Integrating STEAM via virtual reality: a TPACK-focused training model for pre-service secondary mathematics teachers using NeoTrie VR

Introduction: This paper presents the findings from the second iteration of a study aimed at enhancing pre-service secondary math teachers’ competence in integrating immersive virtual reality (IVR) into 3D geometry education. The second iteration builds on the first cycle’s exploratory phase, addressing the need for more structured guidance and hands-on experience in using IVR for STEAM-focused teaching.

Methods: The study involved 33 pre-service teachers who participated in focused training sessions on NeoTrie VR, including collaborative design of teaching sequences, peer feedback, and a final presentation. The TPACK (Technological, Pedagogical, and Content Knowledge) framework was used to assess the participants’ development.

Results: The analysis of the participants’ work revealed significant improvements, especially in the technological components of TPACK. A 15.5% increase in the average score of the final TPACK-based assignment was observed between the first and second cycles, indicating that the structured training led to a higher level of competence in using IVR for teaching.

Discussion: These findings highlight the importance of structured training in IVR for pre-service teachers. By overcoming initial technological barriers and building confidence, the training enabled teachers to effectively integrate NeoTrie VR into their future mathematics teaching, transforming traditional teaching and learning processes.

Introduction

Virtual reality stands out in educational contexts for its strong potential to transform how students interact with and understand complex subjects, like STEAM¹ disciplines, particularly mathematics (Di Natale et al., 2020; Slater and Sánchez-Vives, 2016). According to the systematic review conducted by Tapia (2024), VR in higher education reinforces learning objectives and develops 21st-century skills, such as engagement (71%), creativity (57%), and motivation (92%), fostering autonomy and collaborative work in safe and inclusive environments. Concretely, immersive virtual reality (IVR) represents a significant advance in mathematics education, facilitating interactive experiences that improve traditional methods (Schnack et al., 2019). Thanks to the simulation of realistic environments, the use of Immersive Virtual Reality (IVR) allows students to explore complex concepts in a meaningful way, enhancing the development of mathematical competence, which goes beyond simple computational skills and includes a deep understanding of mathematical principles, problem-solving skills, and the ability to apply mathematical knowledge in various contexts (Corrêa and Haslam, 2021).

Despite these benefits, incorporating IVR into classroom practice presents notable challenges. Awoyemi et al. (2024) emphasize that effectiveness of IVR-based learning depends largely on teachers’ knowledge and training underscoring the need for well-designed professional development programs to fully exploit its educational potential. Integrating these technologies is not merely a matter of adding a new tool, it compels teachers to reconsider the dynamic balance among the three core elements: content, pedagogy, and technology (Mishra and Koehler, 2006), and requires a fundamental re-evaluation of teaching practices and the role of the teacher, moving from the transmission of knowledge to the facilitation of immersive and constructive learning experiences. Within this context, the Technological Pedagogical Content Knowledge (TPACK) model, proposed by Mishra and Koehler (2006), provides a rot lens for analyzing and guiding the integration of these technologies. In essence, TPACK highlights the importance of understanding how technology interacts with specific pedagogical approaches and disciplinary content to support effective teaching and meaningful learning.

NeoTrie VR (briefly Neotrie), an IVR sandbox software designed for constructing and exploring geometric objects, has emerged as a promising tool for fostering spatial reasoning, student engagement, and the understanding of abstract mathematical structures (Rodríguez et al., 2021). Our previous study (Rodríguez, 2024) with pre-service secondary mathematics teachers explored their ability to design didactic activities using Neotrie. Results showed they were able to create teaching sequences that adequately harnessed the potential of the software. However, several limitations were identified: insufficient training with the software, limited didactic content knowledge regarding the targeted mathematical concepts, technical constraints inherent to the sandbox environment, insufficient time for testing and refining activities, and a lack of awareness of potential difficulties secondary students may face when engaging with these tasks.

Although research has documented the pedagogical benefits of IVR and the importance of teacher training in the use of these technologies to achieve optimal effectiveness, few studies have been conducted on how such training should be carried out. The first cycle of this study revealed that, without the necessary training, future teachers find it difficult to get the most out of tools such as Neotrie. This highlights a clear gap in research: determining what training would be necessary and sufficient for teachers in the use of IVR to design high-quality teaching sequences aligned with TPACK for mathematics education.

Since our study is conducted within the cyclical action research methodology (plan, act, observe, reflect), we present in this paper the second iteration of the study. Drawing on the conclusions of the previous cycle, we designed a guided training program on the use of Neotrie. Accordingly, the study seeks to analyse the effect and effectiveness of this training, attempting to fill the gap identified above, being the research question: To what extent can pre-service secondary mathematics teachers design effective and pedagogically robust geometry teaching sequences in Neotrie—aligned with the TPACK framework—after receiving extended, structured training and sustained hands-on experience with the tool?

This study contributes to providing empirical evidence on how pre-service mathematics teachers design their teaching in IVR environments after receiving guided training in the use of these technologies, offering an analysis based on TPACK. The study will contribute to proposing practical guidelines for developing more effective teacher training programs for integrating IVR into mathematics teaching.

