Unpacking Teachers’ Transformative Agency Following Digital Fabrication Workshops on Making Mathematical Manipulatives

Unpacking Teachers’ Transformative Agency Following Digital Fabrication Workshops on Making Mathematical Manipulatives | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Unpacking Teachers’ Transformative Agency Following Digital Fabrication Workshops on Making Mathematical Manipulatives Henrik Stigberg, Susanne Stigberg This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7349219/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Apr, 2026 Read the published version in Digital Experiences in Mathematics Education → Version 1 posted 9 You are reading this latest preprint version Abstract Digital fabrication (DF) presents innovative opportunities for reimagining the use of manipulatives in mathematics education. Manipulatives are fundamental for helping students grasp abstract mathematical concepts. However, integrating DF into teaching practice requires more than just access to technology; it demands a shift in teachers’ transformative agency. This paper presents the experiences of eight teachers who participated in a series of eight full-day workshops over a span of one year, focusing on making mathematical manipulatives using DF. Through interviews, the teachers offered insights into their transformative agency, detailing their sense of purpose, competency, autonomy, and reflexivity. Our results highlight the complexities, opportunities, and challenges encountered by these teachers as they navigated the integration of DF into their teaching practice. Our study led to three key implications: DF enabels teachers to create manipulatives that are pedagogically relevant; DF-created manipulatives support changes in teaching practices, showcasing teachers' transformative agency; and there is a critical need for supportive infrastructure to facilitate teachers becoming makers in education. The paper underscores the potential of DF to transform mathematics education while emphasizing the importance of providing sustained support to realize this potential fully. Figures Figure 1 Figure 2 Introduction In this article, we inquire into how teachers can transform their mathematics teaching with manipulatives after being introduced to digital fabrication tools and techniques. Digital fabrication (DF) is the process of translating a digital design developed on a computer into a physical object, e.g., using a 3D printer or laser cutter (Berry et al., 2010 ). In recent years, DF and making have gained interest in STEM education, providing an opportunity for students to develop creativity and real-world problem-solving skills (Perignat & Katz-Buonincontro, 2019 ; H. Stigberg, 2022 ). Adopting a maker mindset, teachers and students can translate abstract ideas into concrete and meaningful experiences (Blikstein, 2013 ; Ford & Minshall, 2019 ; Presidential Proclamation -- National Day of Making, 2014 , 2014). In this article, we explore how teachers reflect on DF for making their own manipulatives - tangible teaching aids designed to support students’ learning of abstract mathematical concepts. Previous research has demonstrated that introducing DF into teacher training as a method for making manipulatives fosters innovative learning experiences (Akuom & Greenstein, 2021 ; Greenstein et al., 2020 ; Läufer & Ludwig, 2023 ; H. Stigberg et al., 2023 , 2024 ). However, there is limited evidence of teachers’ ability to transform their teaching practices after acquiring DF skills. Specifically, there is a lack of understanding of teachers’ agency, a critical quality for teachers when making meaningful changes to their professional environment (Cong-Lem, 2021 ; Fu & Clarke, 2017 ). Stigberg et al. ( 2023 ) found that when teachers applied DF tools to make their own manipulatives, they developed a strong sense of ownership over these resources, beneficial for enhancing the effective utilization of these manipulatives in the long term. Akuom and Greenstein ( 2022 ) found that DF contributes to pre-service teachers’ pedagogical and conceptual knowledge by enabling them to make agentic design decisions when making manipulatives that promote more learner-centered practices. They suggest that a shift from teachers as consumers to designers and producers of manipulatives enables teachers to take a more active role in utilizing new manipulatives. Despite these findings, the role of DF in fostering teacher agency to transform their teaching practices with manipulatives remains poorly understood. In this article, we unpack teachers’ transformative agency, characterized by sense of purpose, competence, autonomy, and reflexivity (Pantić, 2015 ) after participating in a professional development program, inquiring into DF for making manipulatives. Over one year, we collaborated with eight in-service teachers within a Community of Inquiry (CoI) exploring DF for making manipulatives. CoI theory emphasizes inquiry as both a tool and a norm in collaborative efforts between teachers and teacher educators to enhance practices (Jaworski, 2006 ). While H. Stigberg (2025a) investigated how CoI constructs such as inquiry, engagement, imagination, and critical alignment foster teacher agency, in this article, we analyze teachers’ reflections on the changes in their teaching practices after participating in the CoI. Specifically, we address the following question: How can teachers’ transformative agency be characterized after participating in DF workshops for making manipulatives? In the following, we provide an overview of manipulatives in mathematics teaching and previous research on DF for making manipulatives. Next, we describe teachers’ transformative agency in general and Pantić’s ( 2015 ) framework in particular. We then present our study and its results, concluding with a discussion on how DF workshops can foster teachers’ transformative agency in relation to mathematics teaching with manipulatives. Manipulatives in mathematics education Mathematical concepts are inherently abstract and are represented through symbols, drawings, verbal, real-world situations, or tangible objects such as manipulatives. In education, symbols are often overemphasized, while the ability to switch between different representations is crucial for deepening students’ understanding of mathematical concepts (Duval, 2006 ). Consequently, it is important to encourage teachers to integrate manipulatives into their teaching practices (Brown et al., 2009 ; Holmes, 2013 ; Sowell, 1989 ). When used correctly and over a period of time, manipulatives can positively enhance students’ mathematical understanding, making them essential in mathematical education (Carbonneau et al., 2013 ; Sowell, 1989 ; Uttal et al., 1997 ). However, manipulatives are not inherently beneficial and do not convey mathematical knowledge independently. Teachers must tailor manipulatives to fit the classroom, guide students in their use, and facilitate the transition from concrete representation to other forms, such as symbols (Brown et al., 2009 ; Sarama & Clements, 2016 ; Uttal et al., 1997 ). Despite their potential, Marshall and Swan ( 2008 ) identified several challenges recognized by teachers to use manipulatives in their teaching, including limited access due to economic constraints, material organization, space or time limitations, and issues related to classroom management. Currently, teachers often rely on pre-made manipulatives provided by educational material companies, which limits their ability to adapt these resources to their specific teaching needs. While these manipulatives are often well-designed, teachers are restricted to the intended use defined by the manufacturers, lacking opportunities for customization. Hogan et al. ( 2018 ) examined teacher agency in relation to purchased manipulatives, suggesting that teachers act as agents when selecting from a variety of commercial resources to enhance their pedagogical toolbox. They found that teachers aim to create unique learning experiences tailored to their students’ specific needs, contributing nuance to the debate on commercialization in educational literature. Rather than viewing commercialization as inherently negative, they argue that it offers valuable opportunities for educational enrichment. In contrast, Marshall and Swan ( 2008 ) highlight challenges teachers face in using commercial manipulatives, including insufficient quantities to cover their classrooms, highlighting that the teachers “do not have enough of the equipment [manipulatives] to go around” (p. 342), limited accessibility, and “the cost of manipulatives made their use problematic” (p. 342). Alternatively, teachers can create their own manipulatives using laminated paper, everyday objects like coins or beans, or crafting materials out of wood. However, these homemade manipulatives can introduce irrelevant properties that might impede students’ learning experiences (Carbonneau et al., 2020 ) and may not appear as polished as commercially available options. By utilizing DF, teachers could create manipulatives with the precision and accuracy of commercially manufactured options, while maintaining the flexibility to customize them to their needs, as demonstrated by, e.g., Dilling and Witzke ( 2020 ) making “3D-printed models of graphs of functions for concept formation processes of the concept of derivative” (p. 337). Greenstein and Olmanson ( 2018 ) provided a course where teachers designed 3D-printed manipulatives to support students’ learning of conic sections, the coordinate plane, and the concept of the definite integral in calculus using the rectangle method. To fully capitalize on DF and its opportunities, teachers need transformative agency to embrace changes in their teaching practices with manipulatives. This involves expanding their repertoire beyond off-the-shelf and hand-crafted manipulatives to incorporate DF technologies, thus enhancing their ability to tailor manipulatives to fit their specific classroom needs. While we do not dispute the idea of teachers as agents when purchasing manipulatives, this article aims to explore how DF can potentially improve teachers’ access to manipulatives and possibly broaden their agentic space, facilitating an enhanced integration of manipulatives into their classroom practice. Digital fabrication in education DF is defined as “the process of translating a digital design developed on a computer into a physical object” (Berry et al., 2010 , p. 168). This process is facilitated by tools such as 3D-printers, laser cutters, or vinyl cutters. 3D-printers can create almost any shape by printing successive thin layers of filament, gradually building up the object from the bottom up. They are cost-effective and are easily placed without the need for additional equipment or environmental adjustments. However, printing large objects can be a time-consuming process. Laser cutters and vinyl cutters work by removing material to create the desired shape. Laser cutters can quickly cut or engrave large areas. However, they are limited to two-dimensional cuts, tend to be more expensive, and require sufficient ventilation to handle generated gases. Vinyl cutters, on the other hand, use a blade to cut shapes in piable materials such as vinyl, paper, or leather. DF technologies are often gathered in so-called FabLabs and maker spaces and can be found at universities, libraries, and schools. Over the past decade, the number of these maker spaces has grown (Valente et al., 2017). Individuals attending these places are referred to as makers, forming part of the maker culture - a movement focused on making almost anything using DF tools. The maker culture thrives on the collaborative spirit of sharing personal creations and utilizing the work of others through online platforms like Thingiverse 1 and Printables 2 . Blikstein ( 2013 ) argues that DF and making should play a major role in education, “bringing powerful ideas, literacies, and expressive tools to children” (p. 2). DF has been integrated into various educational settings, predominantly in higher education, engineering, and design courses. It has also been used to create teaching aids for subjects such as anatomy, chemistry, and geometric models in mathematics (Ford & Minshall, 2019 ). Although research on the use of DF for making mathematical manipulatives is limited (H. Stigberg, 2022 ), there are notable examples from teacher education. Greenstein et al. (2019) demonstrated that incorporating DF in teacher education can deepen the understanding of mathematics content, curriculum, and pedagogy among teacher students. Similarly, Barbosa and Vale ( 2025 ) showed that integrating 3D modeling and printing enhances interdisciplinary STEAM learning and problem-solving skills, while also highlighting teacher students’ challenges with mathematical precision and curricular alignment, indicating a need for more pedagogical scaffolding. DF has been employed in teacher professional development programs to enable in-service teachers to make manipulatives. Stigberg et al. ( 2023 ) emphasize DF’s role in relation to customized teaching activities, manipulatives access, and classroom management, concluding that workshops on DF for making manipulatives “allowed teachers to not only familiarize themselves with DF technologies but also foster a strong sense of ownership over the manipulatives they created. This ownership entails: 1) storing the manipulatives in their classroom with easy access for them and their students, 2) creating customized manipulatives tailored to their students and classroom, 3) room for further adaptation, modification, or expansion of the manipulatives, 4) and the option to reuse the manipulatives for teaching various mathematical concepts” (p. 6). Greenstein & Olmanson ( 2018 ) summarize that DF technologies can be a catalyst for pedagogical change by enabling teachers to create their own manipulatives. However, Harron et al. ( 2022 ) identified both affordances, such as facilitating hands-on learning and providing visual support, and constraints, including high costs, tool accommodation difficulties, time limitations, and a sense of pressure to adhere to standardized activities and assessments. While research on DF for making manipulatives has gained traction, the field still requires further consolidation. A particularly overlooked aspect is how teachers can transform their practices by leveraging DF technologies. Teacher agency is a crucial concept for analyzing teachers’ ability to enact change. To date, no study has thoroughly examined and unpacked the characteristics of teachers’ transformative agency following a professional development program for making manipulatives using DF tools. By examining teachers’ transformative agency, we aim to enhance the understanding of the key factors that enable teachers to utilize DF to innovate their teaching practices effectively. Teachers’ transformative agency Agency is a concept that examines the extent to which an individual’s autonomy and influence shape their practices and life situations. It encompasses the freedom to actively strive, take initiatives, and impact