in order to lead teachers to a high degree of self‐reflection. In this context the joint development of PCK and CK provides a basis for instructional experiments. It could be an important future project to implement such design elements also in initial teacher education. Teacher education should become an example for the kind of instruction that is later expected from teachers.

Peter: Learning communities are an indispensable precondition of learning studies. In Lo's book the existence of professional communities is taken for granted and obviously have been common in all of the projects in which learning studies were evaluated. If the professional communities are a necessary condition, it is unlikely that learning studies will flourish in central European countries in the near future. In German speaking countries, e.g. professional communities are not an element of school culture. The culture of many schools can rather be characterized by a mind‐set which Lortie (1975) called “autonomy‐parity‐pattern” by which two rules are considered crucial for smooth interaction between teachers: First, no grown‐up person should interfere in a teacher's classroom (“autonomy”). Second, all teachers are to be treated equally, regardless of their actual competencies, energy invested, and qualities displayed (parity). Lo is not very explicit about the part which was played by the professional communities in which the teachers participated. Practically all examples are taken from externally supported research projects. Can learning studies develop in a culture of “lone fighters”? What kind of infrastructure is necessary at school level and what regional support structures are necessary? Such issues are extremely important if learning studies are introduced into mainstream education.

Gabi: Learning Studies are obviously an effective platform for the professional development of teachers and highly dependent on teacher cooperation. The practical non‐existence of professional communities responsible for joint instructional development is a serious handicap for introducing Learning Studies in Austria. However, we do have teacher training courses where teachers reflect their own practice and work together in small teams to design and evaluate teaching units (Altrichter and Posch, 2009) and we have networks for the professional exchange of experience among teachers. It will take a long time for professional communities to become part of the Austrian educational culture as much as they seem to be in Hong Kong. Much could be learned from the Japanese tradition in which novice teachers are apprenticed into the profession through participation in a lesson study group. Thereby an identity is formed which regards lesson studies as a self‐evident feature of professional activities (Murata, 2011).

Peter: Lo stresses the difference between object of learning and learning objective and sees two problems in the specification of learning objectives: Teachers may feel under pressure to gear their teaching to assessment items, which would distort the true purpose of education (p. 41f). And specifying end results of learning would neglect the “dynamic nature” of the object of learning and would actually limit students’ learning outcomes. For Lo it is “better to pay attention to and try to influence teaching and learning directly rather than hoping to influence the teacher's teaching and the students’ learning by means of changing the assessments” (p. 42). This is a key statement in her book, but is it really an argument against attempts to specify intended learning outcomes and assessment procedures to ensure that teachers and students pay attention to them? In German‐speaking countries, the results of international comparative assessments such as TIMSS, PEARLS and PISA were eye openers with respect to the problematic sides of the educational systems and stimulated a great number of educational reforms, among them also the specification of educational standards because there was an expectation that standards would reduce widespread “laissez faire” in teaching and learning. Furthermore, is there such a big difference between Lo's definition of the indirect object of learning (what the learner is supposed to become capable to do with the content) (p. 50) and the definition of educational standards?

Gabi: There may be no formal difference but a considerable difference in its impact in learning. Standards are static instruments whereas Lo stresses the “dynamic nature” of the object of learning, developing as teachers adjust to students’ reactions. Standards interfere with this learning process of teachers and students. At the same time we have to cope with standards and standards‐based tests. The introduction of learning studies might act as a kind of counterweight to balance out some problematic effects of standards.

Peter: Variation Theory promotes a specific view of learning motivation focusing on the relationship between students and the object of learning: the “relevance structure” (p. 115f). The basic idea behind this is that the meaning of an object of learning for the students’ life experience will affect their motivation to deal with it. This is an important and convincing feature of variation theory but Lo does not say how teachers could provide opportunities for students to develop a favorable relevance structure, perhaps with the exception that the students’ intuitive approaches to objects of learning are taken serious. Learning motivation is an absolutely “critical feature” of any learning process. I suspect that it is not such a problem in the Far East as it is in many European countries.

Gabi: I agree that it may be more difficult to create a relevance structure in our country. We are often faced with classes where students are not interested in learning objects at all and do not want to learn anything. They appear to be saturated and see little function of learning in their lives. The reasons are partly social: competition by web2, smart phones and other social media but also low respect for teachers by students and parents and generally the low status of education in society. I doubt that such influences can be compensated by Lesson Studies. But if anything, Learning Studies would offer a new perspective on the serious problem of motivation.

Summary

Lo's book is an excellent introduction to Learning Studies and to its theoretical basis Variation Theory. It provides a great number of examples of different subjects and age levels. Lo admits that there are not yet enough studies in each subject to generate sufficient examples to generalize the findings (p. 199). However, the examples which she provides illustrate the strength of Variation Theory for nearly every curricular area. Learning Study is a rich occasion to learn for students and teachers but also a challenging and worthwhile occasion to further develop its theoretical basis by researchers. It is not a new instructional method but a new conceptualization of the prime task of teachers which is compatible with many methods. Learning study also provides new and demanding resources for educational action research: “The transmission of the cultural legacy is not a one way process. It requires teachers also to become engaged as learners in the creative process of extending and adapting the cultural meanings presented to their students as objects of learning” (Elliott and Tsai 2008, p. 571). Hattie (2009, p. 22; see also p. 24) sounds quite similar: “The remarkable feature of the evidence is that the biggest effects on student learning occur when teachers become learners of their own teaching”.

About the authors

Gabriele Isak is a secondary school teacher presently seconded to the Institute of Instructional Research and School Development (IUS) of the School of Education of the Alpen‐Adria‐University Klagenfurt.

Peter Posch is a retired Professor of Education and associate member of the IUS. Peter Posch is the corresponding author and can be contacted at: Peter.Posch@aau.at