Pre-service Elementary School Teachers' Ability to Account for the ...

J Sci Teacher Educ (2014) 25:911–933 DOI 10.1007/s10972-014-9407-y

Pre-service Elementary School Teachers’ Ability to Account for the Operation of Simple Physical Systems Using the Energy Conservation Law Nicos Papadouris • Angela Hadjigeorgiou Constantinos P. Constantinou

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Published online: 22 November 2014 The Association for Science Teacher Education, USA 2014

Abstract Energy is recognized as a core idea in science and, hence, a significant learning objective of science education. The effective promotion of this learning objective posits that teachers themselves possess sound conceptual understanding. This is needed for enabling them to organize effective learning environments for their students. In this study, we report on the results of an empirical investigation of teachers’ understanding of energy. In particular, the focus is placed on pre-service teachers’ ability to employ energy as a framework for analyzing the operation of physical systems. We have collected data from 198 pre-service teachers through three open-ended tasks that involved the application of the energy conservation principle to simple physical systems. The results corroborate the claim made in the literature that teachers typically do not possess functional, coherent understanding of this principle. Most importantly, the data serve to identify and document specific difficulties that hamper attempts to use energy for the analysis of the operation of physical systems. The difficulties we were able to document lend support to the idea that it is important to introduce the idea of energy degradation alongside the conservation of energy principle. The findings of this study have implications for the design of preparation programs for teachers, about energy. The findings also provide insights into the limitations of conventional teaching of energy, to which the participants had been exposed as students, in fostering coherent understanding of energy conservation. Keywords

Energy Conceptual understanding Teachers’ education

N. Papadouris (&) A. Hadjigeorgiou C. P. Constantinou Learning in Science Group, Department of Educational Sciences, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus e-mail: [email protected]

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Introduction If teachers are to effectively cope with the challenge of helping students develop understanding in science, it follows that they need to possess adequate understanding themselves. This is of paramount importance for building the confidence needed for organizing and sustaining effective learning conditions (McDermott, Heron, Shaffer, & Stetzer, 2006). Research evidence casts considerable doubt on whether this condition is fulfilled (Burgoon, Heddle, & Duran, 2010; National Commission of Science and Mathematics Teaching for the 21st Century, 2000). Thus, there is a need for developing effective programs for in-service and pre-service science teachers, which, in turn, posits expanding the available research-based knowledge about teachers’ understanding and their needs, in terms of the various conceptual, epistemological or other difficulties they encounter. This paper reports on an exploratory, descriptive study that seeks to contribute in this direction. It sets out to investigate pre-service elementary teachers’ understanding with respect to a core concept of science disciplinary knowledge, namely energy. In particular, we have undertaken a systematic investigation of teachers’ understanding of the features of conservation and degradation, as they apply to the operation of simple physical systems, and the various difficulties they encounter. The research questions we sought to address are as follows: •

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To what extent are pre-service teachers in a position to effectively apply the features of energy conservation and degradation for the analysis of physical systems? What difficulties do they encounter in this respect? To what extent do they appreciate the facility of energy to serve as a framework for system analysis?

The overarching purpose of the paper is to provide a basis for developing courses in teacher education that will address the kinds of knowledge pre-service teachers need to have in order to be able to teach about energy. Indeed, empirical research targeted at the identification and documentation of specific difficulties, could provide valuable insights that could substantially inform and guide attempts to design and structure effective learning environments (McDermott, 1991; McDermott & Shaffer, 1992). Specifically, they could guide the design of activity sequences that (a) address learners’ needs, by explicitly helping them overcome the difficulties they encounter, and (b) utilize their available productive resources as conceptual steppingstones toward more coherent understanding (NRC, 2007; Smith, diSessa, & Roschelle, 1993).

Rationale Why Focus on Energy? Understanding energy is a major learning objective of school science (AAAS, 1993; Chen et al., 2014; NRC, 2012, 2013; Saderholm & Tretter, 2008). The recent

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framework for K-12 science education standards (NRC, 2012) portrays energy as a core concept in the physical sciences. As such, it is considered a wider theme within which it is possible to organize learning experiences for facilitating and sustaining students’ active engagement in science and scientific inquiry over several years. An additional important characteristic of energy that further illustrates its potential from an instructional perspective relates to its crosscutting, unifying nature (NRC, 2012). Energy transcends all science disciplines and provides a powerful framework for interpreting a wide range of phenomena (Arons, 1999; Holton & Brush, 2001). Even though any phenomenon could be analyzed in terms of concepts other than energy (e.g., concepts drawn from the corresponding domains, such as electric current or force for electric or mechanical systems, respectively), energy allows a unifying perspective that could subsume the interpretation of phenomena/systems from different domains of science. Finally, an additional characteristic of energy that further highlights its significance as a learning objective relates to its importance for citizenship. Understanding energy could help one make informed decisions, at a personal level, but also to make sense of the public discussion over topical socioscientific issues, such as energy supply, distribution and utilization (Hinrichs & Kleinbach, 2002). Despite the wide recognition of energy as a significant learning objective, research has consistently demonstrated that the development of coherent conceptual understanding is a rare outcome of conventional instruction (Driver & Warrington, 1985; Duit, 1984; Liu & McKeough, 2005; Solomon, 1992). This study focuses on teachers’ conceptual understanding of energy, which is prerequisite to the promotion of this learning objective among students (Duschl, Schweingruber, & Shouse, 2007). Why Focus on Teachers’ Conceptual Resources and Difficulties? Understanding of disciplinary content is recognized as a main component of pedagogical content knowledge (PCK), which entails the set of resources and knowledge needed to enable teachers to make appropriate instructional choices (Shulman, 1987; Van Driel, Verloop, & de Vos, 1998). Indeed, research literature suggests a strong correlation between teachers’ preparedness, in terms of proficiency in disciplinary content knowledge, and the extent of the impact on students’ learning outcomes (Gess-Newsome & Lederman, 1995). Also, there is evidence that the influence exerted by teachers’ preparedness (or lack thereof) tends to be larger than the impact of other factors that are commonly associated with the quality of instruction and students’ learning, such as, the size or the heterogeneity of the student population in individual classes (Wright, Horn, & Sanders, 1997). Despite the instrumental role of teachers in enhancing science learning, available research has reported rather disappointing findings with respect to their conceptual understanding. For instance, studies that have sought to investigate teachers’ understanding about a wide range of domains of science, including energy, suggest that they often hold non-valid ideas and face a range of conceptual difficulties, which often happen to be similar to those encountered by their students (Burgoon

