Teacher Re-novicing on the Path to Integrating Computational Thinking in High School Physics Instruction

Integrating computational thinking (CT) into STEM disciplines requires secondary teachers to develop their pedagogical content knowledge of computing and content integration. Experienced teachers who choose to integrate CT in their secondary STEM courses may struggle in the same ways as novice teachers as they learn about programming and its potential use within their content areas. This study describes these potential struggles as teacher re-novicing in the context of high school physics. The research team facilitated a week-long computing integration workshop for physics teachers (n = 24) from three countries. The teachers engaged with computational learning activities in Jupyter Notebooks with the goal of developing their capacity to integrate Python in physics applications. Qualitative analysis of teacher surveys supported our theorization of a pathway of CT integration knowledge development. We describe these professional learning needs in four illustrative cases, building a grounded theory for teacher re-novicing as a pathway beginning with computing knowledge, moving through physics applications of computing, and arriving at pedagogical knowledge for physics-CT integration.


Introduction
Computational thinking (CT) has been identified as an essential skill for a technologically integrated future (Kafai & Proctor, 2022;Malyn-Smith et al., 2017;Schnabel, 2011;Wing, 2016). The United States Committee on STEM Education (2018) has advocated for making CT "an integral element of all education" (p. 23). While these assertions about the importance of CT integration in K-12 education have garnered international attention, their vagueness poses challenges for STEM educators who are advocating for actionable, discipline-specific applications of computation (Denning, 2017;Hurt et al., 2023). Furthermore, there are open questions as to how CT can be integrated in other core subject areas (Curran et al., 2019;Hjalmarson et al., 2020;Wang et al., 2022). Our work with high school physics teachers is driven by a conceptualization of CT as discipline-situated computing; we focus on developing teacher capacity to integrate programming within established STEM disciplinary instruction. We take the perspective of Lee et al. (2020) that programming in high school STEM courses develops CT, especially when enacted within a broader goal of furthering student knowledge of modern computation practices within STEM fields. Such a discipline-situated integration of programming demonstrates how CT is more than teaching STEM students to use computational tools and simulations (Graves & Light, 2020). Instead, students should perceive CT as "searching for ways of processing information that are always incrementally improvable in their efficiency, correctness, and elegance" (Li et al., 2020, p. 5).
CT integration in K-12 STEM education also holds significant potential to build students' tolerance for ambiguity and persistence in open-ended problem solving (Barr et al., 2011;Pérez, 2018). Students who aspire to enter the STEM workforce need opportunities to apply authentic CT practices in STEM disciplines (NGSS Lead States, 2013;Serbanescu et al., 2011). Students benefit from learning to program within STEM subjects, and there are many available computing platforms that teachers can use to integrate programming within their STEM instruction (Rich et al., 2022). However, teachers need the requisite unique content and pedagogical content knowledge to create these CT opportunities for their students. Teachers without programming experience may not selfidentify as knowledgeable enough to integrate CT in their instruction (McDonald et al., 2022). Furthermore, "the accessibility and usefulness [of CT] might well be undermined for many by the expectation of training in computer science as a pre-condition" (Li et al., 2020, p. 4). We therefore consider CT integration to be an out-of-field experience (Luft et al., 2020) for many high school teachers because they may lack the formal qualifications or training to teach computer programming.
In this study, we focus on CT integration as an out-of-field experience for high school physics teachers. A teacher's decision to learn how to integrate computer programming within physics instruction is a form of re-novicing when they lack knowledge of computing content and pedagogy. Physics teachers who aspire to integrate CT may struggle in the same ways as new teachers when they negotiate gaps between what they already know and what they have yet to learn (Kenny et al., 2020). Re-novicing requires professional learning support not only in developing knowledge of computing content and practices but also in developing confidence in integrating CT and physics. This paper describes our design and implementation of an online summer Python programming workshop in collaboration with the American Association of Physics Teachers. Our goal was to develop high school physics teacher capacity to integrate CT as an out-of-field experience. Many of the participating teachers had little or no experience with programming but were interested in facilitating CT-integrated physics activities with their students. We analyzed summative survey feedback from the workshop to better understand participating teachers' perspectives about programming in the context of physics and their evolving capacities to integrate CT in their classrooms.

