The analysis of analogy use in the teaching of introductory quantum theory

Abstract

This study analyzes the analogies used in the teaching of introductory quantum theory concepts. Over twelve weeks, the researcher observed each class for a semester and conducted interviews with the students and the instructor. In the interviews, students answered questions about quantum theory concepts, which the instructor had taught them using analogies, and also discussed the effectiveness of these analogies. This study identified 48 analogies used by the instructor over the course of 53 fifty minute classes. The analysis of video recordings of the classes revealed that most of the analogies were constructed at the beginning of the semester during the teaching of the particle nature of waves, which is critical for understanding quantum theory. A large proportion of the analogies were given in verbal format; however, a limited number of pictorial and body motion elements were also used together with the analogies. The analogies were mainly positioned as an embedded activator prior to drawing conclusions about the target. It was also observed that analogies were used as an advance organizer and post synthesizer. In addition, the number of simple and enriched analogies used was similar. A limited number of analog explanations were identified and none of the analogies used indicated strategy identification. The instructor never mentioned the limitation of each analogy during their use in class as well. A large proportion of the analogies used spontaneously included both anthropomorphic and environmental characteristics. Although the presentation medium of the analogies was mainly discourse, the presentation of analogies in role play, story and brainstorming was also identified. In half of the analogy use, the instructor intended their use for clarification of the concepts; however, the use of analogies for introduction of a new topic, gaining attention, increasing participation and discriminating between classical and quantum issues was also observed, indicating a diverse use of analogies. In addition, the interviews revealed that students liked the use of analogies in their classes and believed that they had a positive effect on their understanding of new concepts.

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Introduction

In daily life, individuals tend to use analogy to explain new things to other people in an easy way. Therefore, analogies have great importance in both written and spoken communication (Harrison and Treagust, 1993). They clarify an unknown concept, event, system, or object by considering the properties of a known thing. They can be considered as a subset of models since they make comparisons about the similarities of two things (Coll et al., 2005). Analogies are commonly used by scientists (Coll et al., 2005; Orgill and Bodner, 2006) as well as instructors; therefore, they are precious tools for science teachers. In science classes, instructors use analogies to explain ideas in a simpler way by comparing familiar and unfamiliar domains of knowledge (Mastrilli, 1997; Orgill and Bodner, 2006). For this reason, they are considered to be components of effective teachers' repertoire (Treagust, 1993).

Analogy use in science teaching may provide a route for students' understanding (Coll et al., 2005). Analogies can also play a role in the formation of mental models of scientific ideas (Duit, 1991; Glynn and Takahashi, 1998; Glynn, 2008), so they can be used as primitive elements of mental models on scientific concepts (Glynn, 2007). Since analogies first serve as early mental models, they have the potential for enhancing student learning (Treagust et al., 1994). In the literature, there has been a tremendous amount of research on analogy use in science classes. The research has defined other terms related to analogy, including elaborate analogy (Glynn and Takahashi, 1998; Glynn, 2007, 2008), extended text based analogy (Iding, 1997), bridging analogy (Clement, 1993; Yılmaz and Eryılmaz, 2010), and pictorial analogy (Lin et al., 1996). In addition, in order to use analogies in their instruction, scientists, science educators, and science teachers have also created and presented analogies for specific content by clearly indicating analogs and targets (McKelvie, 2003; Whalley, 2005; Kovačević and Djordjevich, 2006).

Some studies in science education literature examined the analogies used in textbooks of different science domains. One of these examples is the research of Thiele and Treagust (1994a), which examined ten high school chemistry textbooks by using an analogy classification framework developed by the researchers. Due to the criteria checklist, analogies were examined in terms of content, location, analogical relationship, presentation format, level of abstraction, position, level of enrichment, pre-topic orientation, and presence of limitation (see Table 2). In total, 93 analogies were identified in the textbooks. A considerable proportion of the analogies (23%) were about atomic structure and the analogies were used more frequently in the earlier stages of the textbooks. 35% of the total analogies used were structured and functional. Only “verbal” and “verbal and pictorial” analogies had a similar proportion, considering all analogies in the textbooks. Analogs of 87% of the analogies were concrete. In other words, mostly concrete analogs were used to explain abstract targets. By considering the position of the analog relevant to the target, among 93 analogies, most of them (56%) were presented as embedded activators, which were presented after the introduction of the target and just before the conclusions were drawn. Most of the analogies (45%) were explained in a simple way as a “target is like analog”. The analogies used in the textbooks often included an analog explanation (60%), preventing students' unfamiliarity with the analogies used. Although each analogy in the textbooks was examined in terms of a general statement about the limitation of the analogy use or explanation of unshared attributes, the researchers identified no general statements about analogy use and only eight limitations were expressed. In another study, Thiele et al. (1995) examined analogies used in four biology and ten chemistry textbooks and classified them into four categories based on the nature of shared attributes, pictorial representation, analog–target abstraction, and extent of mapping. The results showed that 174 biology and 93 chemistry analogies were used in the textbooks, which shows that there is a greater use of analogies in biology textbooks than in chemistry textbooks. Orgill and Bodner (2006) examined analogies in biochemistry in terms of analogy use. The researchers identified that although science textbooks included analogies, their number was actually few. By slightly modifying Thiele and Treagust's study (1994a), Orgill and Bodner (2006) put forward new criteria to identify an analogy in science textbooks, such as the place of analogies in the book (statements in main texts), the content of the target concept, analogical relationship (not only the external appearance of the target and analog, but also their similar behaviors or functions), presentation format, level of abstraction, level of enrichment, analog explanation, indication of cognitive strategy, limitation of the analogies, and position of the analog relative to the target. However, the terms such as “mnemonics, proverbs, symbols, cartoon depictions without explanations, unclear matches between analog and target, etymologies, and unscientific target concepts” were not considered analogies for the purpose of their study (Orgill and Bodner, 2006).

Although textbooks are important for students' learning, teachers are the actors influencing students' learning through direct interaction. For this reason, it is important to elicit teachers' instructional aids while teaching science. Among the most important research focusing on teachers' use of analogy is the study by Treagust et al. (1989). The researchers examined the nature and frequency of science teachers' analogy use. Seven science teachers, whose experiences ranged from 8–20 years in a senior high school, participated in the study. During four weeks, researchers made observations, took field notes, and conducted some interviews with teachers. The results of the observations of 40 70-minute lessons showed that the teachers were limited in both the number (8) and ways in which they used analogies in their teaching routines. These analogies were simple comparisons. Limited use of analogies was observed. In addition misleading aspects of the analogies were not discussed in the classes. Exemplary use of analogies was infrequent. The research also identified the science teachers' unclear knowledge of analogies, which exposed problems, such as the fact that teachers were often unsure about the difference between analogies and examples. In addition, they did not have a good repertoire of analogies to use in their classes. However, teachers were aware of the advantages and disadvantages of using analogies. The study of Thiele and Treagust (1994b) is one of the good examples of why and how high school teachers used analogies. The researchers focused on four high school chemistry teachers whose experience varied between 5 and 20 years. The researchers observed the teachers during 43 classes over a period of time and all the observations were audio recorded. In addition, field notes, interviews, students' work, and teachers' materials were collected and analyzed. The study revealed that teachers used analogies when students experienced conceptual difficulty with chemistry content. They mainly used analogies spontaneously, which was a direct response to subtle stimuli by students; in other words, the use of analogies was not pre-planned. The teachers tended to use their own experience as a source of analogs. In addition, some analogies used in the classes included a pictorial component. The level of enrichment of the analogies used varied from simple, enriched, and extended, considering the attributes between analog and target. Because some of the analogs were unfamiliar to students, in a great proportion of the analogies (84%), the teachers made analog explanations along with the analogies. Two of four teachers made clear explanations about the break-down of analogies in some particular attributes and highlighted the limitation of the analogies. The researchers concluded that the importance of well-founded content knowledge and experience with how students learned played important roles in teachers' effective analogy use. Finally, Nashon (2004) examined three high school physics teachers' use of analogies in their classes. He observed the classes and conducted informal interviews with teachers and students, and examined class texts and the syllabus. The researcher identified that over 126 40-minute class periods, teachers predominantly used environmental analogies, which were based on the students' socio-cultural environment, and anthropomorphic analogies, which draw on human characteristics.

In addition to how analogies are used in textbooks and classes, how students make sense of analogies is another important kind of research. Orgill and Bodner (2004) conducted research with biochemistry students to understand the usefulness of analogies. The researchers examined how students perceived the use of analogies in biochemistry classes. They interviewed 43 students, examining their use of analogies and opinions about analogies. The results showed that students stated they liked the analogies used in the classes. At the end of the study, the researchers suggested that analogies should be used when the target concepts are difficult, are newly introduced, and cannot be visualized. In addition, they added that the analogies should be used in the classes in a clear way, together with visuals, by explaining analog and target concepts. Podolefsky and Finkelstein (2006), using an experimental design at college level, examined how analogy use influenced students' reasoning on the topic of electromagnetic waves. In the following two semesters, a total of 547 students were randomly assigned to three recitation groups. While a “string analogy” was associated with electromagnetic waves in the first group, a “sound analogy” was presented in the second one. The third group was the control group (with no analogy). The researchers examined both the students' correct and incorrect answers given in the distracters. In this way, they found clear evidence for the effects of different analogies. Finally, Clement (1998) compared experts' (doctoral students/professors) and novices' use of analogies while solving physics problems. He identified that although novices were not as skilled as experts, novices and experts were similar in analogical reasoning. However, he also identified that in evaluating the validity of analogies, experts allocated energy for this issue by making their own analogies. Pittman (1999) indicated that students should be encouraged by their teachers to generate their own analogies. Previous research indicated that analogies have been called “double-edged swords”, which should be used carefully, because users have a high likelihood of generating an alternative conception to the intended scientific ones (Harrison and Treagust, 2006). The effectiveness of analogy use can be increased by considering several issues. One strategy is to give sufficient time for students to compare the analog and target concepts (Orgill and Bodner, 2006). In addition, the analogs should be familiar to many students in order to make the analogies effective (Harrison and Treagust, 1993; Treagust et al., 1994; Orgill and Bodner, 2004; Sarantopoulos and Tsaparlis, 2004). Harrison and Treagust (1993) explained that because some students visualized the analog differently than the teacher explained it, analogies ran the risk of creating alternative conceptions. For this reason, the teacher should check students' understanding in order to prevent them from forming misconceptions (Glynn, 2007). An analogy is a device for introducing new concepts, but an analog–target actually has different basic characteristics. According to Treagust et al. (1994) and Taber (2001), teachers should be careful about analogy use when analogies break down, because unshared characteristics may cause misunderstanding when learners transfer unshared attributes from analog to target. Since no analog shares all its attributes, every analogy breaks down (Treagust et al., 1998). Therefore, in addition to similar characteristics, unshared attributes should be discussed with students (Harrison and Treagust, 1993; Treagust et al., 1994). Treagust et al. (1994) also reported that analogies should have conceptual depth. In addition, students might have difficulty in the transfer of similarities to the target domain if they do not have experience with the analog (Heywood and Parker, 1997). Harrison and Treagust (1993) suggested that analogies should be economical, valid and reliable. Orgill and Bodner (2004) explained that students may tend to use analogies mechanically, which means without considering information for target and using the analog as an answer. For this reason, the presentation of analogies is also important. Harrison and Treagust (1993) suggested that analogies should also be presented as a systematic way to enhance conceptual understanding. One of the well known models of analogy use, Glynn's Teaching-With-Analogies model (TWA), explained a systematic approach to analogy use as:

1. Introducing the “target”;

2. Reminding students about analogous situations, and examining what they know about the “analog”;

3. Identifying the relevant features of the analog;

4. Mapping similarities between the analog and the target;

5. Drawing conclusions about the target;

6. Identifying comparisons for which the analogy breaks down (Harrison and Treagust, 1993; Glynn, 1994, 2007; Thiele and Treagust, 1994a, 1994b; Glynn and Takahashi, 1998).

