This presentation explores the transformative potential of STEAM (Science, Technology, Engineering, Arts, and Mathematics) education in promoting inclusion and creating new opportunities for students with special needs. By integrating these disciplines, STEAM fosters personalized learning experiences that enhance cognitive development, critical thinking, problem-solving, and creative expression for learners with diverse abilities. The discussion highlights the role of inclusive pedagogical strategies in making education more accessible and engaging for students with disabilities. Specifically, it examines how this approach aligns with Luxembourg's educational goals, advocating for systemic support and resources to ensure that all students have the opportunity to realize their full potential.

The integration of artificial intelligence (AI) into mathematics education has sparked increasing interest in its potential for automated examination. This study evaluates the feasibility of using ChatGPT in comparison with the Halomda e-assessment system for constructing and grading mathematics exams. ChatGPT is recognized for its capabilities in solving a broad range of mathematical problems and interpreting handwritten text, including mathematical expressions. Meanwhile, the Halomda system provides a dedicated environment for e-assessment, offering multiple options for answer formats—including multiple-choice questions, algebraic expressions, text, images, and graphs.

Although ChatGPT leverages natural language processing and mathematical reasoning to interpret handwritten answers, prior research has documented inaccuracies in its mathematical solutions. Our findings confirm that while ChatGPT can process mathematical content and formulas, it struggles with accuracy, especially when checking solution steps and handling parameter-dependent answers. Effective exam preparation requires defining both scoring rules and the expected solution path. Solely checking the final answer is insufficient to fully assess a student’s understanding or trace their logical reasoning.

Halomda addresses this need through its task editor, which allows educators to define required solution steps and assign point values to each, enabling detailed and automated evaluation. Conversely, using ChatGPT effectively in this context requires developing precise prompts—a task that demands advanced technical skill and makes exam preparation more complex than using Halomda's structured tools.

This study compared three assessment modes: (a) evaluating handwritten tests, (b) evaluating final answers, and (c) evaluating predefined solution steps, as supported by both systems. Overall, the results indicate that while modern AI models like ChatGPT show promise, they remain less reliable than specialized electronic assessment platforms like Halomda for evaluating mathematics exam solutions.

Eighteen experimentation sessions were carried out in computer classrooms during 2024, in the framework of a study on the use of digital platforms with automatic correction and feedback in the teaching of functions. Nine open-ended tasks were designed focusing on linear, affine, quadratic functions and systems of linear equations, implemented by nine teachers in five high schools, reaching over 300 students aged 13 to 15. Students worked in pairs and both verbal interactions were recorded through audio and on-screen actions. In addition to the platform, the use of various digital artifacts was allowed, including generative AI tools (e.g., Geogebra, Photomath or ChatGPT, among others) (Gaona et al, 2022).

The tasks were characterized as open-ended, i.e., they allowed multiple correct solutions within certain conditions. For example, a quadratic function was requested that intersected the x-axis in two positive values and whose vertex was located in the first quadrant. To respond to this diversity of solutions, the automatic correction and feedback system was designed to distinguish between multiple correct and incorrect answers. From the answers generated by the students, the teachers guided collective discussions in which key concepts of function algebra emerged and conjectures were formulated, favoring a collaborative and enriched mathematical work.

The analysis of the mathematical work was carried out from the theoretical framework of the Mathematical Working Space (MWS) (Kuzniak et al. 2022), considering its semiotic, instrumental and discursive dimensions. The results of the study reveal the didactic conditions necessary for the emergence of a collective MWS, in which interactions between the teacher and the diversity of student productions converge in the configuration and shared understanding of mathematical objects. This evidences active collaboration in the collective construction of mathematical knowledge.

Gaona & Menares (2021): https://doi.org/10.29333/ejmste/11425

Gaona et al. (2022); https://doi.org/10.1080/0020739X.2022.2133021

Kuzniak et al. (2022): https://doi.org/10.1007/978-3-030-90850-8

This qualitative study examines how pre-service and in-service teachers (PSTs and ISTs) experience example generation (EG) tasks implemented within a computer-aided assessment (CAA) system, specifically STACK, with correct/incorrect feedback. Drawing on work by Watson and Mason (2005), EG tasks require learners to create their own examples of mathematical objects that satisfy specified conditions. The tasks are designed to foster conceptual understanding and active mathematical engagement. The study investigates whether this task type, when delivered through a CAA system, preserves its formative potential or whether the nature of the feedback shifts participants’ experiences toward more summative interpretations.

