Prospective teachers’ opportunities to develop PCK from participation in learning study

ABSTRACT

In this study, a learning study was used to enhance prospective teachers’ learning about how to teach a specific topic in mathematics or natural science to 4th-6th graders. It has been argued that participating in learning study can direct prospective teachers (PTs) towards the object of learning, and what needs to be enacted in teaching to make it possible for the learners to learn what is intended. However, less is known about what capabilities PTs develop from planning lessons in collaboration with peers and a teacher educator in learning studies. Our research question concerns what opportunities PTs have to develop pedagogical content knowledge (PCK) when participating in learning studies. We analyzed three groups’ lesson planning on two occasions, once when planning without a teacher educator, and once when planning with a teacher educator in a learning study using theory-informed questions. The software NVivo was used as a tool to code their discussions concerning PCK. For the three groups studied, there were significant differences regarding possibilities for developing PCK under the two conditions.

KEYWORDS:

• learning study
• PCK
• variation theory
• mathematics
• natural science
• prospective teachers
• teacher education

Introduction

In this study, we investigate prospective teachers’ opportunities to develop teaching skills during a learning study in a teacher education course. There is a consensus that teaching requires deep and specific knowledge about the topic taught, as well as knowledge about how students experience the topic (Ball, Thames, and Phelps 2008; Shulman 1987; Ball, Hill, and Bass 2005; Ma 1999). Prospective teachers (PTs) in Sweden practice their teaching skills with students primarily during periods of school-based practicums. During these periods, the PTs work mainly in collaboration with one teacher. Studies suggest that working in a collaborative process with peers in investigations of teaching and learning can help PTs develop their teaching skills during teacher education (Hiebert et al. 2007; Cheng 2014; Royea and Nicol 2019).

Participation in lesson study (Lewis, Perry, and Friedkin 2009) has been shown to develop PTs’ pedagogical competencies, such as observing, reviewing, and planning lessons (Leavy and Hourigan 2016; Lee 2019), as well as leading to development in their pedagogical content knowledge (PCK) (Leavy and Hourigan 2018). Learning study is a type of lesson study in which teachers explore teaching and learning in a single lesson, or a series of lessons, collaboratively, and a theory (e.g. variation theory) is used to focus on the object of learning and create the necessary conditions for student learning (for more details on learning study see Lo and Marton 2012; Marton 2015). Learning study has primarily been used to enhance student learning and for the professional development of teachers in respect of PCK (Nilsson 2014; Mårtensson 2019). It has been argued that learning study and variation theory can help direct prospective teachers’ attention towards the topic being taught and help them realize what needs to be enacted in teaching for students to learn the intended content (Royea and Nicol 2019; Pang and Runesson Kempe 2019). However, we know little about what PTs have the opportunity to learn from such interventions (despite self-reports). This study adds knowledge to the field by providing insights into how learning study can contribute to the development of PTs PCK, especially in terms of identifying students’ understanding of the topic and being able to use this knowledge when planning teaching. The research question is: What opportunities to develop PCK do PTs have when participating in learning study?

Pedagogical content knowledge

Shulman (1986, 1987) proposed the term ‘pedagogical content knowledge’ (PCK) to describe integrated knowledge about both content and pedagogical knowledge. This type of knowledge involves not only understanding the content being taught and the pedagogical issues but also the target group of students. Loughran et al. (2004) suggest that PCK is the knowledge that teachers develop through experience and over time about how to teach particular content to enhance students’ learning. However, Ball, Thames, and Phelps (2008) argue that PCK may need further analytic clarification, and empirical testing. For example, in their practice-based theory of content knowledge for teaching they identified ‘two empirically discernable subdomains within pedagogical content knowledge (knowledge of content and students and knowledge of content and teaching)’ (389).

Based on the rationale that teachers need to acquire a deep understanding of PCK in order to aid meaningful, high-quality student learning, substantial research has been done during the last four decades about how to help teachers develop PCK. One way for teachers to do this is to be involved in researching their own practice (Ball and Cohen 1999; Ermeling, Gallimore, and Hiebert 2017; Grossman et al. 2009; Hammerness et al. 2007). Lieberman and Pointer Mace (2010) argue that the collaboratively planned lessons in a lesson study ‘provide opportunities for teachers to learn from one another, refine their practice, and work with others to deepen their understanding of the complexities of teaching’ (79).