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et al., 2010; Harlen & Halroyd, 1997; Krall, Lott, & Wymer, 2009; Papageorgiou, Stamovlasis, & Johnson, 2013; Rice, 2005; Wandersee, Mintzes, & Novak, 1994). Teachers’ Understanding of Energy: What Do We Know from Prior Research? Research has demonstrated that teachers often hold ideas about energy that deviate substantially from what would be deemed acceptable within the physics disciplinary knowledge (Kruger, 1990; Kruger, Palacio, & Summers, 1992; Summers, Kruger, Mant, & Childs, 1998; Tobin et al., 2012). One of the most prevalent findings includes teachers’ tendency to use the term energy in a loose and unarticulated manner. Specifically, teachers are inclined to assume a rather vague perspective, which portrays energy as something that is somehow needed for any process to take place (Kruger et al., 1992), without offering specific insights into either the nature of energy as a construct or its particular role in these processes. Also, energy is ascribed meanings that are situated in everyday, colloquial discourse and clearly conflict with how this construct is used in formal science communication. For instance, energy is commonly associated with the state of being active (i.e., being energetic). The consequences of this lack of clarity and coherence appear in various ways. One of these relates to teachers’ inability to meaningfully differentiate between energy and other, clearly distinguishable constructs such as electric current, force, heat or momentum (Kruger, 1990; Kruger et al., 1992; Trumper, 1998). Another noteworthy finding, relates to teachers’ flawed interpretations of various forms of energy. For instance, in the case of gravitational potential energy, they tend to believe that objects residing on the ground (as opposed to being located at a certain height above the ground) are not associated with gravitational potential energy. Another example, refers to the well-documented confusion between thermal energy (a form of energy) and heat (an energy transfer process). The findings about teachers’ non-valid conceptualization of various forms of energy (or energy transfer processes), become important in view of the fact that the language of forms of energy is commonplace in conventional teaching of energy (Kruger, 1990; Millar, 2000; Solomon, 1985; Tobin et al., 2012). An additional finding, which warrants mention, relates to the rather fragile confidence of teachers with respect to their understanding of energy ideas. For instance, during interview sessions about energy, teachers have been reported to easily modify or adapt their responses (often in a self-contradictory manner) as a result of further probing on the part of the interviewer (Summers et al., 1998). Teachers’ Understanding of Energy Conservation and Degradation Research findings on the features of energy conservation and degradation, the focus of this study, are also suggestive of inadequate understanding. They reveal teachers’ failure to apply the conservation law in simple systems and their lack of understanding as to its essence. For instance, they illustrate the tendency to assume that energy conservation applies to any individual object, rather than to closed systems (Kruger, 1990; Tobin et al., 2012). This could be possibly attributed to the misinterpretation of the typical formulation of the conservation law, namely that

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energy is neither created nor destroyed and the tendency to apply this law to individual objects, rather than to closed systems. Another common misinterpretation of the conservation law is that the energy involved in a process does not pre-exist. Rather it is produced as the need arises; that is, when a process is to be effected (Kruger, 1990; Trumper, 1998). In a similar manner, in the case of energy degradation, available research evidence suggests that teachers do not typically appreciate the idea that during the operation of any physical system, a part of energy converts into forms of lower quality, in terms of how easily it can be retrieved and taken advantage of (Summers et al., 1998; Trumper, 1998). Despite the interesting findings that have been documented in the extant literature, it is important to note that teachers’ understanding of energy conservation and degradation and their ability to apply those ideas in seeking coherent analyses of system behavior (i.e., formulation of interpretations and predictions), have not been the focus of thorough research.

Methodology Participants The study took place in Cyprus. Participants were 198 student teachers (173 females and 25 males, with a mean age of about 20.5), who were pursuing a bachelor’s degree in elementary education at the University of Cyprus and attended a specific science content course. This was the first science content course they were enrolled in during their studies whereas none of them had been exposed to any specific instruction about energy, other than the conventional science teaching at the precollege level. There are two points that need to be made about elementary teachers in Cyprus and the participants in this study, in particular. First, science in the elementary school is not taught by specialist teachers. There is an expectation that elementary teachers teach all subjects, including science. Second, admission to the academic program of teacher education happened to be very competitive at the time when this study was conducted, in that it posited the accumulation of a very high score in the university entrance examinations. Thus, it could be argued that the participants in this study were of high academic ability. Another noteworthy comment is that the majority of the participants had graduated from high school within either 2 or 3 years prior to this study. Coupling this with the fact that they were of high academic ability, allows using this study to draw tentative inferences as to the learning outcomes of relatively high achievers who had recently completed their enrollment in high school after having being exposed to conventional science teaching (including teaching about energy) throughout elementary and secondary education. Conventional Teaching About Energy in the Local Context Teaching about energy in the local educational system starts from the elementary grades. There are references to energy, starting from the first grade, which are

