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Original Articles

Embodied physics: Utilizing dance resources for learning and engagement in STEM

, , &
Pages 73-106 | Received 17 Sep 2020, Accepted 05 Dec 2021, Published online: 09 Mar 2022

ABSTRACT

Background

Physics is often presented as disembodied, separating learners from opportunities to utilize their bodies as sense-making resources. By ignoring issues of body, ethnicity and culture, these framings limit access to physics for many, including Black girls, who struggle to gain access to physics. Studying the situated, embodied cultural practices of Black girls in physics learning environments provides a window into the range of resources available for physics exploration and illuminates possibilities for culturally relevant physics pedagogies.

Methods

We engaged in micro-ethnographic analysis of video of youth actions and interactions during collaborative activities that combined dance and dance-making practices with physics content.

Findings

Our findings show how (1) dance offered an embodied lens for physics investigation; (2) positioning movement as inquiry gave dancers access to an expanded vocabulary for sense-making; and (3) dance provided opportunities to bring in social and cultural resources as critical funds of knowledge.

Contributions

This article expands the view of funds of knowledge by reintroducing the body, movement, and embodied interaction as resources for learning and engagement and offers an expanded view of physics sense-making that includes cultural embodied resources and foregrounds Black girls, whose voices and experiences are often left out of learning research.

Introduction

This paper examines the complex role of embodied funds of knowledge in physics teaching and learning. Our research goal is to expand understandings of physics knowledge and pedagogy by focusing on the ways that creative and cultural forms of bodily movement can be enlisted in physics teaching and learning. Through a close analysis of teen dancers as they worked to collaboratively construct new understandings of elements of particle physics in an out-of-school workshop called the embodied physics learning lab, we show how utilizing the funds of knowledge of Black girls can provide new levels of access to and engagement with physics and create new possibilities for physics teaching and learning. We begin this discussion with a short vignette that gives a glimpse into the type of work that was happening in the embodied physics learning lab.

In a dance studio, a group of teenage girls gather in the center of the floor, listening intently as their choreographer explains how they will orchestrate a human sculpture as a final tableau for a dance about gravity. Several girls form an outward-facing circle and interlock elbows bending their knees and leaning forward. A smaller circle forms in the center of the larger one, where two girls, facing each other, coordinate their weight, strength, and balance with the other girls, to position themselves with legs extended in a triangle on the backs of those in the outer circle. To support the weight of the two central dancers, the girls must shift their stances to distribute their own weight evenly, push and pull around the circle to distribute the weight across the group, and provide enough force pushing upwards to avoid crumpling. Moreover, they must be able to repeat the activity numerous times in practice, making on the spot adjustments to their handholds and force distributions. This is the work of dancers, but it’s also physics. This activity, part of an embodied physics learning lab for high school girls, reveals how gravity, forces and balance play a significant role in developing choreography. It also reveals how dance can play a critical role in physics engagement ().

Figure 1. Students form structure to explore balance and opposing forces.

Figure 1. Students form structure to explore balance and opposing forces.

Interdisciplinary approaches that include the arts are gaining attention in research on STEM education (Liao, Citation2016). Yet, few studies have explored the possibilities of learning physics through dance (van der Veen, Citation2006). Laws (Citation2002) illustrates the opportunities dance provides for exploring big ideas in physics, underscoring

… the remarkable ability of even young dancers to understand the pertinent physical principles. The fact that they can feel these principles working in their own bodies helps them develop deeper insights than others who only read or hear the ideas described or see them demonstrated. (pp. VIII).

Understanding the value of dance and the various resources it affords for scientific engagement can have a critical impact on physics learning. Physics is the study of matter, its motion and behavior through space and time, and the energy and forces that impact it. Dance, as an art form that centers around the body and its movement in space and time, is an embodied form of physics engagement that places the body in a dialectical relationship with the social, cultural, historical, political, and physical environment (Chappell & Varelas, Citation2020). In current pedagogical practice, physics is often presented in ways that are disembodied, separating learners from opportunities to utilize their bodies and kinesthetic experiences as sense-making resources. Many physics learning environments also position physics as unbiased and culture-free, forcing youth to suppress knowledge and practices that do not support Westernized Eurocentric perspectives (Aikenhead & Elliott, Citation2010). By ignoring issues of body, ethnicity and culture, these framings limit access to physics for many youths. This is particularly true for Black girls, who have struggled to gain access to physics, with only 0.8% receiving bachelor’s degrees in physics, far less than the 11% average seen across other subjects (CEOSE Report, 2017–2018). For Black girls, issues with access to physics begin long before college, in learning environments where their resources and contributions are easily dismissed, erased or excluded, their moving bodies are more harshly managed, and their vocally and physically expressive cultural practices are more likely to be seen as behaviors to be policed than as resources for science learning (Hartman, Citation1997; Morris, Citation2016). Putting dance practices in conversation with physics learning creates space for Black girls to utilize their expressive cultural practices as resources for physics learning. Studying the situated, embodied cultural practices of Black girls in physics learning environments not only provides a window into the range of resources that are available for physics exploration, but it also allows for a shift from the dominant conceptual framing of physics as acultural and disembodied to a physics that is personal, filled with affect and emotion, and grounded in cultural experiences and relational histories, fostering the possibility of a more culturally relevant pedagogy; a physics where Black girls lead the way.

In this paper, we explore theoretically and empirically how specific dance and dance-making practices created space and opportunity for Black girls to bring their cultural and embodied resources to their physics sense-making. We see dance as a creative-embodied arts practice that invites youth to draw on physical modes of expression, social practices, their own cultural repertoires and their creativity to explore ideas individually and collectively, develop and construct representational models, and engage in processes of embodied inquiry. In this study, we aimed to understand how dance supported 15 Black teen girls from two northeastern community-based dance centers in bringing their own resources while also supporting them in better understanding physics concepts and ideas. We look closely at their interactions in the Embodied Physics Learning Lab (EPLL), a program that invited the girls to engage in embodied activities using an interdisciplinary approach that positioned dance not as way of presenting physics understandings, but as a process of inquiry, a way to explore concepts, raise questions, and uncover new ways of thinking about physics. Through a close analysis of the resources they drew from in their interactions in this setting, we show that movement, bodies, emotions and culture can be rich resources that, while sometimes seen as deficits, can be useful in supporting understanding and engagement with physics ideas. We argue that when repositioned as strengths, embodied cultural resources accessed through dance practices can act as powerful funds of knowledge, giving Black girls new paths forward into physics.

