Use of knowledge pieces and context features during the transfer process in physics tasks

ABSTRACT

In this article, we present a qualitative study examining students’ thoughts and strategies while transferring concepts about energy in physics. We include theoretical approaches of existing transfer research and findings from think-aloud interviews with 20 students of different ages and school levels to develop a framework for analysing the transfer process. The results of both traditional transfer studies and modern approaches, such as the ‘Actor-Oriented Transfer perspective’ (AOT) and ‘Coordination Class Theory’ (CCT), are regarded as a theoretical foundation for the framework. Our empirical data involves the statements of students solving a physics task with questions regarding the energy concept, which we used to inductively derive categories for our framework. We conclude that the transfer process is highly individual and that our framework can make this process visible. Knowledge can be transferred with or without a relation to the contextual features of the transfer situation, and it is possible that students describe the context situation itself without relating it to their existing knowledge pieces. Finally, we found four metacognitive strategies that students use while transferring their knowledge. The findings will help teachers to focus on the applicability of knowledge and on practising the use of transfer strategies.

KEYWORDS:

• Transfer process
• physics education
• energy concept

Introduction

The concept of transfer of learning has a long history of research. Since the beginning of the twentieth century, researchers have found evidence for the successful application of knowledge and described this process as (knowledge) transfer. While many different approaches can explain the cognitive and affective aspects of the transfer process, newer research has criticised certain methodological and theoretical aspects of previous transfer studies. Traditional transfer studies are mostly content based, leaving out the perspective of the students that transfer their knowledge and simply measuring what was transferred. Our research project on the other side aims at examining students’ thoughts and the strategies used while solving a transfer task about energy in physics and therefore goes along with modern transfer approaches. Until now, not many specific strategies regarding students’ transfer of physics concepts are known and examined. We want to contribute to closing this research gap by investigating transfer processes and strategies in the domain of the energy concept in physics. The topic of energy is suitable for the study of transfer because the basic concepts are well-known (from an education research perspective) and can easily be applied to different task contexts. We conducted a qualitative interview study to develop a framework for structuring and explaining transfer processes. To this end, we applied transfer mechanisms from traditional and methodological and theoretical approaches from modern studies to form the theoretical foundation of the framework. The results of our study will help to sharpen and expand the knowledge about transfer processes and strategies and show teachers options to foster transfer (strategies) in physics courses.

Theoretical background

Traditional and modern approaches to transfer

From a traditional perspective, a transfer can be defined as the application of existing knowledge to a new situation (Bransford et al., 2000). Factors like deep initial learning and the similarity of the underlying structure of two situations appear to be crucial for achieving a successful transfer from a classical viewpoint (Barnett & Ceci, 2002). Thorndike (1906) introduced the theory of identical elements and influenced several authors in subsequent decades. If the learning situation shares enough of these elements with the transfer situation, students can relate their knowledge, and transfer is possible. This view, which is strongly focused on the transfer situation and not on the person transferring, has led to numerous approaches describing the distance of a transfer performance (for an overview, see Haskell, 2001; Schmid, 2006), such as near and far transfer. In contrast to near transfer, far transfer is based on a problem that is different in terms of the surface structure but still shares a common deep structure with the learning problem (Chi & VanLehn, 2012).

Many of the mentioned transfer approaches focus on analogies between learning and the transfer situation. Based on the work of Gick and Holyoak (1983), analogical reasoning is also prominent in explanations of transfer processes. As noted by Day and Goldstone (2012, p. 154), an analogy can be defined as ‘a match between the systems of relations in two represented situations (‘their deep structure’), regardless of any differences in the objects and features they involve (‘their surface structure’)’. Although the deep structure remains the same, differences in the surface structure of two tasks often result in poor transfer performance (e.g. Gick & Holyoak, 1983).

When it comes to real-world situations requiring a transfer, students may struggle because they do not see the relevance of their existing knowledge in this new environment (Day & Goldstone, 2012). In traditional transfer theories, the importance of the contextual characteristics of a transfer task is underestimated. A key to a successful transfer seems to be the effective differentiation of relevant and irrelevant features of the surface structure. The context of a new situation can hinder transfer, as Day and Goldstone (2012) concluded. However, surface features may also improve the comprehensibility of a task, which makes considering a good balance between abstraction and context information in a transfer task important. Critiques of traditional transfer studies often refer to their handling of context, including a limited definition of context regarding transfer. For instance, the environment of the transfer situation incorporating social aspects is rarely taken into account (Lobato, 2006).

Furthermore, Nokes-Malach and Mestre (2013, p. 188) observed that traditional transfer studies do ‘not capture many of the real world aspects of transfer, such as the use of other resources during the test phase or the role of the learning phase’. This leads to a methodological critique of transfer research. Classical approaches focus on an application task directly following intervention in class. Hence, the test what students do in a specific transfer task after solving a learning task. When only the predefined correct mapping of the initially learned concepts to a new situation is measured, many possible explanations regarding if and how transfer occurs are ignored. If students do not find the correct answer (from the experts’ perspective), transfer simply does not occur. These types of studies which use multiple-choice tasks to measure the transfer performance often show that transfer is rare (Day & Goldstone, 2012). In such scenarios, the processes students execute during transfer are not considered in the analysis of transfer. In addition, motivation and prior knowledge should be part of transfer research, especially because those factors affect the construction of knowledge or representations in a new situation (Nokes-Malach & Mestre, 2013).