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associated with the need to ‘‘save’’ electrical energy at home. There are also references to energy in the third grade (in the context of a unit on heat and temperature) and the fourth grade (in the context of a unit on electricity). In this latter case, the emphasis is on renewable energy sources for producing electricity. In the sixth grade, energy is dealt with as a separate unit. It is introduced in a vague manner as something that is needed for any process or activity to take place and the emphasis is shifted to the presentation of forms of energy, energy sources and the description of specific instances of transformation of energy from one form to another, mostly in the context of electrical devices. This unit also addresses possible ways of producing electricity, including some technologies involving renewable sources of energy. In middle school, energy appears in the eighth grade, were the focus is placed on energy transfers and transformations that take place within different systems. The unit, also, addresses possible ways of producing electricity and emphasis is placed on the distinction between renewable and non-renewable sources. In the tenth grade, energy is dealt with in a separate unit, in the context of mechanics. This unit defines energy as the ability to do work and introduces the energy conservation law, which is essentially restricted to mechanical systems. The emphasis is mostly placed on the quantitative application of this law for the analysis of simple energy problems. The scope of these systems tends to be reduced to idealized situations (e.g., motion along frictionless surfaces) so as to ensure conservation of mechanical energy. Data Collection Data were collected through three open-ended tasks. The first task involves a lawnmower, which is switched off after it had been used for some time (Table 1). In this task, participants are asked to evaluate two given interpretations of how the energy conservation rule applies to this system. According to the first interpretation, the total amount of energy is always constant. It is just transferred from one part of the system to another or converted from one form to another, which, in turn, could be released to bring about additional changes. The second conveys the idea that energy is conserved in that the amount of energy that seems to be missing when the device is switched off, corresponds to the amount expended for producing a specific effect or outcome (i.e., cutting the grass). Both expressions are non-valid. The first seems to ignore the tendency of energy to degrade in quality, by converting to forms that can be retrieved less and less easily. The second violates the energy conservation principle. A correct response to this task involves rejecting both interpretations, using the arguments mentioned above. The second task (Table 2) involves a worker who uses a battery-powered electric drill to perforate a hole on a wall. Participants are asked to compare the amount of energy stored in the system at three different instances: (a) while the electric drill was initially switched off, (b) while it was functioning and (c) after it had been switched off again. Determining the validity of a response to this probe, hinges on how the boundaries of the system are delineated. Thus, if delineated as a closed system, which includes all the relevant objects (i.e., the batteries, the drill, the worker, the wall and the surrounding air), a correct response would be that the

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Table 1 Overview of Assessment Task I An electrical lawnmower, which was functioning for 2 hours, has been just turned off. The following students discuss what has happened to the energy of the blades now that the device has been turned off Do you agree with student 1, student 2 or none of them? Explain your reasoning Student 1 ‘‘The total amount of energy is constant. Chemical energy has been converted to another form. This new form can, in turn, be converted to another form to bring about additional changes and so on’’ Student 2 ‘‘I agree that the total amount of energy remains constant but in a different sense. I think that we should always take into consideration the outcome that has been achieved as a result of the process we are studying. In this case the outcome is that the grass has been cut, and this required a certain amount of energy. Thus, the total amount of energy is actually reduced, the reduction being compensated for by the outcome that has emerged’’

Table 2 Overview of Assessment Task II A worker has switched on a battery-powered electric drill and has used it for some time so as to perforate a hole on a wall. After he had finished, he switched the drill off Let’s assume that we have an instrument that can measure the energy in the system at any instant. Compare the amount of energy at the following three points of time: (1) when the electric drill was initially switched off, (2) while it was functioning and (3) after it had been switched off again. Explain your reasoning

amount of energy remains constant across the three instances. Conversely, if the system is open (e.g., it either excludes the batteries or the air) a correct response would be that the total amount of energy changes, depending on whether there is a transfer of energy into or out of the system. Thus, a correct response would involve, firstly, delineating the system and, secondly, applying the energy conservation law according to the choice of system. For instance, if air is left outside the system, there will be a transfer of energy out of the system and, hence, the amount of energy in this (open) system would decrease. On the contrary, if the system is specified so that it includes the worker, the wall and the air, but excludes the batteries in the drill, there will be a transfer of energy into the system bringing about an increase in its total energy. The third task (Table 3) refers to a solid, rubber ball that is released from a certain height (1.5 m). It falls vertically onto a marble floor and rebounds. Participants are asked to state whether the ball is likely to rebound to a height of (a) exactly 1.5 m, (b) lower than 1.5 m, or (c) higher than 1.5 m. In each case, they Table 3 Overview of Assessment Task III A solid rubber ball is released from an initial height of 1.5 m; it falls vertically onto a marble floor and rebounds State whether it is possible to observe each of the following and under what conditions (if any). In each case, explain your reasoning 1. The ball will rebound to exactly 1.5 m 2. The ball will rebound to a height higher than 1.5 m 3. The ball will rebound to a height lower than 1.5 m

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are asked to justify their answer and state possible conditions that need to be satisfied for each scenario to occur. The correct response is that the ball is most likely to rebound to a height lower than the initial, because of energy dissipation, through heat. Rebounding to the exact same height could only occur in the idealized situation that precludes energy dissipation, whereas the third scenario cannot take place, on any account, since it violates the energy conservation law. We believe that it is not possible to come up with a concise conceptual analysis of this system without drawing on energy. Thus, this task was primarily intended to assess the extent to which participants appreciate the facility of energy (the features of energy conservation and degradation, in particular) to provide a framework for analyzing the temporal evolution of such systems. We anticipated that this would be reflected by the frequency of the energy-based responses provided by the participants. In addition to this, the task was intended to provide insights into how participants who refer to energy draw on its features (e.g., transfer, transformation, conservation, degradation) for evaluating the probability for each scenario (e.g., appreciate that the third scenario is forbidden by the energy conservation principle). One possible limitation associated with the tasks that were employed, is that the anticipated form of data involved primarily textual responses. It would have been possible to use different assessment tools, designed to elicit responses in the form of diagrams or drawings. Student generated drawings could provide a rich source of data that could yield useful insights into their reasoning about energy conservation and degradation. Data Collection Process The assessment tasks were administered to the student teachers who took the relevant science content course in three consecutive semesters. In each case, data collection took place during a regular meeting of the class, by one of the authors in the presence of the course instructor. Participants were informed that the assessment tasks were related to the concept of energy and they were asked to respond individually, in writing. Provided that the science course was intended to address energy, the assessment tasks were administered at the beginning of the course. As shown in Table 4 there is a noticeable variation in the number of responses between the three tasks. The main reason for this is that one of the tasks (Task II) had not been administered in the first two semesters. An additional reason, which, however, has only minor contribution to this variation, is that the three tasks were administered on separate days. Thus, participants who were absent on particular days, did not complete the corresponding task.

