Variation theory: A theory of learning and a useful theoretical framework for chemical education research

Abstract

Instructors are constantly baffled by the fact that two students who are sitting in the same class, who have access to the same materials, can come to understand a particular chemistry concept differently. Variation theory offers a theoretical framework from which to explore possible variations in experience and the resulting differences in learning and understanding. According to variation theory, there are a limited number of features of a given phenomenon to which we can pay attention at any given time. Our experience of that phenomenon depends on the specific features to which we direct our attention. Two individuals who experience the same phenomenon may focus on different features and, thus, come to understand the phenomenon differently. The purpose of this article is to present variation theory as (1) a useful way for instructors to think about student learning and (2) a potentially powerful theoretical framework from which to conduct chemical education research.

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Introduction

How is it that two students who are sitting in that same class on the same day with access to the same materials can come to understand a chemical concept (or any concept for that matter) differently? “Variation theory is a theory of learning and experience that explains how a learner might come to see, understand, or experience a given phenomenon in a certain way” and why two students sitting in the same class might come to understand a concept differently (Orgill, 2012, p. 3391). The purpose of this article is to present variation theory as (1) a useful way for instructors to think about student learning and (2) a potentially powerful theoretical framework from which to conduct chemical education research.

While those two students are both physically present during the same event, their experiences—or, more accurately, their perceptions—of that event will be shaped by a huge number of factors. Any phenomenon will present an individual with innumerable features to which they could attend. One cannot possibly attend to all of them at the same time (van Merriënboer and Sweller, 2005); so the question then becomes, to which features does that person pay attention? The limited number of features to which one attends and the meaning one ascribes to those features will determine an individual's perception of a given event (Marton and Booth, 1997).

If we want people to experience a phenomenon in a particular way, then we need them to attend to certain critical features of that phenomenon. In the chemistry classroom, if we want our students to come to a shared understanding of a given chemical concept, we must then cue them to focus on certain critical features of that concept. Variation theory not only provides a useful way to explain the differences in students' understanding of a particular concept, but also a theoretical perspective from which qualitative educational research studies can be designed in order to identify the differences between what instructors intend for their students to learn about a particular concept and what their students actually learn about that concept.

Background

Variation theory follows from the phenomenographic research tradition (Runesson, 2005). Phenomenography grew out of a series of empirical research studies conducted by a Swedish research group in the 1970s in an attempt to answer the questions “(1) What does it mean that some people are better learners than others?; and (2) Why are some people better at learning than others?” (Pang, 2003, p. 146). Marton (1981) asserts that there are a limited number of qualitatively unique ways in which different people experience or perceive the same phenomenon. Thus, the objective of phenomenographic research is to identify and describe the variation in experiences or perceptions that a particular group of people has of a given phenomenon (Orgill, 2007). Published phenomenographic studies in the areas of chemistry and science education have described the variation in the experiences or perceptions that a particular group of people have had with a given phenomenon (i.e., learning science; see Tsai, 2004), scientific concept (i.e., students' understanding of a mole; see Tullberg et al., 1994), or event (i.e., the results of participating in an innovative chemical engineering course; see Case et al., 2001). In other words, the phenomenon under study in a phenomenographic study can be a phenomenon, a concept, or an event. For this reason and because variation theory is a phenomenographic theoretical framework, in this article we will use the terms phenomenon, concept, and event interchangeably. Later on in the article, we will also use a term from variation theory, the object of learning, synonymously with these terms.

Variation theory, sometimes referred to as “new phenomenography,” reflects a shift within the phenomenographic research tradition that occurred in the 1990s (Orgill, 2012). During that time period, phenomenography was criticized as being a purely descriptive and atheoretical framework. In other words, although phenomenography and its methods could be used to identify and describe the range of experiences a particular group of people had with a given phenomenon, it could not explain why that variation in experience existed. Variation theory can be seen as a more theoretical extension of phenomenography, in that it attempts to explain how people—particularly students—can experience the same phenomenon differently and how that knowledge can be used to improve classroom teaching and learning (Tan, 2009).

Aims of variation theory

To better understand what something is, it is often equally as important to understand and contrast it with what it is not. Thus, in order to discern some aspect of a phenomenon, an individual must experience variation in that aspect. This experience of variation allows the learner to create meaning for the phenomenon.

While there are many potential examples of variation in the teaching and learning of chemistry—some of which we will discuss later in this article—we will begin with a more commonplace example. As noted by Orgill (2012), in order to learn the concept of a ripe banana, one can focus on many features. One such critical feature associated with ripeness is the color of the banana (Fig. 1).

Fig. 1 Stages of banana ripeness.

In order to understand how the feature yellow relates to the concept of ripe banana, one must also experience under-ripe, green bananas as well as over-ripe, brown bananas. This experience of variation in the critical feature of banana color allows the individual to create meaning related to the concept of banana ripeness. It should be further noted, that the gradation of color, from green to yellow to brown, represents a specific continuum in variation within which future experiences will be judged. As such, a blue banana would have no meaning with regards to the concept of banana ripeness within this context.

Banana color is by no means the only critical feature related to banana ripeness. Taste, for example, would be another important feature for one to experience in order to develop a deeper understanding of the concept of banana ripeness. Similarly, one could experience variation in banana size; however, the feature of size is not necessarily related to the concept of banana ripeness. In this way, an individual must filter out some features from others in order to create a meaningful conception. Thus, the individual's perceptions of certain critical features based on experienced variation within and between features allows that individual to construct a mental model of a given concept that is unique to that individual. The overall aim of variation theory is to explain differences in learning and understanding based on the experience of variation in these critical features.