Literature review

The integration of Emerging Technologies such as IVR into the teaching of science, technology, engineering, arts, and mathematics (STEAM) has become so popular because of the impact on teaching and learning process (Silva-Díaz et al., 2022; Khan Soomro et al., 2025). IVR enhances student interest and fosters active participation by providing high spatial immersion and various interactions (Ka et al., 2025), making abstract mathematical concepts more tangible and accessible (Cevikbas et al., 2023). Within this context, NeoTrie VR represents an innovative 3D dynamic geometry software developed by the spin-off Virtual Dor of the University of Almería since 2018, designed to transform teaching through IVR. Its key features—an intuitive design, STEAM integration, a customizable sandbox environment, and multiplayer capabilities—make it both accessible and versatile for classroom use.

Neotrie VR allows learners to enter an immersive environment where they have a comprehensive set of tools to kinesthetically explore mathematical structures, including polyhedra, graphs, tessellations, fractals, curves, and surfaces (for further information, visit the official project website https://www2.ual.es/neotrie/project-neotrie/). This interaction enhances students’ spatial reasoning and visualization skills (Rodríguez et al., 2021; Romero et al., 2023) and promotes the cognitive transition from iconic to analytical visualization (García and Romero, 2024). The software’s dynamic nature helps to correct common misconceptions, such as confusing surface area with volume, by allowing students to explore concepts through dynamic manipulation and hands-on experimentation (García and Romero, 2024). Furthermore, NeoTrie functions as a powerful semiotic mediator, bridging abstract mathematical concepts and concrete virtual representations. Studies also indicate that students report increased motivation and engagement, finding the software fun and intuitive, which stimulates curiosity and a desire to explore (Moral-Sánchez et al., 2022, 2023; Codina et al., 2023).

Despite the growing evidence of IVR’s pedagogical benefits, the effective use of educational technology depends more on teachers’ ability to integrate it into their teaching practices than on the technology itself. Barriers related to technical complexity, cost, and practical classroom management have historically limited IVR adoption (Fransson et al., 2020). However, recent developments in standalone headsets, such as the Meta Quest series, have significantly lowered the entry barrier by offering more affordable, portable, and user-friendly systems, and thus making immersive technologies more accessible to a wider range of educational institutions.

For mathematics educators, integrating IVR poses additional challenges: secondary teachers must face the difficulty of teaching abstract or spatial concepts to students who are at a critical stage of cognitive development. Thus, teacher education programs must prepare future educators to integrate IVR both technically and pedagogically. To better respond to these issues, Awoyemi et al. (2024) propose using Technological Pedagogical Content Knowledge (TPACK) as a framework for instructional design to gain a deeper understanding of the effective integration of IVR in secondary school mathematics teaching (Fragkaki et al., 2020; Koehler and Mishra, 2008, 2009). TPACK is also recognized as an essential model for equipping teachers with the necessary competencies to implement effective STEM practices (Doering et al., 2009; Tondeur et al., 2017). This relevance is further supported by the bibliometric review conducted by Su (2023) on the development of TPACK in future teachers from 2007 to 2022 which highlighted that, recently, many researchers adopted the TPACK framework in teacher education research (e.g., Lachner et al., 2021; Lai et al., 2022), especially in pre-service teacher settings (e.g., Luo et al., 2022; Zhou et al., 2022).

The TPACK framework (Mishra and Koehler, 2006) builds on Shulman’s concept of Pedagogical Content Knowledge (Shulman, 1986), expanding it to address the complex and contextual nature of integrating technology into teaching. It highlights the dynamic interplay between three core knowledge domains: Content Knowledge (CK), which refers to the teacher’s expertise in the subject matter, such as mathematical concepts, procedures, and structures; Pedagogical Knowledge (PK), which involves knowledge of teaching methods, classroom management, lesson planning, and assessment; and Technological Knowledge (TK), which indicates the ability to understand and use various technological tools, from traditional to emerging digital resources. TPACK also emphasizes the intersections of these domains: PCK (Pedagogical Content Knowledge) focuses on how to teach specific content effectively; TCK (Technological Content Knowledge) explores how technology can enhance or transform how content is represented and understood; and TPK (Technological Pedagogical Knowledge) deals with how technology influences teaching strategies and learning processes.

For our study, we have adapted the components of TPACK to the Neotrie software (Figure 1) to provide secondary school teachers with a comprehensive approach to integrating technology by connecting content, pedagogy, and technology use.

Figure 1

Figure 1. TPACK components (central graph in figure is reproduced by permission of the publisher, © 2012 by tpack.org and text boxes with definitions of each component have been adapted by the authors to Neotrie).

In summary, although the effective integration of IVR into the curriculum depends on solid teacher training (Ayanwale et al., 2024; Martins and Baptista, 2024), research indicates that such training remains insufficient representing a key obstacle (Papadakis, 2022). Even when teachers recognize the significant educational potential of IVR, challenges related to integration and inadequate training persist, requiring further research to explore teacher training strategies (Silva-Díaz et al., 2022). This highlights a critical gap that our study seeks to address: there is still little evidence on the specific training secondary school teachers need to implement IVR effectively. In this context, the TPACK framework is particularly relevant for assessing whether such specific training promotes a balanced and in-depth development of the three essential cores of knowledge—technological, pedagogical, and content—necessary for the successful integration of IVR into mathematics teaching.