Conceptualizing CT Integration
With the growing emphasis on making CT relevant and accessible to all students, there are new calls to move away from framing computer science as a standalone field in K-12 education (e.g., Grover & Pea, 2013;Shute et al., 2017). Secondary teachers can work toward strengthening students' access to CT content and practices within their disciplines (Beheshti et al., 2017;Malyn-Smith & Lee, 2012;Weintrop et al., 2016). This access to CT content and practices is especially critical in science education because of the increasing reliance on the power of computational tools to advance science (Hurt et al., 2023). Research has shown that teachers can integrate programming in physics courses to deepen student understanding in both CT and physics (Hamerski et al., 2022;Vieyra & Himmelsbach, 2022).
Our professional learning emphasis on enacting discipline-situated programming as a means of developing both CT and physics knowledge is consistent with Grover's (2021) recent theorization of integrating CT in other subjects. This framework extends longstanding definitions of technological pedagogical content knowledge (Mishra & Kohler, 2006) to include the subject domain and computing as distinct but overlapping fields in K-12 education. Each of these fields has its own set of content, practices, and pedagogies (Grover, 2021).
Pedagogical content knowledge (PCK) describes a teacher's capacity to transform content knowledge into "forms that are pedagogically powerful and yet adaptive to the variations in ability and background presented by students" (Shulman, 1987, p. 15). Grover's (2021) CTIntegration framework considers the PCK necessary for CT integration across three categories: (1) disciplinary knowledge, (2) computing knowledge, and (3) pedagogy. We adapted this framework for the integration of CT and physics in professional learning (see Fig. 1). This adaptation encompasses the disciplinary content and practices related to high school physics curriculum, the computing concepts and practices related to the Python programming language, and pedagogy related to general STEM instructional practices in secondary education. The framework calls attention to the bi-component intersections of physics PCK (Circles 1 and 3), physics-specific applications of computing (Circles 1 and 2), and computing PCK (Circles 2 and 3). Together, these intersections constitute PCK for physics-CT integration (Circles 1, 2, and 3).
This adapted CTIntegration framework met two theoretical aims for our study. First, the framework helped us to categorize our curriculum design and facilitation decisions for the online programming workshop. We assumed that our participants, as practicing physics teachers, already held established knowledge of physics content and practices (Circle 1) and pedagogy (Circle 3). The structure and schedule of the workshop focused on developing integrated physics/computing knowledge (1 ∩ 2) and physics-CT integration PCK (1 ∩ 2 ∩ 3). Second, the CTIntegration framework provided a set of a priori categories for our analysis of participant survey responses about their capacities to integrate CT in their physics classrooms. Teachers' perceptions of what they had learned and what they still wanted to learn framed our theorization of re-novicing as teachers work toward integrating CT in their physics instruction.

CT Integration as Re-Novicing
The term "out-of-field teaching" describes teaching subjects or grade levels for which a teacher lacks formal qualification or disciplinary specialization (Hobbs & Quinn, 2021;Luft et al., 2020). Out-of-field teaching is often the result of an administrative assignment to meet school staffing needs (Ingersoll, 2001), and a teacher's lack of formal qualifications can refer to either disciplinary content knowledge or to discipline-specific pedagogies. High school physics teachers may not study CT Fig. 1 Adaptation of CTIntegration framework for physics teaching (Grover, 2021) explicitly as an element of their undergraduate programs (Caballero & Merner, 2018). Of those physics teachers who did experience CT integration in undergraduate courses, few have had the opportunity to reinforce their learning as pre-or in-service teachers (Sabo et al., 2022). Further, the traditional secondary physics curriculum they are using in their schools and districts likely relies on non-computational means, including experiments and algebraic problem-solving, to develop students' conceptual understanding. Because CT integration requires specialized knowledge, it is out-of-field teaching within the context of an in-field physics course. As such, preparing to integrate computer programming within content instruction constitutes re-novicing as described by Kenny et al. (2020).
Unlike traditional framings of out-of-field teaching as a passive assignment to fill a staffing need, CT integration often represents a proactive choice by teachers to design and implement physics-specific programming tasks within their coursework. They want to provide more authentic STEM experiences for their students by deepening their own knowledge. CT integration as an out-of-field experience is also unique in that the instructional or curricular challenges of computer programming and modeling must be reconciled with physics content and pedagogical content knowledge. Teachers who choose to integrate CT must not only build a disciplinary knowledge of computing; they must also build a working knowledge at the intersection of physics, computing, and pedagogy.

Building Capacity for CT Integration
CT integration requires more knowledge than delivering standalone computational or programming lessons. In designing the professional learning for physics teachers in our summer workshop, we sought to build capacity for CT integration within the traditional high school content and curriculum. Teacher capacity has been generally defined as the "potential for teachers to continue to develop their knowledge, skills, and dispositions… along the continuum in the life-long process of learning to teach" informed by a collaborative community and feedback loops (McDiarmid & Clevenger-Bright, 2008). This cyclical continuum is one of growth from routine expertise to practical adaptability. The idea of capacity as potential for growth is aligned with our conceptualization of CT integration as an out-of-field experience for physics teachers. Teachers working toward CT integration may have differing professional learning needs.
Much of the research on CT professional learning design for science teachers has focused more on providing curriculum and less on developing capacity to design and enact integrated CT experiences (Biddy et al., 2021). A frequent barrier to CT integration in the undergraduate context, similar to what we have observed in the high school context, has been a lack of space in the curriculum to introduce new content (Chonacky & Winch, 2008;Leary et al., 2018;Serbanescu et al., 2011). Other challenges to classroom implementation have been described as lack of CT knowledge, lack of practical and contextual ideas for implementation, and lack of ongoing support (Ogegbo & Ramnarain, 2022).
Professional learning that strengthens PCK, or capacity for CT integration, must involve more than providing training on a specific programming language, computing platform, or CS curriculum. Teachers need the capacity to connect CT content and pedagogy to the wider physics curriculum that they are already responsible for enacting. Therefore, efforts to build capacity for CT integration should be closely coupled to high school physics curriculum and instruction. Expanding teachers' capacity to integrate physics-specific applications of computing should focus on CT practices and activities that support laboratory exploration and quantitative problem-solving. Two common choices for physics-CT integration are (a) data collection and analysis that allows more expanded use of statistics (Backer, 2007); and (b) iterative numerical integration (navigating around the historical need for analytical calculus) that allows students in algebrabased physics courses to study a greater breadth of problems (Chabay & Sherwood, 2008). These CT practices are immediately applicable to the high school-relevant topics of algebra-based mechanics and electromagnetism and emphasize the iterative nature of using CT practices to study a technical subject.
Previous research into high school CT integration (e.g., Hutchins et al., 2019) has described the nature of the integration (the types of activities introduced and how they are assessed) and student learning outcomes (the physics outcomes that CT integration supported and the CT outcomes), but little work has explored the crucial link of PCK and teacher capacity for integrating PCK in classroom instruction. Professional learning can support secondary STEM teachers in this re-novicing journey by providing opportunities to explore CT-physics integrations as learners and then to envision related experiences for their students within their own physics curricula. Designing professional development from both learning and teaching perspectives builds upon teachers' routine expertise in content and pedagogy in the singular physics domain. They learn to adapt their ideas about STEM teaching as they work collaboratively toward CT-related PCK and programming expertise in the context of physics.