Learning study and variation theory

Learning study (Marton 2015) can be described as theory-informed lesson study. It is a form of action research in which a group of teachers (usually three to five) collaboratively plan, enact, and revise a single lesson (or series of lessons) several times in order to enhance student learning by identifying the aspects of a specific object of learning most critical for students’ learning. The theory used most often by the teachers in the learning study process is variation theory (Kullberg, Runesson Kempe, and Marton 2017). Variation theory is a learning theory that can be used for planning and analyzing teaching. Learning is seen as the discernment of aspects of an object of learning not previously discerned (Marton and Booth 1997). The aspects that the learner needs to discern but which they have not yet discerned are called critical aspects. For every object of learning, there are critical aspects, and these may differ from learner to learner, depending on what aspects have previously been discerned. The object of learning is the answer to the question ‘What is to be learned?’ (Marton, Cheung, and Chan 2019; Kullberg, Mårtensson, and Runesson 2016). The learning study process starts with exploration and delimitation of the object of learning in relation to the specific group of learners.

Variation theory ‘offers potential gains to lesson study in the sense that it provides an additional theoretical component to guide decisions about teaching’ (Huang, Gong, and Han 2016, 21). Variation theory provides tools that can help teachers design lessons, and describe and explain student learning. The object of learning and critical aspects are examples of concepts from variation theory that are used as theoretical tools in the learning study process. Variation theory, in contrast to other learning theories, states that the learner needs to experience differences before experiencing similarity (induction) in order to learn something new. Therefore, what varies and what is kept invariant in the teaching situation plays a significant role in what students have the opportunity to learn. In a learning study, the teachers learn to foreground variation (contrast) or invariance (generalization) in order to make the critical aspects more likely to be discernable. Patterns of variation can be used to design tasks and activities. However, a learning study always starts with an exploration of the object of learning and the identification of potential critical aspects for students’ learning. Tasks and activities are then designed using patterns of variation to make the critical aspects discernable for the learners.

Learning study in professional development

Learning study has been shown to have an effect on teachers’ professional development (Holmqvist 2011). For example, a study of teachers who participated in three consecutive learning studies showed that they all changed their way of teaching after the intervention in a similar way (Kullberg et al. 2016). The study showed that after the learning study intervention, the teachers taught several concepts simultaneously and made contrasts between them, instead of handling them one at a time as they did in a lesson before the intervention; thus, they used features of variation theory in their teaching after the intervention. Tan, Amiel, and Yaro (2019) found that elementary school teachers developed a theoretical foundation for their pedagogical actions and decisions after having participated in a learning study. Similarly, Mårtensson (2019) showed how mathematics teachers’ PCK changed and developed through the learning study process. Due to a more thorough use of variation theory over the course of the learning study cycles, the teachers developed a deeper knowledge of students’ different ways of understanding the content and how this could be taken into account in teaching. Nilsson (2014) concludes from her study that the ‘teachers’ discernment of what was experienced as successful and less successful in the different lessons might provide guidance on how different components interact within a teaching situation. Variation theory thus has the potential to become a valuable source of principles for science teaching that are directly useful for both researching and developing teachers’ PCK’ (1811).

Learning study in initial teacher education

Learning study has been included in initial teacher education in different places across the globe, e.g. Hong Kong, Sweden, and Canada. Cheng (2014) and Ko (2012) propose learning study as a model to help PTs develop their instructional design skills and teaching competency in initial teacher education. Pang and Runesson Kempe (2019) suggest that introducing learning study for PTs would also give them a deeper understanding of the learning study approach, and enable them to introduce and practice it in their schools in the future. However, there has been debate over whether PTs are ready to focus intensely on student learning during teacher education (Davies and Dunhill 2008). Challenges have been pointed out in using learning study with PTs, particularly due to the limited teaching experience that PTs have, the time required for a learning study, and difficulties understanding and using variation theory (Davies and Dunhill 2008; Holmqvist 2011; Royea and Nicol 2019). Regardless of these challenges, many studies show that PTs benefit from the experience. There is evidence that participating in learning study may have positive effects on the development of teaching skills (Lamb and Ko 2016; Cheng 2014; Lai and Lo-Fu 2013). For example, Tan (2018) showed that learning study made it possible for PTs to make teaching mistakes and learn from them.