Key concepts of variation theory

The link between phenomenography and variation theory is variation: “describing it (phenomenography) or explaining why it exists (variation theory)” (Orgill, 2012, p. 3391). Phenomenography describes the limited number of qualitatively different ways individuals can experience the same phenomenon. With regard to learning, some ways of experiencing a phenomenon are more meaningful than others. Thus, the way in which a phenomenon is experienced has significant ramifications for learning (Runesson, 2005). The presence of variation creates a potentially noticeable contrast within or between one or more features of a phenomenon. Take, for example, a series of cartoons in which the only feature that is varied is the size of a particular balloon. The variation in size of the balloon would draw attention to the balloon, and cartoon readers would likely begin to wonder why the balloon was changing size, i.e., they would attend to the balloon because of its changing size. At the same time, the readers would most likely ignore many of the invariant features of the cartoon.

An individual's experience of a given phenomenon depends on the particular set of features to which they attend. In order to experience a phenomenon in a particular way, an individual discerns and assigns meaning to certain aspects of that phenomenon. “The aspects of the phenomenon and the relationships between them that are discerned and simultaneously present in the individual's focal awareness define the individual's way of experiencing the phenomenon” (Marton and Booth, 1997, p.101).

For example, as chemical educators, it is our goal to help our students construct a shared (and, hopefully, scientific) understanding of a given concept. To do so, we need them to experience a given learning environment and the material presented in that environment in a particular way, i.e., we need them to notice, recognize the importance of, and make meaning from certain critical features of the concept to be learned (referred to as the object of learning in variation theory). Noticing critical features of a given phenomenon, however, is not a simple process. Variation theory describes this noticing as being related to several key processes and concepts that underlie learning, including awareness, discernment, and simultaneity.

Awareness

How we experience a phenomenon depends on which aspects of the phenomenon are held in our focal awareness. Cognitive research has shown that the human brain is only capable of processing a limited amount of information at any given time (Miller, 1956). Chabris and Simons (2010) demonstrated this in their study known as the “gorilla experiment.” In this study, the researchers created a video in which six players—three in white shirts and three in black shirts—pass basketballs back and forth. Study participants were instructed to count the number of passes made by the players wearing white shirts (i.e., their attention was focused on the players in the white shirts). During the action in the video, a person in a gorilla suit walks through the scene, stops at center stage to thump their chest, and then walks off stage. After the study participants finished watching the video, they were asked how many passes were made between the players in the white shirts. They were then asked if they saw the gorilla. Only about half the study participants had noticed the gorilla. As the participants focused on the task at hand, i.e., counting passes, it was as if the gorilla were invisible. Similarly, students who are focused on a particular aspect or feature of a phenomenon may not notice other features of the phenomenon, even though those features may be important.

In experiencing a phenomenon, we are unable to be aware of all aspects of the phenomenon. Instead, we are only able to attend to certain aspects of the phenomenon. Marton and Booth (1997) note that “[i]f we consider an individual at any instant, he or she is aware of […] certain aspects of reality focally while other things have receded to the background” (p. 108). So which features do we notice and which fade into the background? Experiencing variation in a particular feature may serve to call attention to that feature, thereby allowing it to be noticed while other features may fade into the background.

The particular features brought into focal awareness form the basis of the subsequent construction of knowledge for that experience (Marton and Booth, 1997). “[Q]ualitatively different ways of experiencing something can be understood in terms of differences in the structure and organization of awareness at a particular moment” (Marton and Booth, 1997, p. 100). To readdress the opening question of this article, two students may be sitting in the same classroom at the same time and exposed to the same instructional materials and pedagogies; however, each individual student may attend to different features of the learning event and, thus, come away with a different experience and understanding of that phenomenon. The educational challenge lies in directing students to focus on those aspects deemed critical for experiencing the learning event in a particular manner and doing so in a way that does not excessively tax working memory; in the case of science education, this manner would be the scientifically accepted conception of a given topic.

Discernment

How, then, do students become aware of certain critical aspects of a given phenomenon? In order to be aware of certain aspects of a phenomenon, learners must first discern those aspects from their environment. “To experience something is to discern parts and the whole, aspects and relations” (Bowden and Marton, 1998, p. 33). Discernment is the ability to hold an aspect of a phenomenon in focal awareness and contrast it with its environment in order to construct meaning for that aspect and, subsequently, for the phenomenon. Consider the gorilla experiment described above. Study participants were tasked with counting the number of passes between players wearing white shirts. In order to achieve this task, study participants first had to discern who is a player in a white shirt and who is a player in a black shirt. Each player had to be discerned from the background and then from each other. This experience of variation between the aspect and its environment allows for the perception of that aspect. It should be noted that Marton and Tsui (2004) make a clear distinction between “discernment and being told” (p. 10). The context of experienced variation holds a great deal of information. Discernment is a product of direct experience while being told is non-contextualized and, therefore, lacks a great deal of meaning and significance. As such, variation theory places great emphasis on learners' directly experiencing variation in the critical aspects or features of a given phenomenon.

Simultaneity

It is not enough for a learner to be aware of and discern a single feature of a given phenomenon. In order to truly understand a phenomenon, learners must be simultaneously aware of multiple features of the phenomenon and able to discern the phenomenon from its environment. In other words, in developing an understanding of a concept, it is not enough to be aware of individual features at discrete moments in time. Learners must be simultaneously aware of multiple critical features of a concept. Again, consider the gorilla experiment. It was not enough for the study participants to only be aware of one of the players in a white shirt. Instead, they had to be simultaneously aware of all three players in white and their changing locations as well as the ball moving between them in order to complete the task of counting passes between players in white shirts.

