Learner intuitions about energy degradation Abigail R. Daane, Stamatis Vokos, and Rachel E. Scherr Department of Physics, Seattle Pacific University, Seattle, WA 98119 Abstract: A primary learning goal for energy in K-12 science instruction is that energy cannot be created or destroyed. However, learners’ everyday ideas about energy often involve energy being “used up” or “wasted.” In physics, the concept of energy degradation can connect those everyday ideas to the principle of energy conservation. Learners’ spontaneous discussions of aspects of energy degradation and the second law of thermodynamics include ideas concerning the inaccessibility, usefulness and dispersion of energy. These ideas have motivated us to introduce new learning goals into our K-12 teacher professional development courses. We identify alignments between these learning goals and learners’ informal ideas and discuss instructional implications created by these alignments. Our aim is to create stronger ties between formal physics knowledge and sociopolitical issues by making these learning goals a priority in our professional development. TABLE OF CONTENTS I. INTRODUCTION ............................................................................................................................ 2 II. RESEARCH CONTEXT ..................................................................................................................... 3 A. THEORETICAL FRAMEWORK ........................................................................................................................ 3 B. DATA COLLECTION AND EPISODE SELECTION .................................................................................................. 4 C. INSTRUCTIONAL CONTEXT .......................................................................................................................... 4 III. ENERGY DEGRADATION IN PHYSICS AND PHYSICS INSTRUCTION ................................................... 6 A. THE PHYSICS OF ENERGY DEGRADATION ....................................................................................................... 6 B. PREVIOUS PHYSICS EDUCATION RESEARCH ON ENERGY DEGRADATION AND THE SECOND LAW OF THERMODYNAMICS 7 1. Learners’ everyday ideas about energy compete with canonical physics concepts. ........................... 7 2. Emphasis on energy degradation and the second law of thermodynamics may increase learners’ understanding of energy. ......................................................................................................................... 8 3. Learners’ everyday ideas are productive resources for learning about energy. .................................. 9 IV. LEARNERS’ IDEAS RELATED TO ENERGY DEGRADATION ................................................................. 9 A. ENERGY CAN BE PRESENT BUT INACCESSIBLE. ................................................................................................ 9 B. ENERGY CAN LOSE ITS USEFULNESS AS IT TRANSFORMS WITHIN A SYSTEM ........................................................10 1. Thermal energy is less useful. ............................................................................................................10 2. Sound energy is less useful. ................................................................................................................12 C. ENERGY CAN LOSE ITS USEFULNESS AS IT DISPERSES ......................................................................................12 D. ENERGY TENDS TO END AS THERMAL ENERGY. .............................................................................................14 E. ENERGY’S USEFULNESS DEPENDS ON THE OBJECTS INVOLVED .........................................................................16 V. LEARNING GOALS FOR ENERGY DEGRADATION ........................................................................... 18 A. LEARNERS SHOULD BE ABLE TO DISTINGUISH BETWEEN DEGRADED ENERGY AND FREE ENERGY IN SPECIFIC SCENARIOS. 18 Page 1 of 22 B. LEARNERS SHOULD BE ABLE TO IDENTIFY CHANGES IN DEGRADED ENERGY AS THEY TRACK THE TRANSFERS AND TRANSFORMATIONS OF ENERGY WITHIN AN ISOLATED SYSTEM. ...............................................................................18 C. LEARNERS SHOULD BE ABLE TO EQUATE THE TOTAL ENERGY IN A SYSTEM AT AN INSTANT TO THE SUM OF THE DEGRADED ENERGY AND THE FREE ENERGY. .........................................................................................................18 D. LEARNERS SHOULD BE ABLE TO SHOW THAT THE IDENTIFICATION OF ENERGY AS DEGRADED OR FREE DEPENDS ON THE CHOICE OF OBJECTS IN THE SCENARIO. ................................................................................................................19 E. LEARNERS SHOULD BE ABLE TO IDENTIFY THE OCCURRENCE OF OVERALL ENERGY DEGRADATION. .........................19 F. LEARNERS SHOULD BE ABLE TO ASSOCIATE ENERGY DEGRADATION WITH MOVEMENT OF A QUANTITY TOWARDS EQUILIBRIUM..................................................................................................................................................19 VI. CONCLUSION .............................................................................................................................. 