Literature review

Dance as a resource for embodied sense-making in STEM

Research on embodied cognition in science learning has deepened our understanding of the body, movement, and gesture as resources for learning and communicating knowledge (Goodwin, Citation2000; Stieff et al., Citation2016; Streeck et al., Citation2011). By emphasizing the body’s significant role in sense-making, embodied cognition research has provided new perspectives on the body as a resource for producing and communicating meaning in the exploration of science phenomena (Azevedo & Mann, Citation2018). This research has offered accounts of the roles of the body and collective bodies in collaborative science learning (Danish et al., Citation2020). It has also offered insights on the benefits of exploring physics using augmented reality (Enyedy et al., Citation2015) and provided guidance on how to design science learning environments that capitalize on movement and bodies as tools for learning (Danish et al., Citation2020; Johnson-Glenberg & Megowan-Romanowicz, Citation2017). However, the embodied cognition literature has yet to explicitly address movement as a creative, cultural, and expressive medium. While recent research has focused on how bodies coordinate to perform creative ensemble activity (Ma & Hall, Citation2018), a notable absence of thought remains around ideas of the body and bodies as conversational and expressive—bodies that move individually, collectively, and often in response to one another to create shapes and patterns that tell stories, engage with ideas, and evoke emotions, as is the case with dance. A particular gap exists when it comes to science learning through creative-expressive-embodied dance activities. Our work addresses this gap by focusing on how youth who identify as dancers use expressive movement to engage with ideas as they explore foundational physics concepts with one another in an informal context.

Dance is an inherently embodied art-form that requires sensing, interpreting, and translating kinesthetic, visual, tactile, and auditory inputs into creative-expressive movement that take the form of choreography or improvisation (Cohen Bull, Citation1997). Dance, like all performing arts, lies at the intersection of individual experiences—sensations, emotions, movements, and identity—and the wider cultural sphere (Halverson & Sheridan, Citation2014). It requires cognitive perception, emotional, and kinesthetic knowledge, understandings that are “not merely natural or intuitive, [but] shaped in every aspect by artistic-social ideas and practices” (Cohen Bull, Citation1997). It not only allows for a dancer’s sociocultural context to take shape in and through the body, but also for her to influence the cultural sphere around her. Sklar (Citation2001) has defined dance as movement knowledge that is: “a kind of cultural knowledge;” “conceptual and emotional and kinesthetic;” and an ‘immediate corporeal experience” intertwined with cultural knowledge and conceptual meanings that ‘are not necessarily evident in the movement itself.” Simply put, dance is a physical, ideational, emotional, creative, and cultural way of knowing.

Dance as a physical resource

Dance affords multiple ways of bodily knowing, including through kinesthetic sensing in the muscles, perception through other senses, the ability to focus on internal stimuli inside the body, connecting movement qualities with emotions, and relating to others while moving through space. All of these facets of sensory/bodily experience are coordinated and brought into relationship through the act of dancing (Hanna, Citation2015). Dance training fosters heightened awareness and sensation in all of these sensorial modes, giving dancers access to dance as a physical resource for meaning-making.

Dance as a social and cultural resource

Dance can also be a social, relational and cultural resource. Every culture has its own beliefs and values surrounding dance, and its own esthetics within the art form (Royce, Citation1977). Communities within the African diaspora around the world share a common worldview of dance and music as vital repositories of inherited knowledge, sites for conversations between tradition and modernity placed at the intersection of the material and spiritual worlds (Nicholls, Citation1998; Asante, Citation2001; Glass, Citation2007). For Black communities in the United States, dance has historically been a “medium of expressivity” (Gittens, Citation2012) and a form of resistance in the face of ongoing inequalities and oppressions (Hazzard-Gordon, Citation1990). It is a meaningful part of social life for many Black youth, who use social dance as a means to express their creativity and sense of self, deal with pain, heal, and build solidarity (Gittens, Citation2012; Gottschild, Citation2003).

Dance as an ideational resource

Youth dance practices can also be valuable ideational resources for embodied physics learning. The study of dance-making provides choreographic and improvisational structures for organizing ideas through movement. When students make their own dances, they engage in inquiry that positions them at the center of their learning and allows them to find ways to express ideas that are difficult to capture in words. The choreographic process requires that dance-makers seek out inspiration from various sources and engage in a form of interdisciplinary research (Barrett, Citation2007) that can include reading, writing, physical experimentation, searching for images, and drawing on their own experiences and the experiences of others. Improvisational dance practices foster distributed creativity (Sawyer & DeZutter, Citation2009), allowing youth to collectively generate shared creative products. Improvisation also allows for each individual dancer’s subjectivity to be fore-fronted while communicating complex and “slippery” ideas through the interactions of the collective (McLeod, Citation2007). As each individual dancer improvises, she is also interacting with other improvisers within the collective, and those continual adjustments and conversations bring a unique fluidity to the process of learning, opening up new pathways to understand complex ideas that cannot be accessed in the same way through other methods. Utilizing choreographic and improvisational tools as resources for physics engagement has the potential to “intensify” scientific material “to such a degree as to reveal scientific ontologies that would otherwise be inaccessible” (Coates, Citation2017).

Theoretical tools and perspectives

The funds of knowledge framework is useful for understanding the resources available to minoritized learners in science learning spaces. Funds of knowledge is based on the premise that learning is mediated by the social relations, practices, and artifacts that comprise our experiences (Moll et al., Citation2001). Moll et al. (Citation2001) define it as “the historically accumulated and culturally developed bodies of knowledge and skills essential for household or individual functioning and well-being” (p. 133). The framework has primarily been positioned as a tool for educators to gather resources from outside the classroom to support student learning and engagement within the classroom.

Like other sociocultural perspectives, funds of knowledge emphasizes the interdependence of individual and social processes in the co-construction of knowledge. It characterizes learning as cultural and draws attention to the roles that social and historical experiences play in learning, recognizing family, community, and the individual’s cultural resources and practices as essential assets for designing learning environments. However, researchers who have utilized a funds of knowledge framing have typically limited their view of cultural resources to:

  1. sources of knowledge or information,

  2. ideational resources related to personal background knowledge,

  3. household and community knowledge and experiences,

  4. skills and cultural knowledge used in everyday social contexts, and

  5. world views structured by social factors (Barton & Tan, Citation2009; Moll et al., Citation2001).