Based on experienced variation and prior knowledge, several aspects of a given phenomenon may be discerned (Marton and Tsui, 2004). However, cognitive load limits our ability for simultaneous focal awareness. Thus, again, “the aspects of the phenomenon and the relationships between them that are discerned and simultaneously present in the individual's focal awareness define the individual's way of experiencing the phenomenon” (Marton and Booth, 1997, p. 101).

The object of learning

The act and/or pursuit of learning implies that there is something to be learned. Marton and Booth (1997) describe this something as the object of learning, i.e., what is to be learned by the student. It is the object of learning that is the unique, central focus of variation theory and that distinguishes this theoretical framework from others (Runesson, 2005). (As noted earlier, the terms concept, phenomenon, and event are used interchangeably in this article. To embrace the terminology of variation theory, we will now include object of learning among these synonymous terms.) It is important to note that the object of learning is not a physical object; it is the target concept, phenomenon, or experience at the heart of a learning event. For example, in a second semester general chemistry course, an object of learning might be the concept of chemical equilibrium, while in an organic chemistry course, an object of learning might be the phenomenon of learning how to use arrow-pushing mechanisms to predict the product of a reaction. It is further important to distinguish any representation of the object of learning from the object of learning itself. A chemical equation that includes an equilibrium arrow is a representation of chemical equilibrium. However, this representation is not the object of learning. The dynamic process of chemical equilibrium is the object of learning.

Variation theory allows us, as chemistry education researchers, to examine the learning event—and the object of learning—from three different perspectives by asking the following research questions: (1) according to instructors, what should students learn about a particular object of learning?, (2) what is possible for students to learn about a particular object of learning (based on what they experience during a learning event)?, and (3) what did students actually learn about a particular object of learning? Variation theory examines and triangulates the object of learning from these three different perspectives, each of which will be described below: the intended object of learning, the enacted object of learning, and the lived object of learning.

A learning event involves the interaction of two spheres of knowledge and experience, the teacher and the student (Fig. 2). The teacher facilitates learning and may represent a specific person in the case of a formalized classroom environment or more of an abstraction of expert thought and intention in the case of informal or non-formal learning environments. In all cases, the teacher enters the learning event with some intention for student learning. Similarly, the student represents any individual who enters the learning event in a position to experience and perceive an object of learning and develop a new or altered conception of that object. The overlap in these spheres represents not a shared experience of the learning event but rather the interaction between the teacher and student during that event. This constitutes a space within which learning can take place. This region of overlap is known, appropriately, in variation theory as the space of learning.

Fig. 2 The objects of learning within variation theory. Note: this representation of variation theory has been modified from the model proposed by Rundgren and Tibell (2009, p. 230).

The intended object of learning. Considering the teacher perspective of the object of learning, we can discuss the intended object of learning (see Fig. 2). In developing instructional materials, the teacher (note an inclusive use of the word teacher to encapsulate classroom instructors, curriculum designers, textbook publishers, graphic designers, etc.) intends for student(s) to learn particular concepts (Marton and Tsui, 2004). This intention manifests in the selection, organization, and preparation of instructional materials. The intended object of learning is bound by the teacher's sphere of knowledge and experience.

The enacted object of learning. The act of learning, however, is not defined solely by the teachers' intentions. To paraphrase the poet Robert Burns (1785): the best laid plans of mice and men often go awry. What one intends to teach and what actually happens in the classroom are often two different things. The possibility for learning is dictated by what is actually presented to students and is co-constructed though the interactions that occur between teacher and student and among students within the learning environment (see Fig. 2) (Runesson, 2005). The enacted object of learning constrains the possibilities of experience and, subsequently, for learning. Most commonly, the enacted object of learning is described in the context of a classroom (Marton and Tsui, 2004). However, the learning environment created by any forum (i.e., classroom, textbook, representation, online learning materials, etc.) has the potential to comprise the enacted object of learning. It should be noted, however, that “no conditions of learning ever cause learning. They only make it possible for learners to learn certain things” (Marton and Tsui, 2004, pp. 22–23). Thus, the possibility of learning created by the enacted object of learning constitutes a space of learning for students (Marton and Tsui, 2004).

The lived object of learning. Lastly, from the student perspective, we can discuss the lived object of learning (Fig. 2). Marton and Tsui (2004) identify the lived object of learning as “the way students see, understand, and make sense of the object of learning when the lesson ends and beyond” (p. 22). Students' perception of the enacted object of learning provides the basis from which students construct meaning. Students' experience of the enacted object of learning is informed by the features they discern and of which they are simultaneously aware. This object of learning is often the focus of educational research, i.e., what did students actually learn? Any discrepancies between this lived object of learning and either the intended or enacted objects of learning can provide insight into how curricula or curriculum materials might be modified in order to help students become aware of the critical features of a given phenomenon, a condition that is necessary for learning.

Why study three different objects of learning?. Any study that is informed by variation theory will examine all three aspects of an object of learning—the intended, enacted, and lived objects of learning—and the relationships between these entities. It is not appropriate, for example, to only study the object of learning from the teacher perspective. Other theoretical frameworks might be more consistent with such a study.