one’s circumstances (Eteläpelto et al., 2013 ). Agency is often linked to the ability to change and develop workplace practices through reflection and action (Cong-Lem, 2021 ; Goller & Paloniemi, 2022 ). It involves engaging with issues deemed worthy of solving, thereby influencing change and learning (Billett, 2006 ). Cong-Lem ( 2021 ) conducted a comprehensive review of the literature on teacher agency (TA) to map the field, refine the understanding of the concept, and provide insights for future research. He identified six major themes: (1) the enactment of TA, (2) the role of teacher cognition, (3) influential factors, (4) professional development interventions, (5) TA outcomes, and (6) its change trajectory. Cong-Lem ( 2021 ) emphasizes that teacher professional development, such as coaching, seminars, and workshops, effectively fosters TA. These approaches empower teachers by promoting research, ownership of educational reforms, and technological competencies, which in turn encourage reflective practices. Through examining their pedagogical beliefs and experiences, teachers enhance their agency, leading to transformative change (Cong-Lem, 2021 ). Numerous studies highlight the critical role of teachers as change agents, transforming their practices through professional development (Hauge, 2019 häsantanen, 2015). For example, Insulander et al. ( 2019 ) examined teachers’ agency after participating in a mathematical-didactical professional development program, highlighting that teacher competence enacted in a community setting is a crucial factor in teachers’ agency. Similarly, H. Stigberg (2025) argues that a CoI approach nurtures teacher agency through processes of inquiry, engagement, imagination, and critical alignment. According to Pantić ( 2015 ), teacher agency can be described by four components: sense of purpose, competence, autonomy, and flexibility. She posits that this “model could be used in empirical studies of teacher agency exploring the transformative potential of teachers within the structural and cultural environments across different school, policy and social contexts” (p. 773). In this article, we have applied her framework to examine teachers’ transformative agency, particularly their use of DF for making manipulatives after participating in a CoI, including several DF workshops. Drawing from previous studies, we propose specific indicators for each component. In the following, we will outline key indicators for the components within the framework. Sense of purpose Teachers’ sense of purpose for changing their practices is essential to their transformative agency. This can be demonstrated by their recognition of DF as a valuable resource for making manipulatives and their self-identification with the maker culture. Additional indicators might include their reflections on customizing manipulatives to suit students and classrooms better, developing flexible manipulatives for a range of mathematical concepts (H. Stigberg et al., 2023 ), and utilizing materials that are cheaper and more accessible than purchased manipulatives, provided they have access to DF tools (Harron et al., 2022 ). Competence Competence in the context of making manipulatives using DF encompasses many aspects, e.g., proficiency in operating DF technologies such as 3D printers and laser cutters, using diverse software tools to find, adapt or create digital models, design competence to drive innovation processes, as well as pedagogical and mathematical knowledge to customize manipulatives for the classroom (S. K. Stigberg et al., 2022 ). Autonomy External factors, such as policy, school leadership, and available resources, heavily influence teachers’ ability to change their teaching practices. For instance, Frost ( 2006 ) noted that while strides were made in classroom environment and teaching methods, curriculum content remained constrained mainly by policy, highlighting a significant barrier to teacher agency. Furthermore, resources such as time and access to necessary DF technologies influence teachers’ ability to enact changes. Andersen and Pitkänen ( 2019 ) reported that “lack of time, lack of money, DF machines and other resources” (p. 9) were important factors for not changing activities in school. Reflexivity Cong-Lem ( 2021 ) emphasizes that the transformation of teacher agency often begins with teachers questioning and reflecting on their own pedagogical beliefs and conceptions, making sense of their experiences. Wells ( 1999 ) defines reflexivity in professional development as the metacognitive process of reflecting on the knowledge being created or previously acquired, as well as the tools and practices employed in the process. In our specific context, this means teachers might reflect on the workshops that introduce DF, assess the manipulatives created using DF, and evaluate how their teaching practices have evolved after the workshops. Table 1 Unit of analysis Unit of analysis Potential indicators of teachers’ transformative agency using DF for making manipulatives Sense of purpose How teachers describe their sense of purpose of • the workshops • DF for making manipulatives. • their practice as mathematics teachers Competence How teachers express their competence in relation to • mathematics didactics • DF technologies • design and innovation processes Autonomy How teachers define their autonomy in relation to • school policy and leadership • DF technologies • having time Reflexivity The teachers’ ability to “step outside” themselves and reflect on: • the workshops • the created manipulatives • their manipulative-based teaching practice Methodology To address our research question, How can teachers’ transformative agency be characterized after participating in DF workshops for making manipulatives? , we conducted interviews with seven teachers from three K-7 schools in Norway, all of whom participated in a year-long series of eight full-day workshops. Below, we present an overview of the workshops, alongside details of the data collection and analysis employed in this study. Workshops in DF for making manipulatives Inspired by Community of Inquiry (Jaworski, 2006 ), we (as one teacher educator and one DF expert), together with two teacher education colleagues, conducted eight monthly full-day workshops together with eight elementary teachers (referred to as teachers) with previous experience from using manipulatives to inquire together into DF and its potential to develop practices for making and using manipulatives. In the workshops, we introduced DF tools and techniques, including: DF sharing platforms (e.g., Thingiverse and Printables), 3D modelling and printing using Tinkercad and Prusa printer, 2D modelling and cutting using Cricut vinyl-cutter and Glowforge laser cutter, design thinking process to support the design of new manipulatives. Throughout the workshops, we encouraged teachers to explore the potential applications of the introduced DF technologies. Our objective was to foster critical reflection and enable the teachers to reshape their practices in relation to manipulatives, all while providing them with a range of tools and resources throughout the workshop series. We used the FACS model (H. Stigberg et al., 2024 ; S. K. Stigberg et al., 2022 ) for the first four workshops to scaffold DF skills, arranged in increasing complexity, from finding ready-made manipulatives to designing new ones. FACS stands for Finding, Adapting, Creating, and Sharing manipulatives. Each of these workshops was structured into four components: reflections, lectures, group work, and presentations, drawing inspiration from Frank et al. ( 2011 ). The workshops commenced with group reflections, which fostered discussions on the use of manipulatives in the classroom and encouraged reflection. Subsequently, we provided a brief lecture covering topics such as DF tools and techniques, teaching mathematics, and examples of manipulatives to illustrate mathematical concepts. The main part of each workshop involved collaborative group work, providing teachers with a hands-on, collaborative inquiry experience. Finally, teachers presented their manipulatives and outlined their intended teaching activities. Between workshops, teachers utilized their manipulatives in their classrooms. For more extensive information, the design and implementation of the workshops are described in H. Stigberg et al. ( 2024 )d Stigberg et al. ( 2022 ). During the fifth workshop, teachers gave individual presentations reflecting critically on previous DF workshops, one or more selected manipulatives they had created, and the classroom activities that incorporated these manipulatives (see H. Stigberg et al., 2023 ). In the second part of the series, the workshops shifted focus to extend hands-on experience for teachers. While we continued to share experiences, the emphasis was placed on providing teachers with more autonomy to develop their manipulatives. Our contributions were reduced to brief introductions on topics such as design thinking, programming-based modeling, and sharing on online platforms. Beyond these introductions, our role transitioned to providing support whenever necessary. As the year concluded, we organized a local Maker Faire, inviting colleagues, school management, a nearby science center, and other interested parties. This event provided an opportunity for teachers to showcase their work through posters and talks. A comprehensive summary of all the workshops is detailed Table 2 . Table 2 Overview of workshop content categorized by digital fabrication, pedagogy, mathematical content, and share Digital Fabrication Pedagogy Mathematical content Share Find Workshop 1 Thingiverse Printable Prusa Slicer 3D printer Representations of mathematical concepts Four principles for working with manipulatives (Svingen, 2018 ) Geometrical concepts and properties Example: What object does not fit? In the first four workshops, teachers shared by: Presenting the manipulative and planned classroom activity at the end of each workshop and Sharing experiences from their teaching with the manipulatives at the beginning of the following workshop. Adapt Workshop 2 Adapt/Create Workshop 3 Adapt/Create Workshop 4 Tinkercad Inquiry-based teaching Modelling manipulatives for customized teaching Number concepts and properties Example: Even and uneven numbers pieces Four stage framework for using manipulatives in teaching (Malmer, 1997 ) Modelling manipulatives for customized teaching Position system, positive and negative numbers, spatial geometry Laser cutter Vinyl cutter Inkscape Inquiry-based teaching Using different representations Maker workshops Workshop 5 Workshop 6 Workshop 7 Design thinking Mixing mathematical content to challenge students Presentation of manipulative and critical reflections (H. Stigberg et al., 2023 ) Modeling in 2D and 3D using programming Sharing experiences from their teaching with the manipulatives at the beginning of the workshop Planning Maker Faire, including making posters Contributing to online sharing platforms Maker Faire Workshop 8 Sharing manipulatives to online platform Presenting their manipulatives and posters to invited audience Data collection and analysis Following the Maker Faire, the first author conducted interviews with seven of the eight participating teachers from three K-7 schools in Norway, approximately one to two weeks after the event. Unfortunately, the eighth teacher had to withdraw from the program earlier in the year due to illness. These interviews were designed to facilitate a deeper reflection among the teachers on how their involvement in the CoI on DF for making manipulatives had influenced their overall teaching practices, rather than focusing solely on their agency. The semi-structured interviews took place in the teachers’ respective schools and lasted between 30 minutes and 53 minutes, with an average of 43 minutes. Each interview was audio recorded to ensure accuracy and was subsequently transcribed in full, providing a comprehensive record of teachers’ insights and reflections. We applied Pantić’s ( 2015 ) framework for our interview analysis, focusing on the components of sense of purpose, reflection, competence, and autonomy (see Table 1 ). Each author independently conducted a thematic analysis of the transcribed interviews for each component of the framework, gathering relevant citations with timestamps. Through discussion and comparison, we identified recurring themes that emerged across the data, aligning them with each framework component. Any discrepancies encountered during the coding process were collaboratively addressed and resolved. We developed thematic maps for each component, following the guidelines of Braun and Clarke ( 2006 ), and revisited relevant sections of the transcribed data to ensure the validity of our findings. In the presentation of the results, teachers are referred to by codes T1-T8 (T6 is missing and did not participate in the final interview), providing anonymity while maintaining clarity in analysis. Results Sense of purpose “I finally have a tool to create the things I have always made out of cardboard”, states T2, while T5 is convinced that she “has the motivation to continue” using DF for making manipulatives. Teachers’ sense of purpose for making manipulatives with DF is perceived as more durable, more flexible, and without disturbing elements. The teachers emphasize that manipulatives created using DF are more durable due to the material, but also due to students taking better care of them, and thereby potentially longer-lasting. T5 comments that they created “good manipulatives that are also durable”, while T8 agrees that “these [manipulatives] last so much longer”. T4 elaborates that, “[t]his is more sustainable ... tend to take better care of manipulatives that are durable”. She revisits her statement later in the interview, noting that taking care also can be part of mathematical activities, “the children also have to be involved in [picking up and] sorting, and there is learning in that, in a way, finding all the numbers. What [number] is missing here?”