20 ACKNOWLEDGMENTS ......................................................................................................................... 20 REFERENCES ....................................................................................................................................... 21 I. Introduction Energy conservation is central both in a sociopolitical sense and in the formal study of physics, but the term has a different meaning in each context. In physics, energy conservation refers to the idea that the same total quantity of energy is always present in any isolated system; energy is neither created nor destroyed. In the public consciousness, however, energy conservation refers to the idea that we have to guard against energy being wasted or used up; the energy available to serve human purposes is both created (in power plants) and destroyed (in processes that render it unavailable to us). The Energy Project is a five-year NSF-funded project whose goal is to promote elementary and secondary teachers’ development of formative assessment practices in the context of energy. K-12 teachers are in a special position in that they introduce both formal science concepts and social responsibility to young members of society. Teachers in our professional development courses have spontaneously considered not only the amount and forms of energy involved in physical processes, but also ideas related to the energy’s recoverability and degradation. Some teachers view energy as losing value during certain processes, even as they explicitly recognize the total amount of energy is constant. Others articulate that the quality, usefulness, or availability of the energy may decrease when the energy changes form (for example, from kinetic to thermal) or when the energy disperses in space. We see these ideas as resources from which to build a sophisticated understanding of energy in physics and society, one that is both useful for K-12 teachers and their students and responsible to corresponding topics in formal physics (including energy degradation and the second law of thermodynamics). These ideas might also be the basis for a meaningful model of energy that is in some sense both conserved and used up. Few existing resources support learners in integrating these seemingly contradictory concepts. In this paper, we seek to identify the productive ideas related to energy degradation and the second law of thermodynamics that appear in learners’ spontaneous discussions. We find that learners’ spontaneous discussions about the inaccessibility, degradation, dispersion and usefulness of energy are in agreement with aspects of energy degradation and the second law of thermodynamics. These alignments have motivated us to create new learning goals for our K-12 teacher professional development courses that will support future development of teachers’ ideas. In what follows, we first describe the context and background for the observations of K-12 teachers-as-learners and explain the methodology used to gather and interpret the data (Section II). We next describe the physics concepts relevant to sociopolitical energy ideas and share prior research on learner ideas about these concepts Page 2 of 22 (Section III). By analyzing learners’ spontaneous discussions about energy usefulness, degradation, dispersion and availability, we identify alignments between physics and learners’ intuitive ideas (Section IV). Finally, we introduce learning goals to address the physics concepts that align with learners’ ideas (Section V). Our aim is to create stronger ties between formal physics knowledge and sociopolitical issues by making these learning goals a priority in our professional development. II. Research context In this section we share our theoretical framework, methods for data collection, and instructional context. A. Theoretical framework We take as a premise that learners have rich stores of intuitions about the physical world, informed by personal experience, cultural participation, schooling, and other knowledge-building activities [1-7]. Some of these intuitions are “productive,” meaning that they align at least in part with disciplinary norms in the sciences, as judged by disciplinary experts [8-10]. Learners may only apply these intuitions episodically: at some moments of conversation with instructors and peers there may be evidence of productive ideas, whereas at other moments productive ideas may not be visible [11, 12]. We conceptualize learning as a process of growth through which the “seeds” of learners’ early ideas mature, through experience, to become more logical, coherent, consistent with observed evidence, and otherwise more fully scientific. Effective instruction, in this view, is instruction that provides favorable conditions for growth. This general conceptualization is common to many specific theories about teaching and learning [7, 13-17]. Some research contrasts this general conceptualization with other conceptualizations that see learners as hindered by ideas that are fundamentally flawed, and instruction as repairing or replacing learners’ ideas [10, 18, 19]. Our research is motivated by our experience that attention to learners’ productive ideas is among the most powerful tools for facilitating growth. We find