Table 4 Number of responses per task

Number of responses

123

Task I

Task II

Task III

191

102

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Data Analysis Process Participant responses to the three tasks were subjected to phenomenographic analysis (Marton & Booth, 1997; Wilson, 2004). This type of analysis was intended to map the outcome space, in terms of the variation within the participant responses. Specifically, the response given by each participant to each task was carefully reviewed with the purpose to uncover his/her underlying reasoning. While reviewing the responses we explicitly sought to identify statements that were revealing of certain ways of reasoning about the task. As this process unfolded, these statements were progressively clustered in a (limited) number of categories, which were intended to capture and reflect the qualitatively different ways of reasoning. For instance, an example of two qualitatively different ways of reasoning about the third task (rebound height of ball), distinguishes between the participants who embedded the task in a wider conceptual framework and invoked physics concepts, on the one hand, and those who focused on experiential intuition and gave responses totally dissociated from the science disciplinary knowledge, on the other. These categories are discussed in the results section. It is important to note that the categories of response were not imposed a priori. Rather, they emerged from the data, as a result of a bottom-up approach. Specifically, the response that was under consideration at a certain point was compared and contrasted with the statements that had been identified up to that stage, in terms of what seemed to be their underlying reasoning. In cases when it could be clustered with responses already assigned to a specific category, it was subsumed under that category. This was often accompanied by adjustments in the scope of the categories, or the introduction of subcategories, so as to accommodate minor variations. Responses that could not be classified under any of the existing categories, led to the introduction of additional categories, as needed. Initially, two of the authors worked independently to categorize a randomly selected portion of the data from all three tasks (approximately 25 % overall) and had regular meetings in which they compared their current categorization schemes, with the intent to build common understanding and reach consensus on how to describe the data. As this process unfolded, the categorization scheme converged to a rather stable form, in that revisions became rather rare and less substantial. At that stage, one of the authors undertook to apply this categorization scheme to the rest of the data, whereas the research team continued to have regular meetings so as to discuss ambiguous responses and also possible additional amendments to the categorization scheme. Reliability and Validity In an attempt to evaluate and enhance the content validity of the assessment tasks, each was examined by two academics, who hold a doctoral degree in physics and have extensive involvement in science education research. Additionally, the tasks were pilot-tested, through individual interviews, with a sample of ten pre-service teachers who did not enroll in the actual study. The emphasis in the interviews was placed on the clarity of the probes involved in the tasks and the identification of

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possible sources of confusion. The feedback that emerged from these two sources led to minor amendments. For instance, in the initial version of Task II, the electric drill was powered from a wall socket. Thus, the source of energy for the operation of the drill was essentially an associated power station, which was not mentioned in the description of the task. Thus, the energy analysis of the operation of this system was entangled with the ability to recognize this aspect. We felt that this introduced an unnecessary complication and we decided to shift to a simpler form, which involved a battery-powered drill. Another way in which we sought to determine reliability, included splitting the participants in three groups, according to the semester when they had completed the tasks, and comparing the categorization of their responses, using the Chi square test (Field, 2005). The test for each task yielded non-significant results, suggesting that the distribution of responses across categories remained essentially stable, across the three semesters. Finally, an independent coder repeated the coding process for a randomly selected part of the data (30 %). The comparison of the two categorizations yielded a high level of inter-rater agreement ([85 %). Discrepancies were resolved through discussion and further consultation of the data.

Results Given that the study seeks to describe the participants’ ability to apply the energy conservation principle to given physical systems, we found it useful for the presentation of the results, to organize the responses under general categories that directly refer to this ability. These categories are then considered in greater detail in a second level (sub-categories), which focuses on the reasoning (and its variation) underlying the responses subsumed under each of these general categories. In this section, we present the results from the categorization of participants’ responses to the three tasks, separately. Where useful, the various (sub)categories are illustrated through a quote from an actual participant response. In the last part of this section, we seek to synthesize the results from all three tasks into emergent themes that are indicative of specific conceptual (or other) difficulties encountered by the participants. Assessment Task I: Lawnmower Data analysis led to four main categories of response (Table 5). The first includes the participants who mentioned that energy remains constant in quantity and implied that it tends to convert to less useful forms (f = 6, 3 %) (e.g., ‘‘…Energy remains constant. But it cannot be continually converted into forms that can be taken advantage of so as to bring about useful changes.’’). Even though these participants did not explicitly refer to energy degradation, and it is questionable whether they did appreciate its significance in accounting for the operation of physical systems, it is important to note that their responses were indeed consistent with this idea.

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Table 5 Results of the categorization of participants’ responses to Assessment Task I Categories of responses

f

(%)

Consistency with the conservation principle and direct or indirect reference to degradation

6

3

Consistency with the conservation principle but conflict with (or no reference to) the idea of degradation

120

62

Acknowledgment of the constancy of energy without further elaboration

10

5

Consistency with energy conservation without reference to degradation

73

38

Consistency with energy conservation but conflict with the idea of degradation

37

19

Misinterpretation of the conservation law

55

29

47

25

Energy conservation refers to ideal situations and, therefore, does not hold in real phenomena

4

2

After a process is terminated, energy returns to its source and gets stored in its original form

4

2

Rejection of the conservation law

6

3

Lack of a clear position

3

2

Irrelevant response

1

1

191

100

The amount of energy during a process is reduced by an amount that corresponds to the outcome that was produced