The Current Study
This paper examines how high school physics teachers built capacity for CT integration in the context of a week-long workshop. The context of our study provides an important picture of teachers' perspectives toward CT integration after an initial orientation to the process as they consider potential implementation. We analyzed end-of-workshop survey responses to answer the research question, "How do high school physics teachers experience the development of capacity for computational thinking in online synchronous professional learning?".

Methods
Qualitative content analysis of participant survey responses was performed to better understand how the structure of our synchronous online Python programming workshop built physics teachers' capacity for CT integration in their classrooms. We sought to describe teachers' re-novicing at the intersection of physics knowledge, pedagogy knowledge, and computing knowledge. We followed Maxwell's (2012) interactive approach to qualitative research, in which data collection and analysis informs the development and modification of theory and the refining and refocusing of the research question. This approach shifted our initial research focus from online workshop efficacy toward the theorization of a pathway of professional learning needs for individual teachers. By constructing linkages between survey responses and our adapted CTIntegration framework, we generated grounded theories (Maxwell, 2012) about the varying professional learning needs of teachers who are building their capacity for CT in their disciplinary subjects.

Participants and Setting
This study takes place in the context of a synchronous online summer Python programming workshop. This workshop was advertised by the American Association of Physics Teachers and was facilitated by university physics and computer science education faculty. The physics teachers enrolled in the workshop (n = 24) were from 15 different states in the USA and from Canada and Italy. Their self-reported experiences (which they described throughout the workshop and in the first survey question) with computer programming prior to the workshop varied from no experience to formal computing coursework.
As STEM education professionals who take a constructionist stance (Papert, 1980) in teaching computing, we believed that beginning with integrated CT-physics experiences would increase physics teachers' comfort in learning programming. This workshop was designed to build teachers' knowledge of computing concepts and practices (Circle 2 in Fig. 1) by leveraging their existing expertise in physics domain knowledge (Circle 1) and physics PCK (Intersection 1 ∩ 3). We divided each of the three workshop days into two 3-h sessions using the Zoom video conferencing platform (see Table 1). The learning activities were designed to build capacity for CT integration in physics-situated computing applications (Intersection 1 ∩ 2), while the workshop structure was designed to model computing PCK (Intersection 2 ∩ 3). During reflective conversations between activities, we framed discussions in terms of Physics-CT Integration PCK (Intersection 1 ∩ 2 ∩ 3). Taken together, these design decisions were intended to build teacher capacity at the intersection of Physics-Computing Knowledge, Physics PCK, and Computing PCK.