Learning study can be used as a means to improve PTs’ understanding of the relationships between theory and practice (Royea and Nicol 2019). Royea and Nicol (2019) point out that previous research has shown that learning study may help PTs to ‘continually refine their theorizing about teaching and improve their capacities to apply formal learning theories during their initial teacher education and throughout their future teaching practices’ (3). Using variation theory as a framework in planning and applying lessons may increase PTs’ awareness about the relationship between theory and practice, not only in relation to variation theory but also to the learning theories that they have studied previously. Tan, Amiel, and Cheng (2020) showed how the use of variation theory in learning study helped PTs to identify, for example, taken-for-granted aspects (of the object of learning) that ‘contributed to the difficulties of learning about the topic’ (452). Our study adds to this research by showing how PTs’ PCK can be developed through learning study, in terms of gaining a deeper knowledge of students’ different ways of understanding the content and how this knowledge is taken into account in teaching.

Method and theoretical framework

Two courses at a Swedish university, one in natural science (20 PTs, 4^th semester of 8) and one in mathematics (67 PTs, 7^th semester of 8), in the teacher education program for teaching 4^th-6^th grade students, included learning study as part of the course content as a way to enhance PTs teaching skills. The teacher educators decided which topics should be taught on a general level (e.g. properties of water), but the PTs were asked to delimit the topic to fit one lesson. The groups that chose to participate in the study gave written consent and recorded the lessons and meetings themselves using a video recorder provided by the university. Video recordings from two groups (out of four) from the natural science course and four (out of eight) from the mathematics course were transcribed. Due to technical or other problems, the other groups were excluded from the study. Data from three groups (Surface tension, States of water, Programming) were chosen for analysis, as these topics were felt to be more accessible to a broader audience. In order to study the opportunities that PTs have for developing PCK from learning study, we analyze the video data from the group meetings.

In this study, we analyze group meetings, held during the course, when we asked the groups to plan a lesson without a teacher educator (TE) before the learning study started, and we compare that discussion with the discussion from the first meeting with a TE in the learning study process. The implementation of learning study is described as a list of events in Figure 1 below. Two meetings per group have been analyzed (events nos. 1 and 4 in Figure 1 and Figure 2 below). A TE participated in three meetings (events nos. 4, 6, and 9). A three-hour long seminar on variation theory was given after the first group meeting (event no. 2). In the seminar, concepts like the object of learning, critical aspects, and patterns of variation were described and illustrated. Each group was allocated two to three classes at a nearby lower primary school in which they could conduct their pre- and post-tests and lessons.

Figure 1. List of events in the study.

Figure 2. Identified main categories and subcategories.

During the learning study, three to five PTs worked collaboratively in a group and met with a TE who served as a facilitator in the process. Each meeting was about 30–45 minutes. The learning study meetings were oriented towards a systematic inquiry into the nature of the object of learning and its critical aspects. The TE’s questions emanated from the learning study model and were (variation) theory-based. The questions concerned the nature of an object of learning: i) What does it entail to understand the specific object of learning?; ii) How do students currently understand it?; iii) What do students need to learn in order to develop the required capability (critical aspects)?; and iv) How can these aspects be made visible in the teaching (by means of a pattern of variation and invariance)? A written pre-test was developed and used by the PTs in order to gain insights into their students’ understanding of the topic and to anticipate what might be critical for the students to learn. One lesson was planned collaboratively based on the insights from the pre-test. One PT (or several PTs) enacted the lesson in one class in a local primary school. The lesson was video recorded by another PT. After the lesson, a post-test was conducted in the class. Afterwards, the lesson and the post-test were analyzed (event no. 9, in Figure 1 above), and the lesson was revised and enacted in another class (event no. 10).

