Theorising teaching and learning: pre-service teachers’ theoretical awareness of learning

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Theorising teaching and learning:pre-service teachers’ theoreticalawareness of learningGöran Brantea, Mona Holmqvist Olandera, Per-Ola Holmquistb &Marta Pallab

a Department of Pedagogical, Curricular and Professional Studies,Gothenburg University, Gothenburg, Swedenb School of Teacher Education, Kristianstad University,Kristianstad, SwedenPublished online: 03 Apr 2014.

To cite this article: Göran Brante, Mona Holmqvist Olander, Per-Ola Holmquist & Marta Palla (2015)Theorising teaching and learning: pre-service teachers’ theoretical awareness of learning, EuropeanJournal of Teacher Education, 38:1, 102-118, DOI: 10.1080/02619768.2014.902437

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Theorising teaching and learning: pre-service teachers’ theoreticalawareness of learning

Göran Brantea*, Mona Holmqvist Olandera, Per-Ola Holmquistb andMarta Pallab

aDepartment of Pedagogical, Curricular and Professional Studies, Gothenburg University,Gothenburg, Sweden; bSchool of Teacher Education, Kristianstad University, Kristianstad,Sweden

We examine pre-service teachers’ theoretical learning during one five-week train-ing module, and their educators’ learning about better lecture design to fosterstudent learning. The study is iterative: interventions (one per group) wereimplemented sequentially in student groups A–C, the results of the previousintervention serving as the baseline for the design developed for the next. Theselearning study participants, 79 students from year three of a teacher training pro-gramme, studied the variation theory (VT) of learning. Three lesson cycles werecompleted, each comprising four steps: (1) a pre-test, (2) a 15-min interventiondiscussing VT, (3) a post-test and (4) a delayed post-test conducted eight weekslater. The results indicated learning differences between groups; qualitative anal-ysis identified three categories of student answers, i.e. emergent, premature andunaware, regarding their theoretical understanding. Group C had more studentswith emergent knowledge (36%) than did groups A (20%) or B (17%) atpost-testing.

Keywords: teacher education; learning study; variation theory; object oflearning; critical aspects of learning

Introduction

Teachers’ theoretical knowledge of learning is crucial not only for their teaching butalso for developing their pupils’ learning (Gustavsson 2008; Holmqvist 2011).Lunenberg and Korthagen (2009), when studying how practical wisdom relates totheory and experience, noted that it was difficult for pre-service teachers to find arelevant theory explaining their practical wisdom at a conceptual or generic level.Lunenberg and Korthagen (2009) claim that shorter-duration teacher education mod-ules can be effective, but that implementing them requires considerable expertise tomake connections between theory and practice:

Finally, an even higher level of expertise is needed not only to take care of this connec-tion, but to help novice teachers in developing their own insight into this connection,and to promote their capacity to keep making this connection over and over again intheir future careers. (Lunenberg and Korthagen 2009, 238)

A lack of scientific perspectives on learning and instruction can lead to an absenceof instruction based on theoretical understanding of what is necessary for learning

*Corresponding author. Email: [email protected]

© 2014 Association for Teacher Education in Europe

European Journal of Teacher Education, 2015Vol. 38, No. 1, 102–118, http://dx.doi.org/10.1080/02619768.2014.902437

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mailto:[email protected]

http://dx.doi.org/10.1080/02619768.2014.902437

and a focus on teaching at a procedural instead of a conceptual level. Rittle-Johnson,Siegler, and Alibali (2001) claim that conceptual and procedural knowledge developiteratively. However, teachers in the West more frequently address methods (i.e. pro-cedural knowledge) than content (i.e. conceptual knowledge) when planning theirlessons than do, for example, teachers in South-East Asia (Carlgren and Marton2000; Holmqvist and Wennås Brante 2011). Lack of a theoretical understanding orgeneric perspective at the conceptual level (e.g. regarding what is necessary forlearning), replaced by skill in using various teaching methods, results in a situationin which teachers have many practical tools or methods but no general knowledgeof when particular tools are appropriate. This could result in the weak integration ofprocedural and conceptual knowledge. Instead of scientific theories of learning, stu-dent teachers bring their own lay theories into their teacher education and their ownexperiences of what is necessary in learning and instruction (Sugrue 1997).

It becomes necessary, therefore, to ask: how can initial and ongoing professional devel-opment initiate, support and promote a dialogical conjugation between lay theories,their attendant teaching identities and the broader horizons of teaching and schoolingprovided by research-based approaches to professional growth and renewal? (Sugrue1997, 221)

Agbenyega (2012) notes that the pre-service teachers he studied significantly lackedcompetence in applying learning and developmental theories: this lack weakenedtheir reflection on practice, meaning that their understanding of learning was not thepoint of departure when planning their teaching.