Design of Morning Workshop Sessions
In each morning session, teachers worked in groups of 4-6 in breakout rooms to complete a computational activity designed to be accessible in a high school physics environment. The computational activities were derived from a set of readily deployable/adaptable curricular materials in the form of Jupyter Notebooks created by the research team. The development of these materials is described in Lane et al. (2022), and they are available via this article's supplemental information. Jupyter Notebooks are open-source web applications that support educators in creating documents with text, images, and editable Python scripts (Cardoso et al., 2018). The Jupyter Notebooks were intended to be a critical component of building teacher capacity because teachers could experience the integrated physics/CT curriculum as learners in a collaborative online setting. Due to the editable nature of the notebooks, the teachers could choose the degree to which they followed the structure of the activities and tinkered with the Python program functionality. This freedom was intended to build teachers' readiness to use and modify these resources with their own students, thereby developing their Physics-CT Integration PCK (Intersection 1 ∩ 2 ∩ 3). We were also able to monitor individual teacher progress during the workshop using these cloud-based Jupyter Notebooks. Each of the morning activities (first row in Table 1) was designed to reinforce teachers' existing capacity in physics content and to extend that capacity into the intersection of physics and CT knowledge. We encouraged participating teachers to take on "learner hat" roles (Campbell et al., 2019) as they used CT to collaboratively solve physics problems. Teachers were assigned to the same groups each morning of the workshop to create a sense of community and to promote adoption of researchbased teaching practices (Hatcher et al., 2022). Each breakout room was assigned a workshop facilitator with CT integration experience who observed and offered feedback. Groups were encouraged to use a driver-navigator approach (Williams et al., 2010), in which teachers rotated responsibility for sharing their screens to carry out changes to the program (driver) and for verbally reasoning through the activity to determine next steps (navigator). We chose small groups and the driver-navigator approach both to deepen teachers' programming knowledge and to model researchbased computing pedagogy (Intersection 2 ∩ 3). In the whole-group debriefing sessions, participants were encouraged to switch to "teacher hat" roles (Campbell et al., 2019) as they described the challenges they faced as learners and discussed implications for teaching.
Topics for the morning activities highlighted CT integration in two pillars of the high school physics curriculum typically encountered at the start of the school year: modeling motion and analyzing data. Modeling motion, or predicting the trajectory of an object given forces and a set of initial conditions, is a physics practice (Circle 1) typically encountered in a problem-solving setting. It is usually limited to penciland-paper algebraic problem-solving that produces as an answer either a numerical value (e.g., "How much time passes before the projectile lands on the ground?") or a graph of the predicted motion (e.g., "Draw the projectile's trajectory after it is launched."). This process is typically facilitated with a computer (Intersection 1 ∩ 2) using a graphing calculator to expedite the numerical computation or to generate a graph. Nearly all physics teachers are familiar with graphing calculators. At the start of day 1, we presented the teachers with a motion modeling activity selected from a repository of peer-reviewed computational activities  for them to complete as learners, with the goal of demonstrating the potential of computational physics activities. For this activity, we selected a concept (falling through the earth) that was beyond the scope of traditional high school physics. Our goal was for teachers to experience the potential of CT to transform physics instruction through computer modeling.
Data analysis is a physics practice typically encountered in a lab setting. Nearly all physics teachers are familiar with using spreadsheets to facilitate data analysis, so the day 2 data analysis activity began by encouraging teachers to carry out these same tasks in a Jupyter Notebook, later expanding to additional tasks not typically executed in a spreadsheet. On day 3, we continued with modeling motion in a more scaffolded activity that established both programming practices (e.g., loops, variable updates, arrays) and their applications in motion modeling (e.g., iteration, numerical integration, and trajectory generation).

Design of Afternoon Workshop Sessions
In the afternoon sessions, teachers were offered a choice board of computational integration topics, including assessment of computation-based activities, lab adaptations, visualizations of electrostatics, random number generation, quantum applications, and the use of external datasets. These sessions were designed to be exploratory, with each group working at their own pace and relying on each other's insights and a facilitator's feedback. We also created and introduced a Python helpdesk breakout room where teachers could focus on constructing their foundational computing knowledge (Circle 2) with elements of the Python programming language. We intentionally included more computational integration topics than teachers would be able to explore during the workshop to encourage their continued learning after the workshop concluded. This structure allowed teachers to explore CT integration options based on their interests and capacities.

Data Collection and Analysis
We administered a survey on the last day of the workshop with the following open-response questions: Q1 What first motivated you to participate in the workshop? Q2 What interactions or conversations were most helpful in the workshop? Q3 What types of computational activities would you like to try out with your students? Q4 What else would you like to learn about integrating computation into your courses? How else can we support you in this process? Q5 How does integrating computation in the courses you teach support student learning? Q6 What other feedback would you like to provide?
In this analysis, we focused on Q4 and Q5 because they aligned with building capacity for CT integration. Teachers' responses to these two questions informed our interpretation of how they were navigating CT as an out-of-field experience and the classification of their further professional learning needs using the adapted CTIntegration framework.

First and Second Cycle Coding of Teachers' Responses
We used first cycle open concept coding (Saldaña, 2021) of survey questions Q4 and Q5 to support the generation of grounded theories about professional learning needs (see Tables 2 and 3). The first author coded teachers' perceptions of how they were building their own capacities for CT integration by identifying common themes among survey responses that connected to the workshop's purpose and structure. This author relied on his observations as a workshop leader to contextualize the teachers' comments. These open concept codes are listed in the first column in Tables 2 and 3. The three authors discussed these open codes and agreed that they adequately characterized the teachers' responses. Syntax/language fluency (8): The response mentioned learning about the particular details of the Python programming language "I'd like to make sure I can run into as many errors as possible." Supporting students with limited programming experience (4): The response mentioned attending to students' varying degrees of experience with programming "I'm curious how we can support an introduction to programming for students through a physics lens and 'shelter' them from some of the more technical aspects of computer science."

Intersection 2 ∩ 3 (Computing PCK)
Recurring support/community (4): The response mentioned seeking help from a broader community of physics educators integrating CT with technical or pedagogical questions "Honestly, you've given so many resources, I need time to look at those before I could answer. Just having the community available for help will be great support!" Published resources (5): The response referenced publicly available activities or records of knowledge related to physics-CT integration "I think I need more time to work through activities… programming on my own before I ask my students to." Data collection/experiment (2): The response referenced integrating computational tools with laboratory activities "How to load data directly from a sensor (e.g., Arduino) into a Python coding environment." Intersection 1 ∩ 2 (Physics-Computing Integration) We then used the intersections of the CTIntegration framework as a set of second cycle axial codes (Charmaz, 2014;Saldaña, 2021) to construct linkages between the first cycle open-concept professional learning codes and the workshop goal of developing Physics-CT Integration PCK (Intersection 1 ∩ 2 ∩ 3). All three authors independently coded the first cycle concept codes using the circles and intersections of the CTIntegration framework by re-examining the associated teacher responses. The third author, being uninvolved in the workshop, provided a peer debriefing (Barber & Walczak, 2009) of the data analysis to increase the credibility and dependability (Lincoln & Guba, 1985) of our qualitative findings. The first and second author responded to the third author's questions and revised coding accordingly until consensus was reached.
For example, the first-cycle code of "Supporting students with limited programming experience" was given the axial code for Intersection 2 ∩ 3 (Computing PCK). This group of statements referenced the teaching of computing concepts on their own, without explicit mention of supporting physics learning. All three Feedback to students/interactivity (4): The response discussed student engagement with the CT-integrated learning process "Being able to see how changing variable values changes the outcome without having to repeat many experiments physically will be very valuable. Also students can make predictions and then try them out in the program."