Total

The second category includes the participants (f = 120, 62 %), whose responses were consistent with the energy conservation principle, even though they neglected, or even conflicted with, the idea of energy degradation. These responses fall into three subcategories. The first includes the participants (f = 10, 5 %) who restricted themselves to merely stating that the amount of energy remains constant, without further elaboration (e.g., ‘‘The amount of energy in the system is constant. I disagree with the student who suggests that the amount of energy is reduced during the operation of the lawnmower machine.’’). The second includes the participants who stated that energy is converted to other forms, without addressing its tendency to degrade in quality (f = 73, 38 %) (e.g., ‘‘I agree with the first student. Using energy to perform a task does not reduce the amount of energy. It just changes its form.’’). Finally, the third subcategory includes the participants whose response was consistent with energy conservation but contradicted the idea that energy degrades in quality (f = 37, 19 %) (e.g., ‘‘Energy is constant. Its total amount remains constant. It just converts to other forms, which, in turn, could be released to bring about additional changes and so on forever.’’). The third category includes 55 participants (29 %) who supported that energy is indeed conserved but assumed non-valid interpretations for the idea of conservation. Data revealed three different misinterpretations. The most frequent, which appeared in 47 cases (25 %), rests on the premise that the amount of energy is reduced, the reduction being compensated for by the outcome that was produced (e.g., ‘‘I agree with the student who takes into account the product that emerged from the operation of the lawnmower. Energy is indeed reduced in quantity but this is accompanied by

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the production of the outcome that corresponds to this reduction.’’). The next misinterpretation, which appeared in four cases (2 %), implied that energy conservation does hold if the amounts that have been used up for some purpose are also taken into consideration. (e.g., ‘‘…I believe that the amount of energy is conserved. Thus, the initial amount is equal to the final after adjusting for the energy that disappeared due to friction …’’). In other words, these students seem to imply that energy conservation is an idealization (Portides, 2007) that can be applied only approximately to real situations and phenomena. One might be tempted to interpret this last student statement as a potentially valid description of how energy conservation applies to the lawnmower system. In particular, one could argue that this student suggests that the energy in the lawnmower system is reduced because an amount of energy is transferred outside the system (e.g., to the surroundings) due to friction. However, this interpretation ascribes students with sophisticated understanding of the first law of thermodynamics and competence in dealing with the delineation of the systems boundaries, which does not seem to be supported by the data reported in this study. The data from the next two tasks provide additional evidence that contradicts this alternative interpretation. The third misinterpretation, (f = 4, 2 %) implies that after a process has been terminated, energy returns to its source and gets stored in its original form (e.g., ‘‘…Energy gets converted from one form to another and after the process is over it returns to its initial form and initial value. Thus, there is no change in the total amount of energy.’’). The fourth category includes six participants (3 %) who explicitly stated that energy is not conserved (e.g., ‘‘energy is not constant during the execution of a process. It could either increase or decrease.’’). The fifth category includes three participants (2 %) who stated that both positions could be valid. Interestingly, these participants failed to recognize the apparent conflict between the two positions (e.g., ‘‘I agree with the first student, since the total amount of energy indeed remains constant. However, there could be an amount of energy that is used for producing a specific outcome. If this is not the case, why do batteries go flat?’’). Finally, the last category includes a single participant (1 %) who failed to address the question at hand and, hence, provided an irrelevant response. Assessment Task II: Electric Drill System Participants’ responses to assessment task II fall into three main categories (Table 6). The first includes 15 participants (15 %) whose responses could be deemed consistent with the conservation law, under specific conditions. These responses appeared in two variants. The first was given by 13 participants who stated that the amount of energy in all three cases [(a) when the drill was switched off, (b) during its operation, and (c) after it had been switched off] remained constant and, additionally, stated that energy is transferred to other parts of the system or converts to other forms (e.g., ‘‘the quantity of energy in these three cases will be the same. During the operation of the drill the initial energy simply undergoes transfers and transformations. It does not disappear.’’). The second was

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Table 6 Categorization of participants’ responses to the Assessment Task II Categories of responses Consistency with the energy conservation principle The amount of energy remains constant; it is transferred to other parts of the system or converted to other forms The amount of energy decreases since, a part of energy is transferred to the environment/wall Inconsistency with the energy conservation principle

f

(%) 15

15

13

13

2

2

71

70

The operation of the drill consumes energy

22

22

The amount of energy is greater when the drill is operating rather than when it is switched off

49

48

Irrelevant responses Total

16

15

102

100

given by the remaining two participants, who stated that the amount of energy after the operation of the drill would decrease since, a part of energy is transferred to the environment and to the wall (e.g., ‘‘when the drill is switched off there will be less energy because some amount of energy was transferred to the wall and to the environment.’’). It is important to note that references to energy being transferred to the environment were ambiguous and did not provide insights into the intended meaning of this statement. The validity of the responses in this category is contingent on how the boundaries of the system are set. The first type of response would be valid provided that the system is closed, in the sense that it subsumes all the relevant objects, namely the drill (including the batteries), the air and the wall. Likewise, the second form of response would be valid, had the system boundaries been delineated so as to exclude the surrounding air and the wall. It is important to note that participants did not seem to appreciate the decisive role of the boundaries of the system in applying the energy conservation law. Specifically, none of them referred (at least explicitly) to this idea. The second category includes 71 participants (70 %), whose responses clashed with the energy conservation law. These responses were organized in two subcategories. The first includes 22 participants (22 %) who explicitly stated that the operation of the drill consumes energy (e.g., ‘‘The amount of energy will be decreasing as the drill functions. When the entire amount of energy is consumed, the batteries will go flat and the drill will stop functioning.’’). The second subcategory includes 49 participants (48 %) who stated that energy increases during the operation of the drill. Data suggest that these participants were likely to rely on the presence (or absence) of an ongoing process as an indicator of the amount of energy in the system. In particular, they were liable to conclude that energy is greater when the drill is operating rather than when it is switched off (e.g., ‘‘The amount of energy before it started operating was very small, almost zero. When it was switched on, the amount of energy increased significantly. After the drill had been switched off again, the energy returned to its initial low value whereas the extra amount of energy, it had attained when it was operating, disappeared.’’). If we interpret the