Some of the pre-service teachers in this study indicated that they do prepare their les-sons according to specified requirements and yet they hardly consider theories whenpreparing lessons. (Agbenyega 2012, 145–146)

Gustavsson also found that ‘teachers directed their awareness first of all to differentmethods without connection to the lesson content’ (2008, 160). When planning les-sons, both pre-service teachers and teachers focus mainly on methods, classroomorganisation and relationships with students. Although these are important aspects oflesson planning in order to provide a positive learning environment (Brante 2008;Carlgren and Marton 2000), it is problematic if focusing on them distracts teachersfrom a conceptual focus on what is to be taught, that is, the object of learning.

Furthermore, when pre-service teachers develop their theoretical understanding,they must also understand the relationship between the students’ understanding ofthe content to be learnt and the object of learning (Lo and Marton 2011), as teachersmust ‘live’ the theory in the classroom. This matter is not treated in lay theories butcan be understood in terms of Reckwitz’s (2002) reasoning about practice theory,which is

… knowledge that is more complex than ‘knowing that’. It embraces ways of under-standing, knowing how, ways of wanting and of feeling that are linked to each otherwithin a practice. In a very elementary sense, in a practice the knowledge is a particu-lar way of ‘understanding the world’, which includes an understanding of objects(including abstract ones), of humans, of oneself. (Reckwitz 2002, 253)

One aim of teacher education is to base teaching practice on theoretical perspectives.During teacher education, pre-service teachers are introduced to various pedagogical

European Journal of Teacher Education 103

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theories. To understand the context in which the present study was conducted, wefirst briefly describe Swedish teacher education, which differs from teacher educa-tion in other countries and cultures. Swedish teacher education was a university pro-gramme at Bachelor/Master of Education levels until 2011, when it was changed toa programme of university-level professional degrees at the graduate level:

In its bill ‘Top of the class – new teacher education programmes’ (Govt. Bill 2009/10:89), that was passed by the Riksdag in April 2010, the Government proposed thatthe degree of Bachelor/Master of Education should be replaced by four new profes-sional degrees: a degree in pre-school education, a degree in primary school education,a degree in subject education and a degree in vocational education. There has been acancellation of the requirement in the Higher Education Act that there should be a spe-cial body responsible for teacher education and for research associated with such edu-cation at higher education institutions that have the right to award degrees ineducation. The new education programmes started in the autumn of 2011. (EuropeanAgency for Development in Special Needs Education 2013)

As the present research was conducted in 2010, and the studied students were stillexpected to obtain a Bachelor/Master of Education degree, during their educationtheir theoretical understanding of the conditions for learning was considered asimportant as their teaching skills. The combination of the two types of professionalknowledge is supposed to strengthen the student teachers’ professional development.Finnish teacher education, which also emphasises theoretical studies, devoting aboutone-third of total study time to them (Hellgren 1988), strongly integrates theoretical,subject-specific, pedagogical and practical studies to develop educators with a holis-tic understanding of effective teaching and learning.

Swedish teacher education incorporates periods of vocational training in shortermodules during the programme, starting in the first or second semester. This differsfrom teacher education in which students initially study theory and research, begin-ning field experience in the classroom only later in the training (Carlson 1999). Asecond main characteristic of Swedish teacher education is that the teacher educatorsare supposed to have doctoral degrees and to conduct research as well as teach pre-service teachers, in line with Livingston, McCall, and Morgado’s (2009) suggestionsregarding teaching as evidence- or research-based profession.

Previous findings

Holmqvist (2011) found that how teachers define learning affects their actions, andthat teachers are convinced that learning occurs due to these definitions. For exam-ple, some teachers understand the sociocultural theory of learning as maintainingthat communication and group work guarantee learning, as they convert theoreticalassumptions into classroom action. However, sociocultural theory itself makes nosuch claims. The principle of collaborative learning does not mean that learningmust be done through student collaboration, as collaboration in itself does not ensurelearning, nor does the principle make assumptions as to what is learned by each stu-dent. It is important to ‘avoid the ‘epistemic fallacy’ of transposing ontological mat-ters into epistemological ones’ (Sayer 2000, 90) and to acknowledge thatepistemological approaches are theories and not praxis. Learning is always about‘something’, and this ‘something’ must be handled in various ways that do notensure learning as such. A teacher who believes that lecturing is the best way to

104 G. Brante et al.

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teach will feel satisfied after having lectured, regardless of the content of the lectureor the responses of the students listening to it. Such simplistic understandings ofhow learning theories are translated into classroom action do not help students learn:they take conceptual knowledge of learning, and make it into procedural knowledgethat does not do the theory justice.

The results of a pilot study (Brante and Holmqvist, forthcoming) indicate thatstudent teachers choose certain features of various learning theories that they recog-nise in their everyday work and mix them to form their own home-made theories.Student teachers seem not to embrace any one theory in its entirety or to discern dif-ferences between theories; instead, they take parts of various theories, and under-stand and combine them in new ways – their own ways – that diverge more or lessfrom the actual intentions of the original theories.