Knowledge of all three aspects of an object of learning can be particularly useful to instructors who wish to improve their instructional materials or practices (e.g., Marton and Tsui, 2004). Comparisons between the intended and lived objects of learning can be used to identify differences between what instructors hope students will learn and what students actually learn about a given concept. A comparison between the intended, enacted and lived objects of learning can illuminate why students are not learning what their instructor wanted them to learn about a given concept, since the enacted object of learning—and not the instructor's intentions—creates possibilities for learning. The results of a study informed by variation theory, taken as a whole, can ultimately be used by instructors to revise or design instructional materials and experiences that can be integrated or implemented into a new learning event (a new enacted object of learning) that will ideally lead to their students' developing a desired understanding of a particular object of learning (a new lived object of learning from that future learning event). Similarly, an examination of both the enacted and lived objects of learning may influence an instructor's intended object of learning for a future learning event. In Fig. 2, we have chosen to represent the fact that each object of learning potentially influences the other objects of learning in a future learning event as bidirectional arrows between those objects of learning.

Critical features

Within the phenomenographic research tradition, the researcher is concerned with describing the variety of different ways of experiencing the same phenomenon. As educators, we are much more concerned with getting our students to experience a phenomenon in a scientifically accepted way. To do so, students must notice and be aware of certain features of the object of learning while ignoring others. The features of the object of learning that are important for students to experience in order to develop a particular understanding of that object of learning are the critical features. The critical features are the features of an object of learning that are necessary to distinguish one way of thinking from another (Marton and Tsui, 2004); however, the term is used more often to describe the “features and conditions necessary for learning” (e.g., Rundgren and Tibell, 2009, p. 229). For example, a 2009 paper presented by Park et al. (2009) at the Learning Progressions in Science Conference examined college chemistry students' conceptions of atomic structure. The researchers identified nine hierarchical critical features: divisibility, circular orbits, force, multiple orbits, energy quantization, probability, orbital shape, and wave function. “Making these critical [features] salient to students and facilitating them to figure out the aspects of variation characterizing each concept will enhance student learning about atomic structure” (Park et al., 2009, p. 11).

While educators and educational researchers may deem certain features as critical for developing correct understanding about a given phenomenon, it is possible that those critical features will not be noticed by students or that students will notice some features that the instructors do not deem to be critical. Thus, students will come to a unique understanding of a learning event based on the features, critical or otherwise, to which they discern and hold in their focal awareness. If we, as educators, can get our students to attend to certain critical features of the object of learning, we can help our students construct a more directed understanding of a given object of learning. Variation theory suggests that students' awareness can be focused on these critical features when they are allowed to experience variation in those features.

Significant patterns of variation

How is variation in a critical feature experienced? We are all exposed to a constant barrage of stimuli from the world around us. The ability to perceive a selected stimulus from the onslaught of others is a vital component of learning and, more broadly, survival. Gerow and Bordens (2000) define perception as “the cognitive process of selecting, organizing and interpreting stimuli” (p. 89). With constant exposure to stimuli, our sensory systems have evolved such that we do not perceive the constancy of baseline stimuli. Researchers have found that if a subject is exposed to a new stimulus, such as a sound, that stimulus will be perceived at first; however, with constant exposure to that stimulus over time, the subject no longer attends to or perceives that stimulus (Gerow and Bordens, 2000).

“Typically, we select a few details to which we attend” (Gerow and Bordens, 2000, p. 119). The question then becomes, which details are salient? In order to discern a particular feature from the cacophony of background information, that feature must be presented as different or varied from the background. Thus “[a]ccording to variation theory, a phenomenon and/or its critical features are made visible in a teaching context through variation” (Orgill, 2012, p. 3392). Contrast, generalization, separation, and fusion have been defined by Marton and colleagues (e.g., Marton and Pang, 2006; Marton and Tsui, 2004) as four significant patterns of variation (Guo et al., 2012; Orgill, 2012).

Contrast allows the individual to compare an object of learning or a feature of that object with something it is not. This allows the individual to create meaning for an object or feature by defining it against things that are different from it. As a child, we learn the concept of dog not simply by recognizing dogs but also by noting that they are not cats, or hamsters, or any number of other childhood pets. Similarly, in a chemistry class, a student could develop a concept of an acid by noticing that when the acid is added to a solution containing phenolphthalein, the resulting solution is colorless while the solution that results when a base is added to the same phenolphthalein solution turns pink. The contrast between the color changes of the two solutions serves to call a student's attention to the fact that the acid and base solutions behave differently. Once the student notices the difference in the color of the two solutions, he or she could construct meaning for the concept of acid using both their prior knowledge and other information provided during the learning event. For example, students could add “acid solutions do not turn pink when phenolphthalein is added to them” to their concept of acid based on this described experience of contrast. Their understanding of why acid solutions do not turn pink when phenolphthalein is added to them may then develop during future learning events. It is worth noting that while the contrast between color changes does not ensure that a student will interpret the phenomenon in a scientifically accurate manner, it does serve to draw student's attention, creating the possibility that learning could occur. Ideally, then, the contrast in the behavior of the acid/phenolphthalein and base/phenolphthalein solutions will allow a student to develop their concept of acid as they learn that acids do not behave like bases.

Generalization allows the individual to compare similar instances of the object of learning. “To fully understand an object of learning, the learner must experience many other examples to generalize the meaning” (Guo et al., 2012). Generalizing provides learners experiences that allow them to distinguish between essential and irrelevant features. With regard to the concept of dog, a child might experience large dogs, small dogs, medium sized dogs, brown dogs, grey dogs, multicolored dogs, nice dogs, mean dogs, etc., all of which are generalized to form the child's concept of dog. In the chemistry class, a student might experience strong acids, weak acids, Arrhenius acids, Bronsted–Lowry acids, Lewis acids, etc. By experiencing the same object of learning or feature of an object of learning in multiple contexts, the student is able to develop a broad, robust, and transferable meaning for that concept.