Materials and methods

Building on the first cycle described in Rodríguez (2024), the present study implements an enhanced second cycle whose research design is summarized in Figure 2, showing the key components and sequential steps of the intervention.

Figure 2

Figure 2. Visual overview of the research design, summarizing the key components of the study and the main steps of the intervention. Research Design – Key Components.

The participants of the second cycle of this research were 33 pre-service secondary school teachers, 13 male and 20 female, with average age of 26.4 years (range: 22–39). There were 20 mathematicians and 13 engineers taking the Master’s Degree in Secondary Education Teaching at the University of Almería. In Spain, this master’s degree is compulsory and qualifies graduates for future teaching work at this educational level. The use of Neotrie is included in the teaching guide for the Master’s degree course in which it is developed.

They were selected because they were future secondary school mathematics teachers and part of a course taught by the authors, which ensured full access. Although we also work with in-service teachers using NeoTrie VR, this study focused on pre-service teachers due to their accessibility and to assess how initial training supports the development of teaching knowledge and digital integration.

The course (delivered in two weekly sessions of 2.5 h each, on Mondays and Wednesdays) follows a nine-week structure designed to prepare future teachers to make informed decisions about educational resources and teaching strategies. During the first 4 weeks, students work with a different instructor who introduces key curricular documents, general teaching methodologies, and digital tools such as GeoGebra, Wolfram Alpha, and Kahoot. After this initial phase, students complete a one-month teaching practicum in secondary schools. They then return for the final 5 weeks of the course, led by the first author of this study, which includes a focused intervention on immersive technologies.

In this second phase, special emphasis is placed on the integration of immersive tools, including NeoTrie VR (Rodríguez, 2024). The course is managed through Blackboard, a digital platform that supports content delivery, activity monitoring, and interaction via discussion forums. These combined experiences aim to foster technological fluency and pedagogical reflection through both structured training and authentic classroom connections.

The primary objectives of this iterative approach were to equip future teachers with effective Neotrie usage and classroom implementation strategies, guide them in identifying suitable learning scenarios for virtual reality, facilitate the design of curriculum-aligned didactic activities, and ensure the maximization of the software’s immersive potential.

In the initial session—mirroring the first cycle of our action research (Rodríguez, 2024)—the instructor presents the overall structure of this part of the course, outlining the session-by-session activities and the assessment criteria. The session also includes an introduction to the NeoTrie VR software, with basic guidance on its functionality and a brief overview of its didactic potential in mathematics education.

Students are then invited to visit the Neotrie website and various community activities and social networks. They try out the software, learn how to cast on a computer,² how to manage the delivery of the upcoming tasks in Google Drive; they learn how to move around the Neotrie scenario, how to create and edit a simple figure, and they are given free time to try out some of the activities already included in the software.

To evaluate the initial trial session with Neotrie, students wrote private individual reflections to the instructor. These initial assessments provided personal feedback on their first impressions of the software and its educational potential.

In the following three sessions, students were divided into 10 groups of 2–4 members (G1 to G10) to complete three worksheets—beginner, expert, and advanced—designed to guide their learning of the software (available as Supplementary material). All students engaged with tasks at each level, ensuring a comprehensive exploration of Neotrie’s functionalities. In parallel, they tackled various 3D geometry challenges embedded in the activities. These experiences also served as examples of how to structure sessions within their own didactic units, with careful consideration of the TPACK components.

Across all three user sheets, the activities are carefully scaffolded to support a gradual development of spatial reasoning, from basic object manipulation to complex geometric modeling and analysis. The worksheets are designed to be reproducible and educator-friendly: it includes links to external resources such as how-to guides and instructional videos for each level, ensuring that instructors and learners can independently follow the sessions and replicate the interactive 3D geometry learning experience in their own classroom settings.

Following the scaffolded training sessions on Neotrie, students engaged in an individual task aimed at exploring how the software could be meaningfully integrated into the official mathematics curriculum. To accomplish this, they consulted the national curriculum frameworks (Ministerio de Educación y Formación Profesional, 2022a, 2022b), analyzed relevant learning standards, and reviewed existing projects and activities from the Neotrie community. Based on this research, each student independently drafted a learning situation aligned with curricular objectives and adapted to the secondary education level of their choice.

After the individual phase, students worked with their respective groups to select a mathematical topic and educational level and collaboratively designed a new learning situation—drawing from and combining elements of their earlier proposals. The collaborative design task encouraged a STEM-oriented pedagogical approach, requiring pre-service teachers to apply geometric knowledge (M) to a tangible design problem (T), thereby fostering design thinking and construction skills commonly associated with the Engineering (E) component of the STEM curriculum.