When discussing learning in general, it is understood that the degree to whichteachers use students’ prior knowledge, understanding, experience and ability tohandle objects of learning as points of departure in lesson planning (Shulman 2000)affects student ability to learn. In a learning study (LS) about using fractions whenstudying home economics (Brante and Brunosson, forthcoming), the problem forsome students was their lack of understanding of the concept of doubling. Althoughthe presupposed critical aspects of fractions were considered when planning theinstruction, when enacting the object of learning, not all students could graspthe information because they lacked the necessary prior understanding to follow thelesson. Learning is always about something, and the learner always has some kindof pre-understanding that must be taken into consideration in a learning situation. Inthe present study, the pre-service teachers’ object of learning is variation theory(VT).

Variation theory

This theoretical framework assumes that learning means being able to discern newaspects of an object of learning, to see it in a new, more developed way. It is usedby teachers to design instruction in relation to learners’ prior knowledge (Martonand Tsui 2004) and by researchers to design educational design studies (Holmqvist,Gustavsson, and Wernberg 2008). The principle of variation builds on similaritiesand differences between aspects of the content to be learnt (Lo and Marton 2011).To discern new aspects, one must experience variation of previously discernedaspects. For example, it is seen as necessary to see a variety of colours to discernthe concept of colour: if we were presented with only one colour, we might not dis-cern the concept at all. All objects consist of several aspects to be discerned; how-ever, discernment is based on being confronted with both variation and invariance,and if all aspects of an object vary, discernment will be difficult or impossible(Holmqvist 2011). A very young child learning what ‘mummy’ means may becomeconfused when he or she is at preschool, since all women leaving or retrieving chil-dren seem to be called ‘mummy’. The child may conclude that ‘mummy’ refers toall women and so will call every woman ‘mummy’ for a short period. When thechild understands that only a woman’s own children call her ‘mummy’, invarianceis discerned. When this invariance is recognised, the child knows what woman he orshe may call ‘mummy’.

With reference to more complex objects of learning (e.g. learning theories) or toabilities, learners need to consider various features and values as well as parts of


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wholes and wholes in different contexts. A learning theory can be discerned basedon its defined features; accordingly, in VT it is crucial to discern that the criticalaspects of an object of learning can be discerned by means of contrast, generalisa-tion and fusion. Contrast concerns the ability to distinguish one phenomenon fromanother, for example, by understanding what differs between a feline and a canineor to discern what something is by knowing what it is not. This ability makes it pos-sible to distinguish various phenomena from each other and to separate the aspectsthat characterise a phenomenon. Generalisation concerns the ability to grasp what issimilar between various phenomena, for example, being able to compare a lion to acat in the case of felines. This ability also makes it possible, by discerning differentrepresentations of the same phenomenon, to identify what is general among them.Fusion, finally, ‘allow[s] simultaneous variation in all aspects of the object of learn-ing’ (Lo and Marton 2011, 11). This is accomplished in a learning sequence startingwith the undivided whole, continuing by distinguishing various aspects one at atime, and ending in fusion, a sequence intended to help the learner discern cats ordogs simultaneously even when their representations vary in terms of characteristicssuch as size and colour. By discerning what an aspect of the object of learning isnot, or what defines an object of learning, a conceptual understanding of the contentis developed. In fusion, several aspects vary simultaneously, both the whole and itsparts (i.e. different aspects) being presented at the same time. The discernmentchanges over time and in relation to the aspects presented, as every object of learn-ing is part of a system and every learner changes during the learning process. Loand Marton maintain that ‘discernment, simultaneity, and variation (or difference) gotogether’ (2011, 10).

The relationship between students’ prior knowledge and experiences and theintended object of learning is therefore important. To create an effective learning sit-uation, the intertwined relationship between the learner and the object of learning iscentral: a person’s non-dualistic experience of a phenomenon is unique and impossi-ble to disassemble. Aspects already discerned by the student are seen as not critical,but those yet to be discerned are critical for further learning. Based on this knowl-edge, the teacher designs his or her presentation of the intended object of learning.

In learning situations, the object of learning appears in three different forms: theintended, enacted and lived objects of learning (Holmqvist, Tullgren, and Brante2011). The intended object of learning is what the teacher plans to offer the studentsto discern, while the enacted object of learning is how the object of learning is actu-ally presented and discussed in the learning situation. Finally, the lived object oflearning is the outcome of the learning situation, in the form of a demonstratedunderstanding of the content.

In a learning situation, a specific object of learning is intended to be learned.According to VT, it is essential to focus on the structure of the content and the pat-tern of variation of the object’s aspects enacted in the learning situation. However,the enacted focus in a learning situation can easily shift from the intended object oflearning to something else, as may occur, for example, when a preschool teacherwho intends to teach children the difference between size and number instead startstalking about feelings about the representations (e.g. teddy bears) used in the learn-ing situation (Holmqvist, Tullgren, and Brante 2011). In a situation like this, despitethe preschool teacher’s intentions, the children’s attention will eventually be divertedfrom the intended content towards something else. What is intended to be taught insuch a situation is not obviously or securely connected with what is enacted or with


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what is actually learned (i.e. lived) by the students in that situation (Lo and Marton2011). The lived object of learning, i.e. what the students actually learn, is a func-tion of both the intended and enacted objects of learning. The intended object oflearning is adapted to the students’ prior knowledge, so the enacted object of learn-ing changes in some respects in the classroom. New features, critical for the stu-dents’ learning, appear while others disappear.