Separation allows the individual to discern one feature of an object of learning from other features by varying only the feature of interest while holding all other features constant. This allows the individual to experience and construct meaning for a particular feature of the object of learning, critical or otherwise, independent of each other. Each part is separated from the whole. This pattern of variation may not easily lend itself to a real world example. However, an example of separation would be exposing a child to several dogs each of which are identical in all features except size. One dog would be small. Another dog would be larger, and so on. By keeping all other features constant, the child would be able to discern the feature of dog size and separate that feature from all other features of the concept of dog. The separation of variables lends itself much more easily to the more controlled environment of the classroom. When learning about pH, a teacher might ask students to solve several problems in which the student must solve for the pH of a solution when different volumes of a 1 M strong acid are added to an acetic acid buffer. All other features of the buffer problems would be the same. Thus, the student would be able to separate the influence of the volume of acid being added on the pH of a buffer system from all other variables in the buffer problems.

Lastly, fusion allows the individual to discern variation in several features of an object of learning simultaneously. The experience of multiply varied features facilitates the discernment of relationships between the features of an object of learning. Each part is fused together to create the whole. This is often the child's experience of the concept of dog. The size, smell, color, body shape, and demeanor of the dog are all perceived together and fused to create a unique conception of a dog. In the classroom, the pH of a buffer system might be observed when the volume, concentration, and type of acid added are all varied. All of the individual parts interact to form a specific whole. The students' ability to perceive each component and its specific contribution to the whole can foster a more coherent conception of the concept.

Methodological considerations

Variation theory is not just an explanatory theory. It is a useful framework for guiding qualitative educational research studies that attempt to identify the gaps between teaching and learning. The goals of a study informed by variation theory are three-fold: (1) to describe the variation in instructors' intentions for students' learning about a given object of learning, (2) to identify experienced variation created in the space of learning about a particular object of learning (i.e., to determine what is possible to learn as a function of experienced variation), and (3) to describe the variation in student understanding of a given object of learning after the learning event has taken place. As such, there are three research questions that are typically asked in any study informed by variation theory: (1) what did the instructor intend for students to learn? (the intended object of learning), (2) what is possible for the students to learn? (the enacted object of learning), and (3) what did students actually learn? (the lived object of learning). Before data can be collected and before these questions can be answered in a meaningful way, the researcher must explicitly (1) identify the specific object of learning to be examined and (2) define and limit the student and teacher populations that will be examined in the study.

The type of data collected in a study informed by variation theory depends on the specific research question being asked. The intended object of learning “consists of the concepts and their features that the teacher […] aims to communicate” (Rundgren and Tibell, 2009, p. 229). As the intended object of learning is internalized within the teacher, a retelling of the teacher's perceptions of the object of learning offers insight into the intention behind the curricular and instructional design. The intended object of learning is unique to the individual and can only be expressed as “a second-order description, a description of the phenomenon as experienced” (Marton and Booth, 1997, p. 163). A second-order perspective means that the information received by the researcher is expressed by another party. Thus, teacher interviews and artefacts are used to assess the intended object of learning.

Similar to the intended object of learning, the lived object of learning is unique to the individual student and is expressed as a second-order description. Salient features and students' understanding of the learning event are accessed through students' retelling of the learning experience. This individual retelling of experience may come in the form of individual interviews, written artefacts, or group discussions (e.g., Rundgren and Tibell, 2009).

In contrast to both the intended and lived objects of learning, the enacted object of learning is expressed from a first-order perspective (Marton and Booth, 1997). “It is described by the researcher from the point of view of what is afforded to the learners” (Runesson, 2005, p. 70). Researcher observations of the enacted object of learning are often the primary (and sometimes only) source of data in variation theory literature (e.g., Runesson, 1999). The classroom usually defines the context within which the possibilities for student learning are enacted. This enactment of the object of learning is often captured as audio and video data (e.g., Ingerman et al., 2009). However, the classroom is not the only forum in which an object of learning could be enacted. For example, an ongoing research study is using variation theory to explore student learning from external representations, i.e., in that study, students' interactions with pictures and animations—and not a classroom learning event—are defined as the enacted object of learning (Bussey, 2013). However, in all venues, the enactment of the object of learning is assessed from the researcher perspective and focuses on identifying the variation of features of the object of learning presented to students.

Assumptions of variation theory

As with all theoretical frameworks, variation theory offers a distinctive lens through which to view the world and, more specifically, a particular research project. In viewing the world in a particular way, one makes a series of assumptions that limit and define the impact of extraneous variables on the issues of focus. In variation theory, the central focus is the object of learning and its manifestation through the intended, enacted, and lived objects of learning. In variation theory, there is one main assumption of which researchers should be aware:

“People live in a world which they—and not only the researchers—experience. They are affected by what affects them, and not by what affects the researchers. What this boils down to […] is taking the experiences of people seriously and exploring the physical, the social, and the cultural world they experience.” (Marton and Booth, 1997, p. 13).

The main assumption of phenomenographic theoretical frameworks, like variation theory, is that a person's conceptions and experiences of a given phenomenon are accessible through language (Svensson, 1997). Thus, variation theory looks to capture this experience through the re-telling of experience.