Lobato (2006, p. 435) summarises different methodological requirements for transfer studies. Among those are the prevention of ‘one-trial learning situations to [ensure] that students have the opportunity to understand a procedure, principle or theory deeply enough’ or the better use of transfer tasks that also share surface features with the learning tasks. A third possibility for the methodology of transfer studies could be group assessments, in which students can ‘[utilise] resources and gather additional information’ (Lobato, 2006, p. 435). Moreover, researchers should examine whether students can construct new knowledge (i.e. learn) during a transfer task (Rebello et al., 2005). Knowledge is not considered static and memorised in fixed units; rather, every new situation forces students to rethink, remember and combine existing knowledge and consider aspects of the new situation to eventually construct knowledge explicitly for the new situation. diSessa and Wagner (2005) took up this idea and adapted their ‘knowledge in pieces’ approach to transfer research.

Several new approaches were developed (e.g. diSessa & Wagner, 2005; Lobato, 2012; Martin & Schwartz, 2013; Rebello et al., 2005; Royer et al., 2005; Wagner, 2006, 2010) to answer the critique on traditional transfer theories and studies. In this section, two of these approaches, one with a focus on the fundamental methodological demands on transfer studies and one explaining the cognitive aspects of knowledge construction in a transfer situation, are discussed in more detail. For methodological considerations, the ‘actor-oriented transfer perspective’ (AOT; Lobato, 2003, 2006, 2012) gives insights into how modern transfer studies should be conceptualised. Key to this approach is inductive qualitative methods to explore the ‘nature of novices [generalisation] of their learning activities in semantically rich content domains’ (Lobato, 2012, p. 240). Interpreting transfer situations and students’ answers from an ‘actor’s point of view’ means the abandonment of a predefined, correct concept application. Indeed, the comprehension of transfer situations themselves becomes the subject of the study. The focus on the student in a transfer situation and their thoughts, as well as the construction of knowledge during transfer, provides information about the processes occurring. This even applies if transfer might not have been successful according to traditional measurement methods (Lobato, 2012).

For the cognitive aspects of transfer, the ‘coordination class theory’ (diSessa & Wagner, 2005; Wagner, 2006, 2010) represents a profound basis for modern-approach transfer studies, especially in the field of physics education. diSessa and Wagner (2005) related their qualitative interview analysis with students solving physics problems in a transfer scenario to the ‘knowledge in pieces’ approach (diSessa, 1993). The latter stems from conceptual change research and includes so-called ‘Coordination classes [which] are assumed to encompass the mental resources necessary to operate in a wide range of contexts … and to read out reliably the same information across contexts’ (Dufresne et al., 2005, pp. 188–189). A coordination class is defined as a concept consisting of many knowledge pieces and their relationships amongst each other (Figure 1). Students can form connections out of a selection of their existing, linked knowledge pieces (‘causal net’) and project such coordination onto a new context when dealing with a transfer task (diSessa & Wagner, 2005). This process is called ‘alignment’. An important part of it is ‘readout strategies’ to perceive or evaluate features of the context of the transfer situation. ‘Readout strategies’ are also part of the coordination classes and are activated in specific (context) situations. Coordination classes can include ‘naïve elements’ in the form of technically incorrect knowledge pieces. Further they are newly constructed in every situation and strongly dependent on the respective context. In newer transfer research, the theoretical approach of transfer in pieces became more and more relevant to interpret students’ thoughts during problem-solving and transfer tasks (see, e.g. Podschuweit & Bernholt, 2018).

Figure 1. Alignment during Transfer According to the Coordination Class Theory.

Much like with the actor-oriented transfer approach (Lobato, 2012), context features are considered highly relevant to the construction of coordination classes in a transfer situation. Furthermore, research on problem-solving produces models to distinguish different context features. In an extended context model, Löffler et al. (2018) described surface features and deep-structure features. The former represents the elements that are directly visible and interpretable in the task. The deep structure comprises all subject-related characteristics that form the basis of the problem. Features (both surface and deep structure) that are part of the solution can also be distinguished from those that are irrelevant to the resolution of the problem (Löffler et al., 2018). In addition, both types of features can be part of a scientific model or not related to it. With this model, the authors opened new ways to analyse the use and integration of context features in problem-solving and potentially in transfer research.