This view of cultural resources is still grounded in learning paradigms that assume knowledge is primarily accessed and shared through verbal and written language, images, and physical artifacts. In this paper, we argue for an expanded view of funds of knowledge that reintroduces the body, movement, and embodied interaction as resources for learning and engagement. By attending to movements of the body and of bodies in the moment-by-moment unfolding of creative embodied physics activities, we seek to provide a new lens for understanding sense-making in physics and to offer an expanded view of physics learning that includes cultural embodied resources. We argue that cultural embodied resources are essential funds of knowledge that, when welcomed into the learning space, can lead to deeper and more meaningful engagement (Champion., Citation2018; Nasir & Hand, Citation2008) and provide access to the domain of physics (Nasir & Hand, Citation2008). Understanding how youth draw on these resources could be critical to the process of bringing equity to STEM learning spaces. Considering how these resources serve meaning-making for Black youth dancers and how they relate to their cultural practices, defined by Nasir (Citation2002), as “the constellation of practices historically developed and dynamically shaped by communities in order to accomplish the purposes they value” (p. 489), allows us to center the knowledge of Black girls as an essential asset in understanding physics learning and engagement.

The diagram in below illustrates how our definition of funds of knowledge has expanded to include ideational and material resources (Nasir & Hand, Citation2008) and the cultural and embodied resources youth used for physics learning and engagement. These resources include dance-making tools and technical skills, science knowledge and skills, and the creative process of dance-making; the characteristics of the learning environment; expressive movement and the ways in which dancers’ bodies interact; and the teens’ past and present relationships with one another through their community-based dance centers. While there is significant overlap between each of these resource categories, we focus our analysis specifically on the embodied and cultural resources to show how these resources served in creating the moment-to-moment meaning-making opportunities for youth in the embodied physics learning lab.

Figure 2. Diagram illustrating our expanded definition of funds of knowledge.

Figure 2. Diagram illustrating our expanded definition of funds of knowledge.

Research methods

As part of an exploratory study, we designed and examined an environment that recognized, respected, recruited, and celebrated youths’ prior knowledge, cultural identities, and embodied practices to engage them in the study of physics. Through our personal and professional experiences, we have come to recognize the value of learning through creative embodied experiences. In addition to studying learning at the intersections of STEM and dance, the researchers on our team are dancers, choreographers, dance students, and directors of community-based dance centers. We understand from our own experiences the value of learning and identity work that happens in these spaces. This led to our interest in understanding dance as a tool for engaging with physics and shaped our design and analysis. Our lead researcher, Folashadé is a former dancer from a historically black neighborhood in the northeastern city that is the focus of this study. She has established deep relationships with the two community-based dance centers that are at the heart of this study.

Setting and participants

We selected 15 high-school aged girls from those two community-based dance centers as participants in the Embodied Physics Learning Lab. These dance centers cater to youth from Black and Latino neighborhoods and function as cornerstones of the communities they serve, offering classes to students aged two to adult in multiple dance genres including African, ballet, jazz, modern and tap; fostering relationships between students, teachers, and one another over many years and across generations; and supporting students in developing strong, positive racial identities. Youth participants were recruited based on their age, grade, and interest. The invitation to participate was opened to all high school youth at each dance center who had taken or had planned to take physics in school. Only 15 youth applied to participate—9 girls from one dance center and 6 from the other. All the youth participants had been members of their respective community dance centers for multiple years and identify as Black, although some also consider themselves of Caribbean or Latinx descent. Many of the girls teach younger students at their dance centers or participate in the youth dance company. They attend public and private schools (one was homeschooled), participate in school-based sports and theater activities, and all were either taking school physics at the time or had taken it previously.

As part of the learning lab design process, we engaged in 30 hours of data collection at each dance center, observing and recording classes and rehearsals to develop an understanding of the embodied teaching and learning practices that were valued in each space. This prior exposure positioned us as people who are familiar with the girls and with their community dance center practices and gave us insight into the rich resources afforded in these learning environments, which we consolidated into design principles that guided the development of the learning lab.

Design of the embodied physics learning lab

The learning lab was an exploratory project to investigate learning through embodied activities and to identify principles for design that could inform embodied physics learning in other settings. For this initial iteration of the learning lab, we engaged in a rigorous process of design, meeting regularly with physicists, choreographers, and other dance and learning experts to determine which foundational physics concepts and embodied activities would be included in the 8-week program.

Borrowing from culturally responsive pedagogies and design practices intended to engage children of color by affirming their cultural experiences, practices and ways of knowing, our responsive approach was grounded in a commitment to position youth as knowledgeable and capable doers of STEM and attend to their needs and interests as they developed, shifted, and emerged (Champion, Citation2018). This required that the design and its implementation remain flexible and attend to emergent ideas, issues, and pathways of exploration. As such, we reflected on aspects of the learning lab design each week to understand shifts in participation and engagement and to make changes to activities as needed.

Each session of the learning lab included a relationship-building activity, embodied warm-up, short demonstration of a physics concept, a dance-making activity related to the physics concept, verbal feedback from instructors and peers on the dances made, journal writing, reflective discussions and a closing movement activity. Each session was designed to give physics and dance content equal weight, fostering students’ growth in both domains. The focus for each session is listed below in . In the sessions, students explored gravity and other forces in nature, Newton’s Laws of Motion, repulsion and attraction of charged objects, and the electric forces that hold atoms and elements together by learning and improvising dance phrases, sharing weight across partners, and practicing and analyzing technical dance feats such as jumping and turning.

Table 1. Embodied physics learning lab

For example, youth were asked to explore gravity and forces from their perspective as dancers jumping with a partner to help lift and then rotate them in the air (shown below in ). They felt the forces acting on their bodies and engaged in the question: “How long can you stay in the air; and what must you do with your body to make yourself jump higher or stay longer?” They made sense of what was happening with and in their bodies between each jump, communicating with their partners to figure out what each person needed to do to successfully accomplish the task. They also received feedback from the dance instructor and the physicist in the room: “Keep your center;” “The head is the heaviest thing, so don’t dive into it;” “Push into the ground, and the ground will push back.” As they explored the kinesthetic experience of force and gravity on their bodies, they experienced laughter and joy that came with the surprise of jumping much higher when a lifting partner supported the jump. The activity allowed them to ground their reflections on gravity and the multiple forces that act on “bodies” in space in their experience of jumping.