Because teachers might forget to implement one or more steps of TWA in a dynamic classroom setting (Harrison and Treagust, 2006), Treagust et al. (1998) suggested the Focus–Action–Reflection (FAR) guide, which is the systematic presentation of analogies in three stages. The Focus stage assesses the difficulty, unfamiliarity, and abstractness of the concepts and students' prior knowledge of the concepts. Teachers reviewed experiences familiar to the students to use. In the second stage, which is Action, teachers check student familiarity with the analog. Teachers and students discuss shared characteristics of analogs and targets and establish relationships between them. Finally, they discuss unshared characteristics of analogs and targets. In the final stage, Reflection, the participants draw some conclusions about the usefulness of analogy and discuss improvements before the next use of the analogy. Harrison and Treagust (2006) explained that students' scientific understanding is enhanced when teachers used analogies with the FAR guide.

Another model proposed by Podolefsky and Finkelstein (2007) is the “analogical scaffolding” model. There are three important elements of this model: referent, sign, and schema, which can be considered the corners of a triangle. Referent is described as the thing, such as an event, object, situation, etc.; sign is described as an external representation, such as text, graph, picture, etc.; and schema is a knowledge element explaining sign, in other words, it is a knowledge element articulating the relationship between referent and sign. They examined the effectiveness of students' learning with this model in the context of electromagnetic waves. Because of a progression from concrete to abstract (with layering analogies), they observed that this model scaffolded students' learning. The research explaining different guides for analogy use indicates that analogies are important for students' conceptual understanding.

In contrast to presenting a guide about analogy use, some researchers constructed new analogies to clarify concepts for students better and they explained how analogies might be used in the classes. One of them is Whalley's (2005) analogy about an upper level science concept, which is the photoelectric effect. Whalley (2005) stated two analogies that he used in his classes. In one of the analogies, he pointed out how photon energy is important for liberation of a photoelectron rather than the total intensity. In this analogy, he compared children kicking rugby balls to photons coming to the metallic plate. With the connection of rugby balls thrown intensively by children, he indicated that balls without enough energy cannot cross the bar. In this way, he indicated students why the classical view was impossible. Because this analogy is insufficient to explain kinetic energy gained by photoelectrons, the same researcher constructed another analogy. In this way, he explained how incoming photon energy, work function, and maximum kinetic energy were related with each other with the analog of amount of money to enter the stadium, spending a certain amount of money to enter the stadium, and the leftover money, respectively. Another analogy about the photoelectric effect belongs to Kovačević and Djordjevich (2006). The researchers created an analogy for final-year high school students. Through a visualization of the analogy using a mechanical system, they aided in students' understanding of the photoelectric effect. In the mechanical system (setup), there was a mechanical slide with colored balls at different levels. A black ball was located at the lowest point of the slide. The researchers compared the colored balls to incoming photons, so the potential energy of the colored ball, considering color wavelength, represented the energy of the incoming photon. The colored balls were positioned according to the magnitude of potential energy. For example, a red colored ball with a long wavelength (about 700 nm) was positioned low on the model, and violet balls representing ultraviolet light with a short wavelength (about 350 nm) but with high energy were positioned high on the model. On the other side, the black ball corresponded to the electron in the metallic plate, and the potential energy of the ball at a certain height (potential barrier) corresponded to the work function of the metal, and the kinetic energy of the ball corresponded to the kinetic energy of the electron. When a colored ball without enough energy rolled down the slide, it could not provide enough energy to the black ball to climb the hill after the collision. If the transferred energy is below a certain level, the black ball would fall back to its previous position. When another colored ball with enough potential energy provided enough energy to the black ball to climb the hill after the collision, the ball would make a projectile motion with kinetic energy. This analogy shows that the incoming photon, work function, and kinetic energy are related to each other. Photoelectric effect is one of the important experiments indicating the particle nature of light and the quantization phenomenon. The clearly defined attributes of the analog with the targeted concepts by the researchers made the analogies user friendly. Both of the analogies provide concrete analogs to the target concepts that have quantum nature, so these analogies might be helpful for students to make sense of the quantized nature of energy with the analogies from their environment.

Quantum theory and pedagogical research

One of the theories of interest to chemists and physicists is the “quantum theory” which is the theory of the atomic world and which focuses on not only the description of an atom but also all atomic behavior. The quantum theory is a physical theory that is constructed out of physical ideas, and it is expressed mathematically (Erkoç, 2006, p. XIII). Merzbacher (1998) defined it as a “theoretical framework within which it has been found possible to describe, correlate, and predict the behavior of a vast range of physical systems, from particles through nuclei, atoms and radiation to molecules and condensed matter” (p. 1). It is regarded as a probabilistic physical theory with probabilistic nature (Busch et al., 1996).

Quantum theory was independently approached by two young scientists almost at the same time. In 1925, the German physicist Heisenberg's “Matrix Mechanics”, and in 1926, the Austrian physicist Schrödinger's “Wave Mechanics” were understood as independent theories. However, the English physicist Dirac understood the interrelation between these theories and combined them into an extensive theory, the “Quantum” theory (Penrose, 1989). Because of the new quantum theory, 1926 is considered the golden age of physics. Although Einstein expressed his disbelief in the quantum theory by saying “God does not play with dice”, referring to the probabilistic explanations of the theory, his work on the photoelectric effect is one of the most important elements of this theory, as it indicates the particle nature of light. The nature of atoms and quantum particles, wave particle duality and Heisenberg uncertainty relations, probability, wave-functions, the Hilbert space, the Schrödinger equation, quantization, and matrix representations are the main elements and concepts of this theory.

The quantum theory is accepted as a successful theory in the history of science. It allows scientists to calculate the outcomes of many experiments, and creates new technology based on the behavior of atomic objects (Faye, 2002). The explanations of the forces, which are composed of matter and the physical properties of matter, such as colors, freezing and boiling points, etc., require knowledge of quantum theory (Penrose, 1989), so it has great importance. For this reason, it is imperative for chemistry and physics students to learn about quantum theory.

Until the beginning of the study of quantum theory, scientists were interested in the physical behaviors of macro systems described by classical physics. However, moving from the macro-world to the micro-world with the quantum theory changed all measurement techniques, in addition to interpretations in some parts of physics. Quantum theory is an abstract, mathematical, and counter-intuitive theory (Sadaghiani, 2005). For this reason, students' development of incorrect ideas about the atomic world may be caused by their “misinterpretation of information” based on culture, books, instruction, etc. (Taber, 2008). Much pedagogical research about quantum theory indicates that students had some problems learning quantum theory, such as conceptual problems (Styer, 1996; Singh, 2001; Olsen, 2002; Budde et al., 2002a, 2002b; Müller and Wiesner, 2002; Ke et al., 2005; Wattanakasiwich, 2005; Singh et al., 2006; Özcan et al., 2009; Didiş et al., 2014), mathematical problems (Strnad, 1981; Ireson, 2000; Pospiech, 2000; Sauer, 2000; Gardner, 2002; Sadaghiani, 2005; Wattanakasiwich, 2005), and visual problems (Mashhadi and Woolnough, 1999; Çataloğlu and Robinett, 2002). Students additionally had difficulty in discriminating between classical and quantum concepts (Bao, 1999; Pospiech, 2000; Mannila et al., 2002; Müller and Wiesner, 2002; Olsen, 2002; Sadaghiani, 2005). Instructors also have difficulty in teaching the theory because of the introduction of a new philosophy that is different from the classical one, the abstractness of the concepts, and the lack of analogies and metaphors (Wattanakasiwich, 2005). At this stage, chemistry and physics instructors teaching quantum theory should be introduced to new instructional aids, such as analogies, to help with the teaching of these upper level concepts. Good analogies for upper level concepts are needed; otherwise, students might generate incorrect mental models based on their own incorrectly produced analogies. Research has shown that analogies have a role in the formation of mental models (Duit, 1991; Glynn and Takahashi, 1998; Glynn, 2008). The research of Didiş et al. (2014) indicated that students displayed unscientific mental models about the quantization phenomenon. One of the models of students was the “Shredding Model” which is a coherent conceptual framework analogous to “cutting a cake into slices”. Students relate the discrete nature of physical observables (target) to energy considering quanta taking any value, just as any slice of cake (analog). Displaying this type of mental structure and giving explanations based on an inappropriate analogy for a scientific phenomenon indicate that making sense of the unfamiliar abstract, mathematical, and counter-intuitive concepts requires the construction of correct connections between analogs and targets.

The transition from the classical perspective to the quantum can be accepted as a paradigm shift not only for a scientist but also for students learning science. With the increasing complexity, abstractness, counter-intuitiveness, and mathematical nature of quantum theory, providing appropriate analogies to make understanding the theory easier might allow students to make better sense of the concepts. This study builds on previous research, whose designs varied from experimental, correlational, case studies and content analysis, and enlightened the literature about analogy use from different perspectives such as students, instructors, textbook authors, and researchers. In addition, this research examines students' and instructors' analogy use; however, it differs from the previous research by focusing on the concepts of quantum theory in upper level science classes. To summarize, this study is an exploratory study presenting analogy use in upper level science classes. In addition, it identifies how analogies can be used as an instructional element in the teaching of introductory quantum theory and shows how students at this level respond to the analogies. This research presents the potential analogies for chemistry and physics instructors of quantum chemistry and quantum physics courses at universities and teachers at high schools, who might use these in the teaching of quantum theory.