The theoretical construct PCK (Shulman 1986) together with theoretical concepts from variation theory (Marton 2015) were used as a tool for analyzing the data. PCK refers to certain knowledge that is of importance when teaching a specific subject and distinguishes it from knowledge about a specific subject, content knowledge (CK). The unit of analysis was episodes in which aspects of PCK or CK became prominent in the discussion. Theoretical concepts from variation theory (e.g. critical aspects) were added to provide more detailed descriptions of PCK (see subcategories below). The analysis of the data focused on what PTs take into consideration when planning a lesson. The analysis was conducted in the following way. First, the group meetings were transcribed verbatim. Thereafter, content analysis (Cohen, Lawrence, and Morrison 2017, 563) using NVivo 12 software was applied in the coding of transcripts. During the coding process, three main categories of discussion topics were established: Tasks and organization, CK, and PCK. For each main category, subcategories were created. In total twelve subcategories were identified empirically during the process of analysis.

The transcripts were analyzed and coded in regard to what the PTs (and TE) were talking about. The two subcategories in the first category, Tasks and organization, were identified from discussions about factors such as organization, time management and what tasks to implement (without a specific learning purpose) during the lesson. The factors in this category did not relate to CK and PCK. In the second category, CK, three subcategories were identified: (2.1) PTs’ difficulties with CK were expressed but not further discussed, (2.2) PTs’ understanding of CK was discussed, and (2.3) the learning goal on a general level (curriculum) was discussed. Seven different subcategories were identified within the third category, PCK: (3.1) students’ pre-knowledge, (3.2) specifying the learning goal for a lesson, (3.3) critical aspects (CA) in relation to content, (3.4) CA in relation to students’ understanding, (3.5) CA connected to activities, (3.6) theoretical discussions about variation theory, and (3.7) discussing and creating patterns of variation. For example, the following excerpt from the learning study group in natural science that focused on surface tension was coded as PCK 3.4 – CA in relation to students’ understanding.

PT1: If I was a kid, I would probably have thought that it was the glass that created the surface tension and stopped the water from flowing over the edge.

PT3: Yes, I probably would have thought so too. (coded 3.4)

The following excerpt, on the other hand, was coded as PCK 3.3 – CA in relation to content, since it is about what the students need to know in order to understand what holds water molecules together.

TE: Okay, I interpret what you say as if the students should be able explain surface tension. Then they need to have an idea of what the water molecule looks like, they need to know what it is that holds the molecules together.

PT2: Yes, that is how we were thinking. (coded 3.3)

When curricular factors were discussed in relation to properties of water, this was coded as CK 2.3 – learning goal on a general level. However, the suggestion that surface tension could be a suitable learning goal for a lesson was coded as PCK 2.2 – delimitation of learning goal. A reference to how the water molecule’s structure can create surface tension was coded as CK 2.2 – CK discussed, whereas a reference to what students may need to know in order to understand how water molecules are bound to each other was coded as PCK 3.3 – CA in relation to content.

Discussions that were unrelated to the planning of the lesson were not coded, for instance when the PTs were discussing private matters. Table 1 shows the amount of time coded and the length of each recorded session. Some excerpts have been coded into more than one subcategory due to the fact that the focus was on both students’ understanding and PTs’ understanding of the content.

Table 1. Percentage of time in the group meetings that was analyzed.

	Surface tension	Programming	States of water
Planning a lesson before LS	24 min of 42 min (57%)	33 min of 38 min (87%)	30 min of 44 min (68%)
First meeting in LS with TE	32 min of 34 min (94%)	31 min of 34 min (91%)	33 min of 35 min (94%)

Results

Our findings are illustrated in two parts. First, we show the analysis of our coding of what was discussed during the meetings in terms of aspects of CK and PCK. Then we analyze excerpts from the meetings on a more detailed level, and discuss opportunities to develop PCK from the different meetings. Figure 3 shows the amount of time PTs spent discussing CK and PCK when planning a lesson about States of water in natural science, both without the TE (i.e. not in a learning study) and with the TE. The analysis shows that when planning a lesson without the TE most time was spent on discussing activities that could be used in the lesson (about 35%), the learning goal of the lesson on a general level (about 40%), and organization of the lesson (about 15%), whereas little time was spent on students’ pre-knowledge and more specific delimitation of the learning goal of the lesson.

