Energy is a disciplinary core idea and a cross-cutting concept in the K-12 Framework for Science Education and the Next Generation Science Standards (NGSS). As numerous authors point out, the energy model in these standards emphasizes the connections between energy and systems. Using energy ideas to interpret or make sense of phenomena means tracking transfers of energy across systems (including objects and fields) as phenomena unfold. To support students in progressing towards this goal, numerous representations—both static and dynamic—that describe the flow of energy across systems exist. Static representations work well to describe phenomena where the flow of energy is unidirectional and the dynamics are not a focus but struggle to represent circular energy flows and the temporal order of complex, dynamic phenomena. Existing dynamic representations like Energy Theater are usually qualitative, i.e., they represent energy in ways that differentiate between larger or smaller rates of transfer but do not provide a more detailed quantitative picture. In this article, we present how an existing, empirically tested, static representation called Energy Transfer Model (ETM) can be turned into a dynamic representation that is quantitatively accurate using the freely available 3D animation programming environment GlowScript (https://www.glowscript.org). To do so, we first summarize the central ideas in a model of energy that emphasizes the idea of energy transfer between systems, and we describe how the ETM represents those ideas. Then, we introduce the dynamic ETM and explain how it goes beyond the limitations of its static counterpart and how its quantitative accuracy adds to existing dynamic representations. Lastly, we discuss how the dynamic ETM can be used to integrate computational thinking into the physics classroom.

Energy is a disciplinary core idea and a cross-cutting concept in the K-12 Framework for Science Education^{1} and the Next Generation Science Standards (NGSS).^{2} As numerous authors^{3,4} point out, the energy model in these standards emphasizes the connections between energy and systems. Using energy ideas to interpret or make sense of phenomena means tracking transfers of energy across systems (including objects and fields) as phenomena unfold. To support students in progressing towards this goal, numerous representations—both static and dynamic—that describe the flow of energy across systems exist.^{3},^{5-7} Static representations work well to describe phenomena where the flow of energy is unidirectional and the dynamics are not a focus but struggle to represent circular energy flows and the temporal order of complex, dynamic phenomena.^{5} Existing dynamic representations like Energy Theater^{6} are usually qualitative, i.e., they represent energy in ways that differentiate between larger or smaller rates of transfer but do not provide a more detailed quantitative picture. In this article, we present how an existing, empirically tested, static representation called Energy Transfer Model (ETM)^{3} can be turned into a dynamic representation that is quantitatively accurate using the freely available 3D animation programming environment GlowScript (https://www.glowscript.org). To do so, we first summarize the central ideas in a model of energy that emphasizes the idea of energy transfer between systems, and we describe how the ETM represents those ideas. Then, we introduce the dynamic ETM and explain how it goes beyond the limitations of its static counterpart and how its quantitative accuracy adds to existing dynamic representations. Lastly, we discuss how the dynamic ETM can be used to integrate computational thinking into the physics classroom.

## Emphasizing the connections between energy and systems to interpret phenomena

Nordine et al.^{8} concisely summarize the emphasis on the connection between energy and systems in the NGSS when they state, “in every phenomenon, energy is transferred between interacting systems such that each undergoes a process that increases or decreases its energy.” Thus, describing a phenomenon from an energy perspective becomes a task of localizing and tracking energy when it flows across systems as phenomena unfold. For example, when two billiard balls collide, energy is transferred from one ball to the other, and the speed of one ball will decrease while the speed of the other will increase. Here, the systems where energy is localized are the two balls. However, the systems where energy is stored or between which energy is transferred can also be fields.^{1,2} For example, when a ball falls to the ground, energy is transferred from the gravitational field (between the ball and Earth) system to the ball system as the distance between the ball and Earth decreases and the speed of the ball increases.

## Representing energy transfers between systems

Figure 1 shows a generic ETM. The boxes represent two interacting systems, the text in brackets describes the energy related processes that the systems undergo, and the arrow represents the direction of energy transfer. The ETM comes with a set of rules: 1) arrows representing energy transfer always have to go from one system to another, that is, they cannot come out of or go into “nowhere.” 2) For every energy-increasing process, there has to be at least one energy-decreasing process (and vice versa). These rules represent energy conservation in the qualitative sense that energy always has to be tied to some physical system^{9} and cannot be created or destroyed.