Methodology of research

This qualitative study aimed (1) to examine the analogies used in the teaching of introductory quantum theory concepts and provide some new analogies, (2) to discuss how these analogies are used in university level science classes, and (3) to identify what students think about the analogy use in the classes.

Setting, instructor, and participants

Modern Physics is a four-credit compulsory course for each physics and physics education student. Students took the course in the second semester of their second academic year. Modern Physics is a pre-requisite course for the compulsory Quantum Physics and Quantum Mechanics courses. It is very important for students to make sense of the concepts in this class, because it introduces primary ideas of quantum theory that will be developed in subsequent classes. This course provides students a conceptual background and perspective about the quantum theory; this course was selected intentionally. This course introduces “special theory of relativity, particle properties of waves, wave properties of particles, atomic structure, elementary quantum mechanics, many electron atoms, nuclear structure and radioactivity” (Department of Physics, 2010) to students. The assessment methods of the course were quizzes, homework, two mid-term examinations, and a final examination. Four fifty-minute modern physics classes were taught per week.

The instructor of the course is a full time professor in the department of physics, who has more than 30 years of teaching experience. He also has an upper level teaching certificate and believes in the importance of having pedagogical knowledge as well as the skills and attitudes necessary to teach physics. For this reason, he used pedagogical knowledge in modern physics classes by using several instructional techniques such as analogy, role play, questioning, and examples from daily life.

The participants in this study were 20 undergraduate (second-year) physics and physics education students who were taking the Modern Physics course at a university in Turkey. The academic backgrounds of these two different majors are similar, since all students had to take exactly the same prerequisite physics courses from the physics department. Of all 98 students taking Modern Physics, 20 participants were purposely selected in order to gain more information about their understanding of the analogies used and ideas about analogy use. Students' physics achievement and interests were the main considerations of participant selection for diversity. By following the course over a few weeks, the researcher observed students' willingness and their answers to conceptual questions in the quizzes and to the instructor's questions. Through this process, eight females and 12 males were selected to participate in this study.

Observation and interviews

The research, which was constructed through class observation, was conducted in students' natural environments during an academic semester. The Modern Physics course is taught during fifteen weeks in an academic semester. However, in the first three weeks, special theory of relativity is taught. Because this study is concerned with analogy use in teaching quantum theory, the researcher observed the modern physics classes for the twelve weeks dedicated to quantum theory (4 hours per week). All classes were recorded using a video camera located at the back of the lecture hall and the researcher took field notes about the use of analogy during class. At the end of the semester, the researcher conducted semi-structured interviews with 20 purposively selected students and with the instructor about the analogies used in the classes. In the first part of the interviews conducted with students, they discussed analogies and their effectiveness. In the second part, students answered conceptual questions covering concepts that the instructor had taught with analogies. Each interview took approximately 25 minutes, and each was video recorded. In this way, the instructor's analogy use and students' experiences with the analogies were documented without manipulating the course setting.

Data analysis

Since the data coding provides a formal representation of analytic thinking (Marshall and Rossman, 1999, p. 155), the data obtained from observation and interviews were coded first. The code list was developed from the data in the light of previous literature (Thiele and Treagust, 1994a, 1994b; Orgill and Bodner, 2006) and examined by an external researcher (with a PhD in physics education) in terms of inclusiveness of all codes, and mutual exclusiveness of these codes with each other. Due to the nature of the data, the data obtained from observation and interview were coded in different ways. In the analysis of the observation data, the coding was two-fold. At first, by examining the whole 2700-minute classroom videos, instructors' use of analogy and analogy type explanations was focused. During this, not all video recorded classroom data were transcribed; only the periods indicating analogy use were transcribed. In order to identify and discriminate analogies from other types of explanations, the criteria presented in Table 1 were used.

Table 1 Coding criteria used for the determination of analogies^a

Criteria	Description
a This table was adapted from Orgill and Bodner (2006).
Quantum topic	Instructor's explanation is found in only teaching of the quantum theory during the classes, rather than in the breaks, before, or after the classes. In addition, the classes of the Modern Physics course about the special theory of relativity were omitted from the study because it involved a different theory.
Relationship	Two objects or concepts being compared in the instructor's explanation share more than just similarities in external appearances.
Daily experience	Instructor's explanation is a comparison of a concept of quantum theory with an object or process, which the student could reasonably expect to come into contact with through everyday experience or reading.
Not being an example	A concept of quantum theory in the comparison cannot be an example of the everyday object.

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As given in Table 1, I considered an element as “an analogy” when it was observed in the teaching of quantum topics, and if there was a relationship between what is taught and compared object. In addition, daily experience was important to determine an analogy since Taber (2001) explained “if analogy is intended to help make the unfamiliar familiar, it will only be effective where the analogue is itself genuinely familiar”. After the consideration of these elements to determine the analogies, the new coding list was used to identify analogy use for the second fold of observation data analysis. This list was both developed in the light of previous literature (Thiele and Treagust, 1994a, 1994b; Orgill and Bodner, 2006) and the data itself. Table 2 presents the criteria for identification of the instructor's use of each analogy in particular contexts.

Table 2 Coding criteria used for the determination of how analogies are used^a

Criteria	Description and the codes
a This table was adapted from Thiele and Treagust (1994a, 1994b): Italicized criteria are from the literature and not italicized ones emerged from the data. The topics described for the “Content and Location” category were the chapters of Beiser (2003), which was one of the textbooks, covered for the teaching of the theory.
Content and location	The topics including the concepts of quantum theory, which are being considered by the target concept and location in the curriculum • Particle properties of waves (electromagnetic waves, blackbody radiation, photoelectric effect, light, X-rays, X-ray diffraction, Compton effect, pair production, photons and gravity) • Wave properties of particles (deBroglie waves, waves of probability, describing wave, phase and group velocities, particle diffraction, particle in a box, uncertainty principle, applying uncertainty principle) • Atomic structure (the nuclear atom, electron orbits, atomic spectra, the Bohr atom, energy levels and spectra, Correspondence principle, nuclear motion, atomic excitation, the laser) • Quantum mechanics (introduction to quantum mechanics, the wave equation, Schrödinger' time dependent wave equation, linearity and superposition, expectation values, eigenvalues, eigenfunctions, particle in a box, finite potential well, tunnel effect, harmonic oscillator) • Quantum theory of the hydrogen atom (Schrödinger equation for hydrogen atom, quantum numbers, principle quantum number, orbital quantum number, magnetic quantum number, electron probability density, radiative transitions, selection rules, Zeeman effect) • Many-electron atoms (electron spin, exclusion principle, symmetric and anti-symmetric wave functions, spin–orbit coupling) • Nuclear structure (nuclear composition, some nuclear properties, stable nuclei, binding energy) • Nuclear transformations (radioactive decay, half-life)
Presentation format	How the analogy is presented in the classes
	• Verbal	• Pictorial–verbal	• Body motion-verbal
Position	How the analog is relevant to the target: before, during and after the presentation of the target
	• Advance organizer	• Embedded activator	• Post synthesizer
Level of enrichment	To what extent is the mapping between analog and target
	• Simple	• Enriched	• Extended
Pre-topic orientation	The elaboration of analog domain and indication of the analogical nature
	• Analog explanation	• Strategy identification	• None
Limitations	Presence of any warnings about analogy use
	• Exist	• Not exist
Manner of presentation	Use of the constructed analogy in the class
	• Spontaneous	• Pre-planned
Source domain	Explanations of the analog with human characteristics or from daily life
	• Anthropomorphic	• Environmental
Presentation medium	Medium which the analogy is used
	• Discourse • Role play	• Story format • Brainstorming
Aim of use	For which aims that the instructor use an analogy
	• Introduction of new topic • Clarification • Gaining attention	• Increasing participation • Discriminating classical and quantum phenomena

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Once the codes were identified, the researcher watched specific sections of the video recordings again, bearing in mind these criteria. In this way, the researcher identified the content and location of the analogies, their presentation format, position, level of enrichment, pre-topic orientation, limitations, as reflected in Thiele and Treagust (1994a). In addition, the researcher determined the manner of presentation, source domain, presentation medium, and aim of use. Then, randomly selected video records (not only including fragments with analogies, but the whole 50-minute lecture) were presented to the same external researcher. After the discussion of the codes with the issues about analogy use with the given criteria, we reached consensus about the coding categories.

In contrast to observation data, the verbal data obtained in the interviews were transcribed first, meaning that the verbal data were transformed into written format, and combined with students' written and drawn data provided in the interviews. The coding of interview data was also two-fold. The first part of the coding coded answers to the questions about students' ideas and their recognition of analogies used in the classes (see Appendix). Then, by presenting some conceptual questions that the instructor had taught them using analogies, how much the analogies supported students' conceptual understanding were examined and the findings were compared with students' ideas about analogy use in the classes. In this way, I determined both students' ideas about analogy use and some particular influences of analogy use on students' understanding the concepts.

Reliability, validity, and ethical issues

This research is exploratory research, which does not aim to generalize findings over the settings, and is about the analogy use in upper level science teaching. Towards this aim, the research setting, participants, and related issues were described in detail. In addition, participants were selected by purposive sampling. For credibility corresponding to the internal validity of this qualitative research, prolonged engagement, peer debriefing, and member checking were considered. Collecting data over twelve weeks provided both a prolonged engagement and a saturation of the data about analogy use. The external researcher checked and validated the questions and the codes in the study, which was an important part of peer debriefing. In addition, member checking was done in each interview in order to prevent misunderstanding.

For dependability corresponding to internal reliability, the same external researcher studied the sample data obtained from this study. After detailed discussion on analogies and analogy use, we reached almost full agreement according to Miles and Huberman (1984, p. 63), where a statement of 90% agreement is the cut off point for consensus.

Three important ethical issues (Fraenkel and Wallen, 2000, p. 43) were considered in this study. The access to the research site was obtained after receiving permission from the ethical committee (institutional review board) of the university, the department, and the instructor. Then, the participants were informed about the study and their consent was obtained with their signatures. Probable factors causing physical and psychological harm for participants were excluded from the study by not creating a new environment but rather by doing the research in their natural classroom setting, which eliminated the disturbing interview questions and provided a relaxing environment for the interviews. In addition, to prevent any type of harm to the participants, it was explained the role of the researcher as an overt participant observer during the classes and completed observations by sitting at the back of the lecture hall. The confidentiality of the data was carefully explained to the students; the data were kept private and not used outside of the research aims.

Results

What are the analogies used in the teaching of introductory quantum theory?