Over the next two sessions, each group developed this into a complete teaching unit. The units included essential curricular components such as grade level, topic, rationale, objectives, specific competencies, and core knowledge. A detailed learning situation was outlined, accompanied by a didactic timeline and other relevant elements. While no strict template was imposed, students were encouraged to follow regional curriculum guidelines and criteria used in previous public teaching exams. In addition, they were provided with a rubric based on the TPACK framework to guide the design and evaluation of their units (Figure 1). The proposed learning situations prioritized feasibility within virtual reality environments and allowed for integration with complementary tools such as manipulatives or dynamic geometry software like GeoGebra.

Once the teaching units were completed, each group reviewed the work of another team using the TPACK framework as a reference (Figure 1). Although this was initially designed as a peer-assessment activity, students mainly provided qualitative feedback—highlighting strengths, suggesting improvements, and identifying issues—directly within the shared Google Drive documents. The formal evaluation of each didactic unit across the seven TPACK components (TK, CK, PK, TCK, PCK, TPK, and TPACK) was ultimately carried out by the instructor, based on a detailed rubric (see Figure 1), with special attention to how Neotrie was integrated as both a technological and pedagogical resource.

In the final session, each group presented a 15-min summary of their teaching unit to their classmates. The presentation focused on the main elements of the unit, including curricular alignment, learning objectives, the proposed use of Neotrie and the pedagogical strategies employed. Assessment was carried out both at group level and individually based on active participation in the post-presentation discussion and in the Blackboard forum. This final exchange allowed students to critically reflect on the role of immersive technologies in mathematics education and consolidate their learning from their work.

Results

In contrast to the first cycle, the second cycle featured an extended training phase, consisting of three more sessions. It also incorporated a new individual session dedicated to exploring potential topics for integrating Neotrie into the curriculum, as well as additional sessions for evaluating and presenting the didactic units completed by each group of pre-service teachers to their classmates. These additions promoted deeper curricular alignment, encouraged peer feedback and reflection, and enhanced students’ ability to critically assess the pedagogical use of virtual reality tools in mathematics education.

The collaborative forum on the Blackboard platform played a key role in this process, providing a space for students to exchange ideas, share materials, and offering constructive feedback on each other’s didactic proposals, in the following subsections, we present the results obtained in each of these sessions, following the chronological structure of the intervention. While the analysis addresses various dimensions of the TPACK framework, a final subsection is devoted to a comparative summary of these components across both intervention cycles.

Students’ opinions after the introductory session

After the initial hands-on session, 28 out of 31 students expressed highly positive opinions about its educational potential, particularly for teaching geometry and enhancing spatial reasoning. Many highlighted the tool’s ability to engage learners through interactive features such as the laser, loci brush, and multiplayer mode. However, initial difficulties were noted by seven students, including adaptation to the virtual environment, controller handling, and connectivity issues. Six students suggested the inclusion of introductory tutorials and improved infrastructure for classroom use. Overall, Neotrie was perceived as an innovative and promising educational resource, especially when paired with guided familiarization. A graphic with the themes that emerged in the students’ opinions is presented (Figure 3).

Figure 3

Figure 3. Frequency of emerging themes in student’s feedback on NeoTrie VR, out of 31 participants’ answers (2 did not send any feedback). Files are available at https://drive.google.com/drive/folders/1VwM942mVZBe8zsYi1CIpgD9EbqWXX665?usp=sharing.

Training sessions review

The NeoTrie VR training sequence was structured into three progressive worksheets—Beginner, Expert, and Advanced—designed to build students’ technical and conceptual fluency with the software before designing their teaching units. Each worksheet was accompanied by instructional videos, enabling students to work with autonomy. Groups had up to three attempts to complete the activities and were allowed to correct errors based on instructor feedback. Rather than penalize mistakes, the focus was on ensuring all students reached a level of mastery that would support later curricular integration.

The Beginner worksheet introduced basic navigation and modeling tools. Most students completed it with ease, although many encountered difficulties in the final task: constructing a cube using only the parallel, perpendicular and compass tools. This required understanding spatial relations and tool logic in 3D, presenting a meaningful challenge (see Figure 4). Still, students remained engaged and performed well, with an average score of 9.93 out of 10.

Figure 4

Figure 4. Screenshot of G6 of the Task 4.5 on creating a cube (https://drive.google.com/file/d/18Id8vAVPYCu-L9V4W5z_-HWr8Vs5tUAq/view).

The Expert worksheet introduced transformations and animations (Figure 5). Common issues included improper use of the interpolator tool, missing steps in vertex selection for reflections and rotations, and misunderstandings in intersection and trace-based animation tasks. Although several groups needed guidance, they typically corrected their work and learned from the process. The average score was 9.23.

Figure 5

Figure 5. Screenshot of a video of task 6.9 of G9 on creating a cone as a revolution surface (https://drive.google.com/file/d/17MBciZ_qaKrVRPy4hWuIRyWc34CX-jKW/view?usp=sharing).

The Advanced worksheet involved symmetries, projections, and parametric representations. Challenges appeared in configuring mosaic parameters, visualizing sections in the scanner, and labeling surfaces in the 3D graphing tool. Misinterpretations of unit scales also led to errors in expected equations (see Figure 6 that captures a classroom discussion about unit conversion between decimeters and meters while interacting with labeled plane equations in VR). Although the coordinates of the points are expressed in decimeters, the equation is displayed in meters—resulting in expressions such as x + 2y – z = 0.1 m. Despite these hurdles, most students succeeded in completing the tasks, with an average score of 9.52.