. Compared to purchased manipulatives, the DF-created manipulatives were perceived as more flexible in two ways: providing the opportunity to use the same manipulatives for various mathematical topics, as well as using the same manipulatives for various difficulty levels, enabling differentiated teaching. T2, T3, T4, and T5 all mention their use of the DF-created empty number line (ENL) for diverse teaching activities (See Fig. 1 ). E.g., T2 highlights activities focused on zero with whole and decimal number variations, stressing the need to understand “something in between [whole numbers], because you can also work with a section of the empty number line as a decimal”. T4 varied the ENL with 3D printed cubes and laser-cut numbers, allowing exploration from “simple patterns with color to quite advanced number sequences” with the same tool. T2 describes a second DF-created manipulative for geometry, fractions, and percentages, noting, “geometric shapes are both fractions and percentages” (See Fig. 2 ). T8 shares her shift from using stencils and textbooks to DF-created manipulatives for odd/even numbers, set theory, and whole number addition (See Fig. 2 ). She explains, “We came up with something that you can use for both parts, so it became easier then, less work for me”. The teachers comment that manipulatives were previously often associated with students with special needs. However, their DF-created manipulatives can be used for varying levels of difficulty, allowing all students to use the same manipulative, which conceals who might be working at different mathematical levels. T2 highlights the “unlimited number of tasks [using the same manipulatives], and in terms of differentiation, it is also completely unique.” T5 remarks, “So it seems to have been much easier when we bring in good, durable manipulatives. You can get the kids started with the same manipulatives but with different starting points”. T8 emphasizes the manipulatives’ inclusivity, saying, “Because they are using the same manipulatives, it makes a big difference. It becomes much easier to be discrete about special education when you can create the manipulatives yourself”, supporting a more inclusive classroom environment. T8 sums it up by stating, “And what is brilliant about this [DF-created manipulative] is that you can use it for so many things, which you cannot do with laminated paper in the same way, without giving it more of a special-education feel. This one, everyone uses”. Finally, teachers make a conscious effort to create manipulatives free from distracting features, unlike purchased ones, which they describe as colorful and complex. T3 notes that different colors distract students, saying: “[The students] can have their favorite [color]... While here, … they just accept them because they are all the same color”. T5 adds, “[previously] they started building cars or houses...these [purchased manipulatives] are different colors and...more fun to spin them, as there is a hole through them”. T8 also advocated for simple manipulatives, noting that students overgeneralize, especially with fractions. “To see that this is one half and it is blue, and then...cannot understand that it might as well be red, so the students become so fixated on the appearance”. Competence “I am most satisfied with gaining insight into how to make manipulatives and [that I] starting to think a bit differently”, explains T3. Teachers’ competence can be categorized into technological competence and teaching competence with DF-created manipulatives. Their expertise in DF technology varies; some feel confident using the technology, while others seek more hands-on training. This difference might be influenced by their previous technical experience and their level of engagement in workshop hands-on activities. All teachers demonstrate a willingness to experiment and are not afraid of failing when using DF technologies, despite some feeling uncertain. They express confidence in how to start using the 3D printers at their schools. Before the workshops, no one had attempted to use the printers due to uncertainty about the technology. T4 says, “Several people at our school have used them, so it is not so intimidating to try and initiate it”. T1 states, “Initially, with 3D printing, I had never used it myself, even though we had it here. I never dared to sit down and use it, but”. T8 added, “But now we know it is possible, right? So when it becomes available, it is not difficult to try and start experimenting and learning through trial and error”. All teachers demonstrated competence in finding and printing 3D models. T1 states, “But 3D printing, I can do”. T2 shares, “It is about discovering things and finding tools that students can benefit from using in various contexts”. T3 adds, “We have learned where to find things, what and where to search for, and what can be found”. Some teachers found it challenging to search for manipulatives on online platforms, due to their English language skills. T3 noted, “There is an incredible amount out there, and at the beginning, we spent a lot of time thinking, ‘What do we search for?’ Since things need to be searched in English, you have to be somewhat proficient in it”. Teachers consider modeling in both 2D and 3D more challenging than finding existing manipulatives; still T7 expresses confidence in adapting and creating 3D manipulatives. “With these websites where you can find inspiration and... Tinkercad, being able to edit things yourself, create your own things. I feel I can do that quite well”. However, teachers feel uncertain about operating the laser cutter, mainly because it has been accessible only at the university and not in schools. For example, T1 mentions, “I would probably need a bit more training in it”. T8 added, “I am somewhat unsure about starting with it myself”. Nonetheless, both T2 and T5, who are from different schools, explicitly note that investing in a laser cutter is prioritized because of its usefulness for making manipulatives. All teachers agree that they have enhanced their mathematical teaching competence, although the extent to which they have experimented with an inquiry-based approach using manipulatives varies based on their prior experience and practice. T1, who previously had little experience with inquiry-based teaching using manipulatives, states that theyte have “perhaps become more aware of the manipulatives”. He recognizes the benefits of using manipulatives for more open-ended tasks, like his multiplication puzzle, where “multiple equations could give the same number”. Teachers have explicitly mentioned how making manipulatives together in a CoI has fostered their inquiry-based teaching with more discussions and open-ended tasks. T4 states, “And now there has been more focus on having the kids investigate a bit more, to show something, try it out, talk about it, and find out what they have achieved. Not so concerned with filling out sheets or books or booklets”. T5 says, “I think I have become even more fond of the verbal part of mathematics, and that I have become more confident in it in many ways. There is a greater focus on understanding and talking about math rather than just doing math”. T7 is still hesitant managing whole-class inquiry-based teaching using manipulatives, saying, “A bit uncertain about how that would work, we might need more manipulatives. Maybe present it in a slightly different way. I am not quite sure, have not thought it through very well”. Autonomy Teachers’ autonomy can be characterized by time constraints at schools, access to resources, power structures, and collaboration with colleagues and teacher educators. The teachers would like to have more time to be creative and develop new manipulatives and lesson plans. T3, T5, and T8 explicitly mention it should be regularly scheduled every week for 1–3 hours, while T4 prefers a maker day similar to the workshops, which she finds very beneficial. In contrast, the teachers experience a lack of time within the school day to be creative and design new manipulatives. They mention that no specific time is allocated for this, or that the allocated time is used up with other tasks. “Yes, we have tried and we have made some dice and such, but the dilemma is the time” says T4, and to manage to create manipulatives, she argues that she needs to take “extra time”. T5 explains, she has “hours allocated for working on IT [but they] have instead been used for substitute teaching”. However, DF might help to save time compared to hand-crafting manipulatives, e.g., T1 comments “I am really happy to find things that are already made. We save so much time because it is something we do not have much of, right? It is hectic workdays in school”, while T8 expresses: “Having them [the DF created manipulatives] here meant that you had much less work in preparing, and the students recognize the manipulatives”. The teachers list two types of resources that are important for changing their teaching practice: DF tools and digital models to download. Most teachers do not have access to commercial manipulatives, so providing an opportunity to download digital models or create their own manipulatives gives teachers more autonomy in their teaching and easy access to them, as they are stored in their classroom. Teachers emphasize the importance of easy access to DF tools. Each of the participating schools had one or two 3D printers, which were sometimes poorly maintained and situated in inconvenient locations, such as in the library, where students had access. As T2 expresses, “Yes, well, I was down there checking out the 3D printer today, but someone was using it. So, I could not use it, and the other one is still broken. I talked to [name of IT responsible person] about how bad it is, but I mostly just look at what is available [referring to online platforms such as Thingiverse and Tinkercad]”. Limited accessibility challenges teachers who wish to use the 3D printer whenever possible. None of the participating schools had a laser cutter, which teachers particularly desire because it produces manipulatives more quickly. T5 reveals that her school’s principal announced, “a laser cutter is at the top of the list” when investing in new equipment. The teachers were positive about the online platforms, such as Thingiverse or printables, which allow them to find and download pre-designed models. There is also a wish among teachers for establishing a DF community within their school or municipality, so they are not solely responsible for facilitating all DF-related activities. As T7 mentioned, “…a place where you can go. We briefly talked about how if there were a kind of communal place, like a Maker Space, then the municipality would have it—a place where we could bring our ideas or models and have them made, which might encourage us to do it more often”. The teachers highlight the importance of involving school leadership in the project and presenting the workshop results to them as they hold the power to prioritize investments in DF technologies and can provide the means for teachers to share their experiences with colleagues at each school. For instance, T1 noted, “The assistant principal, she was at the university [participating in the last workshop], … and she said that we must share with each other. So we will likely set aside some time in the fall to share more information about what we have done and how it can be used”. This sharing is crucial, even though teachers might encounter resistance from colleagues who have not attended the workshops. While school leaders have approved all teachers’ participation in the workshops, teachers feel that the project was not consistently prioritized. Consequently, the successful implementation of DF in their practice largely depends on the teachers’ own initiative and engagement. Finally, teachers underscore that collaboration during the workshops with colleagues from the same and other schools, as well as with us as teacher educators, has been essential for transforming their teaching practices with manipulatives. Collaboration with colleagues has been important on two levels. Firstly, interactions with colleagues from different schools provided inspiration, posed challenging questions, and offered valuable tips. Secondly, teachers emphasize the importance of having a colleague from their school with whom they can continue to refine the use of manipulatives in teaching, while also sharing the same set of manipulatives. Reflexivity Teachers’ ability to self-reflect varied in the interviews. Generally, the teachers acknowledge that the DF-created manipulatives have transformed their approach, although in different ways. Most teachers observed that the DF-created manipulatives facilitate collaborative and open-ended inquiry, promoting student collaboration and teacher-student discussions. As T5 remarks, “So, it [the teaching] is perhaps a much more open teaching approach than before”. T4 notes how these manipulatives shifted the focus toward inquiry. “When children work with sheets, it is somewhat about getting it done”, but using the DF-created manipulatives “leads to more reflection and more thought about what you [referring to the students] are doing, and that you can collectively see [different solutions]”. T5 also reflected that her teaching practice has become more inquiry-oriented, with students not immediately seeking help when they encounter difficulties. Instead, they “might also become a bit more open than they have been before, more curious, and wanting to explore more in mathematics”. The teachers also mentioned that students often invent new ways to use the manipulatives and come up with unique solutions in their inquiry with the DF-created manipulatives. T5 shares an example: “However, you do get inspired when you see how the children choose to use it, or when even more questions arise than before”. She had not anticipated that open-ended inquiry with the DF-created manipulatives would also lessen the expectation that the teacher always provides the correct and only answer. Reflecting on their teaching methods before introducing DF-created manipulatives, teachers indicated a greater reliance on textbooks, which typically involved more individual, non-inquiry activities on paper. However, T1 noted that while the workshops and the ability to create manipulatives have transformed his approach in small special-needs groups, they have not impacted his full-class teaching. T1 explained that inquiry-based teaching and the use of manipulatives generate noise and disruption, straying from the usual classroom dynamics. Discussion The concept of teacher agency, while useful for understanding how teachers engage with policy and enact teaching practices, often suffers from imprecise descriptions (Priestley et al., 2015 ). In the context of DF within teacher training, this study seeks to unpack how DF can provide agency to teachers to transform their manipulative-based teaching practices, fostering innovative learning experiences as described by previous research (Akuom & Greenstein, 2021 ; Greenstein et al., 2020 ; Läufer & Ludwig, 2023 ; H. Stigberg et al., 2023 , 2024 ). By applying Pantić’s ( 2015 ) framework, which encompasses four dimensions: sense of purpose, competence, autonomy, and reflexivity, we analyze how teachers change their teaching practices following their participation in a professional development program, inquiring into DF for making manipulatives. The framework aids in pinpointing areas where transformative agency is successful and where challenges persist, such as autonomy and competence. Our article reveals that while DF broadens teachers’ agentic space by enabling manipulative creation rather than mere selection (Greenstein & Olmanson, 2018 ), its adaptation varies across teachers. Our results provide a nuanced view of Pantić’s dimensions of transformative agency post-DF workshops for making manipulatives enriching existing literature by highlighting the complexities, opportunities and challenges faced by teachers, leading to three key implications: DF enables teachers to make relevant manipulatives; DF-created manipulatives support changes in teaching practices; and the results underscore