In the teaching of abstract concepts of quantum theory, a lot of analogies and analogy type elements were used for different aims during the semester. More specifically, in the 53 fifty-minute classes observed, 61 comparisons were made between analog and target situations by the instructor. By eliminating some of the proverbs, etymologies, and ambiguous matches between analogs and targets, as mentioned in the study by Orgill and Bodner (2006), 48 analogies were used during the semester. In this study, in contrast to Orgill and Bodner (2006), proverbs and idioms were not completely excluded from the analogies, because a large majority of the Turkish proverbs and idioms stated a clear relationship between the analog and target. Some of the analogies used in the teaching of introductory quantum theory concepts are presented in Table 3. Each analogy in the table was stated to students by the instructor by indicating the analog and target.

Table 3 Selected analogies used by the instructor during the teaching of introductory quantum theory

Topic	Name of the analogy	Analog	Target	Attributes
a The new analogies were named by the researcher. b The analogies were explained in detail in the “Discussion of selected analogies” section of the article.
Waves	Earning money analogy^a	Managing money	Interference of waves	• Earning money and saving money vs. constructive interference of waves • Earning money and owing vs. destructive interference of waves
Blackbody radiation	Tap analogy^a^,^b	Flow of water (dropping)	Quantization of physical observables	• Water drops vs. quantized energy
Blackbody radiation	Take a liking to someone analogy^a	Harmony of feelings	Radiation	• Take a liking to someone vs. radiating at an appropriate temperature
Photoelectric effect	Strong man analogy^a^,^b	Pulling of different students	Incoming light into different metal surfaces	• Pulling of a student vs. the energy of incoming light • The seated student vs. electron in the metal plate used in the experiment • When the pull is strong to move the students vs. the energy of the incoming light is large • When the pull is not strong vs. the energy of the light is small • Running of the female student not only standing up from her seat vs. having kinetic energy of the photoelectron
Photoelectric effect	Family relationship analogy^a^,^b	Saying the correct word to get permission	Quantum view of photoelectron emission from the surface	• Permission vs. photoelectron • Father vs. metal surface • Asking for permission vs. incoming light • A child's asking several times to his father to get permission vs. intensity of incoming light without sufficient energy • A child's not getting permission from his father vs. inability of the incoming light ejecting a photoelectron from the surface • A child's saying a “word” to convince his father to get permission vs. the frequency of incoming light with sufficient energy • A child's getting permission from his father vs. ability of the incoming light ejecting a photoelectron from the surface
Pair-production	Bear analogy^a^,^b	An adult bear	Need for a nucleus to observe pair production	• Help of adult bear vs. help of nucleus in pair production for the conservation of energy and momentum
Energy of a photon	Good citizen analogy^a	The rules and restrictions for citizens	The amount of energy carried by a photon	• The behaviors of a citizen allowed by rules and regulations vs. a photon's quantized energy by hν
Particle in a box	Ladder analogy^a^,^b	Steps of the ladder	Energy levels	• Moving step-by-step and not stepping between two steps vs. getting only certain energy values and not having continuous energy levels
Particle in a box	Good citizen analogy^a^,^b	The rules and restrictions for citizens	Restrictions on energy values of bound particles	• Good citizen vs. particle in the box • The rules and restrictions for citizens vs. restriction in the energy values of the bound particle • The behaviors allowed by rules and regulations vs. quantized energy levels
Harmonic oscillator	Choppy analogy^a	Blowing hot and cold	Oscillation	• Giving explanations about a topic and saying the opposite in a short time vs. oscillating from the equilibrium in one direction to the opposite direction
Tunneling	Trampoline analogy^a	Bouncing of an object	Behavior of a tunneling particle	• Several bounces on a trampoline vs. several attempts of the alpha particle to tunnel
Models of the atom	Plum pudding analogy	Plums in pudding	Thomson atom	• Plums in a cake vs. electrons in an atom
Models of the atom	Planetary system analogy	Solar system	Rutherford atom	• Planets in the solar system vs. electrons in an atom
Rutherford experiment	Rattlesnake analogy^a	Rattlesnake	Alpha particles	• Rattlesnake vs. positively charged nucleus • Fear of rattlesnake vs. closest approach of alpha particles to the positively charged nucleus
Quantization of angular momentum	Matryoshka doll analogy^a	Matryoshka doll	Quantization of angular momentum	• Matryoshka dolls vs. restriction in the orbital angular momentum values
Non interacting electrons	Freedom analogy^a	Independent person	Free electron	• Having one's way vs. no restriction in behavior of an electron
Binding energy	Nature protects itself analogy^a	Behavior of a mother bird towards young birds in danger	Atomic behavior	• Keeping of a baby bird by mother bird vs. binding energy for a bound electron
Hund's rule	Seating in the lecture hall analogy^a^,^b	Locations of students in the lecture hall	Location of electrons in an atom	• The seats in the lecture hall vs. orbital • The students taking the course vs. bound electrons • The student' preference for sitting vs. Hund's rule
Zeeman effect	Swimming in a drift analogy^a^,^b	The behavior of an object in drift	The alignment of an atom in a magnetic field	• Alignment of a man swimming in a river in the flow direction vs. the alignment of an atom in an external magnetic field
Radioactivity	Richness analogy^a	The amount of money owned	Stability of nucleus	• A middle-class person vs. a stable nucleus • A rich or poor person vs. an unstable nucleus
Radioactive decay	Paper analogy^a^,^b	Paper cut	Half life	• Dividing the paper half vs. the half time of an atom

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How are the analogies used at university level science classes?

The numerical findings of this exploratory study about how 48 analogies are used at a university in upper level science class to teach introductory quantum theory are presented in Table 4.

Table 4 Analysis of the frequency of analogy use in the classes

Criteria	Category	Number	Percentage (%)
Content and location	Particle properties of waves	11	23
	Wave properties of particles	8	17
	Atomic structure	9	19
	Quantum mechanics	6	13
	Quantum theory of the hydrogen atom	7	15
	Many-electron atoms	4	8
	Nuclear structure	2	4
	Nuclear transformations	1	2
Presentation format	Verbal	41	85
	Pictorial–verbal	4	8
	Body motion–verbal	3	6
Position	Advance organizer	8	17
	Embedded activator	34	71
	Post synthesizer	6	13
Level of enrichment	Simple	19	40
	Enriched	20	42
	Extended	9	19
Pre-topic orientation	Analog explanation	6	13
	Strategy identification	0	0
	None	42	88
Limitations	Exist	0	0
	Not exist	48	100
Manner of Presentation	Spontaneous	45	94
	Pre-planned	3	6
Source domain	Anthropomorphic	18	38
	Environmental	30	63
Presentation medium	Discourse	30	63
	Role play	4	8
	Story format	8	17
	Brainstorming	6	13
Aim of use	Introduction of new topic	4	8
	Clarification	24	50
	Gaining attention	8	17
	Increasing participation	10	21
	Discriminating classical and quantum phenomena	2	4

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Content and location

As presented in Table 2, the content of the Modern Physics course was discussed in seven chapters of the textbook (Beiser, 2003). Most of the 48 analogies (23%) were used by the instructor in “Particle properties of waves” teaching of the “electromagnetic waves, blackbody radiation, photoelectric effect, light, X-rays, X-ray diffraction, Compton effect, pair production, photons and gravity” topics. Another unit for which analogies were more commonly used was the topic of “Atomic structure” (19%). This included the teaching of the topics “the nuclear atom, electron orbits, atomic spectra, the Bohr atom, energy levels and spectra, Correspondence principle, nuclear motion, atomic excitation, and the laser”. The instructor sometimes used more than one analogy for a topic according to how that topic lent itself to constructing good analogies. When it is focused on the specific topics explained with the analogies, it was observed that the instructor used analogy mainly while teaching blackbody radiation (6 analogies) and particle in a box (5 analogies). One third of the analogies used were used to clarify the “quantization” phenomenon (i.e. energy, angular momentum), which is a basic idea for the theory. By considering the location of the target concept in the curriculum, it was identified that the instructor used more analogies at the beginning of introducing the concepts of the theory. He continued to use analogies over the semester since students were first introduced to most of the concepts in this course.

Presentation format

The research indicated that although the instructor used pictorial elements while teaching the topics, he also used analogy together with pictorial elements in a limited manner (8%). Most of the used analogies in the classes were verbal (85%). The ladder analogy is a type of analogy presented by a combination of body motions and verbal elements. During this type of analogy, the instructor used the steps in the lecture hall and motivated students.

Position

The instructor mainly used analogies as embedded activators (71%), which is the presentation of the analogies after the introduction of the target prior to conclusions being drawn about the target (Curtis and Reigeluth, 1984 as cited in Thiele and Treagust, 1994a). The use of analogies as an advance organizer, which is the presentation of analog before the examination of target concept, and as post synthesizer, which is the presentation of the analogy after the examination of target concept, occurred with similar percentages, 17% and 13%, respectively.

Level of enrichment

The instructor mostly used enriched analogies (42%), which indicate the shared attributes. However, simple analogies (40%), which state only “Target is like analog” (Thiele and Treagust, 1994a), were also used almost as much as enriched analogies. For example, while teaching the energy quantization in the blackbody radiation topic, the instructor used the analogy “It is just like pulses of the energy” to indicate the discreteness. The instructor constructed simple analogies by himself, without incorporating students. These analogies were used in the instructor's speech, and the construction of the analog–target relationship was limited. In this study, I refer to a simple analogy as “one-shot form” or “direct comparison” because it was observed that most of the enriched and extended analogies were used in “continuous form”, where construction of the analogy takes more time and includes different presentation media (i.e. role play, story format, and brainstorming). Simple analogy has a descriptive role but enriched analogy has an explanatory role (Harrison and Treagust, 2006). 19% of the analogies used were extended analogies with constructing relationships among other attributes. Students might be able to make better sense of analogies presented in this way and thus better understand the target with more attributes.

Pre-topic orientation

The instructor made limited analog explanation (13%). One of the analogies made using analog explanation was a story of a baby bear. The instructor first introduced the major characters of the story as the analog. Then, he constructed the relationship between analog and target. The other two analogs he explained were social environments (i.e. art exhibition) and three of them were to explain the roles of students while presenting the analogies by role plays. The rest of the analogies that the instructor used were also familiar to students. Since the concepts of quantum theory are abstract, counter-intuitive, and mathematical, the instructor helped students by giving analogs from their daily lives, as it was suggested that students' familiarity with analogs is important for the effectiveness of the analogies (Harrison and Treagust, 1993; Treagust et al., 1994; Orgill and Bodner, 2004; Sarantopoulos and Tsaparlis, 2004).

Limitations

During the use of 48 analogies, there were never any warnings regarding their use. He primarily considered analogies with the shared characteristics to help students' conceptual understanding. During the interview with the instructor, he pointed out his use of analogy; however, he never used the term “analogy”, but rather he used the term “comparison”.