“…[T]he only route we have into the learner's own experience is that experience itself as expressed in words or acts. We have to ask learners what their experiences are like, watch what they do, observe what they learn and what makes them learn, analyse what learning is for them.” (Marton and Booth, 1997, p. 16).

In doing so, the underlying assumption is that an individual's retelling of an experience is synonymous with the original experience. This is not to say that the individual is expected to recall every detail of their experience. As noted previously, working memory has a limited capacity. Thus, no one is able to attend to all details and features of an event. Instead, variation theory assumes that the individual's retelling is analogous to their unique experience of the event. It is quite possible that, because an individual will pay attention to certain features of their experience and not to others, the individual's interpretation and retelling of an event will not be the same as what would be described by an outside observer. Thus, some would argue that the main assumption of phenomenographic theoretical frameworks—that conceptions and experiences are accessible through language—is not a valid one (Richardson, 1999; Saljo, 1997). To counter this argument, however, one could acknowledge that although an individual may not—and probably never could—recall all features of an experience that were salient to them at the time they experienced it, the features that remain salient over time are the ones that anchor and continue to structure their understanding of the event and, thus, are the most important, or critical features of that event to the individual that experienced it.

A further limitation of the ‘individual retelling’ methodology lies in the limitations of language. An experience and the words used to describe that experience are not synonymous. As language is socially constructed and individually understood, the audience may understand the vocabulary used by an individual differently from its intended meaning. Furthermore, an individual's ability to articulate their experienced and conceptualized understanding may be significantly different from their actual experience and understanding. Thus, what an individual experienced during an event, what the individual perceived and understood about the event, what the individual recalled about the event, and what the individual said about their recollection of the event might all be different. It should be noted that this critique is not meant to invalidate the personal narrative of an individual's perception of the world, but only to point out the possible discrepancies between the phenomenon, the perception of the phenomenon, and the articulation of the perception of the phenomenon for which the researcher should attempt to account.

Applications of variation theory for chemical education research

We see variation theory as a potentially powerful framework for examining student learning of chemistry and improving chemistry teaching and learning. Despite variation theory's potential for providing both theoretical and practical insights into learning, the literature contains a relatively limited number of research studies that utilize variation theory. Previous studies have examined K-12 teachers' professional development “learning studies” (Marton and Tsui, 2004; Orgill, 2012; Pang and Marton, 2003), as well as students' understandings of physics (Hekkenberg, 2012; Ingerman et al., 2009; Linder et al., 2006; Ling et al., 2006), biochemistry (Rundgren and Tibell, 2009), nanoscience (Swarat et al., 2011), mathematics (Mok, 2009; Runesson, 1999, 2005), computer science (Suhonen et al., 2008), economics (Pang and Marton, 2003), and educational policy (Tan, 2009).

Specific applications of variation theory to the study of chemistry learning are even more limited. As noted earlier, Park et al. (2009) have examined college students' conceptions of atomic structure. Using variation theory and learning progressions, they note that students were able to progress towards the target model of atomic structure by being aware of variations between their own conceptual models and the target model. A more recent study is using variation theory to explore the possibilities for student learning from external representations—pictures and animations—of biochemical concepts (Bussey, 2013).

Overall, in both science education and chemistry education research, variation theory is a potentially powerful, but underused, theoretical framework. Other theoretical frameworks—including conceptual profiles (e.g., Mortimer, 1998), cognitive resources (e.g., Hammer, 2004; Taber and Garcia Franco, 2010), and learning trajectories (e.g., Petri and Neidderer, 1998)—have attempted to answer the question we posed at the beginning of this article, i.e., how is it that two students experience the same leaning event differently? Each of these frameworks offers a unique perspective from which to answer this question. For example, Mortimer (1998) attempts to answer this question from a student perspective through an analysis of student discourse. We find variation theory to be a particularly valuable theoretical framework because it attempts to answer our initial question not just from one perspective but from three perspectives through an examination of the intended object of learning (the teacher perspective), enacted object of learning (the researcher's perspective of the potential for student learning created by the learning environment), and lived object of learning (the student perspective). With this article, we hope to inform the field of variation theory's potential and encourage its use in future chemistry education research studies. In using this framework, however, researchers need to be aware of some of its limitations.

Limitations of variation theory

As with other theoretical frameworks that are used to inform the design of qualitative educational research studies, variation theory has its limitations. In particular, we find that variation theory ignores two important issues that affect how the object of learning is enacted and experienced: (1) the potential effects of students' prior knowledge on the lived object of learning and (2) the potential effects of instructional materials design on the intended, enacted, and lived objects of learning. Each of these factors could influence not only how studies informed by variation theory are carried out, but also the types of research questions that could be addressed through this framework.

The impact of prior knowledge on the lived object of learning

Variation theory, in its original conception, does not explicitly acknowledge the role of prior knowledge on the lived object of learning. As a theory of learning, constructivism posits that new knowledge, as experienced and perceived by the learner, is integrated with students' prior knowledge to construct a new understanding (Bodner, 1986). Individuals interact with and interpret experiential knowledge through internalized, socio-cultural standards and norms in an effort to construct meaning (Ferguson, 2007). However, each individual encounters a unique set of experiences. This history of novel experiences defines a unique cognitive framework and guides the perception and integration of new knowledge within the individual. Thus, prior knowledge is an important element in the construction of conceptual knowledge (Novak, 1990).