that in practice, attending to learners’ ideas requires active engagement by both instructors and peers and stimulates learners’ own resources for problem solving [20-23]. In courses offered by the Energy Project, instructors place a high priority on attending to learners’ productive intuitions. Through the Energy Project, instructors have developed lesson plans and learning targets. They also listen to the disciplinary substance of learners’ ideas, adapting and discovering instructional objectives in response to student thinking [24]. As a result, each Energy Project course has a unique trajectory that emerges from the interaction of learners’ agency with instructors’ judgment of what is worth pursuing [9, 21]. In this paper, we analyze a variety of episodes in which learners show evidence of productive ideas. These episodes do not show instructors responding to the substance of learners’ ideas because at the time that these courses took place, we were not intellectually prepared to attend to learners’ ideas about energy degradation. However, by studying video records of learners’ conversations and developing our own physics understanding, we have come to recognize value in previously overlooked learner ideas. Our new understanding of these ideas has inspired new learning goals, which will shape instructor attention in future courses. Video observations and measurements of effectiveness will feed an iterative cycle of physics model development, improvement of instructional activities, and advancement of learning theory. For us learners’ ideas play the privileged role, consistent with our theoretical stance. Other theoretical perspectives give primacy to canonical understanding and the extent to which learners have or have not achieved it. Regarding the second law of thermodynamics, however, there are two very practical reasons for valuing learners' intuitions as resources for learning, as opposed to evaluating learners' ideas on their alignment (or not) with canonical knowledge. First, if one used an evaluating-student-ideas-for-alignment approach, the list of difficulties would be long and disjointed, partly due to the fact that formal or informal Page 3 of 22 exposure to the second law is often shrouded in mystery and misinformation or unmotivated, inaccessible mathematical formalism. Second, if one were to privilege the typical canonical approach in physics, one would privilege the analysis of reversible processes in idealized situations (e.g., Carnot cycle), whereas everyday experience mainly consists of highly irreversible processes. Thus, rather than thinking of learners' ideas as flawed relative to disciplinary understandings, we value them as productive resources that can grow into rigorous disciplinary knowledge. B. Data collection and episode selection Our data includes examples of learners discussing ideas related to energy degradation and the second law of thermodynamics. The examples are from video records of professional development courses for K-12 teachers offered through Seattle Pacific University as part of the Energy Project. In the Energy Project, professional development courses are documented with video, field notes, and artifact collection (including photographs of whiteboards, written assessments, and teacher reflections). In each course, teachers are grouped into 4-8 small groups, and two groups are recorded daily. As researcher-videographers document a particular course, they take real-time field notes in a cloud-based collaborative document, flagging moments of particular interest and noting questions that arise for them in the moment. Later, the researcher-videographers or other members of the Energy Project identify video episodes to share with a research team. We use the term “episode” to refer to a video-recorded stretch of interaction that coheres in some manner that is meaningful to the participants [25]. These episodes are the basis for collaborative analysis, development of research themes, literature searches, and the generation of small or large research projects. For this analysis, video episodes were identified through (1) initial observations by videographers and (2) a search for key terms in the field notes which could relate to energy degradation (e.g., entropy, spreading, diffusion, thermal energy, wasted). Selected episodes were watched several times to support the creation of detailed narratives and transcripts. On the basis of multiple viewings of the video episodes and analysis of the transcripts and narratives, we identified the productive ideas related to energy degradation and the second law of thermodynamics that appear in learners’ spontaneous discussions. Twelve episodes were isolated and captioned to illustrate learner engagement with issues of energy degradation. These episodes are described in Section IV. C. Instructional context The Energy Project goals for energy learning are specific to our population of teachers-as-learners and include conceptual understanding, sociopolitical relevance, creative flexibility, and representational competence. Our primary conceptual learning goals are as follows: (1) Learners should be able to conserve energy locally in space and time as they track the transfers and transformations of energy