Manner of presentation

A small proportion (6%) of the analogies used by the instructor for well known analogies such as plum pudding and solar system analogies about atomic structure. There were no stimuli by students regarding the use of analogy during the lectures, so there was no systematic use of analogy by the instructor over time. This means the instructor used analogies on his own and used them when needed. The instructor mostly used analogies spontaneously (94%) developed during the lecture period. This manner of presentation might be because he was drawing on his teaching experience and physics knowledge. Many of the analogies were well thought-out in advance and had developed over years, and the teacher deliberately looked for the right moment and setting to introduce them. In this way, he could integrate spontaneous events with the teaching methodology.

Source domain

The analogies used in the teaching of introductory quantum theory were mostly environmental (63%). As seen in Table 1, the analogies used in the classes were analogies from daily life (environmental analogies), which were mostly drawn from the students' social environment, recent news, popular events, or family relationships. Some of the analogies had human characteristics (anthropomorphic traits) (38%). One of these examples is relating a bound particle with a good citizen who obeys the laws of a state. The allowed behaviors for a citizen are similar to allowed energy values (discrete) of a particle. In this way, why the energy of a bound particle could not take every energy value and why we observe energy as levels were explained by human characteristics. These findings about anthropomorphic use of analogies are interesting because the concepts of quantum theory are counter-intuitive, which makes it difficult to find a similar element from the classical world. His ability to make sense of the concepts using human characteristics and environment as analogies also reflects the instructor's well-constructed mental models about the physics concepts.

Presentation medium

The instructor mostly used analogies with discourse (63%). As explained earlier, the instructor used continuous formed analogies in addition to the one-shot forms (or simple analogies). One of the examples of continuous formed analogies is story-type analogy. In addition to the clear statement of the analog–target relationship, more attributes of the analog were allowed to be linked with the target by using story-type analogy (17%). The use of analogies with role play (Aubusson and Fogwill, 2006) provides another example of continuous format analogies (8%). In this type of use, the instructor constructed the analogies along with students. In this study, since it took more time than one-shot use, the instructor also clarified the analog–target relationship further. He mainly stated the relationships when assigning students' roles and during the role play. As with the story format, more attributes were discussed in this type of analogy. Use of analogies in a brainstorming format (13%) is the last type of continuous form of analogy use. The instructor also constructed analogies with students in this format by stating the analogy and then having students interpret the analogy. To make students mentally active, the instructor mainly preferred to: (1) state the topic; (2) before explaining the topic, ask students to participate in the analogy by saying “imagine a situation…”; (3) brainstorm, and get students' explanations about the analog; (4) after students' responses, ask about the situation for the target; and finally, (5) compare the analog and target. This type of use provided evidence that the instructor used analogies as advance organizers.

Aim of use

In the examination of analogies in terms of aim of use, it was identified that the instructor used analogies for five different aims: introduction of a new topic (8%), clarification of taught concepts (50%), gaining students' attention in the classes (17%), increasing students' participation to the classes (21%), and comparing classical physics and quantum physics (4%).

The instructor mainly used analogies in order to clarify the concepts of theory. Since the quantum concepts were so abstract and counter-intuitive, the instructor needed to make them more concrete for students. For this reason, the use of daily life comparisons was particularly important for clarifying the concepts. In addition, keeping students' attention fresh is difficult while teaching unfamiliar and abstract concepts. In these situations, students might be unresponsive to what the instructor is teaching. When students were too passive to ask and answer questions, the instructor used some analogies to motivate them. In addition to keeping students' interest fresh, the instructor aimed to increase students' participation. Large architecture, a linear arrangement of seating, and the large number of students in the class might limit student–instructor interaction. For these reasons, the instructor mainly preferred to combine some analogies with role play and stories, having continuous form. One of the most important uses of analogies was the comparison of classical and quantum issues. Since the Modern Physics course was the only course indicating the change in perspectives and ideas during the transition from classical to quantum physics, the instructor sometimes used analogies to emphasize the discrimination between concepts in these two areas. However, the instructor made a limited number of classical-quantum comparisons using analogies, which was similar to the use of analogy for the introduction of a new topic.

Discussion of selected analogies

This study revealed which and how analogies were used in an upper level class. Table 5 presents the details of selected analogies and the following parts explaining the analogies reflect their use by the instructor.

Table 5 Properties of analogy use in the classes for selected analogies^a

Property of analogy use	Analogies
Categories	Tap analogy	Family relationship analogy	Seating in the lecture hall analogy	Bear analogy	Strong man analogy	Swimming in a drift analogy	Paper analogy	Ladder analogy	Good citizen analogy
a The property of each analogy use was represented by the element having X.
Content and location
Particle properties of waves	X	X		X	X
Wave properties of particles								X
Atomic structure
Quantum mechanics									X
Quantum theory of the hydrogen atom						X
Many-electron atoms			X
Nuclear structure
Nuclear transformations							X
Presentation format
Verbal	X	X	X	X	X				X
Pictorial–verbal						X
Body motion–verbal							X	X
Position
Advance organizer	X		X				X
Embedded activator		X				X		X	X
Post synthesizer				X	X
Level of enrichment
Simple
Enriched	X			X		X	X	X
Extended		X	X		X				X
Pre-topic orientation
Analog explanation				X	X
Strategy identification
None	X	X	X			X	X	X	X
Limitations
Exist
Not exist	X	X	X	X	X	X	X	X	X
Manner of presentation
Spontaneous	X	X	X	X	X	X	X	X	X
Pre-planned
Source domain
Anthropomorphic		X	X		X	X			X
Environmental	X			X			X	X
Presentation medium
Discourse	X	X				X	X	X
Role play					X
Story format				X					X
Brainstorming			X
Aim of use
Introduction of new topic							X
Clarification				X		X			X
Gaining attention
Increasing participation			X		X			X
Discriminating classical and quantum phenomena	X	X

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The tap analogy

As presented in Table 5, tap analogy was used in the teaching of particle properties of waves at the beginning of the introduction of the theory. This enriched analogy was used verbally as an advance organizer in the construction of the analog–target relationship. There was no analog explanation except for when the instructor asked for the Turkish translation of “tap” since he taught the topic in English. He also did not mention the limitations of the analogy and presented it spontaneously. The analogy was environmental, as it was from the students' daily environment. With the presentation of analogy in discourse, he aimed to indicate classical and quantum issues.

This analogy is an example of analogy use in the teaching of the quantization phenomenon. The instructor constructed an analogy to stress the paradigm shift in the transition from classical physics to quantum physics. First, he said “This is a moment of changing physics” and then explained how quantization was the focus of quantum physics. The tap analogy he explained drew on the similarity between water drops (analog) and quantized physical observables (target), where every drop represented a quantum.

Instructor:† It is just like a tap. What is tap? “Musluk (speaking in Turkish)”. Water just flows drop by drop, sound like “pıt… pıt… pıt… pıt…” And every drop is a quantum, just like “hν”. These quanta may be large or small. The emission of quanta is like dropping “pıt… pıt… pıt…” If you increase “pıt–pıt–pıt–pıt (saying fast)”, and if you increase more “pıt–pıt–pıt–pıt (saying faster than the previous ones), it appears continuous…

Without ignoring large or small drops of water (analog), each drop is distinct and not continuous like energy or momentum (target). With this analogy, the instructor explained the discreteness characteristic of the quantization phenomenon, which was new for students, by using a water drop as an analog.

The family relationship analogy

As explained in Table 5, this analogy also belongs to the photoelectric effect of the particle properties of wave unit. It was also used verbally and as an embedded activator to facilitate learning before drawing conclusions about the target. The analogy was extended since it presented more than one attribute between analog and target. Analog explanation was not needed for this analogy and limitations were not mentioned. It was also spontaneously used and it was anthropomorphic. The instructor used this analogy discursively and this was the other analogy discriminating between classical and quantum issues.

For this analogy, the instructor created two imaginary situations. One of them was asking one's father multiple times to get permission (analog₁), and the other was just saying one word to one's father to get permission (analog₂). The first phrase matches with the explanation of light by wave theory in the classical interpretation as the instructor started to explain, and the second one explains light using particle theory in the quantum interpretation. The instructor explained that the consideration of frequency of the light (target₂), rather than intensity of the light (target₁), was important to break off the electron. He also stressed that there was no time lag between an incident photon hitting the surface and emission of the electron from the surface. He explained this analogy as follows:

Instructor: If it is a wave, a wave comes propagating space wave fronts and hits the surface. Another wave hits the surface and another wave hits the surface. In order to break off an electron from the surface, you need time. Maybe you see this type of event when getting permission from your father. You need to ask several times to get permission. You need to go easy on your father before getting permission and you need time for this. However, sometimes just one word is enough to get the permission from your father without spending much time. This is what you told him, and you got the permission! This is quantum physics! This is a new explanation. Welcome new physics! Welcome new habits! With this new explanation, to break off the electron from the surface, you do not need to wait. Just a certain frequency of the incident light is enough to break off the electron from the surface.

This analogy started with the explanation of the classical view: “You need to ask several times to get permission. You need to go easy on your father before getting permission and you need time for this” and explaining that it was impossible to get permission if one's explanations were insufficient to get permission. Then, he said “However, sometimes just one word is enough to get the permission from your father without spending much time. This is what you told him, and you got the permission!” and explained the issues in quantum view for the photoelectric effect. He indicated that the importance of saying the correct word to get permission is analogous to the importance of the energy (or frequency) of incoming light rather than its intensity. This was an excellent analogy to explain the issues (i.e. no need to wait, no time interval for the emission of the photoelectron from the surface) of the photoelectric effect by comparing classical and quantum issues. This analogy stated classical and quantum issues more explicitly than the previous analogy (the tap analogy); however, the instructor used this analogy partially implicitly. If he stated analogs and targets of classical and quantum perspectives explicitly for students after he constructed the analogy, it might be better for students' understanding of the topic.

The seating in the lecture hall analogy

As introduced in Table 5, this analogy was used in the teaching of many-electron atoms, almost at the end of the semester. It was used verbally as an advance organizer through the construction of the analog–target relationship. It was an extended analogy indicating more attributes for Hund's rule. The attributes were the seats in the lecture hall (analog₁), students taking the course (analog₂), and students' seating preference (analog₃), for orbital (target₁), bound electrons (target₂), and Hund's Rule (target₃), respectively. There was no explanation of analogs and/or the limitations of this analogy. The analogy was anthropomorphic. It was used spontaneously in combination with brainstorming with the students in order to increase participation in the class.