Based on the extensive literature on expert/novice differences and the influence of prior knowledge on learning outcomes, we have chosen to acknowledge and integrate students' prior knowledge into a modified model of variation theory, as a key component in assessing students’ lived object of learning (Fig. 3).

Fig. 3 The relationship between prior knowledge and the objects of learning within variation theory. Note: this representation of variation theory has been modified from the model proposed by Rundgren and Tibell (2009, p. 230).

We argue that students' lived object of learning is informed not simply by the features of the enacted object of learning to which students attend but also by their prior knowledge of the concept and related features and concepts. In fact, the features to which students attend in the first place and the subsequent meaning they make may be influenced by their experience with similar objects and features in addition to the situational experience of variation in those objects or features. We also argue that the relationship between prior knowledge and the lived object of learning is unidirectional and temporally bound when seen from a variation theory perspective (see Fig. 3). In other words, a student's prior knowledge upon entering the space of learning will influence the lived object of learning; however, the lived object of learning cannot retroactively alter the base of knowledge the student had prior to the specific learning event under examination in a study informed by variation theory. In making this claim of the unidirectional relationship between prior knowledge and the lived object of learning, we also acknowledge that students' lived object of learning from the learning event under examination in a study informed by variation theory becomes part of the students' prior knowledge for a future learning event and a future study informed by variation theory.

We consider variation theory's failure to explicitly address the effect of students' prior knowledge on the lived object of learning to be a significant limitation of the original conception of variation theory. However, this limitation can be easily addressed by chemistry education researchers. We suggest adding a fourth research question to studies informed by variation theory: What do students know about the object of learning before the learning event takes place? This could be thought of as a pre-lived object of learning, while students' understanding of the object of learning after the learning event takes place could be considered to be a post-lived object of learning. We suggest that researchers assess this pre-lived object of learning through an interview that is implemented prior to the learning event, although such information may also be collected through a questionnaire or pre-test.

The influence of the act of assessing students' prior knowledge—a pre-test of sorts—must be addressed within the research design. By nature, a pre-test makes a student aware of the content they are expected to learn and, thus, potentially influences the learning event (McMillan and Schumacher, 2009). Some of this influence can be diminished by masking the target content in the assessment of prior knowledge by including additional questions or items that are not closely related to the specific concepts under examination (e.g., including questions about equilibrium when bonding is the target concept). Further, as a statement of good practice, we suggest using the same assessment prior to and following the enacted object of learning (i.e., pre-post). By using such a repeated measure, the researcher can assess any learning gains that occur as a result of the learning event while accounting for students' prior knowledge.

It is true that the act of assessing prior knowledge could potentially influence student learning. However, this limitation and threat to internal validity exists for all forms of pre-assessment and cannot be accounted for entirely or completely controlled. Instead, researchers must make note of this potential influence and give it due consideration when developing conclusions. Given that prior knowledge has a significant effect on how students construct new knowledge (Novak, 1990), we believe that the value gained through an understanding of students' knowledge prior to a learning event outweighs the potential limitations caused by an assessment of that prior knowledge.

The impact of instructional materials design on the objects of learning

Variation theory assumes that the enactment of the object of learning is influenced by two parties, the instructor and the student(s). Of these two parties, the instructor is often characterized as an individual who is acting with a singular, unified purpose to create a particular learning environment through the intentional development of resources and implementation of instructional strategies. While this characterization may be true in some circumstances, it is also possible that the instructor is selecting and implementing instructional materials that have been designed by a third party, such as curriculum designers, textbook authors, graphic designers, other instructors, etc. It is, therefore, possible that these instructional materials have been designed with a philosophy or purpose that is different from that of the instructor. It is also possible that the instructor may be unaware of the specific purposes for which the instructional materials have been designed. Thus, there exists the potential for an unintended influence of the instructional materials design on the enacted object of learning.

Consider, for example, the situation where an instructor is assigned to teach a course that uses a context-based curriculum; these materials, organized by the context in which chemistry is applied (e.g., water quality, sustainable living), typically involve a collection of learner-centered activities that have been designed by someone other than the person who is implementing the materials (Pilot and Bulte, 2006; Vos et al., 2010). In this situation, a lecture topic approach to instruction potentially puts the instructor at odds with the instructional materials. Student learning would be influenced by the nature of the students and some combination of the approach of the instructor, the instructional materials design, and the interaction among all components. This potential for instructional materials to influence the different objects of learning should be addressed as an expansion of variation theory.

Since instructional materials—including both physical and virtual resources—are designed for the purpose of facilitating learning (Grossman and Thompson, 2004), they have a unique relationship with the enacted object of learning. These resources, as created by some combination of curriculum designers, textbook authors, instructors, etc., represent a consensus of all responsible parties and are designed with a specific philosophy and purpose. For example, in the case of a publisher's textbook, the team of individuals responsible for producing that volume have written the narrative, sequenced the content and exercises, constructed pictures and diagrams, and added additional learning supports that emanate from their design frameworks (e.g., worked examples, concept maps, glossary, etc.). The instructor may or may not have been part of this team and may or may not share in their philosophy or fully understand how to implement the materials that have been specifically designed to support learning. Thus, the enacted object of learning has the potential to be a hybrid of the instructor's intent and the unintended influence of the instructional materials design. This unintended effect is acting as a confounding variable by influencing the enacted object directly and subsequently affording or constraining the lived object of learning. Understanding the nature and magnitude of this unintended consequence for both the enacted and lived objects of learning represents a fruitful area of potential research, especially given the popularity and availability of digital resources and interactive, digital learning objects for chemical education (e.g., ChemEd Digital Library).