the need for supportive infrastructure for teachers to become makers in education. Digital Fabrication enables teachers to make relevant manipulatives All teachers acknowledge the transformative potential of DF in making high-quality manipulatives. DF enables them to make manipulatives that are durable and flexible, which integrate seamlessly into teaching, enhancing students’ focus on mathematical concepts rather than the manipulatives themselves. This reflection corresponds with Uttal et al. ( 1997 ), who argue “that the manipulatives become highly familiar and hence less interesting as objects in their own right” (p. 50), allowing students to focus on the mathematical concept and not the manipulatives as objects in their own right. Teachers appreciate DF for its ability to create simple, distraction-free objects, contrasting with commercially available manipulatives, which often feature unnecessary distractions such as vibrant colors or complex designs. This echoes Carbonneau et al. ( 2020 ), who advocate for “bland” manipulatives to promote problem-solving. Although none of the teachers commented on hand-crafted manipulatives having distracting features, they are perceived as less durable, which affects their sustained use. While the concept of teachers acting as agents in purchasing manipulatives is valid (Hogan et al., 2018 ), we argue that DF significantly enhances teachers’ access to manipulatives, broadening their agentic space and facilitating easier integration of manipulatives into classroom practices. In conclusion, teachers’ transformative agency is reflected in their preference for DF-created manipulatives, prioritizing manipulatives that are distraction-free and durable, thereby enriching students’ engagement with core mathematical concepts. DF-created manipulatives support changes in teaching practices Teachers reported that DF-created manipulatives shifted their teaching towards a more inquiry-based approach, facilitating student collaboration, enabling students to discuss various solutions, some of which were unexpected by the teachers. This dynamic also encouraged teachers to reflect alongside their students. This aligns with Greenstein and Olmanson ( 2018 ), who highlight that DF technologies can catalyze pedagogical change by enabling teachers to create their own manipulatives. However, not all teachers found DF-created manipulatives transformative across all settings. One teacher noted positive changes in small, special-needs groups but faced challenges with full-class instruction due to perceived noise and disruption, a concern echoed in Marshall and Swan ( 2008 ). Furthermore, it is important to recognize that our results are deeply connected to the context of the workshops the teachers attended, emphasizing inquiry-based teaching. Participation in a CoI encouraged teachers to reflect on their practices and pedagogical beliefs, making reflexivity a key aspect of this process. Through making and using DF-created manipulatives, teachers engaged in ongoing reflection and improvement of their teaching strategies. Navigating the Path to Becoming a Maker in Education Our results underscore that technological competence is essential for teachers to transform their practices, as highlighted by Hauge ( 2019 ) and Vähäsantanen ( 2015 ). Teachers actively engage with maker culture by downloading and 3D printing manipulatives, aligning with Hogan et al. ( 2018 ), who emphasize that teachers act as agents in choosing resources to enhance their pedagogical approaches. In line with Harron et al. ( 2022 ), we see advantages of our workshops, such as facilitating hands-on learning, and constraints of DF technologies, including high costs, tool accommodation difficulties, time limitations, and a sense of pressure for teachers to adhere to standardized activities, lessons, and assessments. Successfully integrating DF technologies requires access to these tools and time—resources often scarce, as noted by Andersen and Pitkänen ( 2019 ) who mention “lack of time, lack of money, DF machines and other resources” (p. 13) as barriers to educational innovation. Increasing DF access can involve utilizing communal Maker Spaces or forming partnerships with universities equipped with DF technologies, as demonstrated in this project, bridging the gap between educational potential and practical implementation. To fully embrace maker culture and contribute to the development of the teaching profession as part of the maker culture, we suggest that teachers be allocated time weekly to cooperate with colleagues and teacher educators in developing their manipulatives. Moreover, they require access to DF technologies, especially laser cutters and 3D printers. It is essential not only to have the equipment but also to ensure easy access, meaning it should be nearby, available, and well-maintained. To address these challenges, we propose fostering closer connections between local makerspaces and schools. Additionally, we encourage teachers to share their digital source files, thereby broadening the repertoire of well-designed manipulatives on online sharing platforms, contributing to the maker culture. Declarations Funding Declaration No external funding. Author Contribution We, the undersigned authors, declare that we have all contributed substantially to the research and preparation of this manuscript, fulfilling the requirements for authorship. H.S had a lead in the scientific work, data collection, and writing process. The analysis was an equally shared workload. S.S contributed to the scientific work and the discussion section in the manuscript. Both authors reviewed and proofread the manuscript. Data Availability Data related to the study were collected after approval from the national Data Protection Official for Research (Norsk Senter for Forskningsdata), following all the regulations and recommendations for research with people. The transcribed data in Norwegian are available from the authors upon reasonable request and with the restrictions regarding protecting study participant privacy. References Akuom, D., & Greenstein, S. (2021). Prospective Teachers’ Design Decisions, Rationales, and Resources: Re/claiming Teacher Agency Through Mathematical Making. In Virtual Annual Meeting of the American Educational Research Association (AERA) . https://bit.ly/3tbXUPP Akuom, D., & Greenstein, S. (2022). The Nature of Prospective Mathematics Teachers’ Designed Manipulatives and their Potential as Anchors for Conceptual and Pedagogical Knowledge. Journal of Research in Science Mathematics and Technology Education , 5 , 109–125. Andersen, H. V., & Pitkänen, K. (2019). 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Whitehouse.Gov. https://obamawhitehouse.archives.gov/the-press-office/2014/06/17/presidential-proclamation-national-day-making-2014 Priestley, M., Biesta, G. J. J., & Robinson, S. (2015). Teacher agency: What is it and why does it matter? In R. Kneyber, & J. Evers (Eds.), Flip the System: Changing Education from the Bottom Up . Routledge. Sarama, J., & Clements, D. H. (2016). Physical and Virtual Manipulatives: What Is Concrete? In P. S. Moyer-Packenham (Ed.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives , (Vol. 7, pp. 71–93). Springer International Publishing. https://doi.org/10.1007/978-3-319-32718-1_4 Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education , 20 (5), 498–505. Stigberg, H. (2022). Digital fabrication for mathematics education: A critical review of the field. 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(2018). Representasjoner i matematikk. 2. https://www.matematikksenteret.no/sites/default/files/attachments/Elever%20som%20presterer%20lavt/P4_M1Representasjoner-i-matematikk_fagtekst.pdf Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology , 18 (1), 37–54. https://doi.org/10.1016/S0193-3973(97)90013-7 Vähäsantanen, K. (2015). Professional agency in the stream of change: Understanding educational change and teachers’ professional identities. Teaching and Teacher Education , 47 , 1–12. https://doi.org/10.1016/j.tate.2014.11.006 Valente, D. J. R. P., Ferretti, F., Martinho, G. P. P. A., Panella, F., & Wanner, M. (2017, November 15). Overview of the Maker Movement in the European Union. JRC Publications Repository. https://doi.org/10.2760/227356 Wells, G. (1999). Dialogic Inquiry: Towards a Socio-cultural Practice and Theory of Education (1st ed.). Cambridge University Press. https://doi.org/10.1017/CBO9780511605895 Footnotes https://www.thingiverse.com/ https://www.printables.com/ Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 07 Apr, 2026 Read the published version in Digital Experiences in Mathematics Education → Version 1 posted Editorial decision: Revision requested 28 Oct, 2025 Reviews received at journal 18 Sep, 2025 Reviews received at journal 18 Sep, 2025 Reviewers agreed at journal 16 Sep, 2025 Reviewers agreed at journal 27 Aug, 2025 Reviewers invited by journal 25 Aug, 2025 Editor assigned by journal 21 Aug, 2025 Submission checks completed at journal 19 Aug, 2025 First submitted to journal 11 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7349219","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":506297393,"identity":"258f071a-a285-4d21-97dd-6804d4fb593d","order_by":0,"name":"Henrik Stigberg","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIie3RsWrDMBCA4ROCaLkHCATaV7DxEAoBv4pEIVmauUsbDAVPLl39GN6SQgcFgbyIdiveqilTB2fL0KFS4tVxxkL1gw8P/uAkA4RCf7DIDy7doDDy71cRBWgvItiRxBFSDhLwBE5EVDBApuxZt9ZAmjL2afdvj4s1o9uMbGa95KZ4vy15A6KgeB+Xu3r5+jQSGTHz/sWauwR4Cxwpzico9bJSOLUkV/3k6/tI0iP5kXoRKYyzs6RBRxogBWV6AvKBDxPjFzNjUShkcSFlXCl3FpGfOUttEnLQs5S91Dt7kKvr6ENts33ef2NdY/eg/0fdPnwInGLWjdVl34ZCodC/6hdXnFeg5gSQZwAAAABJRU5ErkJggg==","orcid":"","institution":"Østfold University College","correspondingAuthor":true,"prefix":"","firstName":"Henrik","middleName":"","lastName":"Stigberg","suffix":""},{"id":506297394,"identity":"2468b942-ec59-45e7-9880-4581c8c78a7f","order_by":1,"name":"Susanne Stigberg","email":"","orcid":"","institution":"Østfold University College","correspondingAuthor":false,"prefix":"","firstName":"Susanne","middleName":"","lastName":"Stigberg","suffix":""}],"badges":[],"createdAt":"2025-08-11 19:23:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7349219/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7349219/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40751-026-00194-3","type":"published","date":"2026-04-07T15:57:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":90392079,"identity":"5abe09f0-df8a-4f14-acea-e8c42e3b13e5","added_by":"auto","created_at":"2025-09-02 08:42:27","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":424044,"visible":true,"origin":"","legend":"\u003cp\u003e(1) Empty number line with whole number digits, (2) and patterns\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7349219/v1/8488a0f24cabe7202ea431ed.jpeg"},{"id":90392084,"identity":"160d646f-808e-4da4-a9f8-c5588e8d9509","added_by":"auto","created_at":"2025-09-02 08:42:27","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":351938,"visible":true,"origin":"","legend":"\u003cp\u003e(1) Fractions and geometry, (2) odd/even numbers, set theory, and whole number addition\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7349219/v1/068c3b254dd74f0e6255a869.jpeg"},{"id":106810671,"identity":"c2877be0-a1c5-4be9-951e-4ecd55474ca0","added_by":"auto","created_at":"2026-04-13 16:16:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1394952,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7349219/v1/e75230f5-948d-4f7d-86dc-490d8a94812f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Unpacking Teachers’ Transformative Agency Following Digital Fabrication Workshops on Making Mathematical Manipulatives","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn this article, we inquire into how teachers can transform their mathematics teaching with manipulatives after being introduced to digital fabrication tools and techniques. Digital fabrication (DF) is the process of translating a digital design developed on a computer into a physical object, e.g., using a 3D printer or laser cutter (Berry et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). In recent years, DF and making have gained interest in STEM education, providing an opportunity for students to develop creativity and real-world problem-solving skills (Perignat \u0026amp; Katz-Buonincontro, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; H. Stigberg, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Adopting a maker mindset, teachers and students can translate abstract ideas into concrete and meaningful experiences (Blikstein, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Ford \u0026amp; Minshall, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; \u003cem\u003ePresidential Proclamation -- National Day of Making, 2014\u003c/em\u003e, 2014). In this article, we explore how teachers reflect on DF for making their own manipulatives - tangible teaching aids designed to support students’ learning of abstract mathematical concepts.\u003c/p\u003e\u003cp\u003ePrevious research has demonstrated that introducing DF into teacher training as a method for making manipulatives fosters innovative learning experiences (Akuom \u0026amp; Greenstein, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Greenstein et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Läufer \u0026amp; Ludwig, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; H. Stigberg et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, there is limited evidence of teachers’ ability to transform their teaching practices after acquiring DF skills. Specifically, there is a lack of understanding of teachers’ agency, a critical quality for teachers when making meaningful changes to their professional environment (Cong-Lem, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Fu \u0026amp; Clarke, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Stigberg et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) found that when teachers applied DF tools to make their own manipulatives, they developed a strong sense of ownership over these resources, beneficial for enhancing the effective utilization of these manipulatives in the long term. Akuom and Greenstein (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) found that DF contributes to pre-service teachers’ pedagogical and conceptual knowledge by enabling them to make agentic design decisions when making manipulatives that promote more learner-centered practices. They suggest that a shift from teachers as consumers to designers and producers of manipulatives enables teachers to take a more active role in utilizing new manipulatives. Despite these findings, the role of DF in fostering teacher agency to transform their teaching practices with manipulatives remains poorly understood.