Figure 6

Figure 6. Screenshot from a video of G4 of Task 9.3 on creating a plane from 3 points and labeling its coordinates and equation (floating-point rounding errors were corrected in later versions of Neotrie [e.g., values like 0.09999999 now appear as 0.1]; https://drive.google.com/file/d/19mm4dnWvunYxs_ssgj2tzUWNQBGKxujK/view).

Overall, the worksheets were effective in scaffolding learning and promoting independent exploration. For future iterations of this study, reducing teacher support, tracking common errors more systematically, and expanding the mathematical depth of certain tasks could enhance the pedagogical value of the training.

Assessment of the group didactic units

After completing the training sessions, 33 individually developed drafts of didactic units were submitted to the instructor, reflecting a rich diversity of approaches to integrating NeoTrie VR into secondary mathematics education. Most activities focused on spatial geometry, transformations, and measurement, highlighting the software’s potential for enhancing 3D visualization and hands-on learning. Units range from simple constructions like prisms and pyramids to advanced problems involving vector operations and analytic geometry. Neotrie is often used to build, manipulate, and analyze geometric figures, fostering active learning and exploration. Several proposals incorporate cultural or historical elements—such as Islamic mosaics or ancient theorems—adding interdisciplinary value. The level of application spans all secondary grades, with a balanced distribution across Compulsory Secondary Education (ESO) and Baccalaureate (post-compulsory and optional). Many students emphasize student engagement and motivation through immersive learning experiences. Some units incorporate GeoGebra for algebraic support or complementary 2D representations. There is a recurring interest in fostering creativity, collaborative work, and critical thinking. Overall, the proposals demonstrate the versatility of Neotrie as both a mathematical and pedagogical tool.

After completing their individual drafts, students participated in group discussions to collectively determine the focus of their final didactic unit. These proposals were shared in a dedicated discussion forum on the course’s Blackboard platform, allowing all students to view each other’s ideas and avoid topic repetition. The next titles and descriptions were verbatim from the proposals of the groups (G1 to G10) in the forum:

G1 Train Station: We propose a learning situation that consists of studying the façade of the 19th century train station building. Concepts such as scale, areas, arcs and symmetries among others will be worked on. Course: 3rd ESO. Students: ibm, asy, acs. Tools: 1, 5, 7, 8, 9, 10, 13, 15, 17, 22.

G2 Mathematical Maze: In our Didactic Unit with Neotrie we propose to the students the elaboration of a maze and some activities (calculation of areas, geometric constructions, etc.) that must be solved by other classmates to reach the goal with the highest possible score. Course: 3rd ESO. Students: jco, ash, cgf. Tools: 1, 2, 4, 5, 8, 9.

G3 Polyhedra in NeoTrie VR (changed later to “Containers”): In this project, students will learn about different properties of polyhedra. Course: 4th ESO. Students: mcc, aos, asr. Tools: 1, 5, 7, 10, 11, 15, 16, 18, 19.

G4 Measuring the World: We will carry out a didactic unit on trigonometry based on students building a clinometer and working on trigonometry by measuring buildings, trees, mountains, etc. First, they will work in the real world, make calculations and measurements with GeoGebra and then transfer everything they have learned to NeoTrieVR. Course: 4th ESO. Students: acf, llp, sde, agr. Tools: 1, 3, 5, 6, 11, 14.

G5 Alhambra mosaics: It is intended that students reproduce different mosaics in the Alhambra. Using Neotrie they will have to calculate the areas to be painted, to know the interior angles of the figures. Course: 3rd ESO. Students: psg, acb, all. Tools: (not indicated).

G6 We design our room: In this activity we will work with vector and mixed products, planes and straight lines. Students will have to create objects such as tables, chairs, etc. using these. Course: 2nd BACC. Students: sle, sml, vpn, erl. Tools: 1, 2, 4, 10, 11, 15, 20, 21.

G7 Soccer Field: Our group will design a learning situation about geometry applied to an example of everyday life: a soccer field. Course: 4th ESO. Students: amp, nrd, mtm. Tools: 1, 4, 9, 10, 11.

G8 Basketball Court: Students design a basketball court to scale in Neotrie, calculating the area of each region while learning plane geometry tools. Course: 3rd ESO. Students: mcg, mjm, rms, fsg. Tools: 1, 4, 5, 6, 8, 9, 10, 11, 14, 15, 17, 19, 21, 22.

G9 Proving our first theorem: Napoleon’s Theorem. We will create an activity providing the statement of Napoleon’s theorem, where students must demonstrate it graphically using Neotrie tools and must make a video in which it appears. Course: 1st BACC. Students: adr, dab, nrg, asg. Tools: 1, 5, 14, 15, 17, 18.

G10 Design your urbanization: In this activity the students will have to use the different Neotrie tools to delimit the different plots and common areas. Calculating also the areas and volumes that are requested. Course: 2nd ESO. Students: mrj, igl. Tools: 1, 2, 4, 5, 7, 10, 11.