That there is a potential influence of instructional materials design on both the enacted object of learning and the lived object of learning seems clear; however, we also claim that instructional materials design can affect the intended object of learning. In other words, the instructional materials available to an instructor might change the instructor's intentions for a learning event. Take, for example, a general chemistry instructor who is preparing to teach a class about the kinetic molecular theory. One of her original intentions is to help her students develop an understanding of the random motion of gas molecules. During her preparations, the instructor might come across a simulation that will allow students to visualize that random motion. One feature of that simulation allows the teacher to show a graph depicting a Boltzmann distribution of the velocities of the gas molecules. Because of this affordance of the simulation, the teacher's goals expand to include the intention that students will understand that, in a sample of a gas, the molecules are moving at different speeds. In this case, the teacher's intentions, and what eventually happens in the classroom, are affected by the instructional materials design. It is worth noting that the relationship between instructional materials design and the intended object of learning is, for the most part, unidirectional. That is, while the instructional materials design may influence an instructor's intentions for a learning event, the instructor's intentions do not often have an influence on the instructional materials design—unless the instructor happens to be a part of an instructional design team.

Recognizing the potential influence of instructional materials design on all three objects of learning, we have chosen to include it as a feature in our modified model of variation theory (Fig. 4). Because the instructional materials are designed to facilitate learning and represent an abstraction of expert thought about a given object of learning, we place instructional materials design in the teacher sphere of variation theory.

Fig. 4 The relationship between instructional materials design and the objects of learning within variation theory. Note: this representation of variation theory has been modified from the model proposed by Rundgren and Tibell (2009, p. 230).

As previously described, instructional materials design has potential effects on each of the objects of learning. The influence of instructional materials design on the intended object of learning is unidirectional. Because this influence is often an unacknowledged one (i.e., the instructor may not acknowledge or recognize that instructional materials design can affect their intentions for instruction), we have chosen to represent this relationship as a dashed arrow.

The influence of instructional materials design on the enacted object of learning, on the other hand, is direct and explicit. Moreover, the possibility exists that a design team operating independently from the instructor could garner feedback from the enacted object of learning that could then be used to modify the instructional materials for a future learning event. For this reason, we present the relationship between instructional materials design and the enacted object of learning as a bidirectional arrow.

The influence of instructional materials design on the lived object is indirect and mediated through the enacted object of learning. As such, the model does not show a direct link between instructional materials design and the lived object of learning.

This expansion of variation theory to include the influence of instructional materials design adds to its utility for chemical education research. When researchers recognize the influence of instructional materials design, unintended or otherwise, on both teaching and learning, they can examine each of the objects of learning from this new perspective by asking such additional research questions as: (1) what did the instructional designers intend for students to learn from their materials?; and (2) in what ways might the instructional materials design and the instructor's intent be interacting?; (3) what influence does the interaction between the instructional materials design and the instructor's intent have on the enacted object of learning?; and (4) what influence does the interaction between the instructional materials design and the instructor's intent have on the lived object of learning?

Using variation theory with the added perspective of the potential impact of instructional materials design on teaching and learning supports research questions that more fully recognize the elements of the learning environment that are influencing student learning. As researchers, we can deepen our understanding of how students learn chemistry and how to better design supportive learning environments by recognizing the instructional materials design as well as the intent and actions of the instructor as separate, but related, entities. In today's classes that are increasing dependent on digital technologies as mediating tools for the teaching and learning process, a model of variation theory that acknowledges the influence of instructional materials design is a particularly useful tool for chemical education research as well as for improving instructional practice.

Proposed expansions of variation theory

Considering the impact of students' prior knowledge on the lived object of learning as well as the influence of instructional materials design on each of the three objects of learning, we propose that variation theory be expanded to include both of these spheres of influence (see Fig. 4). As such, variation theory would now embody five general research questions: (1) what do instructors intend for their students to learn about a particular object of learning (the intended object of learning)?; (2) what is possible for students to learn about a particular object of learning (the enacted object of learning)?; (3) what did students know about a particular object of learning before the learning event occurred (the pre-lived object of learning)?; (4) what did students actually learn about a particular object of learning after experiencing the learning event (the post-lived object of learning)?; and (5) how does instructional materials design impact any or all of the objects of learning? A careful study of these various objects of learning and how they are impacted by instructional materials design can help both teachers and researchers to develop a better understanding of the learning process and the instructional environment.

Conclusions

As both a theory of learning and framework from which to conduct chemical education research, variation theory offers a practical and potentially powerful lens from which to examine chemistry teaching and learning. Within a chemistry learning environment, there are countless features to which a student could pay attention. The features a student notices at a given time and their interpretation of the meaning of those features constitute the student's experience of learning in that environment. As teachers, we hope to cue students to come to a desired learning outcome; however, this is not always achieved. Variation theory offers a framework from which researchers can explore the enacted object of learning in order to explain the differences between what teachers—including both instructors and instructional materials designers—intend for students to learn about a particular concept and what students actually learn about that concept. We have found it to be a powerful theoretical framework in our own research into chemistry learning and teaching, and we encourage its use within the chemical education research community as a mechanism for further examining student understanding of chemistry concepts and as a vehicle for improving instructional materials and practices. Overall, we believe that chemical education researchers can benefit from a knowledge and use of variation theory, while variation theory itself can benefit the input of chemical education researchers. Therefore, we also encourage the chemical education research community to contribute to the further development and maturation of this relatively recently developed framework.

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