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word ‘‘disappeared’’ as a colloquial expression for ‘‘was transferred elsewhere’’, one could argue that, in broad terms, the statement is consistent with the energy conservation principle assuming an open system, which only includes the electric drill but excludes the batteries, the wall and the surrounding air. However, as mentioned earlier, none of the participants referred to the boundaries of the system. The third category includes sixteen participants (15 %) who failed to address the task. Eleven of those (11 %) essentially identified energy with electric current, thereby providing an irrelevant response (e.g., ‘‘energy will go from the battery to the drill and then back to the battery.’’). The remaining five students (4 %) avoided any reference to the amount of energy in the system. Assessment Task III: Ball Rebound Height First Scenario: The Ball Will Rebound to the Initial Height Fifty participants (25 %) deemed this a possible scenario and only five of them (3 %) drew on energy in their response (e.g., ‘‘…Energy is conserved. Consequently, the ball will rebound to the initial height.‘‘). One participant (1 %) omitted to offer any justification (Table 7). 144 participants (73 %) stated that this scenario is not possible. 32 of them (16 %) drew on energy to justify their response and nine of them did so in a manner that explicitly violated the energy conservation principle (e.g., ‘‘during the collision with the ground some of the energy of the ball will disappear and therefore the ball will not be able to rebound to the initial height.’’). 94 participants (48 %) avoided any reference to energy. One noteworthy type of response, given by 22 of these participants, was that this scenario could only be realized under idealized conditions (e.g., ‘‘this scenario may take place if there is no friction during the motion of the ball.’’). 18 participants (9 %) avoided to offer any justification.

Table 7 Summary of responses to the third assessment task per scenario Categories of response

Scenario 1 f

It is possible Energy-based justification

Scenario 2 (%)

50

25

f

Scenario 3 (%)

20

10

f

(%)

174

88

5

3

0

0

36

18

44

21

18

9

129

65

No justification

1

1

2

1

9

5

It is not possible

144

73

175

89

21

11 1

Other justification

Energy-based justification

32

16

32

16

1

Other justification

94

48

126

64

19

9

No justification

18

9

17

9

1

1

No response/irrelevant response Total

123

4

2

3

1

3

1

198

100

198

100

198

100


925

Second Scenario: The Ball Will Rebound Higher Twenty participants (10 %) stated that this scenario is possible. Provided that this scenario violates the energy conservation principle, this finding provides a clear indication as to the insufficient understanding of these participants about the essence of this principle. None of the responses drew on energy, whereas the dominant justification referred to the material that the ball is made of (e.g., ‘‘The ball will rebound to a greater height than that from which it was released, because of its elasticity.’’). Two participants did not justify their response. The remaining 175 participants (89 %) rejected this scenario, though only 32 of them (16 % overall) referred to energy. Eighteen of those (8 %) provided a justification that could be deemed valid, since it did not involve any apparent inconsistencies with the conservation principle (e.g., ‘‘This will not happen because the energy of the ball will be decreasing and converting to other forms’’). The remaining 14 participants (8 %) gave responses that seemed to clash with energy conservation (e.g., ‘‘This cannot happen. An amount of energy gets wasted when the ball collides with the ground.’’). 126 participants (64 %) did not draw on energy and the most frequent response (f = 105, 53 %) was that the ball could not reach the initial height because it was merely released, rather than thrown, downward. Finally, 17 participants (9 %) did not offer any justification. Third Scenario: The Ball Will Rebound to a Lower Height The majority of participants (f = 174, 88 %) stated that this is a possible outcome, though only 36 of them (18 %) drew on energy in justifying their response (e.g., ‘‘This is the most likely case. During the motion of the ball there is energy transfer to the environment. Thus the ball will not have as much energy and it will not be able to climb to the initial height’’). Eleven of those participants (6 %) formulated arguments that were inconsistent with the energy conservation principle (e.g., ‘‘A part of the gravitational energy will get lost and, therefore, the ball will rebound to a lower height.’’). Finally, nine participants (5 %) did not offer any justification. Twenty-one participants (11 %) rejected this scenario, though only one of them (1 %) included energy in her justification (e.g., ‘‘This would only be possible if the ball had not encountered something that would subtract from its energy.’’). Nineteen participants (9 %) did not refer to energy with the most dominant response (f = 6, 3 %) being that the ball is elastic and it should therefore climb higher than the initial height (e.g., ‘‘It is unlikely since the ball is elastic’’). One participant (1 %) did not offer any justification. An Integrative Approach for the Categorization of Responses to Task III In addition to dealing with the responses for each scenario independently, we also sought to shift the unit of analysis to the responses given by each participant to all three scenarios as a whole. In four cases, participants’ responses to the three scenarios involved internal inconsistencies and could not be linked to a coherent

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Table 8 Results of the categorization of students’ responses to all three scenarios

1

Categories of response

f

Conceptually oriented responses

170

88

44

23

126

65

24

12

194

100

Energy-based responses Responses drawing on other concepts 2

Phenomenologically oriented responses Total

(%)

rationale. The remaining 194 responses, which could be indeed subsumed under a coherent perspective, were clustered in two main categories, shown in Table 8. The first includes the responses (f = 170, 88 %) that drew on concepts of physics. It is important to note that only 44 of those (23 %) referred to energy whereas the remaining 126 (65 %) relied on other concepts, force being the most frequently invoked. Provided that participants knew that the task was about energy, on the one hand, and that it is not possible to come up with a concise conceptual analysis of this system without referring to energy, on the other, it would make sense to argue that this finding indicates participants’ inadequate appreciation of energy as a framework for analyzing systems. The second category includes the participants (f = 24, 12 %) who provided responses dissociated from the science disciplinary knowledge and tended to draw on experiential insights and to focus on phenomenological aspects of the system. These responses appeared in two variants. The first includes the participants (f = 7, 3 %) who placed the emphasis on the initial conditions of the motion of the ball. Specifically, these participants tended to focus on whether the ball was either released or thrown downward (e.g., ‘‘Given that the ball was released, rather than thrown, I think that it will not make it to the initial height.’’). The second variant appeared in 17 cases (9 %), in which participants focused on the material that the ball is made of (e.g., ‘‘Because the ball is elastic, it will rebound at least as high’’). Difficulties Associated with Analyzing Systems Using the Energy Conservation Principle In this section, we discuss specific difficulties that seem to have hampered participants’ attempts to apply the energy conservation law for the analysis of the operation of the physical systems involved in the assessment tasks. Tendency to Believe that an Outcome Subtracts from the System Energy Participants often tended to identify the outcome of a particular process with a corresponding amount of energy, which is expended for its production. For instance, in the case of Task II (electric drill), a significant percentage of students (22 %) stated that energy decreases during the operation of the drill by the amount of energy that is consumed for the perforation of the wall. This difficulty also appeared