Figure 3. Percentage of time spent discussing organization, CK, and PCK during group meetings about the topic ‘States of water’ before and during learning study (LS).

During the first meeting with the TE, delimitation of the learning goal and critical aspects in relation to the content for student learning were the main focus of the discussion. How students may experience the content being taught was also discussed, and the activities suggested were connected to the critical aspects. We found similar changes in the three groups (States of water, Surface tension, and Programming) in terms of PCK being discussed more during the meetings with the TE, compared to when the PTs were planning by themselves. Figure 4 shows the analyzed meetings for the group planning a lesson on Surface tension. A difference between this group and the group planning a lesson about States of water is that in the non-TE meeting, the Surface tension group primarily discussed CK in relation to their topic. However, in the meeting with the TE, there was a shift towards discussing critical aspects in relation to the content, that is, what it may be necessary for the students to discern in relation to the content. Hence, instead of focusing on their own understanding of the topic, the PTs focused more on their students’ understanding of the topic. In the meeting without the TE, this group discussed aspects of PCK to a larger degree than the States of water group. Nevertheless, the Surface tension group increased the time spent discussing aspects of PCK during the meeting with the TE. In this group, variation theory was also discussed more from the start of the learning study process.

Figure 4. Percentage of time spent discussing organization, CK, and PCK during group meetings about the topic ‘Surface tension’ before and during LS.

Figure 5 shows the analysis for the group planning a lesson on Programming. In this group, most of the time in the non-TE meeting was spent on the organization of the lesson, and the activities planned in the lesson were discussed in relation to the students (see PCK below). However, the PTs did not discuss what the critical aspects of students’ learning of the topic might be (CA – content, CA – students). In the meeting with the TE, there is a shift towards discussing critical aspects for students’ learning. Only aspects related to PCK were discussed during the learning study meeting. Variation theory and critical aspects connected to the activities were the main focus of the discussion. This group was in their 7th semester of 8 in teacher education (in total four years), and the group had previously conducted a learning study in natural science during the 4^th semester.

Figure 5. Percentage of time spent discussing organization, CK, and PCK during group meetings about the topic ‘Programming’ before and during LS.

Note that the teaching of programming has been recently introduced into the Swedish curriculum for mathematics, and this, we suggest, may explain why the activities in relation to programming formed a major part of their discussion, i.e. it may be an expression of an exploration of the new topic.

Planning a lesson without the TE

In this section, we analyze the PTs’ discussions in the meetings with and without the TE, using the group planning a lesson about States of water as an example. As stated previously, the focus in their discussion without the TE was primarily on what activities to use during the lesson and on time management. The following excerpt shows how the PTs take their point of departure in the activity itself and that it should be fun. This is illustrated by statements such as ‘You want to show something, it gets boring to just … ’ (line 2) and ‘You can do much more fun stuff’ (line 4). The PTs give several suggestions for experiments that could be used. However, at this point, they do not seem to take into account what, on a more detailed level, their students should learn from the activity. Examples of activities seem to be in the foreground in their discussion, not CK or PCK.

Excerpt 1 Meeting without TE, States of water

1. PT2: Should we do experiments …

2. PT1: You want to show something, it gets boring to just …

3. PT3: Water is quite easy [to plan a lesson about].

4. PT1: Were you here on Monday [at a physics class] when we boiled water? Feels like an ordinary thing to do in school but not very inspiring. You can do much more fun stuff.

5. PT1: Can we bring in surface tension as well?

6. PT2: Put water in the freezer, and just before it freezes, you knock on the bottle and the water turns into ice.

7. PT4: We can show that, but we have to have a connection to it, we cannot just do it for fun.

8. PT2: Pour cinnamon on the water, then your finger will not get wet when you put it in the water. It has something to do with surface tension.