\u003c/p\u003e\u003cp\u003eIn this article, we unpack teachers’ transformative agency, characterized by sense of purpose, competence, autonomy, and reflexivity (Pantić, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) after participating in a professional development program, inquiring into DF for making manipulatives. Over one year, we collaborated with eight in-service teachers within a Community of Inquiry (CoI) exploring DF for making manipulatives. CoI theory emphasizes inquiry as both a tool and a norm in collaborative efforts between teachers and teacher educators to enhance practices (Jaworski, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). While H. Stigberg (2025a) investigated how CoI constructs such as inquiry, engagement, imagination, and critical alignment foster teacher agency, in this article, we analyze teachers’ reflections on the changes in their teaching practices after participating in the CoI. Specifically, we address the following question:\u003c/p\u003e\n\u003ch3\u003eHow can teachers’ transformative agency be characterized after participating in DF workshops for making manipulatives?\u003c/h3\u003e\n\u003cp\u003eIn the following, we provide an overview of manipulatives in mathematics teaching and previous research on DF for making manipulatives. Next, we describe teachers’ transformative agency in general and Pantić’s (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) framework in particular. We then present our study and its results, concluding with a discussion on how DF workshops can foster teachers’ transformative agency in relation to mathematics teaching with manipulatives.\u003c/p\u003e\u003cp\u003eManipulatives in mathematics education\u003c/p\u003e\u003cp\u003eMathematical concepts are inherently abstract and are represented through symbols, drawings, verbal, real-world situations, or tangible objects such as manipulatives. In education, symbols are often overemphasized, while the ability to switch between different representations is crucial for deepening students’ understanding of mathematical concepts (Duval, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Consequently, it is important to encourage teachers to integrate manipulatives into their teaching practices (Brown et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Holmes, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Sowell, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). When used correctly and over a period of time, manipulatives can positively enhance students’ mathematical understanding, making them essential in mathematical education (Carbonneau et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Sowell, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Uttal et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). However, manipulatives are not inherently beneficial and do not convey mathematical knowledge independently. Teachers must tailor manipulatives to fit the classroom, guide students in their use, and facilitate the transition from concrete representation to other forms, such as symbols (Brown et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Sarama \u0026amp; Clements, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Uttal et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). Despite their potential, Marshall and Swan (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) identified several challenges recognized by teachers to use manipulatives in their teaching, including limited access due to economic constraints, material organization, space or time limitations, and issues related to classroom management.\u003c/p\u003e\u003cp\u003eCurrently, teachers often rely on pre-made manipulatives provided by educational material companies, which limits their ability to adapt these resources to their specific teaching needs. While these manipulatives are often well-designed, teachers are restricted to the intended use defined by the manufacturers, lacking opportunities for customization. Hogan et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) examined teacher agency in relation to purchased manipulatives, suggesting that teachers act as agents when selecting from a variety of commercial resources to enhance their pedagogical toolbox. They found that teachers aim to create unique learning experiences tailored to their students’ specific needs, contributing nuance to the debate on commercialization in educational literature. Rather than viewing commercialization as inherently negative, they argue that it offers valuable opportunities for educational enrichment. In contrast, Marshall and Swan (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) highlight challenges teachers face in using commercial manipulatives, including insufficient quantities to cover their classrooms, highlighting that the teachers “do not have enough of the equipment [manipulatives] to go around” (p. 342), limited accessibility, and “the cost of manipulatives made their use problematic” (p. 342). Alternatively, teachers can create their own manipulatives using laminated paper, everyday objects like coins or beans, or crafting materials out of wood. However, these homemade manipulatives can introduce irrelevant properties that might impede students’ learning experiences (Carbonneau et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and may not appear as polished as commercially available options.\u003c/p\u003e\u003cp\u003eBy utilizing DF, teachers could create manipulatives with the precision and accuracy of commercially manufactured options, while maintaining the flexibility to customize them to their needs, as demonstrated by, e.g., Dilling and Witzke (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) making “3D-printed models of graphs of functions for concept formation processes of the concept of derivative” (p. 337). Greenstein and Olmanson (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) provided a course where teachers designed 3D-printed manipulatives to support students’ learning of conic sections, the coordinate plane, and the concept of the definite integral in calculus using the rectangle method. To fully capitalize on DF and its opportunities, teachers need transformative agency to embrace changes in their teaching practices with manipulatives. This involves expanding their repertoire beyond off-the-shelf and hand-crafted manipulatives to incorporate DF technologies, thus enhancing their ability to tailor manipulatives to fit their specific classroom needs. While we do not dispute the idea of teachers as agents when purchasing manipulatives, this article aims to explore how DF can potentially improve teachers’ access to manipulatives and possibly broaden their agentic space, facilitating an enhanced integration of manipulatives into their classroom practice.\u003c/p\u003e\u003cp\u003eDigital fabrication in education\u003c/p\u003e\u003cp\u003eDF is defined as “the process of translating a digital design developed on a computer into a physical object” (Berry et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, p. 168). This process is facilitated by tools such as 3D-printers, laser cutters, or vinyl cutters. 3D-printers can create almost any shape by printing successive thin layers of filament, gradually building up the object from the bottom up. They are cost-effective and are easily placed without the need for additional equipment or environmental adjustments. However, printing large objects can be a time-consuming process. Laser cutters and vinyl cutters work by removing material to create the desired shape. Laser cutters can quickly cut or engrave large areas. However, they are limited to two-dimensional cuts, tend to be more expensive, and require sufficient ventilation to handle generated gases. Vinyl cutters, on the other hand, use a blade to cut shapes in piable materials such as vinyl, paper, or leather. DF technologies are often gathered in so-called FabLabs and maker spaces and can be found at universities, libraries, and schools. Over the past decade, the number of these maker spaces has grown (Valente et al., 2017). Individuals attending these places are referred to as makers, forming part of the maker culture - a movement focused on \u003cem\u003emaking almost anything\u003c/em\u003e using DF tools. The maker culture thrives on the collaborative spirit of sharing personal creations and utilizing the work of others through online platforms like Thingiverse\u003csup\u003e1\u003c/sup\u003e and Printables\u003csup\u003e2\u003c/sup\u003e. Blikstein (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) argues that DF and making should play a major role in education, “bringing powerful ideas, literacies, and expressive tools to children” (p. 2).\u003c/p\u003e\u003cp\u003eDF has been integrated into various educational settings, predominantly in higher education, engineering, and design courses. It has also been used to create teaching aids for subjects such as anatomy, chemistry, and geometric models in mathematics (Ford \u0026amp; Minshall, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Although research on the use of DF for making mathematical manipulatives is limited (H. Stigberg, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), there are notable examples from teacher education. Greenstein et al. (2019) demonstrated that incorporating DF in teacher education can deepen the understanding of mathematics content, curriculum, and pedagogy among teacher students. Similarly, Barbosa and Vale (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) showed that integrating 3D modeling and printing enhances interdisciplinary STEAM learning and problem-solving skills, while also highlighting teacher students’ challenges with mathematical precision and curricular alignment, indicating a need for more pedagogical scaffolding. DF has been employed in teacher professional development programs to enable in-service teachers to make manipulatives. Stigberg et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) emphasize DF’s role in relation to customized teaching activities, manipulatives access, and classroom management, concluding that workshops on DF for making manipulatives\u003c/p\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e“allowed teachers to not only familiarize themselves with DF technologies but also foster a strong sense of ownership over the manipulatives they created. This ownership entails: 1) storing the manipulatives in their classroom with easy access for them and their students, 2) creating customized manipulatives tailored to their students and classroom, 3) room for further adaptation, modification, or expansion of the manipulatives, 4) and the option to reuse the manipulatives for teaching various mathematical concepts” (p. 6).\u003c/p\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eGreenstein \u0026amp; Olmanson (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) summarize that DF technologies can be a catalyst for pedagogical change by enabling teachers to create their own manipulatives. However, Harron et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) identified both affordances, such as facilitating hands-on learning and providing visual support, and constraints, including high costs, tool accommodation difficulties, time limitations, and a sense of pressure to adhere to standardized activities and assessments.\u003c/p\u003e\u003cp\u003eWhile research on DF for making manipulatives has gained traction, the field still requires further consolidation. A particularly overlooked aspect is how teachers can transform their practices by leveraging DF technologies. Teacher agency is a crucial concept for analyzing teachers’ ability to enact change. To date, no study has thoroughly examined and unpacked the characteristics of teachers’ transformative agency following a professional development program for making manipulatives using DF tools. By examining teachers’ transformative agency, we aim to enhance the understanding of the key factors that enable teachers to utilize DF to innovate their teaching practices effectively.\u003c/p\u003e\u003cp\u003eTeachers’ transformative agency\u003c/p\u003e\u003cp\u003eAgency is a concept that examines the extent to which an individual’s autonomy and influence shape their practices and life situations. It encompasses the freedom to actively strive, take initiatives, and impact one’s circumstances (Eteläpelto et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Agency is often linked to the ability to change and develop workplace practices through reflection and action (Cong-Lem, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Goller \u0026amp; Paloniemi, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). It involves engaging with issues deemed worthy of solving, thereby influencing change and learning (Billett, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eCong-Lem (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) conducted a comprehensive review of the literature on teacher agency (TA) to map the field, refine the understanding of the concept, and provide insights for future research. He identified six major themes: (1) the enactment of TA, (2) the role of teacher cognition, (3) influential factors, (4) professional development interventions, (5) TA outcomes, and (6) its change trajectory. Cong-Lem (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) emphasizes that teacher professional development, such as coaching, seminars, and workshops, effectively fosters TA. These approaches empower teachers by promoting research, ownership of educational reforms, and technological competencies, which in turn encourage reflective practices. Through examining their pedagogical beliefs and experiences, teachers enhance their agency, leading to transformative change (Cong-Lem, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Numerous studies highlight the critical role of teachers as change agents, transforming their practices through professional development (Hauge, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003ehäsantanen, 2015). For example, Insulander et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) examined teachers’ agency after participating in a mathematical-didactical professional development program, highlighting that teacher competence enacted in a community setting is a crucial factor in teachers’ agency. Similarly, H. Stigberg (2025) argues that a CoI approach nurtures teacher agency through processes of inquiry, engagement, imagination, and critical alignment.\u003c/p\u003e\u003cp\u003eAccording to Pantić (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), teacher agency can be described by four components: sense of purpose, competence, autonomy, and flexibility. She posits that this “model could be used in empirical studies of teacher agency exploring the transformative potential of teachers within the structural and cultural environments across different school, policy and social contexts” (p. 773). In this article, we have applied her framework to examine teachers’ transformative agency, particularly their use of DF for making manipulatives after participating in a CoI, including several DF workshops. Drawing from previous studies, we propose specific indicators for each component. In the following, we will outline key indicators for the components within the framework.