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in Task I (lawnmower). Specifically, some participants tended to believe that adding the amount of energy that corresponds to the outcome produced by the operation of the lawnmower (i.e., cutting the grass), with the amount of energy stored in the system after the lawnmower stopped functioning, is equal to the initial amount of energy, before the lawnmower had been switched on in the first place. It is important to note that students felt that this perspective illustrates the energy conservation principle and failed to recognize that it actually rejects it. Tendency to Believe that Any Change in the Energy of an Object/System Corresponds to Observable Changes in its Macroscopic Features Our data suggest that participants’ reasoning was often undermined by their tendency to believe that changes in the energy of an object/system should necessarily involve observable changes in some of its macroscopic properties (Kruger, 1990; Trumper, 1998). This tendency bears a connection to two misinterpretations of the energy conservation law that appeared in the data. The first, relates to the employment of the presence (or absence) of a running process in a system as the criterion determining whether the system has (or does not have) stored energy. This can be summarized as follows: when a system involves a running process (e.g., an accelerating object, such as the drill bit) then that system has energy; when this process is over (e.g., the object halts to rest) energy disappears. Obviously, this perspective neglects the fact that there are cases when the energy transferred to certain objects does not lead to detectable changes in their properties (e.g., the transfer of energy to the environment, through heat, leads to a negligible increase of its temperature, due to its enormous mass). The second misinterpretation implies that when a process is terminated energy remains stored in the same object (or part of the system), though in an inert form that could be activated at a subsequent stage, as needed. This distorted depiction of the energy conservation law also appears in the research literature in the case of elementary school students (Solomon, 1985). This particular difficulty may also be perpetrated by a tendency to confuse the concepts of energy and action. Lack of Appreciation of the Tendency of Energy to Degrade in Quality Participants did not seem to appreciate the idea that energy tends to degrade in quality and to get stored in forms that cannot be easily retrieved and taken advantage of (e.g., internal energy of air). This idea could serve a productive role in facilitating the development of coherent understanding of energy conservation and it could also help to preempt the distorted depictions of the energy conservation law involved in the previous difficulty. For instance, it could help participants recognize that in cases where energy seems to disappear, it is still conserved though it gets transferred to other parts of the system (e.g., the surrounding air) increasing their internal energy. Also it could serve to highlight that it is possible that the change in the quantity of certain forms of energy might not involve detectable changes in macroscopic features of the relevant objects (e.g., increase of the internal energy of air).

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Lack of Appreciation of Energy Conservation as a Tool for Analyzing the Temporal Evolution of Systems A fundamental characteristic of energy is that it restricts the possible configurations that can be attained by a system, by excluding those that violate the conservation law. Participants did not exhibit sufficient appreciation of this idea. This is evidenced, for example, by the high percentage of participants (77 %), who responded to Task III (prediction of the rebound height of the ball) without referring to energy. This becomes even more interesting taking into account the fact that the lowest frequency of these responses, appeared in the case of the second scenario (the ball rebounds to a greater height), which was most conducive to an energybased response. This scenario could be immediately rejected since it violates the energy conservation law. Another finding that further demonstrates the failure to employ energy conservation for system analysis relates to the participants who erroneously stated that this particular scenario is indeed possible. Despite their relatively low frequency, these responses provide an indication as to the inadequate understanding of the energy conservation law, which should not be dismissed. Tendency to Conceive of Energy Conservation as an Idealization Some participants alluded to the idea that energy conservation holds only under idealized conditions (e.g., cases in which friction is negligible). Even though this idea did not appear prominently in our data, possibly due to the fact that our assessment tasks might have not been sensitive to this aspect, it certainly warrants mention. Presumably, the perspective revealed by this response is reinforced by the common practice in physics teaching to assume ideal conditions when solving quantitative problems involving the conservation of (mechanical) energy. This allows excluding certain intricacies (e.g., friction, air drag etc.), thereby enabling the straightforward application of the conservation law. We argue that this is liable to reinforce the belief that energy is not conserved in real, ‘‘non-idealized’’ situations and we stress the need for engaging learners with explicit epistemic discourse about the role of idealization (Portides, 2007) in the analysis of physical systems. Lack of Appreciation of the Importance of System Choice Energy remains constant in closed systems, that is, systems that do not exchange energy with their outside environment. Thus, appropriately applying the energy conservation law posits the delineation of the boundaries of the system under analysis. For instance, the application of the energy conservation law in the electric drill system (Task II) lends itself to different responses depending on how its boundaries are specified. Participants seemed to be oblivious to the importance of this idea. In particular, none of them referred to, or alluded, to the choice of system associated with his/her response.

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Productive Resources for Building Understanding In addition to the identification of specific difficulties, the data also revealed certain resources, which could serve a productive role in building coherent understanding about energy conservation and degradation. One such productive resource relates to the participants’ tendency to assume that something is lost during the operation of a system. Our data indicate participants’ tendency to erroneously identify this ‘‘something’’ with the quantity of energy. Despite its fallible nature, this could serve as a leverage point and be built upon so as to promote more coherent understanding. Specifically, one could be guided to distinguish between the quantity and the quality of energy and develop the idea that while there is indeed something that gets reduced during a process, this refers to the quality of energy, rather than its quantity. An additional productive resource relates to the participants’ tendency to apply the idea of energy conservation either to individual objects or to open systems. This could serve as a useful resource that could be refined, by incorporating the distinction between closed and open systems, so as to converge to a more informed version that restricts the applicability of energy conservation to closed systems. Also, it could serve to initiate a discussion on the importance of system choice.