Circle 3 (Pedagogy)
Transferable skills (9): The response discussed CT-related learning objectives that apply beyond the physics classroom "Thinking about physics through this computational approach will be a great benefit for my students as they head on to college majors in the STEM field." Intersection 1 ∩ 2 (Physics-Computing Integration) Diversity/expansion in problem solving/understanding (19): The response indicated an interest in using CT to address novel topics or approaches to learning "I think it can model how actual physics is done… to explore larger problems." Intersection 1 ∩ 2 ∩ 3 (Physics-CT Integration PCK) Student readiness to use computation in physics (4): The response evaluates the teacher's observations of student experience with computing "Many of my students already have experience with coding from computer science courses when they come to my class. However, just like with their math skills, through teaching physics they see a relevant application of the skills they have learned." Reinforcement of curriculum (7): The response discusses how CT supports existing learning objectives "[Computation] provides even more representations to help students anchor their conceptual understanding." Don't know/thinking about it (2) The response indicates an uncertainty with how to proceed toward CT integration None authors agreed on this categorization. In contrast, the "Recurring support/community" code required follow-up discussion, since two authors gave it the axial code for Intersection 2 ∩ 3 (Computing PCK) and one gave it Circle 3 (Pedagogy). Discussion focused on how the requested community support included both technical knowledge and pedagogical knowledge and their intersection in the classroom, and consensus was quickly reached. Our identification of circles and intersections were consistent for 8 of the 12 concept themes identified in first cycle coding. Consensus was reached on all classifications after another round of discussions among the three authors. All areas from the adapted CTIntegration framework were evidenced in our analysis except for Circle 1, Physics Content Knowledge. The absence of Circle 1 in responses to these questions is unsurprising as the physics teachers all arrived with disciplinary knowledge and used this knowledge throughout the workshop.

Results
The two cycles of survey response coding deepened our understanding of how the design of the workshop built the teachers' capacities to integrate CT as an out-offield teaching experience. The spectrum of teacher beliefs about building capacity were consistent with our hypothesis that re-novicing is experienced differently by individual teachers who are seeking to integrate CT in their instruction.
Notably, axial codes for responses to Q4 (see Table 2) almost exclusively focused on Circle 2 (Computing Content and Practices) or Intersection 2 ∩ 3 (Computing PCK). No responses to this question indicate that the teachers were thinking of their needs for future development in terms of physics-CT integration. Based on our assumptions in the workshop design (building toward intersection 1 ∩ 2 ∩ 3 from teachers' positions of disciplinary expertise in Circle 1), we expected to see more consistent responses about teaching physics with computation. Instead, most responses focused on student learning and teacher learning of computing. In conceptualizing their needs for capacity development, the teachers identified their need for more knowledge of computing, and how to teach computing, before integrating CT into their physics instruction.
In contrast, axial codes of teacher responses to Q5 (see Table 3) revealed thinking of a CT-integrated ideal in terms of physics-CT integration PCK (intersection 1 ∩ 2 ∩ 3). The qualitative differences in the axial codes across Q4 and Q5 show a discrepancy between the support teachers reported they needed at the time of the workshop and their aspirations for integrating CT. This discrepancy illuminates what re-novicing looks like in this experience and what capacity development needs to look like for these teachers. While teachers all possessed the dispositions necessary to build their professional capacity, their abilities to leverage their developing knowledge base of computing was not evident. This discrepancy prompted us to look within the responses of individual teachers to describe how their workshop experiences were building capacity across the domains of CT integration.

Teachers' Entry Points on the Re-novicing Journey
The breadth of teacher responses we observed across the CTIntegration framework motivated us to consider a set of example cases that represented a continuum of participant entry points to the workshop. We chose four teachers for our examples who answered each survey question completely and exemplified the range of capacity building and professional learning needs that emerged in our code-based data analysis. Our goal here is to plot a hypothetical pathway of re-novicing that individual teachers may follow rather than to make generalizable claims about how all teachers build capacity to integrate CT.