PT4 argues that ‘we cannot just do it for fun’; however, this comment is not taken into account by the other PTs. The group continues to discuss the lesson plan on a general level throughout their meeting (see Excerpt 2). Nevertheless, the activity and the idea that it should be fun are in the foreground. For instance, the group discussed whether it would be more fun for the students if the PTs carried out the experiment instead of showing it as a video clip (Excerpt 2). One PT concludes ‘we can do that. It will maybe make it more fun’ (line 4). What the students should learn from the experiment and what difficulties students may have understanding the content or the experiment are not addressed.

Excerpt 2 Meeting without TE, States of water

1. PT4: There are thousands of experiments on YouTube.

2. PT1: We do a short introduction; we can show a video clip and a short experiment … or do you mean that we should show an experiment [ourselves].

3. PT2 & 3: Yes.

4. PT1: Yes, we can do that. It will maybe make it more fun.

Excerpts 1 and 2 show that organization and activities (coded 1.1, 1.2) are the centers of attention. At the end of the meeting, the group has decided that they should teach states of water and what characterizes the different states (gas, liquid, solid). ‘What we actually want to teach is states of water and what characterizes them … and do experiments that show the states. Then we can look at YouTube to see if there are any fun experiments’ (Excerpt 3, line 1). Two features of water as a liquid are also mentioned (‘surface tension’ and ‘transparency’), but nothing is said about what this means, how to teach this, and how to make it possible for the students to learn this.

Excerpt 3 Meeting without TE, States of water

1. PT3: What we actually want to teach is states of water and what characterizes them … and do experiments that show the states. Then we can look at YouTube to see if there are any fun experiments. It feels like there should be a lot.

2. PT2: But like with liquid, then we can talk about surface tension …

3. PT3: And like transparent … ness

(…)

1. PT3: So, we will primarily describe water’s important …. properties when it is liquid.

2. PT4: Ahh I feel that we have an hour, so we do not have to get into the [water]cycle.

3. PT2: But it is like ice floats in liquid water because … blah blah blah … and we can also mention that it is important because otherwise it would be hard luck on the fish.

In the excerpt above, PT4 (line 5) makes a delimitation to not include the water cycle, and instead focus on the states of water. However, what characterizes the different states and what the PTs want to teach on a more detailed level are not clearly decided upon.

Planning a lesson with the teacher educator in the LS

During the first meeting with the TE, the PTs in the group planning a lesson about States of water start to explain how they want to divide the lesson into different parts where different forms of water would be discussed with the students (coded 1.1, line 2). The TE responds by addressing the need for delimitation of the object of learning and asks what the students are supposed to learn. He says: ‘I need to know what you want them [the students] to learn about the properties of the water’ (coded 3.2, Excerpt 4, line 3). The question directs the PTs’ attention towards student learning, instead of the time and organization of the lesson (line 2).

Excerpt 4 Meeting with TE in the LS on States of water

1. TE: Tell me about your object of learning.

2. PT1: It’s the properties of water, and we thought that the hour we have at our disposal, we’d divide it into three segments: solid, liquid, and gas form.

3. TE: Yes, but let’s take it easy. Because … the properties of water, that tells me nothing. I need to know what you want them to learn about the properties of water. Should they learn all the properties of water?

4. PT3: No, we have decided the property that we should focus on is the states of matter.

5. TE: Then I would rather say that this is your learning object. What do you want them [the students] to know about the states of matter?

The TE’s final question in the excerpt above, ‘What do you want them to know about the states of matter?’ (coded 3.1, line 5), puts the content in the foreground and most likely helps the PTs to focus on a more defined object of learning and what properties of water students should learn in order to explain the states of water in a scientific way. During the meeting, the PTs have a tendency to reason in terms of what they should do or show the students during instruction, while the TE asks what the purpose of the activity is in terms of what the students should learn or understand. The discussion concerns issues related to PCK, and suggestions for activities or tasks to do during the planned lesson are now scrutinized and connected more closely to students’ understanding and learning (coded 3.5).