Discussion and Implications The key finding of this study is that participants were not well positioned to coherently and meaningfully draw on energy conservation for the analysis of the behavior of very simple physical systems. This becomes even more important taking into account that conservation is the aspect of energy that typically receives most emphasis in conventional teaching (Duit, 1984, NRC, 2012). To recapitulate, the data revealed (a) participants’ reluctance to use energy and the conservation principle for the analysis of systems, which, incidentally, happen to be similar to those typically used for introducing this principle in conventional teaching practice, (b) their difficulty to properly apply this law in system analysis and (c) the various misinterpretations they were liable to hold about the meaning of the conservation law. These findings provide further empirical support to the claim made in the literature concerning teachers’ inadequate understanding of energy (Kruger, 1990; Summers et al., 1998; Tobin et al., 2012; Trumper, 1998) and illustrate the prevalence of non-valid ideas, which often happen to be similar to those held by students. Additionally, and most importantly, the findings reported in the study provide useful inputs for any attempt to develop teacher preparation courses. One such input relates to the specific difficulties encountered by the participants with respect to the application of the conservation principle in analyzing the behavior of the physical systems. This could substantially enrich the available research-based knowledge about teachers’ needs. An additional input refers to possible productive resources that could be taken advantage of, for facilitating coherent understanding. These inputs could support and inform attempts to devise professional development courses about energy that could better prepare teachers to undertake the responsibility of the organization and implementation of effective learning

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environments. Finally, they could also be useful for future research so as to further explore the prevalence and nature of specific difficulties, which might have been underrepresented in our data. Implications for Teaching/Learning About Energy Provided that, firstly, the participants in this study were of high academic ability, and, secondly, they had recently graduated from high school after being exposed to conventional teaching about energy in the elementary and secondary grade levels, the findings reported in this study seem to entail some wider implications for teaching and learning about energy in school science. These are discussed next. Importance of Elaborating Energy Degradation in Conjunction with Energy Conservation The findings reported in this study indicate that even though, in most cases, participants were keen to endorse, in principle, the energy conservation law they often provided statements that essentially either violated or distorted its content. This was evident, for example, in cases when participants sought to account for what happens to energy when a running process terminates. To a large extent, this inconsistency in participants’ reasoning could be attributed to the tendency of conventional teaching about energy to totally ignore the idea of energy degradation. Despite the wide recognition of the value of this idea in terms of facilitating functional understanding of energy (Duit, 1984; Kesidou & Duit, 1993; Solomon, 1985) it typically receives scant attention in instruction. The empirical data reported in this study serve to illustrate the consequences stemming from the inadequate teaching elaboration of energy degradation. Also the data highlight the need for the development of research-based teaching innovations intended to address energy conservation and degradation (but also transfer and form conversion) in an integrated manner, and the experimentation with such teaching innovations in classroom settings so as to investigate their facility to promote coherent understanding but also to identify and document possible intricacies involved in this attempt. Importance of Highlighting the Epistemological Role of Energy as a Framework for System Analysis One of the participant difficulties refers to the lack of appreciation of energy (the features of energy conservation and degradation, in particular) as a tool for analyzing the operation of physical systems. This was evident in Task III, in which participants did not seem to sufficiently appreciate energy as a useful tool for reasoning about the rebound height of the elastic ball. We argue that this difficulty is to be expected given the emphases and structure of conventional science teaching about energy. Energy is introduced in the elementary school in a rather vague manner as something that is somehow needed for carrying out various activities and for getting various devices to operate, whereas in secondary education, the emphasis

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is mostly placed on the quantitative application of the conservation of (mechanical) energy in simple systems. Evidently, this approach refrains from explicitly addressing the fundamental question ‘‘what is energy, why is it needed in science and how is it used?’’ Thus, even though it might suffice to help students solve standard quantitative problems, it certainly does not suffice to help them appreciate the epistemological role of energy as an interpretive framework for the coherent analysis of the operation of physical systems. This could provide a plausible interpretation for participants’ demonstrated reluctance to employ energy for analyzing the system involved in Task III and the lack of coherent understanding about energy conservation and degradation they exhibited in all three tasks. From the perspective of a physicist and most other professional scientists, energy can readily be identified as a core concept. This stems from the fact that in all science professional development programs, the energy conservation principle is highlighted as one of a small number of very fundamental laws in nature, which stems from time symmetry. Less often, energy is also highlighted as a crossdisciplinary concept, a unified framework for analyzing a diverse range of systems, yielding information about the underlying mechanisms and also facilitating predictions about what is not possible in their future behavior. Historically, this facility to use energy in analyzing systems from thermodynamics to electromagnetism is equally important in revealing the scientific value of energy. However, it is much less emphasized in science courses as compared to the conservation law. In the classroom, for teachers and students alike, the perception is very different. Energy is an important concept mostly because it appears on the curriculum. The historical and epistemological aspects of the energy framework typically remain hidden away from the accessible information, in favor of the effort to relate energy to quantitative system analysis, with the choice of systems guided almost entirely by the need to simplify and idealize. Teachers and students need opportunities for explicit reflection on what it is that makes energy a core concept. This is particularly challenging because an awareness for its scientific value can only emerge when one gains experience with using energy in diverse domains. In other words, energy can be appreciated as a core concept when it is elaborated as a coherent framework in interdisciplinary science. Only then is the scientific value of energy related to the facility to analyze a broad range of systems and to make predictions. We take the position that explicitly addressing the role of energy as an epistemic tool for system analysis could serve a very useful role in promoting coherent understanding. For a more elaborate discussion of the argument underlying the case of an epistemic approach to energy the reader is referred to Papadouris and Contantinou (2011) and Constantinou and Papadouris (2012). Next Steps Our current research agenda includes the development, and field-testing, of teaching/learning materials for K-6 teachers (but also for physics teachers in higher grade levels), designed with the explicit purpose to capitalize on the epistemic aspects of energy and develop energy as a framework for the coherent analysis of the operation of systems. The findings reported in this study, with respect to

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teachers’ initial ideas, the various difficulties they encounter but also their possible productive resources, provide valuable inputs that could substantially guide and inform the design of the teaching materials. Acknowledgments The study reported in this paper is part of the Projects EKTEMA and EPIKOITE, which were funded by the Cyprus Research Foundation through the Programs PENEK20/02 and ENISX/ 0504/15, respectively.

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