Mary: Seeking More Programming Knowledge
Mary's comments suggested that she was uncertain about how to proceed with CT integration after the workshop. She had previously participated in other workshops focused on programming-based CT integration in physics, but she communicated a mixed sense of confidence after our workshop. She described her time in her breakout rooms as being unhelpful, with "the more advanced folks… spending time looking for alternate ways to do the same thing and leaving the rest of us to muddle through on our own." She elaborated on this statement by suggesting that the workshop be restructured using similar-ability groupings in the breakout rooms. She also wondered if the facilitators could have done more to "make sure everyone in the group was feeling involved." The workshop's approach to positioning teachers as Python learners in breakout rooms with a series of physics-specific Jupyter Notebook activities did not transfer into specific plans for integration in Mary's instruction. There was limited evidence of physics-CT integration PCK with Python programming (Intersection 1 ∩ 2 ∩ 3) in Mary's responses. Mary did not provide evidence that the professional learning would transfer to her teaching. "This toolset is going into my bag and I'll see where I'd put it while I think about next year's course." Similarly, she responded "I don't know" to survey questions about what resources she needed and how computation could support her students' learning. Because her responses generally focused on programming as a tool with which she is still developing proficiency, we categorized her professional learning needs in the domain of computing practices (Circle 2).

Carla: Planning for CT Integration After More Programming Practice
Carla's responses described how she entered the workshop wanting more computing proficiency and ended the workshop still wanting more computing proficiency. Carla wanted to "build her Python skills so that [she could] add programming seamlessly into courses students are already taking." During the workshop, she found value in working collaboratively with other teachers in the breakout rooms and described her interactions with the workshop facilitators as "consistently high quality and 1 3 informative." She described the value of scaffolding with the Jupyter Notebook to make the programming more accessible. Her statements were evidence of her readiness to develop integrated physics/computing content knowledge (Intersection 1 ∩ 2).
Carla's reliance on experts, peers, and scaffolding to work toward her goal of developing a deeper understanding of Python programming supported her re-novicing. Her physics-specific knowledge of the importance of model-building and sensemaking was extended by her belief that computing would provide her students with "another way to view experimental science." Carla shared her intention to modify the electric fields activity for her students and to use some of the data import and curve-fitting activities. She elaborated on these ideas by stating, "I think that integrating computation into my courses would help students see how scientists construct models and how models help us develop unique insights." We interpreted her identification of specific activities and her commitment to model-building with programming as evidence of her progress toward building integrated physics/CT PCK (Intersection 1 ∩ 2 ∩ 3).
At the same time, Carla expressed her need to feel more confident as a programmer before she would feel ready to "fully" integrate computation into her courses. She wanted to be better prepared to anticipate the struggles that her students would face with programming.
I think I need more time to work through activities shared in this workshop and the PICUP libraries . It is good to know that the PICUP Slack [online community] is available when I need assistance with an activity or concept… I'd like to make sure I can run into as many errors as possible programming on my own before I ask my students to walk through these types of activities.
Resolving errors is a known struggle for novice programmers (Marceau et al., 2011), so we observe that Carla's professional learning needs are in the domain of computing practices (Circle 2). However, Carla also has specific ideas about how to extend her existing physics PCK through CT Integration, and she described specific professional learning strategies she wants to use to build her capacity in computing practices. Therefore, these needs are closely aligned with her plans to adapt specific workshop activities for classroom use (Intersection 1 ∩ 2 ∩ 3).

Beth: Engaging in Self-Guided Technical Preparation
Beth began the workshop with the intent to "dust my quarter-century old computing skills off and learn some Python." Beth's experience is an example of our earlier description of how even physics teachers who have foundational CT knowledge have not necessarily maintained that skill set in the high school context. While other teachers expressed their appreciation of the driver-navigator approach to programming in the breakout rooms, Beth offered a different perspective about tinkering with workshop materials.
I had a wonderful time! I did find that I work best independently but enjoyed having someone to answer my questions and helping others with their prob-lems. I found the driving/navigating part distracting. I just want to dig in myself first to construct a basic understanding.
Beth's confidence in integrating her own computing knowledge in her teaching was reflected in her description of several workshop activities that she found to be relevant for her students. Unlike Mary and Carla, Beth responded to questions about the additional resources that she would need to support CT integration by focusing on curriculum (e.g., magnetism visualizations and mechanics simulations). She did not express a need for additional professional learning opportunities related to computing knowledge. Beth perceived that she could develop her computing capacities (Circle 2) on her own in the context of the shared workshop activities. We categorized her further professional learning needs as physics-computing integration (Intersection 1 ∩ 2).

Ingrid: Building Computing Knowledge Within Physics
Ingrid's responses offer evidence of her readiness to integrate CT with physics in her classroom. She did not describe having prior knowledge of computing and she appreciated the patience of her collaborators and the persistent encouragement to ask questions.
It is a somewhat humiliating experience to feel so ignorant-every time I learn something new that is difficult I think it's a good thing since it helps me remember how my own students feel. I'm also really grateful for all the resources and the knowledge that facilitators will be there to help us through the school year.
Ingrid is comfortable with continuing to learn programming through her own teaching with computational activities. She does not perceive her lack of computing knowledge as a barrier to integrating CT with her high school physics students. On her re-novicing journey, she is prepared to continue to construct her computing knowledge (Circle 2) alongside her students in physics-CT integrated activities. She acknowledges that she still needs support with syntax and set-up, but she is comfortable building expertise both on her own and in collaboration with her students.
Some of my students are familiar with coding… so they will be helpful guides for the whole class. I did order the suggested Python for Beginners book for physics and have started working through some of the suggested [YouTube] videos on Python.
Ingrid plans to "start small with kinematics." Kinematics is one of the first topics introduced in a typical high school physics class, so Ingrid's plan affords her options to decide whether to continue with more advanced integrated CT curricula as the school year progresses. She elaborates (emphasis ours): I like the idea of having students do a lab and then code the lab to change variables and see the outcomes numerically and graphically. Being able to see how changing variable values changes the outcome without having to repeat many experiments physically will be very valuable. Also students can make predictions and then try them out in the program. And the more ways a student can represent a scenario to solve a problem, the deeper the understanding. I do think seeing the physics laid out in coding language really does make a conceptual difference in understanding what is going on.
Ingrid entered the workshop with a specific goal of helping her students learn programming, even though she described herself as a novice. Ingrid's statements reveal that she left the workshop thinking about how programming deepens physics learning opportunities and how integrating computing creates more authentic problem-solving opportunities. She had specific plans to further the development of her programming capacity (Circle 2) on her own and through her interactions with her students. This focus on how programming can support learning physics in the classroom places her need for further professional learning in the physics-computing integration intersection (Intersection 1 ∩ 2 ∩ 3).