However, static representations struggle to describe changes in the rate of energy transfer and capture the temporal order in phenomena that involve circular flows of energy. The limitations of a static representation to describe changes in the rate of energy transfer become apparent when we consider a pendulum in air (Fig. 2). Here, the width of the arrows is used to represent the relative amounts of energy that are transferred. While those different widths can represent the relative amounts of energy during a few swings back and forth, they do not reflect, as the amplitude of the pendulum decreases, the changing proportion between (1) energy transferred back and forth among the pendulum system and the pendulum/Earth gravitational field system and (2) energy transferred to the surroundings. When the amplitude is larger, the pendulum moves faster, which in air leads to higher air resistance and thus more dissipation compared to a smaller amplitude and slower pendulum. A static representation of energy transfer across systems cannot capture these complex energy dynamics.^{5} Similarly, existing dynamic representations like Energy Theater^{6} would struggle to capture how the rate at which energy is dissipated decreases over time as the pendulum slows down, because the usage of discrete energy units makes it hard to capture the quantitative details and how exactly the dissipation rate depends on the speed of the pendulum and air resistance.

## Bringing it to life—A dynamic ETM

We use the freely available GlowScript software to turn the ETM into a dynamic representation. GlowScript is based on the accessible programming language Python and runs in the web browser. It can be used across a wide range of devices and operating systems. The animation can be paused and continued at any time and its speed can be set with a slider, allowing one to focus on specific moments as a phenomenon unfolds. Further, one can go into the code and edit the physics equations and definitions. Figure 3 shows a dynamic ETM (dETM) of a pendulum in air (available at https://sites.google.com/view/detm). In the dETM, the white boxes represent the interacting systems in the phenomenon and red fill represents the amount of energy in the respective systems.

## Using the dETM in the classroom

In the following, we discuss how using the dETM instead of the ETM could be useful, based on how the ETM has been used in the classroom as part of a larger unit on energy. Towards the end of the unit, students revisit the pendulum as an example of phenomena that stop. Through a series of activities, students figure out that the pendulum stops because energy is dissipated into the surroundings (Fig. 2). Using the dETM, students could easily get a more in-depth understanding of this process and conclude that the dissipation rate of a moving object due to friction depends on the object’s speed. To do so, students would have to closely observe the dETM of a pendulum in air (Fig. 3). Figure 3 shows how the rate of energy transfer from the “Pendulum” system to the “Surroundings” system has become smaller in the right panel compared to the middle panel. Observing this over several swings and embracing the animation speed and pause functionality leads to the observation that the amount of energy transferred into the surroundings depends on the speed of the pendulum, i.e., faster objects dissipate more energy when traveling through air. This insight is hard to come by using a static representation or a dynamic representation that is not quantitatively accurate. Alternatively, more advanced students could also be guided towards this insight by drawing on the computational modeling aspects of the dETM. Provided with a dETM for a pendulum in vacuum, the teacher could ask students to compare and contrast a pendulum in air (either with experimentation or the dETM) with the dETM for a pendulum in vacuum. Students could then be asked to modify the vacuum dETM so that it matches better with their observations of the pendulum in air.

When students use the dETM as a way to try out their own ideas for how energy is leaving the pendulum, it requires them to specify the drag force and the place where the pendulum’s lost energy is going to. These specifications define the relationships between the pendulum and surroundings. By forcing students to reckon with these system-level interactions, the dETM supports learning about energy transfer via computation. Teachers could also use the dETM in coordination with actual experiments, where students could take observations both of the real-world pendulum and their computational simulation as an alternative way to discover physical principles through experimentation. Both approaches help students better understand the benefits of computation and the role it can play in scientific investigation.

## Conclusion

Using the template and examples at https://sites.google.com/view/detm, teachers can easily adopt the dETM examples to fit their own needs and build new dETMs for other phenomena. We also provide an example for how GlowScript can be used to turn other representations, e.g., Energy Tracking Diagrams,^{5} into a dynamic, computational one.

The dETM template is designed so that teachers can create their own model of systems exchanging energy. In its most basic application, dETM can function similar to a PhET simulation,^{10} serving as an interactive visual model. However, students can also interact with the code and physics equations of the dETM to test how the physical model responds.

This responsiveness to code alterations is one of the ways that doing computation within the dETM can foster a different way of viewing the physical world. When students reckon with their physics knowledge through a computational medium, they learn to organize their ideas in new ways,^{11} aligned with computational thinking^{12} and more authentic ways of doing physics. When students have the opportunity to alter code and manipulate the physical relationships (e.g., adding air resistance to a dETM), they are forced to reckon with the relationship between the physics equations and the real world phenomenon. At its core, doing computation in physics class makes the experience more closely related to authentic physics practices that professionals (scientists, engineers) engage in. The main limitation of using computation is that translating physics knowledge into a computational framework can make it difficult for students to learn new physics at the same time. Therefore, we chose GlowScript (more intuitive syntax) and constructed the dETM template in a way that foregrounds the relevant physics for both dETM creators (teachers) and users (students).