The TE’s questions and focus in the meetings stem from the learning study model and variation theory; hence the questions posed by the TE were theory-based. The concepts object of learning and critical aspects, we suggest, gave PTs an opportunity to discuss and develop PCK. During the meetings with the TE, critical aspects were seen by the PTs at the beginning of the learning study process as general aspects that were important to consider during a lesson, for instance, how the teacher explains something (on a general level), or language difficulties. For example, PT1 in the group planning a lesson about Surface tension said ‘Oh, we have identified a lot [of critical aspects] … one critical aspect is the students’ pre-knowledge and their language abilities’. The TE responded, ‘The critical aspects need to be more explicitly connected to the object of learning. What are the students’ difficulties for learning what you want them to learn?’. In variation theory, a critical aspect is always related to the content taught, and what students need to discern in order to learn the required capability. Excerpt 5 shows how the TE, by posing questions about the content, gives the PTs the opportunity to reflect on what may be critical for students’ learning, for instance, when saying ‘The question is, do they need to know what an atom is in order to understand surface tension?’ (coded 3.4, line 7). Moreover, the TE points out what is not a critical aspect, by making a contrast, ‘How you should explain it – that is not the critical aspect’ (coded 3.3 line 10).

Excerpt 5 Meeting with TE in the LS on Surface tension

1. PT1: Have they [the students] heard about surface tension, molecules, and bonds?

2. TE: (…) What is it they need to deal with … know in order to deal with this object of learning? What do they need to know … do they need to know what a molecule is?

3. PT1: In one way I think so.

4. TE: What else do they need to know?

5. PT1: They need to know how they are bound together.

6. PT2: Something there also with atoms; molecules and atoms maybe go hand in hand.

7. TE: The question is, do they need to know what an atom is in order to understand surface tension? (…)

8. PT2: We talked about this when we did our pre-test [survey], that it is this thing with the bonds between the molecules … so we actually only need to talk about molecules and what’s in between.

[A bit later]

1. PT2: But we had this thing with the structure of the water molecule, how do we explain in the best way also.

2. TE: Yes, but then you are on the next step. How you should explain it – that is not the critical aspect.

The group discussing Surface tension saw students’ language abilities as a critical aspect: ‘We also had students’ language abilities as a critical aspect’ (see Excerpt 6, line 1). The fact that critical aspects are content-specific, not known beforehand, and need to be investigated, since they are dependent on the specific group of learners, was highlighted by the TE (line 2).

Excerpt 6 Meeting with TE in the LS on Surface tension

1. PT7: We also had students’ language abilities as a critical aspect.

2. TE: But that is a more general … that I wouldn’t see as a critical aspect. There are many things that one needs to take into account, and it can have to do with how the classroom looks, who the students are, more general questions, and you can have that in your descriptions but separate from critical aspects, which are more connected to the object of learning. (…) they [critical aspects] are dynamic in a way so when you have had the survey [pre-test], there may be other critical aspects that show up or other critical aspects that you see that they have already mastered. Most likely things [critical aspects] will turn up after your first lesson.

In another group (Programming), a discussion about the object of learning helped the PTs to realize that they need to be more specific about what it is that they actually want the students to discern in order to be able to write an algorithm. Excerpt 6 shows how PTs get insights into a finer level of detail when planning a lesson about a specific object of learning (coded 3.3).

Excerpt 7 Meeting with TE in the LS on Programming

1. PT5: So the object of learning can consist of several critical aspects?

2. TE: Yes, I would say that the object of learning is the critical aspects. That is why the object of learning is dynamic because when you go out and test [the students] it shows that they for instance do not have a problem with ‘following an instruction’ [potential critical aspect in regard to programming], then that critical aspect goes away [is not critical]. Then your object of learning changes, then you should not focus on that. So what you are doing now is trying to find out where the students are. What is critical for these students? And with help from that you formulate your object of learning which is what you will focus on during the lesson …

3. PT6: But then the learning goal could be that they do it step by step [the programming].

4. TE: [Reads what the PTs have written as a learning goal] Have an understanding of what an algorithm is …

5. PT6: Yes, that is what we have now.

6. TE: They [the students] should understand what an algorithm is?

7. PT5: Maybe it should be broken down even more, so it becomes more precise.

8. PT6: In other words, what is it exactly that they [the students] should notice.

The comments ‘Maybe it should be broken down even more, so it becomes more precise’ (coded 3.3, line 7) and ‘what is it exactly they [the students] should notice’ (coded 3.4, line 8) show that the PTs now take both the content and what the students should learn into consideration.