The following is the list of tools employed by student groups during the second cycle, organized by user level.³ Tools numbered 1–16 were already used in the first cycle:

• Beginner level tools: 1. Basic hand actions; 2. Gallery of figures; 3. Photo camera; 4. Palette and pencil; 5. Tape; 6. Protractor; 7. Figure measures information; 8. Copy tool; 9. Scale copy tool; 10. Parallel tool; 11. Perpendicular tool; 12. Rotation tool; 13. Reflection tool; 17. Middle point tool.

• Expert level tools: 16. Sphere, cylinder, cone tool; 18. Angle tool; 19. Compass; 20. Intersection tool.

• Advanced level tools: 14. Coordinate axis; 15. Labeling tool; 21. Graphing calculator; 22. Symmetries.

All materials developed by each group in the subsequent sessions—including didactic units, peer feedback, corrections, and final presentations—were also shared in the Blackboard forum. This open sharing environment fostered transparency, encouraged peer-to-peer learning, and supported collaborative reflection throughout the process.

Quantitative analysis

Initially, each evaluating group was expected to complete an assessment table based on the TPACK framework to evaluate the teaching unit of another group. However, due to time constraints, the detailed evaluation was ultimately carried out by the instructor at a later stage, as summarized in Table 1. Each component was rated on a 5-point scale, with qualitative comments provided for each dimension. These comments were based on the final versions of the didactic units and oral group presentations, which had already been reviewed by their classmates.

Table 1

Table 1. TPACK evaluation summary of didactic units integrating NeoTrie VR.

The overall results (Figure 7) revealed a solid integration of the TPACK components across the teaching units. The average scores were as follows: Technological Knowledge (TK): 4.0, Content Knowledge (CK): 4.3, Pedagogical Knowledge (PK): 4.4, Pedagogical Content Knowledge (PCK): 4.6, Technological Content Knowledge (TCK): 3.9, Technological Pedagogical Knowledge (TPK): 4.4, and Technological Pedagogical Content Knowledge (TPCK): 4.3. These figures indicate that the strongest area among all groups was PCK, suggesting that students were especially successful in designing didactic strategies that supported the teaching and learning of mathematical content. High scores in PK and CK demonstrate their proper grasp of both instructional approaches and curricular objectives. In contrast, the lowest average was in TCK, pointing to some challenges in effectively using NeoTrie VR to enhance or visualize specific mathematical concepts, which were also confirmed by the similar average score obtained in TK.

Figure 7

Figure 7. Average scores for TPACK components.

Qualitative observations

A qualitative analysis of peer-reviewed teaching units revealed several patterns regarding the integration of NeoTrie VR within curricular design.

Overall, most proposals achieved effective alignment between pedagogical strategies, mathematical content, and the technological affordances of Neotrie. These units often featured clear instructional sequences, self-assessment checkpoints, and tasks that promoted spatial reasoning and conceptual understanding, demonstrating solid integration of TPACK elements. However, some units lacked pedagogical coherence, presenting common deficiencies such as insufficient guidance on the use of specific tools and inadequate support for key mathematical concepts, among others, which undermined the clarity and viability of these teaching units.

Considering the units that achieved the highest and lowest ratings, we can deepen our analysis under the analytical lens of the TPACK framework. Among the highest-rated units were Basketball Court (G8), Containers (G3), and Napoleon’s Theorem (G9). Basketball Court (G8) achieved a perfect score (35/35) due to its well-structured pedagogical design, alignment with realistic classroom dynamics, and effective use of Neotrie’s tools to model and analyze geometric figures meaningfully. Containers and Napoleon’s Theorem were commended for their clear articulation of learning objectives and their ability to connect abstract mathematical ideas—such as volume, surface area, or triangle centers—with interactive construction tasks that fostered spatial reasoning and student autonomy, including the use of video tutorials within Neotrie. Measuring the World (G4) also scored highly, but the omission of key mathematical content (e.g., trigonometric reasoning) or assessment criteria weakened its pedagogical coherence. In contrast, the Alhambra Mosaics (G5) and Football Field (G7) units received the lowest overall scores. Although both were based on visually appealing and potentially rich mathematical contexts, they presented a lack of detailed student instructions and limited use of Neotrie’s capabilities—particularly in areas such as symmetry construction, tessellation, or the dynamic comparison of geometric transformations. The shortcomings were especially evident in Alhambra Mosaics, where otherwise engaging mathematical concepts were insufficiently supported, reducing the clarity and feasibility of the tasks. These cases underscore the importance of complementing attractive mathematical contexts with carefully scaffolded tasks that fully leverage the immersive features of virtual learning environments.

Changes in the use of NeoTrie VR tools across two cycles

To better understand students’ technological engagement, we analyzed the NeoTrie VR tools used in the teaching units developed by each group. Tools were categorized by level of complexity (Beginner, Expert, Advanced), and their frequency of use was recorded.