At the beginning of the class, the instructor wrote the title “Hund's Rule” on the board and turned back to the class. Then he started to explain the concept by stating “The order…” and he recognized a female student was just coming into the lecture hall. He did not complete his sentence and instead he told the class “Let's follow her!” The instructor and the students in the class watched the location of the incoming student in the lecture hall. Then he told the class, “She sat down here” by indicating where she was sitting. Then he developed the analogy further:

Instructor: (Asking the class) Have you followed her? What can you say about her motion? Let's analyze!

Student A: She sat down in the seat where she wanted to sit.

Student B: She sat down in the seat closest to door.

Then a male student entered the lecture hall. Again, the instructor said, “Let's follow him!” and again the instructor and students watched the location of the incoming student in the lecture hall. Another student in the class then interpreted the new student's motion:

Student C: He sat down in the seat near his best friend.

A third student then entered the lecture hall, and the instructor again said, “Let's follow her!”

Student D: She also sat down in the seat near her best friend.

Instructor: The first motion you saw was that everyone sat down in empty places, which represents an empty state. Second, she and he (gesturing to the first and second students who entered late), they sat down in places where they felt a little bit more free. What do we mean by that? She did not sit down just next to him, but left a seat in between. He (the second incoming student) did the same thing. You see, he left an empty seat next to him so he would feel free. You did the same thing also! If you look at the distribution of the classroom, every student sat down in a place that is separated a little bit from the others. Electrons follow the same rules. What does the rule say? If there are two electrons left out after distributing, these two electrons, the last electrons in the atoms do not sit next to each other, but prefer sitting in separate states. Let's explain with an example…

After this analogy, the instructor continued to explain the concept through physical examples. It is emphasized that spontaneous use of analogies constructed by teachers may mislead science learning (Treagust et al., 1989). For this reason, spontaneous use of this analogy actually had the potential risk of creating misconceptions about Hund's Rule. This analogy might break down if students tended to sit next to or near their friends instead of sitting in the empty parts of the lecture hall at the beginning. The instructor did not acknowledge the students' observation and interpretation that students tend to sit next to their friends. By acknowledging that the analogy might break down if all the students did not sit apart from each other but instead tended to sit near their friends, the instructor would be stating a limitation of the analogy. This acknowledgement would help the students to develop a clear understanding of Hund's Rule. If the limitations of the analogy were stated explicitly, this type of use might be an example for the careful use of analogies in the classes.

The bear analogy

As mentioned in Table 5, the bear analogy was also used in the teaching of Particle properties of wave unit in the clarification of Pair production. It was used as a post synthesizer by telling a story verbally. It was an enriched analogy. This analogy was one of the analogies where analog explanation was observed. After the teaching of the pair production, the instructor started to tell a story. He first gave an analog explanation by telling the story. In the analogy, the help of an adult bear (analog) was related to the help of a nucleus in pair production for the conservation of energy and momentum (target). The analogy was environmental and it was spontaneously used. There was no explanation about the limitations of this story-formed analogy.

Instructor: (Explaining the figure drawn on the board) Charge and energy is conserved, and linear momentum is conserved. It is conserved with the help of a nucleus. So, it means that, if you do not have a nucleus, if you perform this experiment in a vacuum, you cannot have this production. So, a nucleus helps this photon to create a pair as if a nucleus stays behind, remains behind, and the photon does whatever it is going to do. Do you know the story of baby bear?

(A noise in the class)

Instructor: (Starting to tell the story) There are a baby bear and a mother bear. The hunters chase and kill the mother bear and then the baby is left alone. It eats toxic mushrooms, herbs because it does not know what they are. It dreams some bodies attack it. One day, while the baby bear is moving, it comes across a tiger. The baby bear is shaking because it is afraid of the tiger. While they are looking at each other, the tiger moves back without attacking. The baby bear thinks that it frightened the tiger. While it was proud of itself, it saw the father bear by looking back. The father was standing at its back. It protected the baby from any danger. So the nucleus is like that…

That was a different experience for students since the lesson was teaching quantum concepts. It was observed that students were motivated and focused on what the instructor was saying. They liked the story because the instructor told this story in the last five minutes of the class, just before ending the class. In this way, he regained their attention, he summarized the pair production, and he ended the class.

The strong man analogy

As explained in Table 5, this analogy also belongs to the photoelectric effect topic of the Particle properties of waves. It was also used verbally and as a post synthesizer to strengthen the students' understanding through role play. By giving roles to some of the students in the class, the instructor gave the analog explanation. With this analogy, the photoelectric effect was simulated in the class, introduced anthropomorphic elements, and showed extended use of analogy with more attributes. It was spontaneously used and the instructor never mentioned its limitations. The instructor used this analogy to increase participation in the class.

After summarizing the photoelectric experiment for different metal plates (aluminum, copper, etc.) by showing the figure and explanations written on the board, the instructor asked himself, “How should we represent that?” Then, the instructor approached the student sitting at the end of the first row of seats.

Instructor: (While coming from the desk toward the students) Yes… Come here (asking a male student)!

(The student stood up from his seat and he stood near the seat of a female student. The instructor explained the roles of the students by saying “hold the female student's hand and pull her” to the male student and “do not move easily when he pulls” to the female student)

Instructor: Now… Hold her hand and pull her up! (Asking to male student)

(The male student was holding the hand of the female student and pulling her towards himself. He was pulling very strongly. Other students in the class were laughing because she was not moving.)

A student: Her arm will be broken!

(Then the female student stood up from her seat and moved toward him)

Instructor: He is trying to remove her from her seat. Now repeat the experiment! Pull again. Pull her hand! (shaking his hand). Yes. You see he pulled her from the seat. He pulled very strong. But it was difficult to get her up. It depends on how strongly she is bound. This strength is ϕ (indicating the formula on the board). That is known as “work function” of materials. It depends on the type of the materials. How strongly she is holding on. And, after pulling her from her seat, he applied more force and she started running. So she has extra kinetic energy. She gained extra kinetic energy. So, there are two things: Work function is in fact equal to the amount of energy that he is using to move her from the desk. This is known as the work function of the particular material or particular student. Now (looking at the students sitting at the other corner of the class). These two (indicating two male students)! He is going to pull him! Lets repeat it!

(The male student was pulling and the other male student was not moving so the other students in the class were laughing at the situation).

Instructor: Pull! You see it is not easy. Try harder! (Speaking to the pulling student). Yes. Try harder!

(The male student was still pulling but the other male student was not moving)

Instructor: Look that he (indicating the pulling one) is not strong enough to pull him up! That's why, if it is below a certain frequency, if the strength of the incoming wave is not enough, so nobody came out! So, if it is below this energy (indicating the work function on the board), the energy of the wave is below work function, you cannot expect electron! The original energy of the wave is “hν“ which is E (indicating its place on the board). This energy first goes into work function! This is the minimum energy required to expect the electron. Here, he does not move (indicating the male student), so the energy was below this minimum energy “work function”. What he did to her (indicating the male and female students), he pulled her up and she gained kinetic energy. This is maximum kinetic energy of the electron (indicating the formula on the board hν = ϕ + KE). As a result of this extraction as you see, maximum kinetic energy of the electron you see is the difference between the energy of the photon minus work function of the material in question or in the experiment. This is, you see, another result. The kinetic energy increases linearly with the frequency of light. This is the very fundamental for photoelectric effect!

This was also an excellent analogy indicating the clear relationship between analog and target by saying “Work function is in fact equal to the amount of energy that he is using to move her from the desk. This is known as the work function of the particular material or particular student”. The instructor explained the target by directly indicating the analog in the role play, and finally he ended by using both of them together.

Strong man analogy, which I called so, was as important for the explanation of the important issues of the photoelectric effect as family relationship analogy. The analogy used took eight minutes to compare analog and target. With this analogy, the instructor related the pulling of the male student (analog₁) with the energy of incoming light (target₁), and the seated students (analog₂) with electrons in the metal plate (target₂). In addition, when the pull is strong enough to move the seated student (analog₃), it corresponded to a large amount of energy from the incoming light (target₃) and when the pull is not strong enough (analog₄), it corresponded to a small amount of energy from the light (target₄). In addition, when the female student did not only stand up from her seat but also started running (analog₅), this action represented the kinetic energy of the photoelectron (target₅). One more attribute could be added by the instructor to indicate the difference between classical and quantum perspectives. If the instructor gave roles to more than just one student to pull the seated student (male or female) and the student does not move from his/her seat, he could indicate the importance of the frequency of the incoming photons to eject an electron from the surface, not the intensity of the incoming photons (target) which were related to the number of students pulling the seated ones (analog). In spite of some limitations, this analogy was a good example of how analogies might be incorporated into lectures using role play, and it was also a different experience for students majoring in science at the university level.

This analogy also indicated the risk of its break-down while constructing it with the students spontaneously. It might also break down as previously explained in the seating in the lecture hall analogy. However, in this case, the instructor directed the role play well. More clearly, there were two probabilities for the pulled students: being pulled up or staying in his or her seat. Both probabilities were observed in the class and the instructor used both attributes to explain the target. This success can also be attributed to the experience of the instructor, since he recognized that the first part of the role play with male and female students could not make sense of all the roles and behaviors of the target, he then organized the second role play with the two male students.

In the interview with the instructor, he stressed the importance of this type of activity for students' enjoyment while learning. He stated that he could increase interaction and make students participate mentally and physically in the classes by using analogies and analogs from daily life.

The swimming in a drift analogy

As presented in Table 5, the swimming in a drift analogy was used in the teaching of the Zeeman effect in the Quantum theory of the hydrogen atom. It was used as an embedded activator to clarify the concepts. It was an enriched analogy explaining the behavior of an atom in an external magnetic field (target), which related it to the behavior of a man swimming with the flow of a river (analog), and was anthropomorphic. The instructor drew the figure indicating the external magnetic field and an atom in the field on the board. Without drawing a new figure for the analogy, the instructor explained the analogy in the figure by saying “river” for the external magnetic field, “you” for the atom, “drift” for the flow of river, thereby using both verbal and pictorial elements. There was no analog explanation or presentation of the limitations of the analogy. It was also spontaneously used during the discourse in the teaching of the Zeeman effect.

Instructor: We are talking about putting an atom in a magnetic field, in fact we mean a hydrogen atom in the magnetic field in this case. The hydrogen atom has a magnetic dipole moment. This is μ, magnetic dipole moment (drawing the figure on the board)! So, suppose we have such an atom with a dipole moment μ in external magnetic field. Let's say its angle is θ (indicating the angle between magnetic dipole moment and magnetic field). What happens here? How do they interact with each other? What do you think happens?

(None of the students gave answers to the instructor's questions. He waited for students and after he did not receive a response, he constructed the analogy.)

Instructor: Suppose you are swimming in a river. The river is flowing and you have an angle to cross the river. What happens?

A student: It pulls me in its flowing direction!