Figure 3. Students engage in partner lift/jump activity to explore dance and physics.

Figure 3. Students engage in partner lift/jump activity to explore dance and physics.

In another set of activities, youth explored physics content and the science practice of modeling through improvisation and choreography. They engaged in sense-making through improvisation and imagery, mobilizing dance to animate concepts in particle and quantum physics, such as the periodic table of elements and the formation of the universe. As a synthesizing activity, they engaged in re-presentation of physics concepts and ideas, interpreting, combining, reformulating, and translating the physics ideas that were interesting to them and presenting them in an embodied form. Working in small groups, the dancers engaged in iterative processes of creation and feedback. They were encouraged to be explicit about the choices they made regarding what aspects of their physics concept to represent, as well as be aware of which aspects they misrepresented, and which were not represented. They presented these final dances and shared what they learned at the culminating performance on the EPLL’s final day.

Data collection and analysis

As we observed their engagement in the learning lab, we were interested in understanding (1) how the girls utilized the ideational, cultural, and embodied aspects of dance as resources for their physics learning and engagement; and (2) how those embodied resources would support or create new pathways of access to physics. To answer these questions, we collected ethnographic data in the form of video, field notes, participant journals, surveys, and interviews. We looked across a range of activities to determine the ways dance acted as a resource, supporting meaning-making and engagement. Data for this analysis comes from video data and field notes of activities that were specifically focused on moments when the girls worked collaboratively in small or large groups to make sense of physics ideas. Across the 8 weeks of the program, there were six such activities. We narrowed our focus to those that were captured on video from beginning to end and that had supplemental data from journal entries, surveys, and interviews to further inform our analysis.

To understand the richness and complexity of their talk, movements, gestures, gaze, and other interactions in the context of their embodied explorations, we reviewed video that captured the studio space as participants engaged in each of the collaborative activities. In the first phase of analysis, we identified shifts in engagement and sense-making, noting how the girls positioned themselves, how they positioned science, and what information, ideas, and movements they brought into the space. We watched and re-watched the videos, breaking each episode down into observational turns of “talk” and noting what happened at each turn. We noted their different movement styles, emotional responses, differences in levels and types of participation, and moments of sense-making (Norris, Citation2012). We defined sense-making as enacted, made visible through action and interaction, and we identified those moments not only in their verbal exchanges, but through shifts in their physical responses.

We looked closely at participant interactions, developing rich descriptions of what we observed. Given that dance includes changes in space, time, and energy simultaneously, breaking down the data into small descriptions to capture overlapping actions that happen very quickly in real time was essential to the analysis. We attempted to slow time by creating a multimodal transcript for each activity using the presentation software Keynote. These multimodal transcripts helped us to describe the moment-to-moment interactions, movements, relationships, and ideas that spread as activities unfolded by utilizing captioned annotated video, photos, and descriptions of movement to reconstruct and understand what was happening. This process allowed us to track who was paying attention to whom at each moment and to see how ideas flowed around the room, and how they were communicated verbally and nonverbally.

Findings

For this article, our analysis focuses on one activity that took place on the fifth day of the program, an improvisational exploration of the periodic table. We present this activity as a case of collaborative embodied engagement because it involved all fifteen program participants in interaction with one another as they engage with new physics information.

The activity was co-designed by the research team, which included the physicist and choreographer who facilitated the activity. It developed out of a conversation from the previous week’s activity, a trip to the museum to engage with “choreographic objects,” an interactive exhibit designed by choreographer William Forsyth that encouraged physical problem solving. The girls became interested in the ways that movement could be used to raise questions and solve problems. Prior to the improvisation activity, the group had been engaged in a discussion about positive and negative charges, which included a demonstration of static electricity and a movement activity in which they embodied positive and negative charges, moving toward or away from each other depending on their assigned charge. For the improvisational exploration of the periodic table, the girls were asked to spread out and move around the space as if they were the elements—to use their bodies to express certain physical characteristics of elements like the lightness of hydrogen, the dense, heaviness of iron, the softness and explosiveness of sodium, and the intermittent radioactive glow of radium. The activity was intentionally designed to accomplish three goals: (1) to help the girls understand how electron structures affect the elements’ physical properties, (2) to reposition the periodic table of elements as more than just a poster on the wall, as an object with which they could interact, get information, and relate, and (3) to introduce improvisation as a choreographic tool that would allow them to express their understanding of physics concepts to others. Because improvisation is a medium for creative physical expression, dynamic, unscripted collaboration and communication between dancers, the improvisational exploration would naturally afford opportunities for the girls to bring in multiple resources from their dance training, their social networks, and lives outside of the learning lab. To understand how and what resources they brought in, we looked at four critical moments in the activity: the unveiling of the periodic table; the exploration of the lightest gas, hydrogen; the exploration of a heavier element, iron; and a later exploration of sodium, a soft metal. We contrast these examples to show three important ways that dance provided resources for the girls in connecting to physics.

Through discourse, annotated video stills, and narrative descriptions, we have constructed and present an empirical illustration that shows (1) how dance offered an embodied lens for physics investigation; (2) how positioning movement as inquiry gave dancers access to an expanded vocabulary for sense-making; and (3) how dance provided opportunities to bring in social and cultural resources as critical funds of knowledge.

Dance as an embodied lens for physics investigation

Investigating the elements of the periodic table through dance provided a comfortable entry point, a familiar way of working, and an invitation to develop new relationships with familiar science resources—the traditional school resources that are oft presented as settled and static and represent the dominant epistemologies that have shaped physics teaching and learning in ways that marginalize black girls. The periodic table was one such resource. When the periodic table was introduced as a resource in the context of a discussion about elements, molecules and electrons, the girls initially had a strong negative reaction.

Excerpt 1.1: Introducing the periodic table

Dr. V:So, anyone come across this before?

Dr. V and Mariah unroll a large poster of the periodic table of elements

Stacia:Ugh!

Michele:Oh no!

Stacia and Ayanna turn their faces away and Michele puts her head down on the floor

Ayanna:Put it away!

Tameka

and Alison:No!

Stacia:Uh uhh!

Ayanna:Put it away! Put it away! Put it away!