The number of groups in each cycle depended on the total number of students, resulting in eight groups in Cycle 1 and 10 groups in Cycle 2. Although all 10 groups were evaluated in Cycle 2, we adjusted the data to reflect eight groups in each cycle for comparison purposes. Since the table reports absolute (not relative) frequencies, this proportional adjustment ensures a fair and balanced comparison between the two cohorts. Table 2 shows the absolute number of tools used at each level. Together, these results reveal a shift toward more diverse and complex tool use in the second cycle, suggesting increased technological fluency and integration.

Table 2

Table 2. Absolute and relative frequencies of NeoTrie VR tools used by user level across the first and second cycles (eight groups each).

In the first cycle, students primarily relied on beginner-level tools, such as object selection, movement, face coloring, and extrusion. These tools were intuitive and sufficient for producing simple geometric constructions. The use of expert-level tools (e.g., intersections, reflections, and symmetry tools) was present but limited to a few groups. Advanced tools—including animation, scanning, parametric equations, or the 3D calculator—were virtually absent.

By contrast, in the second cycle, the tool usage became both more diverse and more aligned with didactic objectives. All groups had previously completed scaffolded training sessions, allowing them to explore Neotrie’s capabilities in depth. As a result: beginner tools were still widely used, but in more complex combinations; expert tools were more frequently integrated into the didactic units, often used to model transformations, projections, and dynamic figures; advanced tools saw a notable increase, with multiple groups using animation, curve tracing, 3D projections, and mathematical surfaces to support higher-level reasoning and curricular content.

This shift reflects not only an improved command of the software but also a deeper understanding of how specific tools can serve pedagogical and mathematical goals. In particular, the integration of tools such as the scanner or interpolator helped students transition from static visualization to more dynamic and exploratory learning environments.

The evolution in tool use from the first to the second cycle illustrates a clear growth in technological-pedagogical thinking. While students in the first cycle were primarily exploring possibilities, those in the second cycle demonstrated a more intentional and curriculum-aligned use of NeoTrie VR—laying the foundation for future implementation in real classroom contexts. This broader and more strategic use of Neotrie tools in the second cycle aligns with greater technological content knowledge, that is, the pre-service teachers showed a growing ability to select and apply the appropriate Neotrie tools to display the mathematical contents. The combination of scaffolded training and individual curriculum integration tasks appears to have helped students better understand how technology can enhance content delivery and learner engagement.

Comparison of TPACK-based evaluation between cycles

A comparison between the two intervention cycles reveals notable differences in the integration of TPACK components. In the first cycle, students’ proposals were assessed based on four key dimensions—originality, mathematical content, software mastery, and presentation—each scored from 0 to 5, as described and reported in Rodríguez (2024). These dimensions corresponded to combinations of TPACK elements such as TK, TPK, PCK, and TPACK. In the second cycle, a more comprehensive TPACK-based rubric was used (Figure 1), covering the full range of the model: TK, CK, PK, PCK, TCK, TPK, and TPACK. This broader evaluation allowed for a more fine-grained analysis of the teaching proposals and revealed new challenges, especially in pedagogical content knowledge and in the full integration of technology with pedagogy and content.

To better understand the evolution in pre-service teachers’ technological and pedagogical integration, Table 3 offers a qualitative assessment of the TPACK components observed in each intervention cycle, based on the students’ written teaching units and the instructor’s analysis. In the second cycle, each component was assessed using a structured rubric (see Figure 1), which guided the instructor’s evaluation based on explicit indicators derived from the students’ work. These indicators reflected how the didactic units incorporated technology, pedagogical strategies, and mathematical content in alignment with the curriculum. In contrast, the first cycle employed a simpler set of categories that broadly mapped to some TPACK dimensions but lacked the specificity of the second cycle’s rubric.

Table 3

Table 3. Comparison of TPACK outcomes: first vs. second cycle.

While the second cycle employed a detailed and structured evaluation rubric aligned with the TPACK framework, the first cycle was assessed through broader categories. The comparison highlights both the progression in specific dimensions and the challenges in achieving full integration.

Although a basic comparison of component scores across both cycles is possible, we decided not to include a direct quantitative analysis, as the evaluation criteria and training conditions varied significantly. In the first cycle, students were assessed after only one exploration session with minimal guidance, and the rubric was based on broader categories. In contrast, the second cycle involved structured training, peer review, and a more detailed TPACK-based rubric. Therefore, any direct comparison of scores would risk misrepresenting the actual learning progression.

Nevertheless, a rough comparison based on the average total scores (15.38 in Cycle 1 and 17.75 in Cycle 2, out of 20) suggests a 15.5% improvement, which—despite the differing conditions—can be viewed as an indicator of positive development in TPACK-related competencies.

Discussion

The comparative results between the first and second cycles of this study reveal important insights into how scaffolded training in immersive technologies like NeoTrie VR can enhance pre-service teachers’ technological and pedagogical integration capacities and enable us to affirmatively answer our research question.