Instructor: It pulls you in its direction. It moves you in the flow and you go adrift. So that's what happens here (turning back the topic). Dipole moment of the atom tends to align with the magnetic field. So, there is a rotation. So, μ, magnetic dipole moment tends to rotate. In what direction? In the direction of magnetic field. Like this (showing the figure that explained the analogy). Eventually it comes, in this direction, to align with the magnetic field. When there is rotation, what effect do we have? There is torque…

This analogy is special because its use combines verbal and pictorial elements. The instructor recognized the similarity of the figure of an atom in an external magnetic field and that of a man in a river, and he used this opportunity to construct an analogy, which was supported by the previously drawn figure. The use of this type of analogy that included a pictorial element also presented some evidence about the instructor's well-founded subject matter knowledge and experience by recognition of implicit elements in the classes, integrating them into instructional techniques, and using them for the clarification of the concepts for students' better understanding.

The paper analogy

As indicated in Table 5, the paper analogy was used in the teaching of radioactive decay in the last topic of the semester, which was “Nuclear transformations”. It was also used differently by the instructor, who visualized the analogy using body motions in combination with verbal elements. This analogy was an advance organizer to introduce the concept of a half life. In addition, it was an enriched analogy that constructed an analog–target relationship between dividing the paper half (analog) and the half life (target). The instructor did not use analogy explanation or admit the limitations of the analog. It was spontaneously used by discourse and had environmental characteristics.

While the instructor was explaining nuclear decay, he said that “I want to give one more concept and finish”. Then, he picked up a piece of paper. Showing it to the students, he constructed the analogy:

Instructor: Now, this is a paper. It has a certain length. I folded it into two and I am tearing it (tearing). I have this (showing half of the original paper). What is this? What is left in my hand?

Students: Half!

Instructor: Half of it! Now folded, and I did the same (tearing the folded parts). Rest?

Students: Half.

Instructor: Half of the half! Now, I folded again. (After tearing the paper) Now? Half of the last half! And we continue (tearing the last half)! There is a certain life time for halving the initial. Then the next halving, next halving. This is known as the half life of this element.

One of the special uses of analogies is its use combined with body motions. This analogy was constructed by concrete visual elements by showing how the atomic mass is reduced by tearing the paper.

The ladder analogy

As mentioned in Table 5, the ladder analogy was used in the first explanation of quantization phenomenon for particle in a box in the Wave properties of particles. It was used as an embedded activator by means of body motions and verbal elements. That means the analog–target relationship was enriched by the steps of the instructor on the steps in the lecture hall (analog) to explain discrete energy levels (target). There is no analog explanation and limitations about the analogy. It was used spontaneously from the students' daily environment during discourse to increase the participation.

Instructor: Because there is n². Energy can take only certain values. Like a ladder (stepping in the lecture hall). Steps of the ladder like energy levels. Energy is discrete. Where these things observed, in atoms, in small regions!

By moving step-by-step and not stepping between two steps (analog) he showed having only certain energy values and not having continuous energy levels (target). This analogy was also stated in the textbook (Beiser, 2003) and in the interviews students mentioned about this visualized analogy in the class.

The good citizen analogy

As explained in Table 5, the good citizen analogy was used in the teaching of energy quantization in the particle in a box case in Quantum Mechanics. It was used as an embedded activator by verbally extending the attributes. With this analogy, the particle in the box (target₁) was matched with a good citizen (analog₁); restriction in the energy values of the bound particle (target₂) was matched with the rules and restrictions imposed on citizens (analog₂) for being a good citizen; quantified energy levels (target₃) was matched with the behaviors allowed by rules and regulations (analog₃). In this way, energy quantization for a bound particle was explained by analogs to the restricted rules to be obeyed by citizens. In this way, the quantization was clarified by indicating human characteristics for the behavior of the atomic system. There was no analog explanation and he also did not mention the limitations. The instructor used the analogy spontaneously by alluding to Socrates' life.

Instructor: There are restrictions. You cannot have your way! There are rules that you have to obey. Just like there are laws for the state. We respect the laws! So the particle in this box cannot just say “I can do everything” and it says “I do the right things, only right things. So the quantization of this energy equal to (drawing the figure on the board) E₁, E₂ is four times E₁, E₃ is nine times E₁. This is quantum mechanics! This is such a quantum effect!

In the teaching of the particle in a box topic, the instructor constructed the good citizen analogy, which I named, from a social context, similar to what Sarantopoulos and Tsaparlis (2004) suggested. In his explanation of the quantization of the energy of a particle in a box, the instructor used it with an idiom by saying the good citizen will not have his own way and he compared the restriction of the energy values of a bound particle with the rules and restrictions imposed on citizens.

What do the students think about analogy use in the classes?

The instructor's diverse use of analogies in modern physics classes can be considered as a different experience for students. Because the instruction of upper level physics concepts is mainly constructed on advanced calculus knowledge, the classes include advanced mathematical expressions and direct teaching with limited interaction with the students. The analysis of the interview data showed that students were aware of the analogies used in the classes. One of the students stated, “The instructor constructs good analogies in the classes”. In addition, they thought that analogy use was one of the strong points of the instructor's pedagogical methodology. In the interview of the instructor, he explained that he constructed the tap analogy with the flow of water drops from a tap to indicate discreteness. He stated that he used this analogy to discriminate between Newtonian physics and quantum physics. He also added that he believed students who understand quantization correctly remember this analogy or construct other analogies, and explain quantization correctly.

Students mainly stated that they liked the analogy use in the classes and they believed that analogies were important elements in making the concepts concrete. One of the students stated the importance of analogy thus: “We observe the nature and try to explain the new thing. Then, we ask 'what does it look like?’ and we make analogies to explain it”. Therefore, students believe analogies were effective elements in their understanding of modern physics concepts, just like the mathematical and visual elements.

The students also believed that the instructor constructed effective analogies in the classes, thus better facilitating their understanding and comprehension of the concepts. In the interviews, students mostly indicated the instructors' use of the ladder analogy for energy quantization as an effective analogy that they remembered. Students, who remembered this analogy from the classes, explained the targeted physics concept in addition to the analogy while solving the conceptual questions in the interviews. In addition, six of the twenty students could explain at least one conceptual question by using the same analogy (e.g. ladder analogy, good citizen analogy, tap analogy, etc.) as the instructor and four of them could construct different analogies. One physics student explained quantization with his own analogy, stating that quantized energy is like paying an installment with small amounts. After he stated energy was in packets, he clarified this issue as getting money from someone who lent in small amounts, such as 3 liras per loan, and with the values the lender allowed someone to pay him back. In this way, the student explained the quantized energy levels using an analogy.

Although physics and physics education students had similar ideas about analogy use by the instructor and the analogies used in the classes, one difference between these two groups of students can be reported as the recognition of “analogy” as a term. Since the physics education students take pedagogy classes in their program, in the interviews they demonstrated their theoretical knowledge of analogies and they used the term “analogy”, rather than referring to it as a “comparison”. While stating analogies, some students clearly indicated unshared characteristics of the analog and target. One student, from the physics education program, also stated that he could use analogies frequently in daily life. He believed that analogies are the most powerful elements of language, explaining that he could communicate better by using analogies, and that individuals needed to imagine and link two different things in order to make sense of the unknown by using the known.

Conclusion and discussion

This study showed that although the concepts of quantum theory were abstract and counter-intuitive, analogies can be constructed and used for the teaching of a wide range of topics at the university level. In the observation of 53 fifty-minute classes, it was identified that 48 analogies were used by the instructor. In comparison with the results of previous research (Treagust et al., 1989; Nashon, 2004), the construction of such a large number of analogies by only one instructor is remarkable. This exploratory research revealed that in the teaching of quantum theory in an upper level course, most of the analogies (23%) were constructed in the Particle properties of wave unit in teaching electromagnetic waves, blackbody radiation, photoelectric effect, light, X-rays, X-ray diffraction, Compton effect, pair production, photons, and gravity close to the beginning of the semester. The presentation format of the analogies was largely verbal (85%); however, a limited number of pictorial and body motion elements were used in conjunction with the analogies. The analogies were mainly positioned as an embedded activator (71%) prior to drawing conclusions about the target; however, it was also observed that analogies were used as advance organizers and post synthesizers. The number of simple and enriched analogies used was quite similar; these numbers were 40% and 42%, respectively. A limited number of analog explanations (13%) were identified and none of their use indicated strategy identification. Similarly, of the analogies used in the classes, the instructor never mentioned the limitations of each analogy. A great proportion of the analogies (94%) were used spontaneously, both with anthropomorphic (38%) and environmental (63%) characteristics. Although the presentation medium of the analogies was mainly discourse (63%), the presentation of analogies in role play, stories, and brainstorming was also identified. In half of the analogy use (50%), the instructor aimed for clarification of the concepts. However, the use of analogies to introduce a new topic, gain attention, increase participation, and discriminate between classical and quantum issues can be considered evidence of diverse use of analogies.

The instructor not only used the analogies already existing in the literature, but also constructed a large number of new analogies, including some of the selected ones presented in Table 3. The statement of like and unlike characteristics between the analog and target might be the result of the instructor's outstanding physics knowledge (Treagust et al., 1994). In addition, Table 5 presents how analogies were used in the classes by presenting some of their properties. In this case, the family relationship analogy was a good example of the comparison of classical and quantum theories with its extended used of attributes. Another analogy with more attributes was good citizen analogy, which was an example of how it clarified quantization phenomenon. The bear analogy presented the use of analogy in story format as a post synthesizer to gain students' attention in the last few minutes of the class. The strong man analogy presented how analogies could be used with role play for increasing participation. This analogy also indicated the instructor's well-founded physics knowledge, as he analyzed all issues to be taught about the topic and revised the role play to include more attributes. As with the previous example, seating in the lecture hall analogy was an example of the spontaneous use of analogies that included students. In this case, brainstorming was preferred as the advance organizer; however, this analogy had the potential risk of break-down if something is wrong in the spontaneity. For this reason, this can be accepted as the instructor's avoidance of the probability of the break-down of the analogy. The tap analogy was a good example of enriched analogies presented through discourse. While swimming in a drift analogy was an example of how an analogy might make use of a pictorial element, paper analogy and ladder analogy were analogies that were used differently from the literature. These analogies used body motion combined with verbal explanations, indicating that the presentation of concrete visual elements might be important for students' learning. In the interviews, most of the students referred to the ladder analogy as effective for their understanding of the quantization of energy.