within, into, or out of systems of interest in complex processes and (2) Learners should be able to theorize mechanisms for energy transfers and transformations. Our progress toward some of these goals is reported elsewhere [4, 26- 33]. We structure our energy instruction around a substance metaphor for energy, which supports a model of energy as conserved, localized, transferring among objects1, and transforming among forms [27, 28]. These features constitute a powerful conceptual model of energy that may be used to explain and predict energy 1 The description of energy as being located in objects can be a concern for gravitational and other forms of potential energy, which are properly located in a system of objects or in a field, rather than in individual objects. In our instructional contexts, we allow learners to locate such forms of energy either in isolated objects, in systems of objects, or in fields, as appropriate to the level and learning goals of the course. This approach allows for iterative negotiation and refinement of the meaning of systems, an important learning goal in the study of energy. Alternatively, learners may identify a field as a new kind of (nonmaterial) object that can contain energy. Page 4 of 22 phenomena [2, 34-38]. Though this substance metaphor has limitations [34, 39, 40], its benefits for our specific instructional goals outweigh its possible disadvantages [27]. In our courses we use Energy Theater, a learning activity that is based on a substance metaphor for energy [28]. In Energy Theater, each participant identifies as a unit of energy that has one and only one form at any given time. Groups of learners work together to represent the energy transfers and transformations in a specific physical scenario (e.g., a refrigerator cooling food or a light bulb burning steadily). Participants choose which forms of energy and which objects in the scenario will be represented. Objects in the scenario correspond to regions on the floor, indicated by circles of rope. As energy moves and changes form in the scenario, participants move to different locations on the floor and change their represented form. The rules of Energy Theater are:  Each person is a unit of energy in the scenario.  Regions on the floor correspond to objects in the scenario.  Each person has one form of energy at a time.  Each person indicates their form of energy in some way, often with a hand sign.  People move from one region to another as energy is transferred, and change hand sign as energy changes form.  The number of people in a region or making a particular hand sign corresponds to the quantity of energy in a certain object or of a particular form, respectively. For learners who have become comfortable with Energy Theater, we offer a second representational activity called Energy Cubes. This representation is similar to the Energy Theater representation except that units of energy are represented by small cubes that move among object areas marked on a horizontal white board or sheet of paper. Different sides of the cubes are marked to signify different forms of energy. As energy transfers and transforms, learners move and flip the cubes on a whiteboard. The Energy Cubes representation is similar to Feynman’s description of energy as a child’s set of blocks [41] but with added features: the location of the cube shows the location of the energy and each side of the cube shows a different form of energy. A snapshot of Energy Theater or Energy Cubes illustrates the energy located in each object at the instant of the snapshot, consistent with understanding energy as a state function. Energy is associated with each object based on perceptible indicators that specify the state of that object. An Energy Theater snapshot may also include energy units in transit between objects. Such energy-in-motion is ontologically different than the energy contained in objects: over a time interval, it reflects processes of energy transfer. Heating or performing work are processes that imply a choice of time interval – a choice that defines an initial state, an a priori specified final state, and a specific connecting story. In physics, an arbitrarily defined set of objects can comprise the system of interest. In Energy Theater, learners decide which objects are of relevance to particular energy processes, typically including all objects that play a significant (as judged by them) role in the processes. The system, therefore, is made up of all interacting objects and is by construction isolated (no energy comes in or out during the time evolution of the system). In this paper, we use the term system to refer to isolated systems, i.e., systems that include all interacting objects. A scenario is a unique story involving the objects comprising the system that has a predetermined time development. That is, the initial and final states of the system are known in advance or assumed in advance. Energy Theater and Energy Cubes represent the scenario; they do not represent causal agents (forces, temperature gradients, pressure differences, electric potential differences). Coordination of the energy story with the story of these causal agents occurs during the negotiation among the participants. Learners who use these