Discussion
Developing the capacity to integrate CT was the start of a re-novicing journey for the high school physics teachers who attended our online Python programming workshop. Our instructional design, built upon our hypothesis that teachers could learn to integrate CT in high school physics through discipline-specific programming applications, garnered mixed perceptions from participants of their capacity building gains. Our analysis reveals the complexity of designing professional learning to meet the unique programming knowledge needs of all teachers who are interested in CT integration as an out-of-field experience.
We assigned each of four teachers a unique location on the CTIntegration framework (see Fig. 2) based on their professional learning needs. We located Mary on the boundary of Circle 2 (Computing Content and Practices), where she perceives her need for additional Python programming knowledge as a barrier to integration. She is out-of-field in her capacity to integrate physics and CT. By contrast, Carla is located within Circle 2. She acknowledges a need for additional computing knowledge but is already thinking of activities (however "small") that she can pilot with her students. She is therefore much nearer the intersection of Circles 1 and 2 (Physics Content and Practices and Computing Content and Practices). Beth, meanwhile, is situated in the intersection of Circles 1 and 2, where she describes herself as selfsufficient and ready to try an array of activities. Finally, Ingrid sits securely in the central intersection, describing the greatest capacity for CT integration as a result of her workshop experiences. Although she acknowledges that she has room to grow in her Python programming knowledge, she believes that she can build this capacity as she engages in physics activities with her students.
Carla and Mary needed to develop routine expertise (McDiarmid & Clevenger-Bright, 2008) related to the computing practices that their students would need to perform in CT-integrated activities. In contrast, Beth and Ingrid described a need for adaptive expertise (McDiarmid & Clevenger-Bright, 2008) related to particular applications of computing practices in the physics context. Because Beth and Ingrid describe computing as an integral part of learning physics, they perceive CT integration as the logical next step in the development of their teaching practice. Carla and Mary describe computing as an external set of skills they need to master before integrating computing into their existing curriculum. These different perspectives on computing suggest different capacities for CT integration, and by extension, different professional learning needs.
We further interpret these cases to offer a grounded theory of re-novicing as teachers build their physics-CT integration PCK. Teachers may be at different points along a theoretical pathway toward building capacity to integrate CT in physics teaching. We had anticipated that teachers at our workshop would be comfortable learning computation in the context of ready-made physics activities. They would begin at the 1 ∩ 2 intersection and progress toward 1 ∩ 2 ∩ 3. In contrast, the survey responses and case studies we presented show that some teachers need an entry point of Circle 2 before progressing through Intersection 1 ∩ 2 and toward Intersection 1 ∩ 2 ∩ 3. For teachers like Mary, the entry point is the development of a working knowledge of computing content and practices (Circle 2). This knowledge becomes a prerequisite for building PCK for disciplinary integration. Teachers in Circle 2 may benefit from a more general introduction to computational thinking practices and skills before engaging in the collaborative integrated CT-physics activities that we facilitated in the workshop.
Even though Carla's professional learning needs also focused on knowledge of computing content and practices (Circle 2), she was still supported by our workshop's professional learning approach. She expressed her willingness to build her students' programming knowledge through integrated CT-physics planning and teaching (e.g., "running into as many errors as possible"). The workshop design was also aligned with Beth's and Ingrid's professional learning needs. The lack of a general introduction to CT practices and the Python language was not a barrier to their re-novicing journeys. Ingrid's entry point in intersection 1 ∩ 2 ∩ 3 provided evidence that some teachers are comfortable learning computing within the context of their own teaching. She is envisioning and embraces the learning opportunities for both her and for her students as she integrates physics and coding in her teaching.
A "one-size-fits-all" approach to professional learning may not support all teachers who begin the re-novicing journey toward CT integration in the physics classroom. Some teachers might have experienced a rich computationally integrated undergraduate physics curriculum or earned a formal credential in computer science, while others may not have worked with computing beyond rudimentary spreadsheet applications. However, there is more nuance in building CT integration capacity. Teachers' beliefs about the depth of programming expertise required to introduce these ideas to their students will vary. There may be a tension between a teacher's belief that they should have content expertise to be a good teacher and a workshop approach that suggests that this content expertise can be constructed through discipline-specific programming experiences within and beyond the workshop. By conceptualizing CT integration as an out-of-field experience for many physics teachers, designers of professional learning can attend not only to the development of PCK but also to the CT dispositions (e.g., tolerance for ambiguity) that teachers may bring to these professional learning opportunities.