Transfer processes and strategies

Transfer processes are described in various forms. The aforementioned readout strategies (diSessa & Wagner, 2005) can be seen as a part of a transfer process during the alignment. Nokes-Malach and Mestre (2013) developed a framework for interpreting and analysing the transfer process based on both traditional and modern transfer approaches as well as their own study involving novice problem-solvers in mathematics and science. The authors see transfer as a dynamic process that includes the activation and application of knowledge components. The framework consists of different stages, including transfer processes like ‘sense-making’ and ‘satisficing’ and four basic mechanisms adopted from traditional approaches, namely ‘identical rules’, ‘analogy’, ‘knowledge compilation’ and ‘constraint violation’. Transfer is seen as a two-step process consisting of the construction of a context representation and the generation of a solution for the transfer problem. The roots of the strategies ‘sense-making’ and ‘satisficing’ lie in the coordination processes in transfer noted by Dufresne et al. (2005). ‘Sense-making’ is considered as an act of determining whether the solution meets the student’s requirements, whereas in ‘satisficing’, the constraints from the environment (such as the task affordances, the learning setting, or the social situation) play a role while an individual is evaluating if he or she is satisfied with a solution (Nokes-Malach & Mestre, 2013).

Research regarding the ‘actor-oriented transfer’ approach also includes some form of transfer strategies or processes with the description of ‘noticing’ as an important part of the transfer process (Lobato et al., 2012). Different task contexts trigger different transfer strategies, and the noticing of context features, therefore, becomes central. Lobato et al. (2012) demonstrated that features (of tasks or activities) students explicitly notice during a mathematics class directly influenced their noticing and argumentation in a transfer task.

It is worth noting that notions like processes, mechanisms or strategies are often used as synonyms in transfer research. In our work, we will use the term ‘transfer process’ to denote the procedure a student executes while solving a transfer task. We will call the subprocesses during this process transfer strategies.

Students’ energy concept in physics

In parallel to the research on prior knowledge related to energy (see, e.g. Harrer et al., 2013; Watts, 1983), Neumann et al. (2013) described various levels of development within a whole energy concept. The levels differ not only in terms of content but also in their complexity: the least complex level contains the knowledge of energy forms and sources. For this purpose, fragmented knowledge in the form of individual knowledge elements (or pieces) is sufficient. Links between pieces of knowledge are required for understanding the next levels of the energy concept, namely energy transfer and transformation as well as energy degradation or dissipation. Both levels require the linking of individual knowledge pieces to form a net of interrelated knowledge. The most complex level of the energy concept is the conservation of energy, consisting of more difficult and less comprehensible connections between individual knowledge pieces (Neumann et al., 2013). Those four levels of energy concept development can also occur in parallel. As the authors mention, there is a possible fifth level, called ‘energy devaluation’, which respects the idea of entropy. While the levels of understanding the energy concept in physics are not hierarchical, Neumann et al. (2013) recommended structuring initial learning about energy by the described sequence of these levels. Nordine et al. (2011, p. 693) note that focusing on energy transformation during instruction can help students to ‘make sense of everyday phenomena’. This insight is notable regarding transfer processes, because students have to deal with everyday phenomena in transfer tasks (e.g. the task used in our study). The relevance of energy as a topic of research in (physics) education is high, as it is described as ‘a cross-cutting core concept’ (Podschuweit & Bernholt, 2018, p. 727) with importance in different science disciplines as well as political, societal and practical meaning.

Aims and objectives

Our study set out to examine students’ thoughts and the strategies they use in a physics transfer task as well as the transfer process itself.

We pursued the following research questions:

1. Which strategies are applied by students during a transfer situation in physics (topic: energy) and how is the transfer process structured? (RQ1)

2. How do students deal with their existing knowledge pieces and with context features of the task in a transfer situation in physics? (RQ2)

Method

Participants and settings

We wanted to respect the methodological criticism on traditional transfer studies. Therefore, we consciously decided not to conduct an intervention study with a specific learning task but rather focused on students who had recently completed the topic of energy in a physics course at their school.

We conducted 12 qualitative think-aloud interviews with 20 students to assess the mental processes occurring during transfer. Students participated alone or in small groups. There were ten students from two classes from lower secondary school taking part in groups of two or three. These groups were formed on students’ request and the participation was voluntary (so not every student of the two classes took part). Other students from upper secondary school were recruited (also on a voluntary basis) from different classes and schools through their teachers, who were in contact with our university. Four of those students participated in groups of two and two of them alone. Finally, we also asked students from our university of teacher education to participate voluntary. Four of them took part in our study, all of them doing the interviews alone. The interviews took place at the participants’ school or home to provide an environment familiar to the students. For younger students, parents had to give permission for participating in the interviews.

To achieve a large variability of participants, we deliberately recruited students from various school levels (see above) and spanning different ages (14–35, M = 17.4, SD = 4.9). This wide range of backgrounds of the participants is justified by the exploratory character of the study and is typical for qualitative think-aloud studies (Ericsson & Simon, 1993; Sandmann, 2014).

Think-aloud interviews

Protocols of think-aloud interviews allow for the development of detailed categories for the intended framework (Konrad, 2010). As a starting point to ‘think aloud’, students were given a written physics task on the topic of energy with an illustrated map of a locally well-known outdoor climbing park as a real-life context (Figure 2).