representations consistently produce in-depth analyses of energy scenarios and communicate these analyses in detail to instructors, peers, and researchers [28], enabling studies such as this one. Page 5 of 22 III. Energy degradation in physics and physics instruction Energy Theater and its associated representations foreground certain aspects of energy, described above. Other aspects of energy are not apparent in these representations, including the idea that energy is not only conserved but also used up. In Section A, we describe the physics of energy degradation. In Section B, we identify literature discussing student understanding of these ideas. A. The physics of energy degradation In everyday language, learners may refer to certain quantities of energy as lost or used up, prompting concerns as to whether or not they are committed to the concept of energy conservation. Another possible interpretation is that learners are referring to ideas related to energy degradation. Energy degradation depends on a specific system (which comprises all relevant objects in a specific scenario), a specified time evolution of that system, and a specified or putative final state. Degraded energy at time t associated with , the system of all relevant objects evolving from some initial state to a specified final state is energy at time t that will not be available for the performance of work during the remaining time evolution of the system [42].2 In order to avoid requiring our learners to integrate models of force and energy prematurely, we define degraded energy equivalently as energy unavailable for the process of mechanical energy transfer (with the provisos of the previous sentence). For example, in a gasoline-powered car, thermal energy that dissipates to the environment as the engine runs is lost in that it cannot be used to propel the car; it is degraded. Energy change associated with the performance of work (or mechanical transfer) is related to free energy change in physics (“free” in the sense that it is available for use).3 The total energy (which remains constant in Energy Theater) is, at every instant, the sum of the degraded energy and the free energy (of the system, within the confines of specific initial and final states bridged by specified time development). Concerns about conserving energy (in the sociopolitical sense of guarding against energy waste) may be interpreted as concerns about preserving free energy. In physics, energy degradation is associated with movement toward equilibrium in a quantity whose gradient can be harnessed for the performance of work (such as temperature, pressure, or concentration). When a partition is removed between a vacuum and a cube of gas, the gas expands from the area of high concentration into the volume that was a vacuum. This expansion process reduces the pressure difference between the two volumes and degrades the energy that was associated with the filled cube. The expansion also spreads energy more equitably through the system [43]. Energy can also spread through mixing: for example, when a hot gas and a cold gas come into contact with each other, the initial temperature gradient between them is reduced. In this case, the energy spreads in phase space by increasing the range of possible momenta of the particles. In real, irreversible processes, energy spreads within objects, to other objects, through space, by mixing, in phase space, or a combination of these.4 This spreading is accompanied by an increase in entropy [43]. In other words, energy spreading, energy degradation, reduction of gradients, and entropy production are all features of real, irreversible processes. This co-occurrence prompts a degradation-oriented statement of the second law of thermodynamics: Energy degrades in irreversible processes. 2 Degraded energy as defined here is therefore not a state function. 3 Free energy as defined here is not a state function but rather the difference between state functions and may correspond with the work-related part of Gibbs or Helmholtz free energy changes depending on specific conditions. Our use of free energy corresponds to exergy [74], a term not widely used in physics instruction. 4 Not all energy that spreads spatially is associated with irreversibility and energy degradation. For example, compressed springs that are arranged radially as spokes around a fixed center may be released, pushing blocks radially outward on a horizontal frictionless surface: the spatially localized energy in the springs spreads radially outward, but could bounce back from a fixed circular obstacle and re-compress the springs. Page 6 of 22 Since energy degradation is defined relative to a specific set of objects interacting over a time interval through specified processes and with specified initial and final states, changes in any of those parameters can change the status of the energy (from degraded to free, or vice versa). For example, thermal energy that accumulates in a car as a result of the engine running may be identified as degraded in the system consisting only of the car and the warm surrounding air, because it cannot be used to propel the car. However, that same thermal energy may be identified as free in a different system that would include freezing