Method

There have been two main traditions in studying teachers and teaching in recent dec-ades: the psychometric and phenomenological perspectives (McQualter 1985). Basedon phenomenological research, the phenomenography approach (Marton 1981,1986) has evolved with a focus on people’s qualitatively different experiences of thesame phenomenon. In the present study, a phenomenographic-inspired approach wasused when the pre-service teachers’ expressions of the same phenomenon, i.e. VT,was studied, qualitatively categorised and described. Their expressions were catego-rised and the qualitative differences between their experiences were studied throughpre-, post- and delayed post-essays. Three different designs, used to explain the the-ory during a lecture, were implemented in three different groups of students; in allother parts of the module the students were offered the same learning aids. Thisapproach was intended to help pre-service teachers develop their knowledge of acertain learning theory, i.e. VT. By offering contrasts between different theoreticalperspectives during the interventions, VT was described in relation to constructivistand sociocultural theory, with which the pre-service teachers were already familiar.This approach was intended to make it easier for the students to identify the charac-teristics of VT by highlighting similarities and differences among the three theories.By focusing on those aspects of learning on which VT is based (e.g. a focus on con-tent, while keeping method/procedural knowledge in the background), the criticalaspects students must discern in order to learn the content, and how the aspects ofthe object of learning are handled and varied in a learning situation, thereby becamediscernible to the learner. We expected that the student teachers would be able todiscern what VT is and is not.

The method used to collect data on the interventions in the present study was the‘LS’, a kind of ‘lesson study’ (Lewis 2002) with systematic and iterative steps bothto collect data and to change practice so as to improve learning (Holmqvist,Tullgren, and Brante 2011; Lo and Marton 2011). In this model, the teacher worksin a team with other researchers and/or teachers to form a collective critical groupthat jointly develops and refines the interventions. Other studies in this tradition con-ducted by teacher/researchers studying their own work, but without the collaborativeaspect, have aimed to change teaching practice and influence student learning(Pienaar and Lombard 2010).

A LS starts with pre-lesson meetings with the teachers. The teachers choose ateaching area that they have found difficult to teach and that they want to study andbetter understand. During the pre-lesson meetings, the teachers also design a lessonand test to measure student progress during the interventions. The interventions con-sist of three parts: a pre-test, a lesson and post-test and a delayed post-test, in thiscase eight weeks after the intervention. After each intervention, a post-lesson meet-ing is conducted in which the teachers discuss and analyse the video-recorded lessonand the learning outcome. The benefits of video recording in helping students


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improve their understanding of the classroom have frequently been exploited forthree decades (Harris 1983), but this time video recording was used in the teachertraining programme instead. The aim of the post-lesson meeting is to design arevised lesson, in an attempt to devise a lesson that facilitates student learning betterthan the previous one. Each intervention was administered to a different, but equiva-lent, group of learners. In this LS, the pre-test was designed to capture how studentteachers understood VT; previous experience of teaching pre-service teachers indi-cated that they find it difficult to understand this theoretical framework. We assumedthat they would initially (in the pre-test questions) write mainly about variation ofmethod, student engagement and/or educational context, avoiding the issue of sub-ject-area content; this assumption is supported by previous research (Agbenyega2012; Gustavsson 2008). Of the few student teachers (i.e. 9 of 79) who expressedideas close to those of VT on the pre-test, at least one had probably read parts of thetextbook in advance, as the examples she cited were similar to those found in the lit-erature (Holmqvist 2006).

Participants

The participants were from the third year of a teacher education programme. Thestudent teachers (n = 79) were divided randomly into three groups, i.e. A = 30,B = 24 and C = 25. The number of subjects was the same in all tests. We did notconsider gender, as only seven male students were studied. The same teacher educa-tor taught all three groups.

Data collection

The data were collected via pre-tests, post-tests and delayed post-tests in all threegroups (total, 237 tests) and via three video-recorded interventions. The results ofthe first studied lesson were used as a starting point for designing the next lesson,and so on.

Three lesson cycles were completed in the LS, each comprising four steps.Before and after each lesson, pre-lesson and post-lesson meetings were held. Thefirst step was a pre-test that participants completed by writing essay-formatresponses to the open-ended question ‘In what ways can variation be used in teach-ing’? A qualitative analysis identified three qualitatively different categories ofanswers, i.e. emergent, premature and unaware, in terms of students’ expressed theo-retical knowledge. This pre-test was followed by a 15-min intervention (i.e. lesson)in which various aspects of VT were presented and discussed. After the lesson, thestudents repeated the same test as a post-test. The tests were conducted immediatelybefore and after the intervention and repeated in all three groups. Finally, eachgroup of students completed a delayed post-test eight weeks after the intervention,answering the same question once more. This allowed us to compare the pre-serviceteachers’ knowledge before and after the intervention, and to compare the resultsbetween the groups.