In addition to yelling out, “No!” and “Put it away!,” three of the girls turned their heads away from the facilitators and the paper, as shown in below. Not only did their gaze shift, but they literally hid their faces. The girls’ reactions demonstrate a negative association with the periodic table, a common resource in high school science classrooms. In this moment, it was not a meaningful resource for them because they associated it with negative experiences from their chemistry, biology, and physics classes in school. Studies have shown that people assign certain values to material resources based on their cultural schemas and past experiences (Rivera Maulucci, Citation2010). We argue that in this case, the girls’ experiences with school science framed the way they viewed the usefulness of the periodic table and shaped their initial resistance to engage with the poster in our session. Their resistance provided an opportunity for reframing their relationship to the periodic table and their understanding of what can count as a resource in science learning. The embodied activities that followed created space for their physical and cultural expressiveness, and in turn, shifted their relationship not only to the periodic table, but to physics in general.

Figure 4. Girls physically turn their faces away from the periodic table as others shout “No!” “Put it away!.”

Figure 4. Girls physically turn their faces away from the periodic table as others shout “No!” “Put it away!.”

A different relationship with the periodic table

The unveiling of the periodic table was a critical moment for the learners in the EPLL. In this moment, facilitators acknowledged the students’ feelings and proposed to them a new way of thinking about the elements and of looking at the periodic table. They invited the girls to claim space for themselves in this thought process by embodying the physical characteristics of multiple elements in relation to one another. Exploration began by contrasting hydrogen, the lightest element with only one electron, with the densely packed elemental structure of iron.

Excerpt 2.1: Dancing the elements (Hydrogen)

Mariah:We’re going to imagine ourselves as hydrogen

Mariah gently lifts her arms to the side and takes large, soft steps to move around the space as she says,

Mariah:Okay, so hydrogen is a gas and it’s the lightest element, right? So, it basically floats everywhere.

Mariah:So, can you float … through space?

The girls spread out in the space and begin taking large, slow steps to move around the room. They move in a variety of ways. Some girls imitate Mariah’s lifted arms and soft steps, adding their own interpretations, while others slither more organically. A few girls immediately incorporate movements from ballet. As they make eye contact with one another, they begin to mimic each other’s movements, adding their own unique variations

Mariah:Now, really feel like you could imagine—to get the sensation of hydrogen, you’re in a big, puffy white cloud, and you’re floating through space

The girls continue with arm movements and soft steps moving slowly around the room. As they meet one another, there is soft laughter.

Mariah:Nice floating!

There is light chatter around the room as many of the girls use long arm and straight leg movements to travel across the room. The girls watch and mimic one another. As they scan what others are doing and make eye contact, some smile, acknowledging the “silliness” of the activity and start to laugh at themselves as they evaluate how they must look

Mariah:But you know what, hydrogens don’t talk

The girls giggle loudly, then the chatter dies down and they continue to float silently around the room. When they encounter other dancers, they make eye contact, but no longer giggle. Some are focused on themselves and their own movements in the mirror

Mariah:They just move

Mariah moves with and through the girls and ends up on the opposite side of the room

Mariah:And they share electrons

The girls found many creative ways to move their bodies and travel around the space as they enacted the feel of hydrogen and its single electron. Their exploration was filled with laughter as they scanned the room to see what others were doing, often mirroring and building on each other’s gestures. Exploring through an embodied lens centered the girls in their own investigation and empowered them to explore multiple ways of expressing the physical properties of hydrogen. It provided the girls with a different way of relating to the elements. In a sense, their bodies replaced the periodic table. Embodied exploration allowed for a celebration of their skills as dancers and the movement expressiveness dispositions that they bring into the room as Black girls (Elmesky, Citation2007). It made room for joy in the learning experience, contributing to a shift in the girls’ perceptions of and feelings about science. It also provided expanded access for meaning-making.

Access to an expanded vocabulary for sense-making

The improvisational dance activity positioned movement as a form of inquiry, allowing for a deep exploration of the information and ideas represented in the periodic table. Through movement, the girls explored the periodic properties and differences between elements, considering how atomic numbers and electron configurations would affect the physical and chemical properties of each element. Positioning movement as a form of inquiry gave these dancers access to an expanded vocabulary for meaning-making. Engaging in improvisational embodied exploration provided opportunities to utilize dance-making resources in conversation with the science ideas, to communicate through symbolic devices such as stylization and metaphor, and using spheres of communication, such as specific movement qualities, and dance styles (Hanna, Citation2008).

For example, at the start of their exploration of hydrogen the girls moved around the room awkwardly, looking to each other for validation and confirmation, and giggling nervously as if they were unsure of what exactly to do. Mariah’s question, “Can you float?” provided a prompt, a way to think about how to embody lightness. Several of the girls took it up by incorporating ballet movements into their improvisations. Their knowledge of dance technique and practices became useful for expressing lightness. Taking dance classes at their community-based dance centers, learning choreography and training in ballet, which asks dancers to appear lighter than air, gave them a movement vocabulary to pull from that helped them engage in the exploration. show multiple moments of the embodied hydrogen improvisation when dancers were moving in ways consistent with the style of ballet, with chests lifted, long necks, arms positioned overhead with softened wrists and energy reaching through stretched fingers. Specific ballet movements are also recognizable in their hydrogen dances including coupé, a position where the foot is pointed and brought to the ankle of a supporting leg; arabesque, a position balanced on one foot with the other leg extended behind; and plié, a soft bent knee. They drew from their technical knowledge and training and utilized the movements and style of ballet as a sphere of communication (Hanna, Citation2008) to express the idea of hydrogen as light and airy.

Figure 5. Girls moving in ways that were consistent with the style of ballet.

Figure 5. Girls moving in ways that were consistent with the style of ballet.

Figure 6. Girls using different specific ballet movements as resources.

Figure 6. Girls using different specific ballet movements as resources.

Not only were the girls able to draw on their dance vocabulary as a resource for engagement, but they also used their bodies as physical resources. When the facilitator prompted them to “get the sensation of hydrogen,” she invited them to engage with the idea kinesthetically and sensorily, to get a feeling for the phenomenon. Enacting the “lightness” of hydrogen with their bodies allowed them to make real connections to the idea of how hydrogen moves through space with only one proton and electron. In their post-activity reflections, the girls talked about how the physical act of embodying hydrogen allowed them to experience a “different perspective of the role of molecules,” to better understand the relationships between the elements, and to better remember the differences. This reaction was dramatically different from their initial reaction to the periodic table. This experience of dancing hydrogen created a pathway to physics access by redefining scientific inquiry as a creative and embodied process for which they already had the tools to explore. The next excerpt shows how cultural resources contributed to shifts in the girls’ experiences of physics.