Figure 2. Task for the Qualitative Interview Study.

In the first step, participants had to find a situation within the map that was related to energy. There were then further questions as well as additional hints as guidelines for analysing the selected situation regarding some of the aforementioned levels of the energy concept (Neumann et al., 2013). The task enabled a variety of approaches and included different situations from which to choose (e.g. a freefall tower, a zip wire, a cable car or even a fireplace).

Students had to verbalise all their thoughts. The think-aloud interviews followed a standardised procedure and were audiotaped and transcribed verbatim (in German). All 12 interviews were conducted by the same person (one of the authors, with a background in science education) to contribute to the standardised procedure of the study. The interviewer gave an introduction to the process at the beginning, asked the participants to continuously think aloud and gave them the previously defined, additional questions or hints if needed. However, the interviewer did not give any feedback on the content of the participants’ responses and did not answer questions from the students regarding the topic, as it is usual for the think-aloud method (Konrad, 2010). In group interviews, the interviewer left the discussion to the students and only intervened if no one said anything more or if there were uncertainties regarding the procedure of the interview.

Transfer task and analysis

A mixed method of deductive and inductive derivation of categories (codes) as part of qualitative content analysis (Kucskartz, 2018) was chosen to develop the framework. To ensure a high quality of the study, we paid particular attention to two points: the development of the transfer task (our test instrument), and the testing of the developed framework, by comparing the results of coding from different, independent coders.

The (transfer) task used for the interviews must trigger cognitive processes that can be verbalised or are naturally verbal (Charters, 2003). In our task, students were asked about the basic levels of the energy concept (Neumann et al., 2013) through short written questions (Figure 2). The questions allowed different solutions and thus met the requirements of the ‘actor-oriented transfer’ approach. In addition, hints and further tasks were prepared for students who answered all other questions in a short time or had difficulties, respectively.

After developing the framework in the first phase, we tested it in a multistep procedure. Firstly, transcripts were coded with the initial framework by the two authors. In the process of finding consensus, one-third of codings and every single (sub)category from the framework were discussed. The framework was subsequently revised; the transcripts were coded again, and finally, coding units for the next stage of coding were determined. In this step, two experienced students studying science education at the university of the teacher education were recruited as independent coders. They were not familiar with the initial data analysis and independently coded one-fourth of the interview transcripts (i.e. three interviews) using the previously determined coding units. The intercoder agreement, calculated with MAXQDA (Rädiker & Kuckartz, 2019), resulted in Kappa κ_n = .66 (Brennan & Prediger, 1981). According to Landis and Koch (1977), this represents a substantial agreement of the two raters.

Coding the interviews in the described multistep procedure resulted in a framework. Guided by theoretical considerations about transfer approaches and the analysis of our interview data, we delineated descriptions for every category of the framework.

Results

First, we will present the developed framework to be able to show which strategies students apply during transfer and how their transfer process is structured (RQ1). Afterwards we present the results of how students specifically deal with their existing knowledge pieces and the context features of the task by giving explanations of the categories of the framework and showing examples from the transcripts of the interviews (RQ2).

Results for Research Question 1 (RQ1)

We based the framework on the understanding that concepts are built of knowledge pieces and are always newly constructed in a different (transfer) situation. This understanding is in line with the coordination class theory (diSessa & Wagner, 2005) which describes the application of knowledge as a process of connecting existing knowledge pieces and aligning those to the actual contextual situation. This distinction between the knowledge (pieces) of a student, the features of the context of the task, and the alignment of those two elements, induced us to deductively derive three main categories for our analysis of the think-aloud transcripts and hence for our framework for transfer processes in physics (Table 1). These categories are as follows: (1) the description and analysis of context features; (2) the mention and connection of knowledge pieces without relation to context; and (3) the alignment of knowledge pieces with context features.

Table 1. Framework to Describe Transfer Processes in Physics Regarding the Topic of Energy.

(1) Description and analysis of context features	(2) Mention and connection of knowledge pieces	(3) Alignment of knowledge pieces with context features	(4) Metacognitive strategies
1a: Description of cr* context features	2a: Mention or description of non-content-related or naïve knowledge pieces	3a: Coordination of ncr** knowledge pieces with cr* context features	4a: Formulating assumptions or questions
1b: Description of ncr** context features		3b: Coordination of ncr knowledge pieces with ncr context features	4b: Taking the perspective of a subject
	2b: Mention or description of a content-related fact or notion	3c: Coordination of a fact/notion with cr context features	4c: Making references to one’s own experiences
		3d: Coordination of a fact/notion with ncr context features	4d: Drawing conclusions
	2c: Description of a content-related relation or concept	3e: Coordination of a relation/concept with cr context features
		3f: Coordination of a relation/concept with ncr context features
	2d: Description of a content-related physical formula or abstraction of a relation	3g: Coordination of a formula/abstract relation with cr context features
* cr: (physics) content related; ** ncr: not (physics) content related		3h: Coordination of a formula/abstract relation with ncr context features

We also decided to include a fourth main category considering the metacognitive aspect of transfer. This category is comparable to the readout strategies in the coordination class theory (diSessa & Wagner, 2005) or the transfer processes, strategies and mechanisms from traditional transfer approaches. The specific subcategories from this fourth main category – referred to as (4) metacognitive strategies – as well as the subcategories from the other three main categories (Table 1) were derived inductively from the interview data.