One open-ended question was used through the study, dealing with an issue pre-vious groups of student teachers found difficult to grasp. The aim was to assess howthe pre-service teachers’ understanding of the concept of ‘variation used in teaching’(an important assumption in VT is that variation of critical aspects of the content iscrucial for learning) qualitatively changed between the pre- and post-tests, and


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whether or not this change would persist after eight weeks. The delayed post-testwas used to demonstrate whether sustained or generative learning (Holmqvist,Gustavsson, and Wernberg 2007), i.e. learning beyond the immediate learning situa-tion, had occurred.

It was possible to describe and compare differences in group results in terms ofthe differences between pre- and post-test outcomes attributable to what the studentswere required to discern during the lessons. As the pattern of variation changed inthe interventions, it was possible to describe the aspects of VT that seemed criticalfor the student teachers to understand. The results of the delayed post-test were sup-posed to indicate whether what was learned was retained or even further developed.

Intervention

The three interventions differed in the pattern of variation used during instruction(see Table 1), i.e. the focus of the lessons was changed to facilitate the students’need for information to help them understand the object of learning, as describedbelow. Lessons two and three (in new groups of pre-service teachers) were alteredbased on analysis of the answers on the pre- and post-tests in combination with anal-ysis of the video-recorded previous intervention. Our conjecture, in line with VT,was that these changes would change the pre-service teachers’ opportunities to dis-cern the lesson content, and that the differences in handling the object of learningwould result in differences in how the students learned.

The first intervention used contrast by requiring that the students discern differ-ences between the three learning perspectives, i.e. constructivism, the socioculturalperspective, and VT. After that, features of VT were discussed, including conceptssuch as discernment, variation and simultaneity and patterns of variation such ascontrast, generalisation and fusion. In the first intervention, various concepts andpatterns were illustrated using the example of felines. We asked the student teachersto discern what is catlike in a feline through variation, simultaneity, generalisationand fusion. We then asked the students to contrast felines with dogs, after which thestudents went on to discern critical aspects of tigers and lions. However, what con-stitutes a critical aspect was not explicitly explained, as the students encountered theconcept only in terms of the representations (i.e. dogs and cats). It seemed as thoughthe general principle was overlooked: as the students focused exclusively on the par-ticular representations, they remembered only the examples. As a point of departureof the study was the tendency of student teachers to continue to see variation interms of method rather than content, the intervention tried to engender an under-standing of variation in the latter conceptual sense. When analysing the first post-test, however, we found that many participants still understood variation in terms ofvariation in method instead of in aspects of the object of learning (see Table 3).

Table 1. Patterns of variation when discussing the concepts ‘patterns of variation’ and ‘criti-cal aspects’ in VT.

Patterns of variation Critical aspects

Cycle 1 Variant InvariantCycle 2 Invariant InvariantCycle 3 Invariant Variant


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For this reason, the design of the second intervention, in the second group ofpre-service teachers, was changed. The lesson started with an example illustratingthe differences between varying representations of the content to be learnt (e.g. fruitsin different shapes, sizes, numbers and colours to learn colours) compared with rep-resentations varying in only one aspect of the content (e.g. similar balls of differentcolours to learn colours). The focus of the second intervention was thus changed topoint out what aspects of an object of learning are. Then the pre-service teacherswere presented with various aspects of the three learning theories. The concepts ofcontrast, generalisation and fusion were omitted as they seemed to confuse the stu-dents, hindering their ability to discern what characterises VT. Two major changeswere thus made between the first and second interventions; however, the mainchange in this intervention was in how the examples used varied in the lesson, theconcept of critical aspects being mentioned only in connection with one example.This made it difficult for the students to separate the concept from the representationand gain a generalised understanding of the principle as such; instead, they mighthave understood the overall presentation only as an example, overlooking the con-ceptual level.

In the third intervention, the focus on VT emphasised critical aspects of theobject of learning, explaining the theoretical assumption that these are aspects notdiscerned but that need to be discerned to enable the students to advance their learn-ing, vs. aspects already discerned by the learner and therefore not critical for furtherlearning. Critical aspects are the ‘keys’ to student learning. In this case, the criticalaspects of the object of learning were in the foreground and the difference betweenaspects in general (not critical for further learning) and critical aspects (a key consid-eration in VT) was highlighted. By focusing on different critical aspects of theobject of learning, in relation to different representations used in the lesson (e.g.using apples of different colours to point out that colour is not critical in definingwhat an apple is), the students were forced to focus on the content and on thevariation of aspects of the object of learning separated from its representations(e.g. separating colour from the object apple), which advanced their understandingto a more abstract, conceptual level. The third lesson seems to have affected thelearning outcome even more (see Table 3) in terms of the qualitative analysis oftheir expressed experiences.