\u003c/p\u003e\u003cp\u003eSense of purpose\u003c/p\u003e\u003cp\u003eTeachers’ sense of purpose for changing their practices is essential to their transformative agency. This can be demonstrated by their recognition of DF as a valuable resource for making manipulatives and their self-identification with the maker culture. Additional indicators might include their reflections on customizing manipulatives to suit students and classrooms better, developing flexible manipulatives for a range of mathematical concepts (H. Stigberg et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and utilizing materials that are cheaper and more accessible than purchased manipulatives, provided they have access to DF tools (Harron et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eCompetence\u003c/p\u003e\u003cp\u003eCompetence in the context of making manipulatives using DF encompasses many aspects, e.g., proficiency in operating DF technologies such as 3D printers and laser cutters, using diverse software tools to find, adapt or create digital models, design competence to drive innovation processes, as well as pedagogical and mathematical knowledge to customize manipulatives for the classroom (S. K. Stigberg et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAutonomy\u003c/p\u003e\u003cp\u003eExternal factors, such as policy, school leadership, and available resources, heavily influence teachers’ ability to change their teaching practices. For instance, Frost (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) noted that while strides were made in classroom environment and teaching methods, curriculum content remained constrained mainly by policy, highlighting a significant barrier to teacher agency. Furthermore, resources such as time and access to necessary DF technologies influence teachers’ ability to enact changes. Andersen and Pitkänen (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) reported that “lack of time, lack of money, DF machines and other resources” (p. 9) were important factors for not changing activities in school.\u003c/p\u003e\u003cp\u003eReflexivity\u003c/p\u003e\u003cp\u003eCong-Lem (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) emphasizes that the transformation of teacher agency often begins with teachers questioning and reflecting on their own pedagogical beliefs and conceptions, making sense of their experiences. Wells (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) defines reflexivity in professional development as the metacognitive process of reflecting on the knowledge being created or previously acquired, as well as the tools and practices employed in the process. In our specific context, this means teachers might reflect on the workshops that introduce DF, assess the manipulatives created using DF, and evaluate how their teaching practices have evolved after the workshops.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eUnit of analysis\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit of analysis\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePotential indicators of teachers’ transformative agency using DF for making manipulatives\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSense of purpose\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHow teachers describe their sense of purpose of\u003c/p\u003e\u003cp\u003e• the workshops\u003c/p\u003e\u003cp\u003e• DF for making manipulatives.\u003c/p\u003e\u003cp\u003e• their practice as mathematics teachers\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCompetence\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHow teachers express their competence in relation to\u003c/p\u003e\u003cp\u003e• mathematics didactics\u003c/p\u003e\u003cp\u003e• DF technologies\u003c/p\u003e\u003cp\u003e• design and innovation processes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAutonomy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHow teachers define their autonomy in relation to\u003c/p\u003e\u003cp\u003e• school policy and leadership\u003c/p\u003e\u003cp\u003e• DF technologies\u003c/p\u003e\u003cp\u003e• having time\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eReflexivity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe teachers’ ability to “step outside” themselves and reflect on:\u003c/p\u003e\u003cp\u003e• the workshops\u003c/p\u003e\u003cp\u003e• the created manipulatives\u003c/p\u003e\u003cp\u003e• their manipulative-based teaching practice\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eTo address our research question, \u003cem\u003eHow can teachers’ transformative agency be characterized after participating in DF workshops for making manipulatives?\u003c/em\u003e, we conducted interviews with seven teachers from three K-7 schools in Norway, all of whom participated in a year-long series of eight full-day workshops. Below, we present an overview of the workshops, alongside details of the data collection and analysis employed in this study.\u003c/p\u003e\u003cp\u003eWorkshops in DF for making manipulatives\u003c/p\u003e\u003cp\u003eInspired by Community of Inquiry (Jaworski, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), we (as one teacher educator and one DF expert), together with two teacher education colleagues, conducted eight monthly full-day workshops together with eight elementary teachers (referred to as teachers) with previous experience from using manipulatives to inquire together into DF and its potential to develop practices for making and using manipulatives. In the workshops, we introduced DF tools and techniques, including:\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eDF sharing platforms (e.g., Thingiverse and Printables),\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e3D modelling and printing using Tinkercad and Prusa printer,\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e2D modelling and cutting using Cricut vinyl-cutter and Glowforge laser cutter,\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003edesign thinking process to support the design of new manipulatives.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThroughout the workshops, we encouraged teachers to explore the potential applications of the introduced DF technologies. Our objective was to foster critical reflection and enable the teachers to reshape their practices in relation to manipulatives, all while providing them with a range of tools and resources throughout the workshop series. We used the FACS model (H. Stigberg et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; S. K. Stigberg et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) for the first four workshops to scaffold DF skills, arranged in increasing complexity, from finding ready-made manipulatives to designing new ones. FACS stands for Finding, Adapting, Creating, and Sharing manipulatives.\u003c/p\u003e\u003cp\u003eEach of these workshops was structured into four components: reflections, lectures, group work, and presentations, drawing inspiration from Frank et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The workshops commenced with group reflections, which fostered discussions on the use of manipulatives in the classroom and encouraged reflection. Subsequently, we provided a brief lecture covering topics such as DF tools and techniques, teaching mathematics, and examples of manipulatives to illustrate mathematical concepts. The main part of each workshop involved collaborative group work, providing teachers with a hands-on, collaborative inquiry experience. Finally, teachers presented their manipulatives and outlined their intended teaching activities. Between workshops, teachers utilized their manipulatives in their classrooms. For more extensive information, the design and implementation of the workshops are described in H. Stigberg et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)d Stigberg et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). During the fifth workshop, teachers gave individual presentations reflecting critically on previous DF workshops, one or more selected manipulatives they had created, and the classroom activities that incorporated these manipulatives (see H. Stigberg et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In the second part of the series, the workshops shifted focus to extend hands-on experience for teachers. While we continued to share experiences, the emphasis was placed on providing teachers with more autonomy to develop their manipulatives. Our contributions were reduced to brief introductions on topics such as design thinking, programming-based modeling, and sharing on online platforms. Beyond these introductions, our role transitioned to providing support whenever necessary. As the year concluded, we organized a local Maker Faire, inviting colleagues, school management, a nearby science center, and other interested parties. This event provided an opportunity for teachers to showcase their work through posters and talks. A comprehensive summary of all the workshops is detailed Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eOverview of workshop content categorized by digital fabrication, pedagogy, mathematical content, and share\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDigital Fabrication\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePedagogy\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMathematical content\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eShare\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFind \u003c/p\u003e\u003cp\u003eWorkshop 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThingiverse\u003c/p\u003e\u003cp\u003ePrintable\u003c/p\u003e\u003cp\u003ePrusa Slicer\u003c/p\u003e\u003cp\u003e3D printer\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRepresentations of mathematical concepts\u003c/p\u003e\u003cp\u003eFour principles for working with manipulatives (Svingen, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eGeometrical concepts and properties\u003c/p\u003e\u003cp\u003e\u003cem\u003eExample: What object does not fit?\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eIn the first four workshops, teachers shared by: \u003c/p\u003e\u003cp\u003ePresenting the manipulative and planned classroom activity at the end of each workshop\u003c/p\u003e\u003cp\u003eand\u003c/p\u003e\u003cp\u003eSharing experiences from their teaching with the manipulatives at the beginning of the following workshop.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eAdapt\u003c/p\u003e\u003cp\u003eWorkshop 2\u003c/p\u003e\u003cp\u003eAdapt/Create\u003c/p\u003e\u003cp\u003eWorkshop 3\u003c/p\u003e\u003cp\u003eAdapt/Create\u003c/p\u003e\u003cp\u003eWorkshop 4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eTinkercad\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInquiry-based teaching\u003c/p\u003e\u003cp\u003eModelling manipulatives for customized teaching\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNumber concepts and properties\u003c/p\u003e\u003cp\u003e\u003cem\u003eExample: Even and uneven numbers pieces\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFour stage framework for using manipulatives in teaching (Malmer, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1997\u003c/span\u003e)\u003c/p\u003e\u003cp\u003eModelling manipulatives for customized teaching\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePosition system, positive and negative numbers, spatial geometry\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLaser cutter\u003c/p\u003e\u003cp\u003eVinyl cutter\u003c/p\u003e\u003cp\u003eInkscape\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInquiry-based teaching\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUsing different representations\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eMaker workshops\u003c/p\u003e\u003cp\u003eWorkshop 5\u003c/p\u003e\u003cp\u003eWorkshop 6\u003c/p\u003e\u003cp\u003eWorkshop 7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDesign thinking\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMixing mathematical content to challenge students\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePresentation of manipulative and critical reflections (H. Stigberg et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModeling in 2D and 3D using programming\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c4\" namest=\"c3\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eSharing experiences from their teaching with the manipulatives at the beginning of the workshop\u003c/p\u003e\u003cp\u003ePlanning Maker Faire, including making posters\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eContributing to online sharing platforms\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaker Faire\u003c/p\u003e\u003cp\u003eWorkshop 8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSharing manipulatives to online platform\u003c/p\u003e\u003cp\u003ePresenting their manipulatives and posters to invited audience\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eData collection and analysis\u003c/p\u003e\u003cp\u003eFollowing the Maker Faire, the first author conducted interviews with seven of the eight participating teachers from three K-7 schools in Norway, approximately one to two weeks after the event. Unfortunately, the eighth teacher had to withdraw from the program earlier in the year due to illness. These interviews were designed to facilitate a deeper reflection among the teachers on how their involvement in the CoI on DF for making manipulatives had influenced their overall teaching practices, rather than focusing solely on their agency. The semi-structured interviews took place in the teachers’ respective schools and lasted between 30 minutes and 53 minutes, with an average of 43 minutes. Each interview was audio recorded to ensure accuracy and was subsequently transcribed in full, providing a comprehensive record of teachers’ insights and reflections.\u003c/p\u003e\u003cp\u003eWe applied Pantić’s (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) framework for our interview analysis, focusing on the components of sense of purpose, reflection, competence, and autonomy (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Each author independently conducted a thematic analysis of the transcribed interviews for each component of the framework, gathering relevant citations with timestamps. Through discussion and comparison, we identified recurring themes that emerged across the data, aligning them with each framework component. Any discrepancies encountered during the coding process were collaboratively addressed and resolved. We developed thematic maps for each component, following the guidelines of Braun and Clarke (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), and revisited relevant sections of the transcribed data to ensure the validity of our findings. In the presentation of the results, teachers are referred to by codes T1-T8 (T6 is missing and did not participate in the final interview), providing anonymity while maintaining clarity in analysis.