For every interview, we created a document portrait with MAXQDA to compare the whole process of transfer in the sense of a sequence of the codings. The examples (Figure 3) show two representative transfer processes that are different in terms of the amount and sequence of the coded categories (the coloured squares are representative of the length and place of codings within the transcripts; main category 1 is blue, 2 is green, 3 is orange and 4 is purple). In group interviews, we coded subcategories to the statements of the students individually, except when it was a direct response to a statement of another group member (the response had to be directly related to and about the same topic as the first statement). But the whole transfer process of a group was seen as one process containing all the coded statements of the group members.

Figure 3. Document Portraits of Transfer Processes from Two Different Interviews.

All the analysed transfer processes have discernibly different sequences of coded categories. This uniqueness of (verbalised) thought processes including the connection of knowledge pieces, the analysis of context features, the alignment and use of strategies is independent of the age and school level of the students. This means, that there are no patterns of sequences of categories that could describe transfer processes of a specific group of participants. Some of the coded categories (like category 1) are far less frequent than others and some appear regularly (like category 4), which is visible in the selected document portrait (Figure 3, purple squares). The portrait on the left shows a transfer process of a group of students from lower secondary school, the one on the right the transfer process of a student of the university of teacher education. These diagrams are shown as representative of the transfer processes from the 12 interviews.

Results for Research Question 2 (RQ2)

The following section presents an explanation of each category of the framework to show how students deal with their knowledge pieces and the context of the transfer task. Some explanations are provided with an example of a student’s statement to illustrate the deliberations behind the derivation of the respective category. The comments from the original transcripts in German were translated into English.

1. Description and analysis of context features: Context features can be related or unrelated to the solution or the subject matter of the transfer task. We found statements in our interview data where students described or analysed both variants of context features, so we defined two subcategories: one for the description of content-related context features (1a), and one for the description of non-content-related context features (1b). These two subcategories include exclusively statements that have no knowledge pieces aligned to the described context features. As an example, one student analysed the map of the rope park and identified context features that could be considered as addressing energy transformation. The student stated that ‘somewhere there is this one [points to the map of the climbing park], this is the highest point where you can abseil, so to speak. It’s a high tree from which you can jump out into nothingness, and then it slows you down quite a bit and lets you down there until you’re back on the ground.’ For statements such as these, we derived the first subcategory (1a): only features of the task context are described, and there is no link in the description to existing knowledge pieces the student has regarding the topic of energy. If there was neither a direct reference to a possible solution to the transfer task nor a reference to knowledge pieces about energy, we coded subcategory (1b) of the first main category, as in the following example statement: ‘Well, I have to look at the picture first and, uh, there I see the different starts and there it has different colours of starts and finishes, maybe it has something to do with the difficulty of these, uh, tracks, but I don’t know much more about that now.’ Here, the colours of the track signs are not relevant for an answer to the questions of the transfer task.

2. Mention and connection of knowledge pieces: We based this main category on the coordination class theory’s concept of knowledge pieces that are newly built in every situation (diSessa & Wagner, 2005). If a transfer task triggers specific individual knowledge pieces or causes the connection of these to a more complex concept, this main category was applied to the respective coding unit, as long as no link to any context feature was made (apart from the text of the task). We found different levels of individual or connected knowledge pieces in the form of transferred concepts in the statements of the students.

   The first subcategory (2a) includes all individual or connected knowledge pieces that are not content-related to the task or even technically incorrect. We also allocated prior knowledge, or so-called ‘p-prims’ (diSessa & Wagner, 2005), to this category but only without any direct link to a context feature of the task. One student, for instance, tried to explain how energy was calculated but remembered the wrong formula: ‘There is the formula m times v equals energy.’

   The other three subcategories differ in terms of complexity regarding the amount of (connected) knowledge pieces or the form of representation. Statements that included individual knowledge pieces that are not interconnected were compiled in the second subcategory (2b). This included statements where students described or listed numerous forms of energy without linking them to the context of the task, as is the case with this statement: ‘Now, forms of energy, I would say kinetic energy, potential energy and thermal energy’.

   When students connected two or more knowledge pieces to describe a relation or concept, we applied the third subcategory (2c). The relation or concept had to be content-related and technically correct, like this statement: ‘In a closed system, no energy is lost, but, uh, friction creates heat, which is surely lost. So more simply not lost, we can’t use it, let’s say so. Energy that we can’t use anymore. But nothing is lost, so it is always some form of energy’. Here the student connected various knowledge pieces (e.g. the closed system, friction, heat, energy form, etc.) to explain the concept of energy conservation; there was, nonetheless, still no link to the actual context of the task.