From the pedagogical research about the quantum theory, scientists use analogies to introduce new concepts during the development of science. Thomson's description of an atom as a plum pudding and Rutherford's model of an atom as the solar system are good analogies for understanding the atomic world. However, they are analogies for early ideas and cannot explain the quantum theory. This means the analogies have a limited ability to explain all issues of the targets and they also have unshared characteristics. One of the important issues identified in this research is that only shared characteristics of the analogies were explained by the instructor. Unshared characteristics of the analogies were never mentioned and limitations of the analogies were never explained implicitly or explicitly. Many researchers indicated the importance of explanations of the analogs' shared and unshared characteristics with the targets (Harrison and Treagust, 1993; Thiele and Treagust, 1994b; Treagust et al., 1994, 1998; Taber, 2001) because each analogy has the potential to break down and create misconceptions about the concept.

As Whalley's (2005)rugby ball analogy indicated the importance of the energy of incoming light for the liberation of photoelectron rather than the intensive light without insufficient energy (as rugby balls thrown intensively by children), the instructor indicated the same issue when teaching the same concept (photoelectric effect). In the family relationship analogy, the instructor explained the process of asking the father for permission (as intensive light without insufficient energy) as an analogy to indicate the impossibility for liberation of electrons and also explained that saying one word (not intensive light with sufficient energy) and getting permission was analogous to the possibility for liberation of electrons. Although both of the analogies are useful in explaining the photoelectric effect, the use of these analogies might be improved by stating each attribute between analog and target explicitly for students. For this reason, teachers or professors, who have well-organized mental models about the topics they teach, should consider how students understand their explanations while they are constructing analogies.

This research identified that the analogies were often used spontaneously. Similar to the way in which Whalley (2005) described his experience, the instructor used some analogies spontaneously in order to respond to students' needs at that moment in the class. In other words, he used analogies sometimes as a “remedy” for students' misunderstanding (Treagust et al., 1989). However, some research indicated that the spontaneous use of analogies constructed by teachers may mislead science learning (Treagust et al., 1989; Thiele and Treagust, 1994b). Thiele and Treagust's (1994b) research design was similar to that of this research since the researchers examined chemistry teachers' analogy use. The findings about the instructor's spontaneous use of the analogies are parallel for both studies. However, in terms of the findings on analog explanation, one of the findings of Thiele and Treagust's (1994b) research is not parallel with this research. Although chemistry teachers made explanations in a great proportion of their analogies, the instructor in this study made very limited analog explanations. This lack of explanation may be because the instructor in this research considered analogies only as a tool, and not an instructional methodology. Since the instructor was a physics professor, his limited knowledge about analogy use might be the reason for this approach. In addition, the audience was second-year university level students majoring in science (physics and physics education). The instructor might consider that these students – in contrast to high school students – already had experience with the analogs. Previous literature (Harrison and Treagust, 1993; Treagust et al., 1994; Orgill and Bodner, 2004; Sarantopoulos and Tsaparlis, 2004) suggested the importance of familiarity with the analogs on the effectiveness of analogies; the instructor used familiar analogies with the students. Treagust (1993) suggested that teachers should select the analog from the students' own world in their explanation of the topic. Duit (1991) also suggested that analogies from students' real world experience facilitated the generation of their sense of intrinsic interest. In this study, for the familiarity of the analogs for students, the analogies were drawn from their own experiences. For this reason, the instructor's selection of the analogies from a familiar environment is a good way to explain concepts more easily. When the analog is unfamiliar to students, it might limit students' conceptual understanding (Treagust et al., 1994). The analogies used in the classes have both environmental and anthropomorphic characteristics, as defined in Nashon's (2004) study of high school physics classes. In other words, the analogies were drawn from the social environment with which the students were familiar. The use of anthropomorphic analogies helps students to make sense of abstract and counterintuitive concepts. As they gain human characteristics, these concepts are concretized for the students to facilitate their understanding. This characteristic presented a similarity between the analogies observed in this study and those preferred in the research of Sarantopoulos and Tsaparlis (2004). The researchers explained that analogies having strong social contexts were an important requirement for effective instructional analogies. They implied that social relevance and enjoyment made the classes interesting and not boring.

As Thiele and Treagust (1994b) identified with high school chemistry teachers, the instructor in this study used pictorial components together with the analogies; however, it was quite limited. When comparing analogy use in textbooks to that of instruction, instruction has some advantages because the instructor may provide more attributes immediately by interacting with students. Since this study included the possibility of direct interaction with the students as it was required, our findings differed from the findings on the presentation format regarding the use of analogies in textbooks (Thiele and Treagust, 1994a). There is an additional difference from previous literature: this research identified that the instructor used three analogies that combined body motion with verbal explanations. This combination can be considered as one of the advantages of instruction over textbooks in terms of providing a kind of visualization.

As Treagust et al. (1989) identified from the teachers, the instructor was aware of the advantages and disadvantages of using analogies. In this research, the instructor used these advantages and he used the analogies for five different aims such as the introduction of a new topic, clarification of previously taught concepts, gaining students' attention in the class, increasing students' participation, and comparing classical and quantum physics. Analogies may increase students' motivation and interest (Treagust et al., 1989; Thiele and Treagust, 1994b). These aims showed that in addition to addressing the cognitive domain of learning, analogy use contributed to the affective domain of learning as the instructor used analogies for motivational aims (Duit, 1991).

Constructing good analogies requires instructors to blend pedagogical knowledge with subject matter knowledge. The results of this study demonstrated that evidence of the instructor's expertise might contribute to the use of analogies in the classes. The instructor never mentions the “analogy” as an instructional strategy. Rather, his well-founded physics knowledge and considerable teaching experience enabled him to construct new analogies about the concepts of quantum theory in upper level science teaching and make good use of these analogies. This supports the requirement of these two issues in order to use analogies well, as explained by Thiele and Treagust (1994b).

This study identified that the instructor used the analogies in four different ways: with direct comparisons (simple); in conjunction with role play (Tsai, 1999); in story format; and in brainstorming. Aubusson and Fogwill (2006) explained that role play combined with analogy enabled knowledge transfer from analog domain to target and generated deeper understanding. Therefore, the use of analogies with role play can be integrated into the classes with pedagogical knowledge combined with subject matter while teaching science. Orgill and Bodner (2006) indicated the need for giving sufficient time for students to compare the analog and target concepts; the instructor in this research gave students sufficient time in three different presentation mediums such as brain storming, role play, and story type. Since these analogies had continuous form and their construction took more time than the simple analogies, the students had time to relate analog and target. In addition, stating more attributes in some of the analogies might facilitate the construction of analog–target relationship.

Second year university students taking the Modern Physics course believed that analogy use was one of the strong points of the instructional methodology of the instructor and that analogies are effective elements for enhancing their understanding of the concepts of quantum theory. Some of the students could recall analogies used in the classes and the concepts targeted by those analogies. The reason the ladder analogy might have been the most recalled could be the visual support of the analogy by the instructor going up and down the steps of the lecture hall while explaining the concept. These findings from 20 students are also similar to the results of the research conducted by Orgill and Bodner (2004), in which they identified that biochemistry students liked and remembered the analogies used in the classes. This parallelism supports that the ideas about analogy use in the classes might be context independent. Some of the students (four students) constructed their own analogies to explain a specific concept and these analogies were similar to the instructor's analogies in terms of being environmental; however, they were mutually independent analogies. Students' construction of their own analogies is important for the development of mental models and thus learning (Glynn, 2007). In addition, the research of Podolefsky and Finkelstein (2006) showed the positive influence of analogy use on students by inferential statistics. However, this research supported students' ideas about the positive influence of analogies on their conceptual learning by testing their understanding with conceptual questions in the interviews. Although the examined concepts and research methodologies were different, this research indicated that students had a clear understanding of the concepts that the instructor explained using analogies in the classes.

This research was exploratory research examining the university level science classes teaching quantum theory. In addition to reflecting what might be happening in upper level science classes through the influence of an instructor (e.g. his knowledge, motivation, etc.), it indicated the possibility of use of instructional methodologies in classes with large architecture, a linear seat arrangement, and a large number of students limiting the student–instructor interaction. The analogies that emerged from the instructor's well-founded physics knowledge might be helpful for chemistry and physics instructors teaching the concepts of quantum theory in the future. In addition, how these analogies are used and students' beliefs may help develop new instructional designs in university physics, chemistry, and science classes. In science instruction, no matter whether it is high school or university level, analogies might be used effectively alongside good instructional design.

The results of the observational data and the data obtained from the second part of student interviews support the idea that the use of analogies is effective in classes. At first, giving analogies from a familiar environment, stating some differences between analogs and targets (Harrison and Treagust, 1993; Treagust et al., 1994; Orgill and Bodner, 2004; Sarantopoulos and Tsaparlis, 2004), and constructing conceptually deep analogies (Treagust et al., 1994) were some evidences about effectiveness. In addition, the instructor provided students the required time to think (Simons, 1984 as cited in Orgill and Bodner, 2006). Finally, this research indicates that the use of analogies in classes might be a result of instructor's well-founded content knowledge and experience about how students learned as Thiele and Treagust (1994b) concluded in their study. However, well-founded content knowledge and experience might not always be enough to guarantee good use of analogies. As McDermott (1991) stated, what we teach is sometimes different from what students understand. So, in order to provide correspondence between taught and understood concepts, as science educators, we need to use effective techniques in classrooms. Analogy is one such effective technique for helping students reach a correct understanding of the scientific concepts by using similarities with nature; however, it is important to keep in mind that teaching effectively using analogy requires careful planning (Taber, 2001).

Appendix: interview protocol

1. Analogy is a kind of technique to clarify the “unknown” by using the properties of the “known”. When considering the modern physics classes over the semester, do you recall the instructor using any analogies? Did he explain any unfamiliar concepts by means of familiar ones?

2. If Yes, which analogy was the most effective one for your understanding of the explained phenomenon?

3. Do you think the analogies are helpful for your understanding of the concepts of the quantum theory?

4. There is a list of conceptual questions about the important issues of quantum theory. Please select one of the following questions and explain your answer using an analogy:

• What is the importance of Planck's constant (h) for quantum theory?

• What does the photoelectric experiment explain about the nature of light?

• Suppose the electron in the hydrogen atom obeys classical mechanics rather than quantum mechanics. What would you expect to observe in the spectrum?

• What are the failures of the Bohr's postulates about the quantum theory?

• Can you give an example for a physical situation of particle in a box?

• What do the quantum numbers explain? Discuss for the Bohr atom and a quantum mechanical model of atom.

Acknowledgements

I would like to extend special thanks to Professor Dr Şakir Erkoç (Atomic and Molecular Physicist), Professor Dr Ömer Geban (Chemistry Educator), Middle East Technical University, Bülent Ecevit University, and the Scientific and Technological Research Council of Turkey (TÜBİTAK) for their precious support.

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Footnote

† All quotations attributed to the instructor and students stated in the classes are the original quotations with the explanations in English since the study was conducted at an English medium university.

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