Social and cultural resources as critical funds of knowledge

Creative embodied engagement with physics ideas provided opportunities for the girls to bring in and utilize a range of social and cultural embodied resources. Because of their prior dance training, ballet was a cultural form with which these girls were familiar. However, the exploration of the elements allowed them to utilize cultural forms outside of their technical dance training and to capitalize on their social connections and relational histories with one another.

Excerpt 2.2—Dancing the Elements (Contrasting Hydrogen and Iron)

Mariah condenses her torso by curving her spine and tucking her head, rounding her arms like angel wings and says,

Mariah:Good, now let’s contrast that with one we didn’t talk about—but we’ll talk about it right now—with the element iron, right?

Mariah:So, iron has a pretty full electron sphere and so it is really densely packed, and really strong

Nia begins stomping her feet, her center of weight close to the floor.

Mariah points to Nia and says,

Mariah:Exactly!

LaKeysha then begins stomping on the other side of the room in a sharp staccato rhythm. Mariah lifts her feet high and places them down slowly as she says,

Mariah:Heavy, dense, beautiful!

The girls explode with an array of different movements. A few continue stomping their feet, moving through space, while others make closed fists and punch into the air.

LaNiah comes face to face with Tameka, and with bent knees they begin whipping their bent arms in circles from shoulders to waist, their face squished in intense scowls. They are engaging in a movement style called krumping. They stomp their feet in sync with their arm movements, and face off in a quick dance battle, before stopping to smile and moving on to new partners.

Tameka walks away to another group of girls and starts her krumping dance again, and those girls join in. LaNiah begins to krump in front of Katherine, who krumps back.

Katherine walks away and begins krumping with Jaleesa. The girls are laughing and making excited exclamations.

Mariah:You’re iron, move through space

The girls krump with partners, stomping to move through space as they laugh out loud. As they move from partner to partner, their laughs and vocalizations escalate and increases in volume. LaNiah stops in front of LaKeysha and begins to do the battle dance.

Mariah:Good

LaKeysha:Stop!

LaNiah responds to LaKeysha,

LaNiah:I was krumping!

Stacia begins to clap, snap, and tap her thighs as she steps in a rhythmic pattern that travels across the room. As she passes LaNiah, she joins in replicating the pattern. Jaleesa and Nia join in when Stacia passes them, and together, they create a musical rhythm that becomes the loudest sound pattern in the room.

Mariah:Good, so yeah, feel how different that is from the experience of floating …. Let’s go back to hydrogen for a moment … your floating sensation … and let’s feel how different those two … experience gravity, experience the world … Floating.

This excerpt reveals how cultural dance resources helped make physics content more personal to the girls. As they transitioned from embodying hydrogen to embodying the qualities of iron, the dancers continued to draw on information about the elements to construct their improvisational dance explorations. However, there was a stark contrast in the types of movements they used to represent iron. Dancers transitioned from moving with their chests lifted as they embodied hydrogen to more grounded movements with bent knees and concave upper bodies to embody iron. The contrast in movement style occurred as soon as the facilitator introduced the elemental characteristics of iron. Nia initiated a heavy stomping movement when she heard the words “really densely packed and strong.” Her expression was met with encouragement from the facilitator, who pointed to her and yelled out, “Exactly!” This instructor feedback was a pivotal moment in the exploration, as it highlighted the girls’ funds of knowledge and created an opening for them to bring in their cultural movement styles as resources to express their ideas about the heaviness and density of iron ().

Figure 7. Girls dancing iron (a) movements change from lifted to grounded; (b) Nia begins to stomp and is acknowledged by the facilitator.

Figure 7. Girls dancing iron (a) movements change from lifted to grounded; (b) Nia begins to stomp and is acknowledged by the facilitator.

When dancers realized that stomping was an accepted form of movement, it immediately expanded the variety of movements they used to express the density of iron. Dancers quickly began drawing on movements from their own vernacular, movements from African Diasporan dance styles. One student began a form of dance called krumping, a style that gained widespread popularity in Black communities in Los Angeles in the early 2000s. While an infinite number of ways exist to portray “heavy, strong and dense” movements as presented in the iron imagery (Studd & Cox, Citation2019), krumping was selected and introduced by a dancer who recognized that the quick, strong, direct and bound movement qualities found in the arm and shoulder movements of krumping would be a fitting representation. Krumping spread among the group because it was a shared cultural resource among the girls, and because others recognized that it was deemed acceptable in this space. The girls began to trade movements in small groups, enjoying each other’s contributions with laughter and building on each previous movement, a practice that can be found in the freestyle battles of many Black vernacular dance traditions. Krumping became a powerful expressive embodied resource for the girls to experience and connect with the physics material. It allowed them to fulfill the improvisational prompt in a way that carried a shared emotional meaning for themselves and their classmates. When their resources were validated through facilitator feedback that honored their contributions, the girls brought in more culturally specific resources and were able to integrate those cultural resources seamlessly ().

Figure 8. Girls krumping with one another in pairs and small groups.

Figure 8. Girls krumping with one another in pairs and small groups.

Stepping was another such resource. A Black vernacular dance style originating in the early 1900s that features rhythmic stamping and body clapping, stepping is most closely associated today with Black fraternities and sororities. The girls associated it with the density and weight of iron. When Stacia began to move around the room with a stomping and clapping rhythm, Jaleesa picked it up quickly and joined in as they passed one another. The two continued to travel through the room, keeping rhythm with each other, and other dancers joined in with the rhythm as they saw or heard it. By the end of the iron improvisation, half the room was clapping together in rhythm. Utilizing cultural dance styles to embody and express the qualities of iron created a sense of social cohesiveness and a sense of belonging for this group of girls.

As these examples show, dance became a medium for the youth to put their cultural resources to work, to find value in their own knowledge, develop solidarity with one another through group membership (Bourdieu, Citation1986), and connect with physics in a personal way, all of which worked to expand their pathways of access to physics. By locating physics as happening within krumping and stepping (at least representationally), and not just in the world of science classrooms or sterile laboratories, the girls began to see their worlds as part of the domain of physics, and themselves as physicists ().

Figure 9. (a) Stacia begins a stepping rhythm; (b) The rhythm is picked up by others.

Figure 9. (a) Stacia begins a stepping rhythm; (b) The rhythm is picked up by others.