Limitations
Our study offers an in-depth look at physics teachers' experiences in learning CT in the context of an online workshop but is limited in its sample size and duration. We did not seek to make generalizable claims about the relationship between the workshop experience and capacity building. Furthermore, the short duration of this professional learning (a 1-week summer workshop) did not afford us the opportunity to relate the teachers' self-described capacity for CT integration to actual CT integration in the following school year or beyond. Therefore, we focused our research question on the teachers' experiences with the workshop and emphasized capacity as being developed "along the continuum in the life-long process of learning to teach" (McDiarmid & Clevenger-Bright, 2008).
We must also acknowledge that our grounded theories are built upon limited insight into teachers' educational backgrounds and teaching contexts. These insights are based on interpretation of responses to six survey questions and researcher observations and interactions during the workshop. Our analysis of capacity to integrate CT may not capture intention or interest levels for carrying out CT integration.
Finally, the four illustrative cases were chosen based on the completeness of teachers' answers and as such may not have captured the perspectives of teachers who gave less verbose answers. However, our analysis did not find any additional themes mentioned by other teachers that were not represented in these four cases.

Implications
Based on this theory of teacher re-novicing, CT-integrated professional learning may need to support teachers in developing computing capacity apart from disciplinary applications. We structured our professional learning under the assumption that the teachers would learn CT integration without deep programming knowledge based on our own experiences learning computing in domain specific contexts. Some teachers who seek re-novicing may best be served by engaging in a different approach to professional learning, situated first within the domain of computing knowledge with a clear path toward computing activities that leverage their disciplinary knowledge. To further expand on Luft et al.'s (2020) concept of out-of-field teaching, professional learning needs to be differentiated for teachers who are near out-of-field versus far out-of-field. This conceptual orientation shifts the goal of professional learning toward CT-integration that prioritizes the learning of enough computing knowledge for teachers at different points on the re-novicing journey to feel prepared to integrate CT in their instruction.
CT-integrated professional learning also needs to attend to the tensions introduced by a teacher's expectation of content expertise prior to integrating CT. While developing computing-domain knowledge, teacher educators need to help teachers establish reasonable expectations for how much expertise is "good enough" to achieve their CT integration goals. They can also emphasize opportunities for continuing education in the form of web-based resources and knowledge community forums. Working through ambiguity should be at the center of CT-integrated education (Barr et al., 2011;Pérez, 2018). Teachers must experience and accept this ambiguity in order to facilitate CT learning with students.
Further research is needed into the depth and breadth of computing knowledge at the start of the re-novicing journey for teachers whose professional learning needs are in the domain of computing practices. It would be unreasonable to expect teachers to complete an entire undergraduate curriculum in programming before introducing introductory-level CT-integrated activities, but what level of expertise do they need to progress? How does this need for capacity development vary based on teachers' academic background and motivation? To make CT more accessible to teachers from a diversity of starting points, we suggest querying their motivations and experience (especially with an eye toward their perceptions of their own re-novicing journey) early in the professional development and, in the case of online video conferencing platforms, being purposeful in populating breakout groups based on individuals' sense of preparedness.
The pathway outlined in the "Discussion" section is evocative of an inbound trajectory within a community of practice from peripheral membership to central membership (Wenger, 1999). We chose not to use communities of practice as a framework for this study since the workshop likely did not extend over sufficient time to reasonably establish a local community of practice. Additionally, since we have data about these teachers at one point in time, we cannot trace out their individual trajectories over time. However, this similarity suggests that the communities of practice framework would be useful in the design and evaluation of longer-term development of physics teachers' capacity for CT integration.
This grounded theory of re-novicing traces physics teacher professional learning as a series of entry points from computing knowledge to physics-CT integration. There may be a similar pathway for computer science teachers who want to integrate physics concepts into their instructional practices, beginning with physics knowledge and progressing toward integration.

Conclusion
We have conceptualized CT integration as an out-of-field teaching experience that requires physics teachers to be re-noviced. Our analysis of survey responses from a CT-integration workshop revealed teachers' varied needs for CT integration knowledge and informed our development of grounded theories for professional learning. Re-novicing is a pathway that begins with building computing knowledge and moves toward physics-CT integration PCK. This pathway can inform the design of CT-integrated professional learning that supports teachers in developing computing capacity, attends to their differing expectations of computing expertise for classroom integration, and cultivates their beliefs and attitudes as CT teachers.
Because of its inherent computational orientation, physics is a naturally accessible discipline for CT integration. When integrating CT in other STEM fields, the specific uses we outlined (modeling and data analysis) are equally applicable in different contexts. The diverse professional learning needs exhibited in this study are also likely to be found when integrating CT into other STEM fields. An expanded collaboration between STEM teachers and STEM + CT practitioners may identify and address these needs. Professional learning should attend to the tension between an expectation of teacher expertise and the reality of re-novicing as teachers begin CT integration. A critical part of developing the capacity of STEM teachers is the purposeful normalization of re-novicing if teachers are to enact CT integration as an out-of-field experience that increases the rigor and relevance of their disciplinary STEM instruction.