Data analysis

The answers on the pre-, post- and delayed post-tests were categorised in three qual-itatively different pools of meaning, progressing gradually from a weak expressedunderstanding to a more developed understanding. The analysis was inspired byphenomenography and by the pre-service teachers’ expressed experience of whatvariation in VT is. The aim was to determine whether the pre-service teachers devel-oped a scientific/conceptual understanding or a procedural understanding (focusingon variation of methods). The highest level of understanding, the emergent level,encompasses and extends all lower levels of understanding; in an emergent under-standing of VT, the student expresses that variation entails deliberate variation ofaspects of the taught content in order to advance understanding. To be categorisedas emergent, an answer must emphasise that parts of the content are aspects that canbe varied, for example, ‘by showing different aspects of the object of learning,enabling the students to discern what is/is not the object of learning; by giving them


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contrasts, generalization, and fusion. Simultaneity – wholeness’ (post-test, studentteacher A18).

The next lower level of understanding is labelled premature, which implies theexpressed partial understanding of what variation means from a VT perspective, andthat the written answer does not describe VT well enough to belong to the emergentcategory. For example, ‘If you want to teach a student what characterizes, for exam-ple, a dog, the student must be able to distinguish what characterizes a dog fromwhat characterizes, for example, a cat. The student must be able to compare in orderto see differences’ (post-test, student teacher B6). This student conveys the idea thatit is possible to vary the content, but it is unclear whether the answer can beregarded as indicating a genuine understanding of the theory of variation as it refersonly to the example used in the intervention.

The lowest level of understanding is labelled unaware, which indicates that thepre-service teacher has not expressed a scientific description of the assumptionsabout variation in VT. The following is one such answer: ‘As a teacher, you varyyour teaching. You can vary your goals, so you do not stick to your old way ofteaching. You could let your pupils direct the education more, and sometimes theteacher organizes the lesson so that everybody is involved’ (post-test, student teacherC24). Answers categorised as unaware do not mention variation of aspects of thecontent; instead, they focus on variation of method (i.e. procedural knowledge).

Results

The focus of the analysis is the qualitative differences in the pre-service teachers’understanding of VT regarding the core concepts patterns of variation and criticalaspects. Specifically, we follow whether and how they improve their understandingand move between the unaware, premature and emergent understanding levels in thepre-, post- and delayed post-tests. To support the qualitative analysis, some quantita-tive measurements were made. The pre-test results indicate that in total 27 of 30(group A), 21 of 24 (group B) and 22 of 25 (group C) pre-service teachers’ initialexpressions were characterised as unaware and 3 of 30 (group A), 3 of 24 (B) and 3of 25 (C) were characterised as premature. None of the pre-service teachers’ initialexpressions was categorised as emergent. The post-test results indicate that the pre-service teachers’ expressions at the unaware level decreased to 13 of 30 (group A),12 of 24 (group B) and 14 of 25 (group C) at the same time as their expressions atthe desired emergent level increased to 6 of 30 (group A), 4 of 24 (group B) and 9of 25 (group C). From the perspective of overall improvement, summing the pre-ser-vice teachers’ expressions at both the premature and emergent levels, the increasewas from 13 of 30 (group A) to 12 of 24 (group B) and 14 of 25 (group C). Thisindicates that the students in group C changed their expressed awareness the most, amatter that is further analysed. Another important result is that the pre-service stu-dents’ expressions categorised as unaware decreased the most in group C. Examplesof expressions in the different categories are presented in Table 2. The answers onthe pre-test (Table 2) indicate that, with very few exceptions (i.e. 9 of 79), the pre-service teachers consider variation as something achieved by changing the method,alternating between different places or involving students in planning and imple-menting the lessons.

The results indicate improved learning between the different lessons givengroups A, B and C, suggesting a gradually more powerful lesson design during the


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study. The most powerful design, i.e. lesson C, resulted in an increase of 9 students(36%) in the qualitatively highest category, almost double the number in groups Aand B, indicating that the students did discern that the variation in question con-cerned the content and not the method. This is a strong indicator of this interven-tion’s effect in terms of improving learning more in group C than in the othergroups (i.e. group A, 20% and group B, 17%). Concurrently, there was a higher per-centage decrease (64%) in the lowest category (i.e. unaware) in group C than in theother groups. In group B, the strongest increase was in the middle category, prema-ture, from 3 to 11 student responses. In group A, nearly half of the students (14)remained in the unaware category in the post-test.

The results of the delayed post-test, which was administered eight weeks afterthe research lessons and after input from an additional lesson and literature reading,indicate that the knowledge seems sustainable in all groups. Even better, all groupsseemed to have developed their knowledge further with the aid of the additional

Table 2. Examples of answers from the different categories expressed at the tests.