Discussion and conclusions

Our analysis of the meetings, both without and with a TE, shows that PTs to a large extent focus on the organization of the lesson and activities to be conducted during the lesson. In the meetings without the TE, there seems to be a lack of reasoning about what the students should learn, or about possible difficulties that students may encounter with regard to the specific content. In the meetings both without and with a TE, the PTs often struggled with their own understanding of the specific content to be taught (CK).

We add new knowledge to the field by showing how certain aspects of PCK and CK came into the foreground and had potential to be developed in the PTs’ discussions about planning a lesson. We found that when PTs collaboratively plan a lesson in their 4th (of 8) semester in teacher education in natural science, and in their 7^th (of 8) semester in mathematics (Programming), this may not necessarily develop their teaching skills with regard to teaching the specific topic, since our study showed that they focused primarily on teaching at a general level, addressing mainly organization of the lesson, time management, and activities considered to be fun. No distinct learning goals were in focus during these initial lesson-planning meetings, and little attention was given to students’ learning and the potential difficulties students may encounter in relation to the topic. However, during the learning study meetings with a TE, we found a significant shift towards matters related to PCK (cf. Nilsson 2014). For all three groups, the difference between the two meetings (without TE and with TE) can be seen as a shift from a focus on the activities students should carry out to a focus on students’ learning. Our findings are in line with previous studies indicating that learning study has positive effects on PTs’ development of teaching skills (e.g. Lamb, Ko, and Lamb And Po Yuk Ko 2016; Lai and Lo-Fu 2013), and PTs’ awareness of students’ difficulties with learning the topic (Tan, Amiel, and Cheng 2020).

In the learning studies analyzed, the TE guided the PTs’ attention to students’ understanding of the topic being taught, using theory-based questions emanating from the learning study model and variation theory. Our study shows, like Royea and Nicol (2019), that PTs had some difficulties with the theoretical concepts used in variation theory, e.g. critical aspects are seen as ‘all things’ that are important in a teaching context. Teaching methods and activities became, during the learning study, increasingly based on students’ understanding of what is taught, students’ possible difficulties in understanding the content, and critical aspects. We are aware that in this study, we have analyzed only the first meeting with the TE in the learning study. We believe it was important to analyze the first meetings since they show what prospective teachers’ focus on when planning lessons and how PTs are challenged to focus more on students’ learning. Further research is needed to explore PTs’ teaching skills, and how participating in a collaborative practice such as learning study may affect PTs’ skills with regard to planning, enacting and evaluating teaching.

The study contributes to the development of a tool for analysis (a coding scheme) (cf., Ball, Thames, and Phelps 2008). The use of variation theory to inform descriptions of PCK, we suggest, can contribute to a more precise description of what PCK may entail. The study also has implications for teacher education practice. It indicates, for example, that even when PTs have had several periods of practicum, they may still focus on organization and activities (before conducting learning study). This raises questions about the opportunities provided to develop PCK during teacher education. The study illustrates that prospective teachers, by conducting learning study together with teacher educators, most likely have greater opportunities to learn CK and PCK than when taking on the task of lesson planning without such support. The role of the teacher educator appears to be vital in directing the PTs’ attention towards the object of learning, and towards the use of theory when planning and analyzing teaching and student learning. We propose that variation theory can assist in focusing on what is critical for students’ learning, and make it possible to examine teaching and learning on a detailed level. Participation in collaborative processes such as lesson study or learning study during initial teacher education would also prepare PTs for working collaboratively to plan teaching, and provide professional learning (theoretical and practical) that is directly useful for planning lessons when working in schools (cf., Bulterman-Bos 2020; Elliott 2012; Pang and Runesson Kempe 2019).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Department of Pedagogical, curricular and professional studies.