   We also found that students explained matters with a physical formula. This represents a more abstract way of describing a relation or concept of two or more knowledge pieces, as indicated by the following statement: ‘I know that the total energy, i.e. E total, should actually be E potential plus E for the motion, hence kinetic, plus, uh, the spring energy or ½ times D times s square. So, at the moment I have this formula in my head, just like that [laughs], maybe I will write it down [takes paper and pen].’

3. Alignment of knowledge pieces with context features: This category for alignment was deductively defined as our third main category. We found students connecting their knowledge pieces with features of the context of the transfer task, conducting an alignment according to the coordination class theory (diSessa & Wagner, 2005). Aligning knowledge pieces with context features is a meaningful activity during which (parts of) the solution of a transfer task can emerge.

   Based on the first and second main categories, we included two types of context features and four subcategories for the (interconnected) knowledge pieces, respectively. The crossing of these two times four factors results in eight variants of alignment (Table 1). A student could, for instance, coordinate a content-related context feature like a cable car with a single, not interconnected knowledge piece like electric energy (subcategory 3c): ‘Then, uh, electrical energy, here, with the cable car’. In principle, every combination of the subcategories of main categories one and two is possible. However, in our interviews, we found predominantly those subcategories which included content-related context features (3a, 3c, 3e, 3 g; marked in grey in Table 1).

   The most frequently found subcategory was the coordination of a relation or concept with content-related context features (3e), like in this statement: ‘Yes, generally in the rope park, you use the different height differences, so to speak, and then it changes, or, there is a movement, when he is higher up and then slides down, from a potential to a kinetic energy. And that’s what you’re doing now in this rope park, you use exactly these forms of energy. The conversions, so to speak … Hmm [long pause].’ This subcategory was coded more than twice as much (76), than the second most coded subcategory (3c, 32). Other subcategories were found only twice (3b, 3f), once (3d) or not at all (3 h).

4. Metacognitive strategies: We summarise statements that show metacognitive procedures in this category as metacognitive (transfer) strategies. Such strategies show how and why transfer can occur. The following four subcategories were derived inductively:

   • (4a⁣⁣⁣⁣⁣⁣⁣) Formulating assumptions or questions: Students formulated questions to themselves or their peers to question their solution approach or exhibit uncertainty in solving the transfer task. They also made assumptions about what they saw as a possible solution to the task. We combined those two strategies in one subcategory because they are difficult to distinguish. The questions or assumptions should foster or bring forward the other processes (such as the description of a context feature or an alignment) to classify these as real transfer strategies, as seen in this statement: ‘Given this fire, it would actually be heat energy, wouldn’t it? Isn’t fire part of heat energy?’

   • (4b) Taking the perspective of a subject: Students often described (hypothetical) actions of a subject (e.g. person or animal) in the task context. They took the ‘I’, ‘you’, ‘we’ or ‘one’ perspective and explained or discussed the situation from this (fictional) view. For example, one student stated: ‘I quickly imagine that when I climb from the ground onto the tree … and, as it were, with the stairs to the first platform [pointing to the map], my energy changes with every step … and I only notice this when I jump down’. The student thought and talked about the situation step by step, taking a task subject’s perspective.

   • (4c) Making references to one’s own experiences: Students used similarities with familiar situations to argue about the transfer task. Analogies related to tasks that were discussed in school during the initial learning about energy or to everyday experience in out-of-school situations. There is an action of comparison in this transfer strategy, as illustrated in the following discussion about the freefall tower in the rope park:

     S1: That is, that is, yes. That’s the example when you jump on the trampoline. So, yes, on the trampoline you just go up again, but here you just fall down again.

     S2: Yes. Yes, actually it is similar, so you come, you, eh, tie yourself up, then you jump down and then you are … ’

     S1: … caught.

     S2: Afterwards again a little bit upwards. Actually, it is similar to that, like the trampoline.

     By identifying and describing similarities or differences in the transfer situation and their experience, students could incorporate their findings when solving the physics task.

   • (4d) Drawing conclusions: This strategy involved students’ (active) reflection during the transfer process, resulting in new insights about the transfer task or topic. Triggers for drawing conclusions from review can be contextual features, newly combined knowledge pieces or following the process of alignment. Drawing conclusions during transfer is predicted by several modern transfer approaches (e.g. from the ‘Preparing for Future Learning (PFL)’ approach). This is in line with the idea that knowledge is always newly constructed in every (transfer) situation, and new knowledge pieces can be added by reflecting on the given task. While we found conclusion-drawing in our interview protocols, the instances were somewhat rare. One example is this reflection about the occurrence of energy forms: ‘Now I’ve got more with the ropes and the … yeah, that was actually the first thing that came to my mind. … But actually, it has much, much more forms of energy, now that one starts to think like that, it’s like this, everywhere, actually, in everything [laughs].’