Unaware Premature Emergent

You can use the variation in,for example, classroomenvironment, changing theclassroom, let the childrenparticipate in deciding.Using differentenvironments outside,inside and so on. Usingdifferent ways to reportthings, not just the test oran oral presentation.Different groupings.Working with variousthemes are good, then youget into a lot of variety andmany forms of expression

What should students learn?What are the difficultieswhen learning? Not focusingthe method, but instead whatis to be learned. Discernwhat you have to learn – tobe able to distinguishbetween green – red.Separate what you’relearning, something canmean a lot and lookdifferent. Similarities –Differences

By varying the object oflearning you want students tolearn. It is important to findout what it is that thestudents find difficult with theobject of learning. Then youvary its difficult parts tomake it more visible to thestudents and to createopportunity for them to beable to understand what is tobe understood. To understandwhat something actually is, Ialso have to get access towhat it is not

In as many ways as yourimagination and creativityallow. It is possible to varythe teaching in very manyways

You can vary the object oflearning and see it fromdifferent perspectives. Forexample, an apple does nothave to be green all thetime, but can also be red, indifferent shape and differenttaste

Variation according to thevariation theory highlightsthe learning object indifferent ways so it becomesclear what is to be learned.This implies that teachershave to find out whatstudents know and what theydo not know. By that, I as ateacher can define what thecritical aspect of learning isfor the pupils. Variety iscreated by illuminating forexample fractions in differentways by their numericalrepresentations, images,characters and so on, but it’sthe same part of the learningobject (fractions) that isilluminated


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Table

3.Alltheresults.

Tests

Pre

Post

Del

PPre

Post

Del

PPre

Post

Del

PGroups/Categories

A(N

=30)

B(N

=24)

C(N

=25)

Emergent

0%(0)

20%

(6)

37%

(11)

0%(0)

17%

(4)

29%

(7)

0%(0)

36%

(9)

40%

(10)

Premature

10%

(3)

33%

(10)

40%

(12)

12,5%

(3)

46%

(11)

50%

(12)

12%

(3)

32%

(8)

36%

(9)

Unaware

90%

(27)

47%

(14)

23%

(7)

87,5%

(21)

37%

(9)

21%

(5)

88%

(22)

32%

(8)

24%

(6)


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input, i.e. the additional lesson and reading material, which means that the designseffectively prepared the students for further learning (Bransford and Schwartz 1999).Measuring longitudinal knowledge acquisition up to the delayed post-test entailssome methodological considerations. All three groups received the same inputbetween the post-test and the delayed post-test, namely, a study book on VT andLS, and one more lesson on VT. This made it possible to study whether, and how,the students in the three groups benefitted from the additional learning materials toprepare themselves for future learning (Bransford and Schwartz 1999). The resultsindicate an interesting difference between the groups, namely, that the pre-serviceteachers in group C expressed more qualitatively changed expressions than did thepre-service teachers in the other two groups in the long term. It seems as thoughgroup C became better prepared for generative learning as a result of the third inter-vention, as it prepared them to profit more from the study book and the extra lessonthan the rest of the pre-service teachers.

The post- and delayed post-test results indicate that the learning outcomesimproved in all student teacher groups, but more so in group C. Although it is impos-sible to have complete control over what the three groups did between the post- anddelayed post-tests, all three groups were formally treated the same. As we could con-trol what the pre-service teachers were offered during the interventions, the resultsare based on the analysis of differences between the pre-service teachers’ expressionsbetween the pre- and post-tests within and between the three groups; to find outwhether the results are sustainable over time, the delayed post-test is used. Betweenthe pre- and post-tests, the results improved slightly more in group B than in groupA, driven mainly by the fewer expressions still categorised as unaware in group B; ingroup C, the number of expressions in the emergent category increased more than ingroups A and B, while expressions in the unaware category decreased the most.

Notably, the premature category changed the least between the post- and delayedpost-tests. It is also evident that the largest change between the post- anddelayed post-test results is in the unaware category, which could mean that knowl-edge of VT increased over time or that the pre-service teachers developed theirunderstanding after the module.

However, if we analyse the results at the individual instead of the group level,the number of changes in expression between the post- and delayed post-test resultsis interesting. By examining how each participant is categorised in the post- anddelayed post-tests, we can see how their expressed understandings changed over thetest period. Of the 79 respondents, 34 (43%) are categorised the same in both tests,i.e. 9 emergent, 14 premature and 11 unaware, which might indicate that it is diffi-cult to change one’s understanding (Shulman 1986) within a short period, as wassuggested by Lunenberg and Korthagen (2009). Only 12 of 79 (15%) respondentsexpressed less understanding of VT after eight weeks, i.e. between the post- anddelayed post-tests. Their understanding has declined from, for example, emergent topremature or from premature to unaware (three respondents even declined fromemergent to unaware). It is a positive sign, however, that 85% retained theirexpressed understanding. Perhaps the decreased results are explainable in light ofSwidler’s (2001) distinction between what people know and what they express or bythe fact that the pre-service teachers did not develop their conceptual knowledge anddid not reach a more generic level of understanding. In total, 33 of the 79 studentteachers (42%) displayed improvement in their knowledge of VT between the post-and delayed post-tests.