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eSense of purpose\u003c/p\u003e\u003cp\u003e\u0026ldquo;I finally have a tool to create the things I have always made out of cardboard\u0026rdquo;, states T2, while T5 is convinced that she \u0026ldquo;has the motivation to continue\u0026rdquo; using DF for making manipulatives. Teachers\u0026rsquo; sense of purpose for making manipulatives with DF is perceived as more durable, more flexible, and without disturbing elements.\u003c/p\u003e\u003cp\u003eThe teachers emphasize that manipulatives created using DF are more durable due to the material, but also due to students taking better care of them, and thereby potentially longer-lasting. T5 comments that they created \u0026ldquo;good manipulatives that are also durable\u0026rdquo;, while T8 agrees that \u0026ldquo;these [manipulatives] last so much longer\u0026rdquo;. T4 elaborates that, \u0026ldquo;[t]his is more sustainable ... tend to take better care of manipulatives that are durable\u0026rdquo;. She revisits her statement later in the interview, noting that taking care also can be part of mathematical activities, \u0026ldquo;the children also have to be involved in [picking up and] sorting, and there is learning in that, in a way, finding all the numbers. What [number] is missing here?\u0026rdquo;.\u003c/p\u003e\u003cp\u003eCompared to purchased manipulatives, the DF-created manipulatives were perceived as more flexible in two ways: providing the opportunity to use the same manipulatives for various mathematical topics, as well as using the same manipulatives for various difficulty levels, enabling differentiated teaching. T2, T3, T4, and T5 all mention their use of the DF-created empty number line (ENL) for diverse teaching activities (See Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eE.g., T2 highlights activities focused on zero with whole and decimal number variations, stressing the need to understand \u0026ldquo;something in between [whole numbers], because you can also work with a section of the empty number line as a decimal\u0026rdquo;. T4 varied the ENL with 3D printed cubes and laser-cut numbers, allowing exploration from \u0026ldquo;simple patterns with color to quite advanced number sequences\u0026rdquo; with the same tool. T2 describes a second DF-created manipulative for geometry, fractions, and percentages, noting, \u0026ldquo;geometric shapes are both fractions and percentages\u0026rdquo; (See Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eT8 shares her shift from using stencils and textbooks to DF-created manipulatives for odd/even numbers, set theory, and whole number addition (See Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). She explains, \u0026ldquo;We came up with something that you can use for both parts, so it became easier then, less work for me\u0026rdquo;.\u003c/p\u003e\u003cp\u003eThe teachers comment that manipulatives were previously often associated with students with special needs. However, their DF-created manipulatives can be used for varying levels of difficulty, allowing all students to use the same manipulative, which conceals who might be working at different mathematical levels. T2 highlights the \u0026ldquo;unlimited number of tasks [using the same manipulatives], and in terms of differentiation, it is also completely unique.\u0026rdquo; T5 remarks, \u0026ldquo;So it seems to have been much easier when we bring in good, durable manipulatives. You can get the kids started with the same manipulatives but with different starting points\u0026rdquo;. T8 emphasizes the manipulatives\u0026rsquo; inclusivity, saying, \u0026ldquo;Because they are using the same manipulatives, it makes a big difference. It becomes much easier to be discrete about special education when you can create the manipulatives yourself\u0026rdquo;, supporting a more inclusive classroom environment. T8 sums it up by stating, \u0026ldquo;And what is brilliant about this [DF-created manipulative] is that you can use it for so many things, which you cannot do with laminated paper in the same way, without giving it more of a special-education feel. This one, everyone uses\u0026rdquo;.\u003c/p\u003e\u003cp\u003eFinally, teachers make a conscious effort to create manipulatives free from distracting features, unlike purchased ones, which they describe as colorful and complex. T3 notes that different colors distract students, saying: \u0026ldquo;[The students] can have their favorite [color]... While here, \u0026hellip; they just accept them because they are all the same color\u0026rdquo;. T5 adds, \u0026ldquo;[previously] they started building cars or houses...these [purchased manipulatives] are different colors and...more fun to spin them, as there is a hole through them\u0026rdquo;. T8 also advocated for simple manipulatives, noting that students overgeneralize, especially with fractions. \u0026ldquo;To see that this is one half and it is blue, and then...cannot understand that it might as well be red, so the students become so fixated on the appearance\u0026rdquo;.\u003c/p\u003e\u003cp\u003eCompetence\u003c/p\u003e\u003cp\u003e\u0026ldquo;I am most satisfied with gaining insight into how to make manipulatives and [that I] starting to think a bit differently\u0026rdquo;, explains T3. Teachers\u0026rsquo; competence can be categorized into technological competence and teaching competence with DF-created manipulatives.\u003c/p\u003e\u003cp\u003eTheir expertise in DF technology varies; some feel confident using the technology, while others seek more hands-on training. This difference might be influenced by their previous technical experience and their level of engagement in workshop hands-on activities. All teachers demonstrate a willingness to experiment and are not afraid of failing when using DF technologies, despite some feeling uncertain. They express confidence in how to start using the 3D printers at their schools. Before the workshops, no one had attempted to use the printers due to uncertainty about the technology. T4 says, \u0026ldquo;Several people at our school have used them, so it is not so intimidating to try and initiate it\u0026rdquo;. T1 states, \u0026ldquo;Initially, with 3D printing, I had never used it myself, even though we had it here. I never dared to sit down and use it, but\u0026rdquo;. T8 added, \u0026ldquo;But now we know it is possible, right? So when it becomes available, it is not difficult to try and start experimenting and learning through trial and error\u0026rdquo;.\u003c/p\u003e\u003cp\u003eAll teachers demonstrated competence in finding and printing 3D models. T1 states, \u0026ldquo;But 3D printing, I can do\u0026rdquo;. T2 shares, \u0026ldquo;It is about discovering things and finding tools that students can benefit from using in various contexts\u0026rdquo;. T3 adds, \u0026ldquo;We have learned where to find things, what and where to search for, and what can be found\u0026rdquo;. Some teachers found it challenging to search for manipulatives on online platforms, due to their English language skills. T3 noted, \u0026ldquo;There is an incredible amount out there, and at the beginning, we spent a lot of time thinking, \u0026lsquo;What do we search for?\u0026rsquo; Since things need to be searched in English, you have to be somewhat proficient in it\u0026rdquo;.\u003c/p\u003e\u003cp\u003eTeachers consider modeling in both 2D and 3D more challenging than finding existing manipulatives; still T7 expresses confidence in adapting and creating 3D manipulatives. \u0026ldquo;With these websites where you can find inspiration and... Tinkercad, being able to edit things yourself, create your own things. I feel I can do that quite well\u0026rdquo;. However, teachers feel uncertain about operating the laser cutter, mainly because it has been accessible only at the university and not in schools. For example, T1 mentions, \u0026ldquo;I would probably need a bit more training in it\u0026rdquo;. T8 added, \u0026ldquo;I am somewhat unsure about starting with it myself\u0026rdquo;. Nonetheless, both T2 and T5, who are from different schools, explicitly note that investing in a laser cutter is prioritized because of its usefulness for making manipulatives.\u003c/p\u003e\u003cp\u003eAll teachers agree that they have enhanced their mathematical teaching competence, although the extent to which they have experimented with an inquiry-based approach using manipulatives varies based on their prior experience and practice. T1, who previously had little experience with inquiry-based teaching using manipulatives, states that theyte have \u0026ldquo;perhaps become more aware of the manipulatives\u0026rdquo;. He recognizes the benefits of using manipulatives for more open-ended tasks, like his multiplication puzzle, where \u0026ldquo;multiple equations could give the same number\u0026rdquo;. Teachers have explicitly mentioned how making manipulatives together in a CoI has fostered their inquiry-based teaching with more discussions and open-ended tasks. T4 states, \u0026ldquo;And now there has been more focus on having the kids investigate a bit more, to show something, try it out, talk about it, and find out what they have achieved. Not so concerned with filling out sheets or books or booklets\u0026rdquo;. T5 says, \u0026ldquo;I think I have become even more fond of the verbal part of mathematics, and that I have become more confident in it in many ways. There is a greater focus on understanding and talking about math rather than just doing math\u0026rdquo;. T7 is still hesitant managing whole-class inquiry-based teaching using manipulatives, saying, \u0026ldquo;A bit uncertain about how that would work, we might need more manipulatives. Maybe present it in a slightly different way. I am not quite sure, have not thought it through very well\u0026rdquo;.\u003c/p\u003e\u003cp\u003eAutonomy\u003c/p\u003e\u003cp\u003eTeachers\u0026rsquo; autonomy can be characterized by time constraints at schools, access to resources, power structures, and collaboration with colleagues and teacher educators.\u003c/p\u003e\u003cp\u003eThe teachers would like to have more time to be creative and develop new manipulatives and lesson plans. T3, T5, and T8 explicitly mention it should be regularly scheduled every week for 1\u0026ndash;3 hours, while T4 prefers a maker day similar to the workshops, which she finds very beneficial. In contrast, the teachers experience a lack of time within the school day to be creative and design new manipulatives. They mention that no specific time is allocated for this, or that the allocated time is used up with other tasks. \u0026ldquo;Yes, we have tried and we have made some dice and such, but the dilemma is the time\u0026rdquo; says T4, and to manage to create manipulatives, she argues that she needs to take \u0026ldquo;extra time\u0026rdquo;. T5 explains, she has \u0026ldquo;hours allocated for working on IT [but they] have instead been used for substitute teaching\u0026rdquo;. However, DF might help to save time compared to hand-crafting manipulatives, e.g., T1 comments \u0026ldquo;I am really happy to find things that are already made. We save so much time because it is something we do not have much of, right? It is hectic workdays in school\u0026rdquo;, while T8 expresses: \u0026ldquo;Having them [the DF created manipulatives] here meant that you had much less work in preparing, and the students recognize the manipulatives\u0026rdquo;.\u003c/p\u003e\u003cp\u003eThe teachers list two types of resources that are important for changing their teaching practice: DF tools and digital models to download. Most teachers do not have access to commercial manipulatives, so providing an opportunity to download digital models or create their own manipulatives gives teachers more autonomy in their teaching and easy access to them, as they are stored in their classroom.\u003c/p\u003e\u003cp\u003eTeachers emphasize the importance of easy access to DF tools. Each of the participating schools had one or two 3D printers, which were sometimes poorly maintained and situated in inconvenient locations, such as in the library, where students had access. As T2 expresses, \u0026ldquo;Yes, well, I was down there checking out the 3D printer today, but someone was using it. So, I could not use it, and the other one is still broken. I talked to [name of IT responsible person] about how bad it is, but I mostly just look at what is available [referring to online platforms such as Thingiverse and Tinkercad]\u0026rdquo;. Limited accessibility challenges teachers who wish to use the 3D printer whenever possible. None of the participating schools had a laser cutter, which teachers particularly desire because it produces manipulatives more quickly. T5 reveals that her school\u0026rsquo;s principal announced, \u0026ldquo;a laser cutter is at the top of the list\u0026rdquo; when investing in new equipment. The teachers were positive about the online platforms, such as Thingiverse or printables, which allow them to find and download pre-designed models. There is also a wish among teachers for establishing a DF community within their school or municipality, so they are not solely responsible for facilitating all DF-related activities. As T7 mentioned, \u0026ldquo;\u0026hellip;a place where you can go. We briefly talked about how if there were a kind of communal place, like a Maker Space, then the municipality would have it\u0026mdash;a place where we could bring our ideas or models and have them made, which might encourage us to do it more often\u0026rdquo;.\u003c/p\u003e\u003cp\u003eThe teachers highlight the importance of involving school leadership in the project and presenting the workshop results to them as they hold the power to prioritize investments in DF technologies and can provide the means for teachers to share their experiences with colleagues at each school. For instance, T1 noted, \u0026ldquo;The assistant principal, she was at the university [participating in the last workshop], \u0026hellip; and she said that we must share with each other. So we will likely set aside some time in the fall to share more information about what we have done and how it can be used\u0026rdquo;. This sharing is crucial, even though teachers might encounter resistance from colleagues who have not attended the workshops. While school leaders have approved all teachers\u0026rsquo; participation in the workshops, teachers feel that the project was not consistently prioritized. Consequently, the successful implementation of DF in their practice largely depends on the teachers\u0026rsquo; own initiative and engagement.\u003c/p\u003e\u003cp\u003eFinally, teachers underscore that collaboration during the workshops with colleagues from the same and other schools, as well as with us as teacher educators, has been essential for transforming their teaching practices with manipulatives. Collaboration with colleagues has been important on two levels. Firstly, interactions with colleagues from different schools provided inspiration, posed challenging questions, and offered valuable tips. Secondly, teachers emphasize the importance of having a colleague from their school with whom they can continue to refine the use of manipulatives in teaching, while also sharing the same set of manipulatives.