surrounding air – a different system participating in different possible scenarios, due to a temperature gradient that was not present in the system of only a car and warm air. This gradient could be used, in theory, to power some other process. The addition of new objects into the scenario or reconsideration of the boundaries of the system can introduce new gradients and increase the free energy of the system. Thus, degraded and free are not properties of units of energy; rather, they are qualities of the distribution of energy among interacting objects. B. Previous physics education research on energy degradation and the second law of thermodynamics 1. Learners’ everyday ideas about energy compete with canonical physics concepts. Students’ ideas about energy often include sociopolitical associations with energy sources and consumers that are not consistent with the ideas taught in physics instruction [44-54]. Primary and secondary students categorize fuels, food, and natural phenomena (e.g., the sun) as sources, and humans, animals and cars as users or consumers of energy [51]. Sources are sometimes identified as energy itself, instead of entities from which energy originates. The same source-consumer model was found pre- (ages 10+) and post- (ages 13+) instruction. Among student-identified sources, fuel has a particularly strong association with energy [e.g., 47, 54]. One preliminary study highlights a student’s description of energy as “something that can do something for us…say like gas or something” [47]. The “energy as a fuel” framework [54] is seen as problematic in that fuel is a material substance whereas energy is not. Some researchers argue that these ideas must be confronted to improve students’ understanding of energy [51, 53]. Some of this same research characterizes students’ ideas as not only “obstinately persistent” but also “messy,” stating that students’ “socially acquired meanings are not consistent or logical” [51]. For example, when asked whether exercise causes a gain or loss of energy, some students argue that exercise both uses up and builds up a person’s energy simultaneously [51]. This perspective highlights the context-dependence of students’ ideas, a feature also observed in other areas. However, it characterizes students’ sociopolitical ideas as difficulties; little mention is made of their potential productive alignment with free energy. We will argue that the idea that energy “can do something for us” is a productive resource for learning about free energy [55]. Students tend to apply their everyday ideas (e.g., energy as fuel) to real world situations in lieu of energy topics from canonical physics (e.g., the principle of energy conservation) [49, 50, 56-62]. Studies involving secondary students in several countries, including Germany, the Philippines, and the United Kingdom, have elicited student responses to questions regarding the principle of energy conservation. Of 171 post-instruction German students, less than 15% mention conservation when asked to explain various phenomena, such as the motion and displacement of a ball rolling without friction along curved paths (down one curve and up another curve) [49]. Students instead use everyday experiences to describe where the ball ends up on the second curve, determining its destination by distance travelled rather than by height [50]. One year later, “most students did not make use of any knowledge stemming from physics instruction. Some students who tried to employ such knowledge failed” [50]. In another study, only 5 of the 75 students (< 7%) “gave satisfactory answers to the questionnaire as a whole,” which included both quantitative and qualitative questions about energy post-instruction [58]. Also after instruction, 23 students (> 30%) still referred to conservation as saving energy or recycling, even though the questionnaire asked for scientific answers. The evidence suggests that over 50% of these students have “considerable difficulties with the basic concept of energy and its related ideas, and their application to everyday situations” [58]. Page 7 of 22 Students also rely on their everyday experiences to explain phenomena related to the second law of thermodynamics and the concept of irreversibility [61-63]. One study reports on 34 clinical interviews with 15-16 year old students from a range of physics classrooms regarding their qualitative ideas about the second law of thermodynamics [61]. The majority of these students describe energy as a substance that is used up, after completing four years of traditional physics courses. At the university level, research on student understanding of heat engines identifies difficulties in relating energy efficiency to the overall increase of entropy in the system [64]. University students also view entropy as a conserved quantity post- instruction in introductory physics courses [65] and confuse the concepts of energy and entropy when discussing ideas about the second law of thermodynamics [66]. In advanced undergraduate chemistry courses, students’ understandings of entropy are described as “limited, distorted, or wrong” [67]. Students in these courses often define entropy as disorder and consider visual disorder and entropy to be synonymous. K-12 teachers, in professional development and in their own classrooms, use “inappropriate conceptual meanings” [68] of energy degradation including: a) energy transfer or transformation indicates degradation, b) degradation reduces total energy or occurs only when energy is not conserved, c) internal energy is unrelated to degradation, and d) degradation is heat, which teachers seem to define as “a process of losing energy or losing the availability of energy” [68]. These studies highlight the challenge of supporting student learning of the first and second law of thermodynamics, especially if the goal is to build on learners’ intuitive ideas. 