Discussion

Our objective was to substantiate known transfer strategies and processes from previous work in transfer research. Thereby we aimed to develop a framework to describe, analyse, and compare transfer processes in physics education, based on think-aloud thought protocols from students solving a physics task. For the topic of energy, we now have a reliable framework, which includes different aspects of traditional transfer theories as well as requirements of modern approaches like the AOT. With our framework, we can answer (part of) the questions about which strategies students use during transfer (RQ1), how transfer processes look like (RQ1) and how students deal with their knowledge pieces and with the context features of the transfer task in a transfer situation (RQ2).

For research question 1 (RQ1) we looked for transfer strategies that students used while solving or discussing the transfer task. Even if we could only infer that a student applied the respective metacognitive strategy from the given statement, we tried to find patterns of procedures in the transcribed interviews. Four strategies could be coded reliably; presumably, however, this list is not yet complete. While we do not claim to integrate all previously studied mechanisms and strategies, the four strategies found in the interviews can be related to the theoretical approaches reviewed. The first metacognitive strategy is ‘formulating assumptions or questions’ (4a). This strategy aids the construction of a representation of the context situation. According to Nokes-Malach and Mestre (2013), it represents the first step in a transfer process. Students activate their knowledge or knowledge pieces when they formulate questions to themselves or explore possible answers when developing assumptions. We see the latter as a part of ‘sense-making’; indeed, it is a reflection upon the given situation. When solving the transfer task in groups, students also asked questions to their classmates in social interactions during the transfer process. This indicated, in turn, that students integrated and interpreted the environment of the transfer task (Nokes-Malach & Mestre, 2013). The second strategy we outlined (‘taking the perspective of a subject’, 4b) is also aimed at the social interaction and sense-making process. According to Lobato et al. (2012), ‘noticing’ means selecting, interpreting, and working (with) the given features or regularities. This can be simplified when students think the situation through in a (fictive) acting person’s perspective. It helps students to better align their knowledge pieces in the future.

We located the other two strategies in the framework in the second step of the transfer process model by Nokes-Malach and Mestre (2013). ‘Making references to one’s own experience’ (4c) is essentially the same strategy or mechanism as making analogies or looking for identical elements. In our study, students remembered previous experiences from classes or outside the school environment and related them to the actual transfer situation. This strategy does not merely involve looking for deep structure features of the task to be similar to the learning situation (which was the intention of the traditional description of identical elements in transfer research); instead, the strategy of making references to one’s own experience is very individual and depends strongly on the prior knowledge of students. Therefore, the deep structure in the traditional sense plays a role for ‘successful’ transfer, and, at the same time, all the context features and existing knowledge pieces can be the trigger for this strategy.

The last of our framework’s four metacognitive strategies (‘drawing conclusions’, 4d) is a process containing the reflection after finding an answer or assumption to the transfer task. The alignment (or, simply, the connection) of knowledge pieces within the context situation can lead to new insights and the inclusion of new knowledge pieces. In simpler words: students can learn during transfer. If students actively reflect and look for such conclusions drawn from the transfer situation, they actually apply this strategy. We see this as a part of ‘satisficing’ or ‘sense-making’ in the two-step transfer process, but also see some similarities with the traditional mechanisms of transfer, including ‘knowledge compilation’ and ‘constraint violation’ (Nokes-Malach & Mestre, 2013).

To answer research question 2 (RQ2) we took approaches of existing transfer theories like the coordination class theory (diSessa & Wagner, 2005) as a starting point to empirically develop the subcategories for the main categories 1, 2 and 3 of our framework. The process of coding of the statements of the students led to several deviations from our initial theory review.

In main category 1 (‘Description and analysis of context features’), we could not distinguish all dimensions of the context model by Löffler et al. (2018). Based on our data, we decided to differentiate between context features that are related to a possible solution and those unrelated. We chose not to describe surface and deep structure features because this is primarily a distinction made by experts (and regarding the AOT, we wanted to see the transfer from the actors’ point of view). Moreover, we were unable to decide which context features would have been surface or deep-structure features because the chosen situation dictates which features are relevant for the solution. Therefore, two subcategories were enough to code the statements of the participants.

One can assume that during a transfer, only alignment (according to the coordination class theory) occurs. Instead, we could show that the sole description of context features (main category 1) or the mention and connection of knowledge pieces without any link to the given context (main category 2) are possible. The latter is triggered by information from the transfer task when students connect their knowledge pieces while ignoring the given context situation. This is particularly interesting because abstraction of knowledge is widely discussed in the literature of transfer (e.g. Lave, 1988; Wagner, 2010) and context-based instruction (Bennett et al., 2007; Taasoobshirazi & Carr, 2008). Some of the participating students transferred part of their knowledge in an abstract form, without any relation to previously learned context situations or the context of the transfer task. We can, therefore, assume that, during transfer, knowledge pieces can be connected to form an abstract concept that is independent of its context, even if knowledge pieces were learned via context-based instruction.