\u003c/p\u003e\u003cp\u003eReflexivity\u003c/p\u003e\u003cp\u003eTeachers\u0026rsquo; ability to self-reflect varied in the interviews. Generally, the teachers acknowledge that the DF-created manipulatives have transformed their approach, although in different ways. Most teachers observed that the DF-created manipulatives facilitate collaborative and open-ended inquiry, promoting student collaboration and teacher-student discussions. As T5 remarks, \u0026ldquo;So, it [the teaching] is perhaps a much more open teaching approach than before\u0026rdquo;. T4 notes how these manipulatives shifted the focus toward inquiry. \u0026ldquo;When children work with sheets, it is somewhat about getting it done\u0026rdquo;, but using the DF-created manipulatives \u0026ldquo;leads to more reflection and more thought about what you [referring to the students] are doing, and that you can collectively see [different solutions]\u0026rdquo;. T5 also reflected that her teaching practice has become more inquiry-oriented, with students not immediately seeking help when they encounter difficulties. Instead, they \u0026ldquo;might also become a bit more open than they have been before, more curious, and wanting to explore more in mathematics\u0026rdquo;.\u003c/p\u003e\u003cp\u003eThe teachers also mentioned that students often invent new ways to use the manipulatives and come up with unique solutions in their inquiry with the DF-created manipulatives. T5 shares an example: \u0026ldquo;However, you do get inspired when you see how the children choose to use it, or when even more questions arise than before\u0026rdquo;. She had not anticipated that open-ended inquiry with the DF-created manipulatives would also lessen the expectation that the teacher always provides the correct and only answer. Reflecting on their teaching methods before introducing DF-created manipulatives, teachers indicated a greater reliance on textbooks, which typically involved more individual, non-inquiry activities on paper. However, T1 noted that while the workshops and the ability to create manipulatives have transformed his approach in small special-needs groups, they have not impacted his full-class teaching. T1 explained that inquiry-based teaching and the use of manipulatives generate noise and disruption, straying from the usual classroom dynamics.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe concept of teacher agency, while useful for understanding how teachers engage with policy and enact teaching practices, often suffers from imprecise descriptions (Priestley et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In the context of DF within teacher training, this study seeks to unpack how DF can provide agency to teachers to transform their manipulative-based teaching practices, fostering innovative learning experiences as described by previous research (Akuom \u0026amp; Greenstein, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Greenstein et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; L\u0026auml;ufer \u0026amp; Ludwig, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; H. Stigberg et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2023\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). By applying Pantić\u0026rsquo;s (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) framework, which encompasses four dimensions: sense of purpose, competence, autonomy, and reflexivity, we analyze how teachers change their teaching practices following their participation in a professional development program, inquiring into DF for making manipulatives. The framework aids in pinpointing areas where transformative agency is successful and where challenges persist, such as autonomy and competence. Our article reveals that while DF broadens teachers\u0026rsquo; agentic space by enabling manipulative creation rather than mere selection (Greenstein \u0026amp; Olmanson, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), its adaptation varies across teachers.\u003c/p\u003e\u003cp\u003eOur results provide a nuanced view of Pantić\u0026rsquo;s dimensions of transformative agency post-DF workshops for making manipulatives enriching existing literature by highlighting the complexities, opportunities and challenges faced by teachers, leading to three key implications: DF enables teachers to make relevant manipulatives; DF-created manipulatives support changes in teaching practices; and the results underscore the need for supportive infrastructure for teachers to become makers in education.\u003c/p\u003e\u003cp\u003eDigital Fabrication enables teachers to make relevant manipulatives\u003c/p\u003e\u003cp\u003eAll teachers acknowledge the transformative potential of DF in making high-quality manipulatives. DF enables them to make manipulatives that are durable and flexible, which integrate seamlessly into teaching, enhancing students\u0026rsquo; focus on mathematical concepts rather than the manipulatives themselves. This reflection corresponds with Uttal et al. (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), who argue \u0026ldquo;that the manipulatives become highly familiar and hence less interesting as objects in their own right\u0026rdquo; (p. 50), allowing students to focus on the mathematical concept and not the manipulatives as objects in their own right.\u003c/p\u003e\u003cp\u003eTeachers appreciate DF for its ability to create simple, distraction-free objects, contrasting with commercially available manipulatives, which often feature unnecessary distractions such as vibrant colors or complex designs. This echoes Carbonneau et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), who advocate for \u0026ldquo;bland\u0026rdquo; manipulatives to promote problem-solving. Although none of the teachers commented on hand-crafted manipulatives having distracting features, they are perceived as less durable, which affects their sustained use.\u003c/p\u003e\u003cp\u003eWhile the concept of teachers acting as agents in purchasing manipulatives is valid (Hogan et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), we argue that DF significantly enhances teachers\u0026rsquo; access to manipulatives, broadening their agentic space and facilitating easier integration of manipulatives into classroom practices.\u003c/p\u003e\u003cp\u003eIn conclusion, teachers\u0026rsquo; transformative agency is reflected in their preference for DF-created manipulatives, prioritizing manipulatives that are distraction-free and durable, thereby enriching students\u0026rsquo; engagement with core mathematical concepts.\u003c/p\u003e\u003cp\u003eDF-created manipulatives support changes in teaching practices\u003c/p\u003e\u003cp\u003eTeachers reported that DF-created manipulatives shifted their teaching towards a more inquiry-based approach, facilitating student collaboration, enabling students to discuss various solutions, some of which were unexpected by the teachers. This dynamic also encouraged teachers to reflect alongside their students. This aligns with Greenstein and Olmanson (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), who highlight that DF technologies can catalyze pedagogical change by enabling teachers to create their own manipulatives. However, not all teachers found DF-created manipulatives transformative across all settings. One teacher noted positive changes in small, special-needs groups but faced challenges with full-class instruction due to perceived noise and disruption, a concern echoed in Marshall and Swan (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eFurthermore, it is important to recognize that our results are deeply connected to the context of the workshops the teachers attended, emphasizing inquiry-based teaching. Participation in a CoI encouraged teachers to reflect on their practices and pedagogical beliefs, making reflexivity a key aspect of this process. Through making and using DF-created manipulatives, teachers engaged in ongoing reflection and improvement of their teaching strategies.\u003c/p\u003e\u003cp\u003eNavigating the Path to Becoming a Maker in Education\u003c/p\u003e\u003cp\u003eOur results underscore that technological competence is essential for teachers to transform their practices, as highlighted by Hauge (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and V\u0026auml;h\u0026auml;santanen (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Teachers actively engage with maker culture by downloading and 3D printing manipulatives, aligning with Hogan et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), who emphasize that teachers act as agents in choosing resources to enhance their pedagogical approaches.\u003c/p\u003e\u003cp\u003eIn line with Harron et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), we see advantages of our workshops, such as facilitating hands-on learning, and constraints of DF technologies, including high costs, tool accommodation difficulties, time limitations, and a sense of pressure for teachers to adhere to standardized activities, lessons, and assessments. Successfully integrating DF technologies requires access to these tools and time\u0026mdash;resources often scarce, as noted by Andersen and Pitk\u0026auml;nen (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) who mention \u0026ldquo;lack of time, lack of money, DF machines and other resources\u0026rdquo; (p. 13) as barriers to educational innovation. Increasing DF access can involve utilizing communal Maker Spaces or forming partnerships with universities equipped with DF technologies, as demonstrated in this project, bridging the gap between educational potential and practical implementation.\u003c/p\u003e\u003cp\u003eTo fully embrace maker culture and contribute to the development of the teaching profession as part of the maker culture, we suggest that teachers be allocated time weekly to cooperate with colleagues and teacher educators in developing their manipulatives. Moreover, they require access to DF technologies, especially laser cutters and 3D printers. It is essential not only to have the equipment but also to ensure easy access, meaning it should be nearby, available, and well-maintained. To address these challenges, we propose fostering closer connections between local makerspaces and schools. Additionally, we encourage teachers to share their digital source files, thereby broadening the repertoire of well-designed manipulatives on online sharing platforms, contributing to the maker culture.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u003cp\u003eNo external funding.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eWe, the undersigned authors, declare that we have all contributed substantially to the research and preparation of this manuscript, fulfilling the requirements for authorship. H.S had a lead in the scientific work, data collection, and writing process. The analysis was an equally shared workload. S.S contributed to the scientific work and the discussion section in the manuscript. Both authors reviewed and proofread the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData related to the study were collected after approval from the national Data Protection Official for Research (Norsk Senter for Forskningsdata), following all the regulations and recommendations for research with people. The transcribed data in Norwegian are available from the authors upon reasonable request and with the restrictions regarding protecting study participant privacy.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkuom, D., \u0026amp; Greenstein, S. (2021). Prospective Teachers\u0026rsquo; Design Decisions, Rationales, and Resources: Re/claiming Teacher Agency Through Mathematical Making. 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Manipulatives are fundamental for helping students grasp abstract mathematical concepts. However, integrating DF into teaching practice requires more than just access to technology; it demands a shift in teachers\u0026rsquo; transformative agency. This paper presents the experiences of eight teachers who participated in a series of eight full-day workshops over a span of one year, focusing on making mathematical manipulatives using DF. Through interviews, the teachers offered insights into their transformative agency, detailing their sense of purpose, competency, autonomy, and reflexivity. Our results highlight the complexities, opportunities, and challenges encountered by these teachers as they navigated the integration of DF into their teaching practice. Our study led to three key implications: DF enabels teachers to create manipulatives that are pedagogically relevant; DF-created manipulatives support changes in teaching practices, showcasing teachers' transformative agency; and there is a critical need for supportive infrastructure to facilitate teachers becoming makers in education. The paper underscores the potential of DF to transform mathematics education while emphasizing the importance of providing sustained support to realize this potential fully.\u003c/p\u003e","manuscriptTitle":"Unpacking Teachers’ Transformative Agency Following Digital Fabrication Workshops on Making Mathematical Manipulatives","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-02 08:42:22","doi":"10.21203/rs.3.rs-7349219/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-28T15:35:10+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-18T21:32:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-18T08:45:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"236875664818474228523004724762720532472","date":"2025-09-16T13:12:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"271612945923183166709862879208066568398","date":"2025-08-27T09:49:36+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-25T09:07:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-21T07:44:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-20T00:33:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Digital Experiences in Mathematics Education","date":"2025-08-11T19:11:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"digital-experiences-in-mathematics-education","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"deme","sideBox":"Learn more about [Digital Experiences in Mathematics Education](http://link.springer.com/journal/40751)","snPcode":"40751","submissionUrl":"https://submission.nature.com/new-submission/40751/3","title":"Digital Experiences in Mathematics Education","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"805f2d84-16a3-4987-a5f9-ab3ce8f27632","owner":[],"postedDate":"September 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-13T16:14:38+00:00","versionOfRecord":{"articleIdentity":"rs-7349219","link":"https://doi.org/10.1007/s40751-026-00194-3","journal":{"identity":"digital-experiences-in-mathematics-education","isVorOnly":false,"title":"Digital Experiences in Mathematics Education"},"publishedOn":"2026-04-07 15:57:22","publishedOnDateReadable":"April 7th, 2026"},"versionCreatedAt":"2025-09-02 08:42:22","video":"","vorDoi":"10.1007/s40751-026-00194-3","vorDoiUrl":"https://doi.org/10.1007/s40751-026-00194-3","workflowStages":[]},"version":"v1","identity":"rs-7349219","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7349219","identity":"rs-7349219","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}