The more extensive guided training phase implemented in the second cycle, in which students participated in differentiated activities and had time to master the software progressively, led to a notable improvement for most pre-service teachers in one of the three core knowledge domains, Technological Knowledge (TK), as well as in the components derived from it, Technological Pedagogical knowledge (TPK) and Technological Content Knowledge. This was evidenced by the average scores obtained in the TPACK evaluation, which also reflected a substantial improvement over the previous cycle. The comparison between the two cycles also reflects a shift from tool-centered exploration in the first cycle to more curriculum-aligned integration in the second one. In the first cycle, students primarily relied on basic construction tools and tended to reproduce familiar 2D classroom activities in a 3D environment. By contrast, in the second cycle, the guided training enabled students to purposefully use a wider range of Neotrie tools—such as interpolation, compass, symmetry, and intersection—in ways that supported spatial reasoning and multiple representations. Several groups also included GeoGebra as a complementary tool for algebraic verification or dynamic 2D analysis, demonstrating increasing fluency in the integration of digital resources, as observed in previous studies (Codina-Sánchez et al., 2022; Rodríguez et al., 2021). These findings align with previous research suggesting that pre-service teachers are more likely to integrate digital tools into their future classrooms when they have personally experienced their effectiveness and pedagogical affordances during their training (Agyei and Voogt, 2012; Tondeur et al., 2012).

An additional key factor contributing to the improvement of TK, TPK, and TCK was the peer assessment process. Each group of students was not only required to develop their own didactic unit, but also to critically evaluate those of their classmates—identifying technical and conceptual flaws and suggesting improvements. On the other hand, the last session (Final Presentation) allowed students to present the definitive version of their teaching units to peers, receive feedback, and reflect collectively on the integration of VR in mathematics education. This exchange, followed by further discussion in the Blackboard forum reinforced their ability to justify pedagogical choices. This dual role—as designers and evaluators—fostered deeper reflection on the pedagogical potential and constraints of specific tools, thus reinforcing their TPACK development from multiple angles in a collaborative setting. These results reinforce the idea that learning through collaboration and authentic assessment tasks is highly effective in teacher education contexts (Koh et al., 2017).

Regarding the other two core TPACK domains, CK and PK, the average scores were high and indicated an overall satisfactory knowledge. However, some pre-service teachers showed gaps that revealed fairly limited pedagogical content knowledge. Although they designed tasks that adequately incorporated the required Neotrie tools, these tasks demonstrated limited depth in their treatment of mathematical content. The activities mainly required arithmetic calculations, which posed no challenge or cognitive demand for the students for whom they were intended. This can be attributed to gaps in the students’ didactic training on how to teach mathematics conceptually. Greater mastery of both CK and PK could have enabled them to design tasks more closely aligned with curricular expectations, thereby encouraging deeper mathematical thinking (Kilpatrick et al., 2001).

One of the main contributions of this study is the development of a rubric-based TPACK assessment framework, tailored specifically for evaluating the integration of immersive technologies like NeoTrie VR in mathematics education. While TPACK is often evaluated through self-reports or standardized questionnaires (Schmidt et al., 2009; Sahin, 2011), this study proposes a practical and formative approach, aligned with the current educational legislation in Spain that emphasizes authentic and criteria-based assessment. The rubric developed in this study proved useful not only for the instructor but also for students to understand the multifaceted nature of effective technology integration.

Finally, it is worth noting that the didactic units developed during the second cycle remain drafts, yet they represent a promising foundation for future iterations. Rather than starting from scratch, the third cycle of this program (implemented in the academic year 2024–25) took a new direction: students were not asked to design new teaching units, but to assess and revise the ones produced in the previous cycle. This was done using an enhanced version of the TPACK rubric developed in this study. Working in small groups, students commented on the pedagogical and technological strengths and weaknesses of the units, proposed improvements, and rewrote sections to increase curricular alignment and mathematical depth. Greater independence was given during Neotrie training sessions, encouraging students to detect and correct technical errors, expand mathematical problems, and engage in deeper reflection. In addition, students created video reflections structured around key prompts (first impressions of Neotrie, classroom experiences, lessons learned, and potential future use), offering a rich qualitative complement to the rubric-based evaluations. This evolving design reflects a broader design-based research (DBR) methodology, where proposals are continuously refined through iterative cycles of design, implementation, analysis, and revision (Cobb et al., 2003). By having subsequent cohorts engage in the evaluation and improvement of previous materials, we foster not only cumulative knowledge building, but also a stronger sense of professional agency. This iterative model of teacher training supports deeper TPACK development and aligns with calls for more sustainable, practice-based approaches to educational innovation.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors without undue reservation.

Ethics statement

Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.

Author contributions

JR: Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Formal analysis, Software. MG: Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Formal analysis, Supervision.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The authors have received partial support from the group of Innovation and Research in Science and Mathematics Education (HUM886) of the Regional Government of Andalusia.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that Generative AI was used in the creation of this manuscript. Parts of this manuscript were written and edited with the assistance of ChatGPT (GPT-4o), developed by OpenAI (https://openai.com/chatgpt). The authors reviewed and verified the content for factual accuracy and originality. A record of the initial and final prompts is included in Supplementary material.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feduc.2026.1725968/full#supplementary-material

Footnotes

^STEAM emphasizes the creative and design process by adding the Arts to the core STEM disciplines (Science, Technology, Engineering, and Mathematics) (Yakman, 2008).

^http://www.oculus.com/casting

^https://www2.ual.es/neotrie/guia-2024/

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