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Although these results are satisfactory, they could be improved still further.Many students still lack, or are unable to articulate, an understanding of the core VTconcepts patterns of variation and critical aspects essential for learning. Resolvingthis misunderstanding might require more than one module, and the pre-serviceteachers examined here did continue to study this matter in ensuing coursework.Their professional development did not end with this study, which gives us aglimpse of the difficulties of teaching pre-service teachers.

Discussion

Pre-service teachers’ knowledge of learning theories is important for their dailywork in the classroom, though they found these theories difficult to understand dur-ing their pre-service training. In this study, student teachers were exposed to VT andits core concepts patterns of variation and critical aspects when being taught what isnecessary for learning. This is a complex object of learning, as many parts constitutethe whole. In this study, the students were not expected to achieve a sophisticatedunderstanding of such a complex object of learning, but simply to understand thatthe variation referred to was not in method but in content. All the students wereadministered the same initial intervention, namely, a comparison between VT andtwo other theoretical perspectives to highlight what differentiates VT from the oth-ers; after that, the focus was on VT alone. To help the students learn about VT, dif-ferent aspects of VT were emphasised in the three interventions. Helping thestudents discern the difference between varying methods and varying aspects ofthe content did not facilitate the pre-service teachers’ learning. In the next interven-tion, the pattern of variation was invariant as were the critical aspects. In this way,no aspect was put in the foreground or background, as is required in VT (Martonand Booth 1997). Finally, in the third intervention, several examples were used toillustrate what critical aspects are. This allowed the students to distinguish the mean-ing of the concept from the object, to be able to generalise to other representations.The pre-service teachers’ test results after the three interventions indicate that learn-ing occurred and was facilitated by the interventions, that is, planned and enactedlessons based on VT did improve the student teachers’ understanding. The studentteachers’ expressed awareness was qualitatively analysed based on the data fromtheir knowledge expressed on the tests and the video-recorded interventions.

The present results indicate that differences in how various aspects of a complexobject of learning are presented influence learners’ ability to discern the object oflearning, as the only factor that differed among the groups was the interventiondesign. The tests were administered immediately before and after the interventions,as well as after eight weeks. The largest difference was between the pre- and post-tests, instead of between the post- and delayed post-tests, which might be surprisingas only 30–50 min had elapsed between the pre- and post-tests. The effects of differ-ences in design, in terms of differences in learning outcomes, have been demon-strated in many learning studies. VT asserts and the present LS demonstrate that it iscrucial to understand what constitutes a critical aspect in order to discern the differ-ence between variation in method and variation in the aspects of the object oflearning. In this study, the context or the relationships between actors in the learningsituations did not vary; the only difference was the intervention design in terms ofdifferent patterns of variation of aspects of the object of learning. By keeping thefocus on what constitutes a critical aspect, through maintaining an invariant


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background in terms of patterns of variation, the students in the last intervention(group C) were able to distinguish critical aspects at a generic level, as distinct fromthe particular example. VT conjectures that, to enable the learner to generalise, sepa-ration of the aspects of the object from the representation itself is needed to make itpossible to generalise this aspect to other objects (Lo and Marton 2011). In this case,the third intervention offered the students the opportunity to separate the concept(i.e. critical aspect) from the representation, as several different representations wereused. That this succeeded is indicated by the increased number of student teachersdisplaying an emergent level of understanding on the post-test. More pre-serviceteachers in group C seemed to possess conceptual-level knowledge than in the othertwo groups.

The results of the study indicate the importance of explicitly identifying theimplications of learning theories for classroom instruction in teacher education, tomake the studied theories useful in practice for the student teachers in learning situa-tions. Although these theories do not give teachers ready-made tools to use in teach-ing, they can be used as guiding principles for designing and analysing classroomlearning, in this way providing their teaching with a scientific basis.

AcknowledgementsThe authors would like to thank Kristianstad University and University of Gothenburg forsupport. We are also indebted to the teacher students taking part, and to the reviewersfor their important comments at earlier versions of the manuscript.

Notes on contributorsGöran Brante is a senior lecturer in Education in the Department of Pedagogical, Curricularand Professional Studies at the University of Gothenburg, Sweden. His main research interestis teachers’ professional life and teacher education.

Mona Holmqvist Olander is an associate professor in Education in the Department ofPedagogical, Curricular and Professional Studies at the University of Gothenburg, Sweden.Her main research interest is learning and learning study. She is a council member of WorldAssociation of Lesson Study (WALS).

Per-Ola Holmquist is a bachelor of education and teacher at the teacher education atKristianstad University, Sweden.

Marta Palla is a master of education and a teacher at the teacher education at KristianstadUniversity, Sweden.

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Documents

Theorising teaching and learning: pre-service teachers’ theoretical awareness of learning