In the iron example, the girls navigated the space as dancers, attending to one another as people in the space and building on each other’s movement ideas. However, as the next excerpt will show, they were also attending to the science ideas that they were working to represent. As they engaged in this process of embodied imagining, the girls began to seek alignment between their embodied characters and the metaphor of sodium’s reactivity with water, exploring some of the limits to model-making.

Excerpt 3—Dancing the Elements (Sodium)

Mariah demonstrates a wiggly, gooey, sensation in her body as she travels to the middle of the room as she says,

Mariah:Alright, we’re going to go on to sodium, which is a soft metal, not like iron that’s hard, but it’s soft, so it’s kind of like buttery

Mariah:So, feel a buttery sensation, like as if you were butter

Dr. V:Sodium is also really dangerous and reactive

The girls giggle and chatter as they move with loose torsos and slide their feet with bent knees

Mariah:So, find your buttery … Nice quality of buttery … But here,listen up

The girls pause to watch and listen to Mariah

Mariah:Sodium has another property … when it mixes with water, itwants to give away its electron … and it explodes!

Mariah unexpectedly jumps in front of Stacia, throwing her arms in the air. Stacia is surprised by this action, and says,

Stacia:Woo!

The girls erupt in laughter as Mariah quickly runs in front of other dancers, throwing her arms up in front of their faces. They jump back as if startled as well.

Mariah:So, find your … go from your buttery movement …

The girls run and jump from partner to partner, each time making different shapes with their bodies in the air

Mariah:Alright, now find your buttery and pair with someone and give away your electron

Alison:Oh, we’re back to buttery?

Mariah:Well, yeah, so sodium is both. So, on its own it’s buttery, and if it comes near water, it explodes

LaKeysha:So, who’s water?

Edna:We’re not water though.

Exploring the physical properties of sodium through dance required the girls to engage in a dynamic and fluid process of embodied imagining. In a sense, as dancers enacting the properties of the elements, the girls were tasked with “becoming” each element. They had to shift their ways of thinking about who they were and what they would need to do as they characterized each element. Drawing on both external and internal stimuli, they became more aware of the intricacies of the scientific content and began to question their own model-making.

In becoming sodium, they were provided with information about two different characteristics of the element: the “buttery” quality of the soft metal and its volatility when mixed with water. As the facilitator introduced these contrasting properties, she asked the girls to transition from “buttery” to “explosive” movements by asking them to “find your buttery and pair with someone … and give away your electron.” This language of “pairing” attends to both the science and the dance. Pairing in this moment meant to find a partner to improvise with and to share an electron. The facilitator was speaking to the girls both as dancers and as the element “characters” they portrayed, drawing on dance partnering as a resource for making sense of electron pairing.

The girls bought into their roles as sodium and their corresponding engagement with science was evident in the next few turns of talk, beginning when one student asked, “Oh, we’re back to buttery?” When the facilitator responded by explaining that sodium is both buttery and explosive when it comes near water, two girls reminded her that no one was playing the role of water. Their response revealed a developing understanding of the reactive relationship between the elements and their recognition of the inadequacy of their embodied model. They understood that they could not truly represent sodium’s explosive pairing with water if every dancer was embodying sodium in this improvised model.

This breakdown makes visible the ways that movement exploration created opportunities for questioning and pushback on the facilitator. When the girls called the facilitator out on her broken metaphor, they were holding her to account for the critical conceptual content needed to represent the reaction accurately. They were interrogating their model as they created it. Their question was not taken up by the facilitator but was quickly taken up by another student in the room who encouraged the others to “just pretend” there was water in the space. In that moment, the girls resolved the issue for themselves in a way that allowed them to remain true to the model they were building. However, we might also imagine this moment as an opportunity for the girls to iterate on their model and rebuild it with dancers playing the roles of both sodium and water, raising new questions about the physical properties of water and what happens to it at the moment of reaction with sodium.

Many have criticized traditional instruction and its dynamic of teacher as sole authority, showing evidence that instructional moves and participation structures that position teachers in more symmetrical relationships with students lead to deeper learning (Tabak & Baumgartner, Citation2004). The moment of breakdown in this example makes evident the opportunities for symmetrical engagement that arise when physics is explored in a dance space that centers the embodied knowledge of young people. In this space, the girls were empowered to ask their own questions and to invent and own their solutions, and the instructional moves of the facilitator provided a form of scaffolding, encouraging the girls to generate and assess information about the model they were building in ways that are typically relegated to teachers (Cazden & Beck, Citation2003; Herrenkohl & Guerra, Citation1998). The girls felt the agency to suggest a solution and to provide a path forward so that their exploration could continue. Their ideas, questions, personalities, and bodies were welcomed and celebrated resources in the space as they engaged in collective knowledge building (Cress & Kimmerle, Citation2018). As a result, they experienced a totally different way of interacting with the periodic table than they had in school science spaces.

Expanded pathways of access to physics for black girls

The opportunity to explore and express physics understanding through socially and personally meaningful cultural practices caused a shift in how the girls related to physics content, how they thought about themselves, and how they thought about what parts of themselves belonged in the physics learning space, and in their experience of epistemic power. Creative dance activities made physics more vital and alive in their bodies and made it personally and culturally relevant, such that the girls began to see themselves and their worlds as part of the domain of physics. This process had an immediate effect on their relationship to the periodic table. By the end of the improvisation activity, the energy of the room had shifted and some expressed not only that they had enjoyed the exploration of elements’ “personalities,” but also that they might use this technique to help them study at school. As one dancer wrote in her journal: “New things I learned: relationships between molecules (movements helped me remember more).” Another student notated: “Use movement to retain information—> muscle memory.”

By moving from a resistant “this is not for me” perspective toward a realization that they could use something they love and understand—dance—to build their own relationship with the physics material, the girls began to redefine for themselves what it meant to engage in physics inquiry and model-making. Dance became an embodied and creative resource that they could see themselves using in science inquiry. They could begin to conceive of themselves as “dancers” and as “physicists.”

The EPLL expanded their access to the domain of physics by showing them how much their dance training had already prepared them to understand the physical laws of nature and practice the creativity and experimentation essential to science. As Ayana said at the final performance, “One of my biggest takeaways from the program so far is realizing the relationship between gravity and dance. It was interesting to see how closely related physics and dance were, especially since I don’t typically associate the things I learn at school with the choreography taught at dance.” Students felt they could apply this process of learning to other learning situations.