When looking for what students transfer, it was difficult to distinguish the four levels of energy concept development (Neumann et al., 2013). This corresponds to the authors’ conclusion that the levels are developed in parallel. In our interviews, we can see that this also applies for transfer (at least for our group of 20 participants). We decided to distinguish the complexity of statements regarding energy and not primarily the four levels mentioned. This approach resulted in subcategories describing the number of knowledge pieces that were noted or connected during alignment (main category 3) or without linking them to the context situation (main category 2). In addition, we added a subcategory for statements that included abstract explanations like formulas or described equations, respectively. Several students argued with, for instance, a formula of a particular energy form, such as kinetic energy. After having learned about this in class, students remember a formula during transfer because the required knowledge pieces are already connected through the formula.

The alignment of (connected) knowledge pieces with context features (main category 3) is a merging of the first two main categories of the framework. Some subcategories of the alignment were not found in our transcripts. We have thus highlighted the common subcategories in Table 1. Other subcategories are possible in principle, but rare. An example would be the alignment of a non-content-related context feature with a (physically correct) formula (subcategory 3 h). Nevertheless, it is likely that when a student mentions a formula, they show the connection with a content-related feature of the context situation.

After discussing the different aspects of the categories in our framework, we now want to specify what a transfer process is (RQ1). We argue that an individual transfer process while solving a task is the sum of all subcategories coded in the unique sequence. It is thus possible to compare transfer processes from different students, for example with document portraits (see above). We found that those processes were quite different regarding the amount and sequence of the coded subcategories, so it was impossible to see a pattern among them. The way we define a transfer process is different to existing approaches like the two-step transfer process of Nokes-Malach and Mestre (2013), because our definition respects the individual procedure of a student (visible in the sequence of the coded subcategories) and not a predefined sequence of transfer steps.

Moreover, the use of metacognitive strategies varied, which we attribute to the different experiences students had with the topic of energy, the environment of the transfer situation and the transfer task itself, which allowed for different approaches of solving and thinking about the task. This finding can be seen as an advantage of the task applied in our study. We assume that students, based on their prior knowledge and the transfer situation, think differently in every (transfer) task. However, in tasks used in traditional transfer studies, the thoughts of students are not sufficiently captured.

Conclusion and limitations

With the framework developed based on existing transfer theories and an inductive process of analysing think-aloud interviews with students of different ages and school levels, it is possible to describe and compare transfer processes in physics. The study was actor-oriented, which means that the thoughts and solution approaches of the students were central to the development of the framework. We considered not only what is transferred but also, with the metacognitive strategies included in the framework, how and why transfer occurs. The framework is intended for analysing transfer in tasks with questions that allow different solutions and ways of thinking. It thereby differs from traditional transfer research but respects certain mechanisms that are known from those studies. In addition, we do not merely consider the task (context) or the knowledge pieces of participants, but notably the interconnection between those two aspects.

We recommend for teachers to plan their physics lessons explicitly with later transfer strategies and the task context as well as the knowledge pieces of their students in mind. There should be a focus not only on understanding the deep structure of the problems discussed in class, but also on dealing with context features regarding the surface structure of a problem, on learning metacognitive strategies and on how to apply those strategies in a transfer situation. We suggest including specific transfer tasks during physics classes for practicing. While teaching the concept of energy, highly contextualised tasks (like we used in our study) with open questions and with a variety of different solutions could foster the use of metacognitive strategies. Students would have to think about their experience from previous instruction or from out-of-school observations, formulating assumptions and questions and drawing conclusions while solving the problem. We also recommend including different features of context that help students put themselves in the transfer situation. As we saw in our interview analysis, students often think about actions of a (fictive) person showed in a picture or mentioned in a task description. They then take the perspective of this subject to think through possible solutions to the questions. This approach and further relation of the task to everyday life could be a useful way to actor-oriented transfer exercises. To initiate the training of specific transfer strategies like those described in our framework, teachers should give hints and develop tasks that include prompts (e.g. to formulate assumptions or to think the situation through from the perspective of a subject).

Transfer tasks during instruction should be used after students have learned the main concepts of energy forms, energy transformation and degradation etc., because a proper amount of knowledge pieces are a prerequisite for building concepts in a transfer situation. In a transfer task the main focus will be the discussion about the use of strategies for the alignment of those knowledge pieces with context features.

Our study is restricted to physics and the topic of energy. For other domains and maybe even for other physics topics, different strategies or alignment processes may be more suitable. There is also no quantitative data to empirically prove the frequency of use of the described strategies or other parts of the framework. In an ongoing study to pursue this aim, we develop a measurement instrument for quantitative transfer studies in physics. Such studies will show if the use of transfer strategies can be replicated in a larger sample than we had with the 20 students participating in think-aloud interviews.

It remains to note that the framework only covers part of the transfer process. We assume that further metacognitive strategies exist. According to the actor-oriented transfer approach, future (quantitative) studies should also include the measurement of motivation and social aspects.

Data availability statement

The data that support the findings of this study are available from the corresponding author, D.G., upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Swiss Federal Government under ‘Projektgebundene Beiträge’ PgB P-9.