2. Emphasis on energy degradation and the second law of thermodynamics may increase learners’ understanding of energy. Many researchers tout an increased focus on energy degradation in K-12 classrooms as a way to increase student understanding [49, 51, 59, 61, 62, 69-72]. In one study, lessons that focused on energy degradation significantly increased student learning of the principle of energy conservation [53]. Some researchers offer middle school curricula that include degradation [70, 71]. However, little research into the effectiveness of this approach exists currently. Some researchers recommend a stronger emphasis on free energy in physics curricula [55, 73-75]. The use of free energy as it relates to gradients in a quantity (e.g., temperature or pressure) is recommended as a central focus in secondary education over the use of energy transfers and transformations because these ideas are more fundamental and offer a reason for the changes that occur [73]. One study promotes the use of the term “fuel energy” for free energy, responding to secondary students’ ideas regarding sources and users [55]. Emphasis on the second law of thermodynamics may also improve student understanding of energy in secondary education. Many studies suggest the use of “energy degrades” as a K-12 appropriate conceptual version of the second law of thermodynamics [55, 58, 62, 76]. For example, teachers can increase student understanding of energy conservation by also using the Running Down Principle: “In all energy changes there is a running down towards sameness in which some of the energy becomes useless” [69]. Another study introduces entropy to 10th grade students as a part of an energy curriculum [76]. After instruction that focuses on both entropy and free energy, students demonstrate limited success in correctly answering questions about the second law of thermodynamics in terms of entropy. The results indicate that secondary students can be successful in learning about entropy and the second law of thermodynamics, though the challenges are great. Some research suggests that attending to the metaphorical representations of the second law of thermodynamics and entropy may improve the effectiveness of instruction [43, 67, 77-83]. Many metaphors for entropy have been analyzed for their usability including entropy as disorder, freedom, energy spreading, and information [83]. Among these, energy dispersal has been argued to be one of the most promising metaphors in helping students to build a qualitative connection between sociopolitical aspects of energy, science energy, and entropy [67]. This conceptual metaphor uses the idea that as energy spreads, gradients Page 8 of 22 are decreased and entropy increases. However, this metaphor has not yet been evaluated for effectiveness in the classroom [83]. 3. Learners’ everyday ideas are productive resources for learning about energy. Overall, the literature on student learning of the first and second law of thermodynamics characterizes learner ideas as different from, and in competition with, what they learn in science courses. Some argue that “students are evidently inadequately prepared and/or are unable to use the energy concept and the principle of the conservation of energy in order to explain simple experiments. They prefer to use explanations with which they are familiar from their environment. On the whole, the tenacity of these notions is surprising and instruction is not very successful in changing them” [57]. Even when concepts such as degradation are introduced into the classroom, researchers report that learners lack the ability to connect their ideas to concepts covered in physics instruction, saying, “It is obvious…that students are far from the physicist’s conception of energy degradation” [61]. A primary task of education research, in this account, is to identify learner misconceptions or difficulties so that instruction can be designed to address them specifically. We share these researchers’ sense of the importance of learner ideas for instruction. However, we see these ideas not as obstacles to learning but as potentially productive resources for sophisticated understanding [3,82]. Research using a resources theoretical perspective has been conducted for the concept of energy [8, 84], but not energy degradation. We argue that learners’ everyday ideas about saving and wasting energy contain the seeds of correct canonical physics concepts: The intuition that energy can be “lost to us” is a productive idea as applied to irreversible processes in the real world. The outcome of our analysis is to propose learning