Discussion and implications

Through this study, we hoped to expand understanding of the ways that cultural and embodied resources can support physics learning and engagement by offering an empirical analysis of Black girls engaging in physics activities in a creative dance space. Specifically, we focused on the embodied and cultural resources made available through dance and the ways that these largely unrecognized and unappreciated resources create new pathways of access to physics. We argue that dance as an expressive art form and set of practices provides access to embodied creative, kinesthetic, and cultural resources that, when positioned as strengths rather than deficits, are useful in supporting physics understanding and the development of positive relationships to physics.

Embodied exploration of physics through dance supported sustained engagement, invited youth to engage in inquiry using multiple movement vocabularies, and offered Black girls opportunities to connect personally and culturally to physics concepts and ideas. The girls’ willingness to bring their cultural dance resources (i.e., ballet, krumping, stepping) into the space to represent the physical characteristics of different elements is noteworthy for several reasons. First, it highlights their physical representational fluency, their ability to easily recognize appropriate representational forms and articulate ideas using the different movements styles in their repertoires (Champion, Citation2018). Exploring physics through dance improvisation in the learning lab centered this specialized type of knowledge and positioned the girls as embodied experts in their investigation. However, youth without dance training can still call upon the embodied communication resources in their movement vocabularies to express complex science ideas and can benefit from opportunities to practice using embodied communication resources.

Secondly, it reveals the value of having shared cultures and histories in the science learning space. Inviting the girls to engage through creative expressive movement provided space for them to make relational, historical, and cultural connections that crossed contexts, time, and space (Vossoughi et al., Citation2020). In the improvisation activity, many of the dance movements spread through the group because some girls shared histories and relationships from their regular dance classes. However, when deemed appropriate, they also brought in culturally popular movements, like stepping and krumping, that were part of a shared vocabulary of all the girls in the EPLL. These movements resonated through the group quickly. Because the girls shared cultural embodied vocabularies, movements could be easily recognized and picked up by the next person. This supported their ability to communicate their ideas and build on one another’s ideas, making it easier to stay focused on the conceptual ideas in the representational models they were creating. Because of their shared social connections and cultural resources, they felt welcomed to express themselves fully as Black girls as they engaged with the science. They felt comfortable being themselves as they learned. The idea of bringing one’s own whole self to one’s work is not a small issue for Black girls who are often excluded, treated more harshly and have their contributions minimized in science learning spaces because of their cultural practices (Annamma et al., Citation2019; Epstein et al., Citation2017). The work done by the girls in the embodied physics learning lab highlights the necessity of including embodied resources if educators are interested in more equitable pedagogy.

This work has shown that the embodied cultural resources of dance can be valuable funds of knowledge for Black girls. The transformative nature of this study underscores the power in the theory of funds of knowledge while expanding upon it. Considering the embodied resources of dance as funds of knowledge that youth can bring into a learning space allows us to recognize the value of Black bodies in STEM spaces and to “attune our attention” to see the strengths in their cultural ways of knowing (Rosebery et al., Citation2015). It makes visible the ways that the cultural repertoires of Black girls can be resources for learning when they are welcomed rather than managed, as is often the case in formal STEM learning environments. With this in mind, we can begin to reimagine physics and our ideas about who can do it and how.

We have presented a model that sees physics as inherently physical, an exploration of expressive bodies moving, interacting, and colliding through space and time, widening the lens on physics engagement, and offering a broader definition of what counts as physics learning. Whereas art forms like dance are often positioned in contrast to the sciences as ways of knowing, this work shows dancers developing and utilizing meaning-making strategies that challenge those ideological separations that have led to narrow perceptions of science as disembodied, emotionless, purely objective, and lacking creativity (Bowman, Citation2004; Brickhouse, Citation2001) and to equally narrow perceptions of art as frivolous, irrational, and non-cognitive. This work also prompts us to consider the ways in which science itself can be oppressive and exclusionary, particularly for Black girls. Physics teaching is often grounded in assumptions about the resources and contributions of Black girls, assumptions that lead to the policing of their bodies in ways that have a profound effect not just in the moment but for their entire futures. We have challenged and dismantled those assumptions, showing that their bodies, creativity, and cultural practices can play an important role in their physics learning.

Learning environments can support or restrict pathways for engagement with physics depending on the approaches they take (Nasir & Vakil, Citation2017). A focus on creative embodiment can disrupt the dominant culture of physics and the power dynamics of traditional science classrooms which typically require Black girls to demonstrate resilience instead of inviting them to experiment, play, and make mistakes as they learn to think critically (Wright & Riley, Citation2021). While school science spaces may not generally offer fair treatment of cultural and personal resources, dance learning spaces with culturally relevant methodologies that focus on building strong relationships and positive disciplinary identification (Bell et al., Citation2017) can act as safe, fertile settings for healing, growing, and epistemic expansion. It is important to understand the relevant factors that went into creating such a space, how these ideas might apply in other contexts, who can and should take them up, and what levels of expertise are necessary.

In our embodied physics learning lab, all the girls and all but one facilitator (the physicist) identified as dancers and had previous dance training. This allowed us to engage in activities that centered the dance knowledge of the participants and allowed the researchers and facilitators to utilize our own disciplined perception (Stevens & Hall, Citation1998) to interpret the girls’ actions and interactions as dancers in the space. However, a dance background is not necessary to engage in these types of embodied activities. One only needs a body to draw on embodied resources. The value in this work is that it proposes a new way of seeing physics and a new lens for engaging in physics inquiry. Positioning dance as a form of inquiry allows room for youth to bring in their own creative ways of moving. Much of the focus of the learning lab was on engaging youth in processes of exploration that involved iteration and revision and provided space for youth to discover and raise new questions and interrogate their answers. They were encouraged to engage as whole beings and to recruit their entire repertoire of cultural and social practices for sense-making.

To move toward transformative equity in science education, it is vital that we study informal learning environments that are developed, implemented, and populated by people of color. Examining the situated, embodied cultural practices of Black girls in these spaces helps us to recognize how youth voices and experiences are often left out of learning, and to understand the value of centering youth as vital to their own science learning experiences. It also pushes us methodologically to centralize the meaning-making of black girls outside of the oppressive, white, masculine norms of schooling. Black girls remain an untapped resource for STEM creativity and innovation. It is critical that we center and celebrate their knowledge resources as we re-imagine what physics learning could be.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Science Foundation award DRL-1713393.

References