goals that originate from learners’ productive ideas and form a coherent concept of energy degradation that is appropriate for K-12 instruction. IV. Learners’ ideas related to energy degradation Learners in our courses have spontaneously discussed ideas about energy that our instruction was not designed to support. We provide examples of learners considering elements of energy degradation without explicit instruction or encouragement. Their ideas include: (A) energy can be present but inaccessible; (B) energy can lose its usefulness as it transforms within an isolated system; (C) energy becomes less useful as it disperses; (D) energy tends to degrade; and (E) energy’s usefulness depends on the choice of objects under consideration. Below we describe these ideas and give examples of their use by learners in our courses.  Energy can be present but inaccessible.  Energy can lose its usefulness as it transforms within an isolated system.  Energy can lose its usefulness as it disperses.  Energy tends to degrade.  Energy’s usefulness depends on the objects involved in the scenario. Figure 1. Learners’ ideas related to energy degradation. A. Energy can be present but inaccessible. Some learners describe energy being used up during a process, even as they explicitly acknowledge that the total amount of energy is constant. In the following episode, learners discuss the energy involved when wind creates waves on water. Four elementary teachers (whose pseudonyms are Joel, Rosie, Hannah, and Page 9 of 22 Marissa) decide that energy transfers from the wind to the water, and then try to determine what happens to the energy after that. Hannah states that the energy in the water waves is “not absorbed, because it has to continue on to go someplace.” Marissa asks what happens to the energy if the wave hits a wall. Joel suggests the wave “goes through this mass and hits every individual particle.” He asks, “Does every single thing take a little bit of energy away until it eventually dies off?” Joel’s word “it” might refer to either the energy or the wave dying off. In the ensuing exchange, Rosie interprets Joel’s question as a suggestion that the energy dies off. Rosie and Hannah then agree that the energy is “gone,” but pause to clarify the meaning of that assertion. Rosie: But it can't ever die though, right? Isn't that what we decided? Hannah: No, but it can though, because look at batteries, a battery is stored energy, and when it's gone, it's gone. Rosie: It's gone! Hannah: It's gone somewhere, but it's gone. Rosie: It's not really gone. It's just not there. Instructor: It's gone somewhere. Hannah: Right, exactly. Instructor: It's just not in the battery anymore. Rosie: Right, oh, but we just talked about dissipate, so that's the same thing as saying gone away from us. After Joel’s question Rosie counters, “but it can’t ever die,” possibly referring to conservation of energy. Hannah responds with a reference to batteries, which are sources of energy that are said to “die” when all possible chemical energy has been transformed to electrical energy. Hannah describes the energy in batteries as eventually being “gone.” Though Hannah does not initially specify whether she means gone out of existence or gone to another location, she later says, “It’s gone somewhere, but it’s gone,” supporting the location interpretation. Rosie affirms that “it’s not really gone; it’s just not there.” She relates this idea to dissipation, which she seems to understand as a condition in which the energy is inaccessible (“gone away from us”). Rosie, Hannah, Joel, and Marissa retain their commitment to energy conservation when they assert that the energy of the water wave must “go somewhere” when it hits the wall. However, they also attempt to reconcile this commitment with their sense that the energy “goes away from us” as part of that process. In other episodes below, learners recognize that energy may become inaccessible even as its quantity is unchanged (e.g., Dennis in Section IV.B, Vicki in Section I.C, and Jean in Section IV.D). B. Energy can lose its usefulness as it transforms within a system Learners describe the usefulness and availability of energy during various energy processes. They distinguish between more or less useful energy and also explain how the usefulness changes during a process (e.g., energy becomes less useful when it transforms from kinetic to thermal energy). These informal descriptions of usefulness seem to correspond to the physics concept of degradation. 1. Thermal energy is less useful. In our courses, some learners describe a transformation into thermal energy as a loss of useful energy. This idea is also present in the Next Generation Science Standards, in which one standard (PS3.D) pronounces thermal energy as a “less useful form” of energy. However, thermal energy can be useful in a situation where a temperature gradient drives a process (e.g., steam runs a turbine). In the following episode, Dennis, a secondary teacher, distinguishes between useful energy and energy that has lost its usefulness. He also identifies the change in usefulness during a process. Responding to a question about a block sliding across the floor, Dennis says, “The molecules are heating up in the lower Page 10 of 22