The research responds to the growing interest in how digital tools can support formative assessment practices in mathematics education (e.g., Kinnear, 2022). Semi-structured interviews were conducted with both PSTs and ISTs after they had engaged with a STACK quiz containing open-ended GE tasks designed to elicit exploration and reflection.

Findings reveal contrasting perspectives between PSTs and ISTs. PSTs often struggled with the open-ended format of the tasks and expressed uncertainty due to the lack of exploratory feedback, which reduced their perception of the tasks as formative. In contrast, ISTs generally viewed the tasks more positively, appreciating their potential for promoting self-assessment, deeper reflection, and autonomy in mathematical reasoning.

The study contributes to the broader discussion on digital formative assessment by highlighting the tension between task design, feedback (correct/incorrect), and user interpretation.

References:

Kinnear, G. (2022). Comparing example generation with classification in the learning of new mathematics concepts. Research in Mathematics Education, 1-24. https://doi.org/10.1080/14794802.2022.2152086

Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Routledge.

Geometric constructions are a common topic in mathematics education across many countries. In Japan, practical drawing skills were historically taught in the subject “Drawing” within the Arts curriculum, while mathematics has traditionally focused on logical thinking and proof. About 85 years ago, “instrumental drawing” was incorporated into mathematics education, requiring students to understand the mathematical structure behind constructions before creating figures.

The emphasis on geometric constructions varies internationally—some countries prioritize precise constructions using rulers and compasses, while others focus more on theoretical understanding. With the rise of dynamic geometry software (DGS) such as GeoGebra，Cinderella, and Desmos, construction activities have increasingly shifted from analog tools to digital or blended environments. While DGS offers precision and dynamic manipulation, it has been noted that students may struggle to grasp construction procedures and underlying concepts due to reduced physical, hands-on experience.

Traditional tools like rulers and compasses still play a valuable role in helping students understand the essence of constructions and geometric reasoning. As a third approach, this study proposes the use of an electronic compass tool that combines the strengths of both analog and digital technologies. The tool we developed replicates the shape and function of a physical compass: the pencil is replaced by an electronic pen, and the needle point includes a sensor that captures digital data. It records both the coordinates of the circle’s center and the arc drawn with the digital compass as digital ink data.

This tool enables detailed tracking of students’ drawing processes—such as speed, sequence, and revisions—allowing educators to visualize their trial-and-error efforts and gain insights into their understanding. This enhances formative assessment in geometric construction activities. Looking ahead, we explore the potential of using this data for automated evaluation and personalized feedback.

This study reports on the participatory development of an interactive digital platform titled STEAM Education and Culture, created using the new features of Google Earth. The platform maps and documents diverse cultural practices and artefacts from various regions of Tanzania to foster the integration of cultural relevance into the teaching of science subjects. To evaluate its educational potential, 20 science subject teachers from Tanzania, Kenya, and Uganda were engaged in a virtual focus group discussion. Teachers perceived the platform as a potential for offering instant, visual access to indigenous knowledge and artefacts that are often inaccessible in conventional classrooms. However, to make the platform pedagogically practical, participants recommended the inclusion of sample science concepts linked to each artefact, example lesson plans, and professional development for teachers on how to use Google Earth effectively. As a result, nine teachers from the three countries volunteered to co-develop culturally contextualised lesson plans and expand the platform’s regional content. Further development will be reported in the upcoming articles. This project demonstrates the value of participatory design in creating inclusive, place-based STEAM resources that foster both educational relevance and digital innovation in African contexts.

Thirty-two mathematics education students - most with no formal musical background - participated in a course that linked musical activity with mathematics teaching. Initially, they engaged in live composition exercises under the guidance of a lecturer from the music department—a pianist and composer specializing in fostering creativity through music. Later, with support from a lecturer in mathematics education, students were instructed to create and record a five-part musical soundtrack to accompany a mathematics teaching unit. Each piece was intended to represent a mathematical concept from a pedagogical perspective and was accompanied by a written explanation of its educational significance.

Students employed a variety of digital and analogue technologies in creating their compositions, including GeoGebra simulations of shifting parabolas, digital editing with pre-recorded audio samples, and accessible musical tools such as xylophones, drums, and bells. The compositions reflected a broad range of musical interpretations in the context of mathematics teaching. For example, equality in equations was represented by performing the same notes sequentially on piano and strings; ascending and descending movements on the keyboard portrayed vertical and horizontal shifts of a parabola; identical chords in different octaves illustrated triangle congruence; errors in solution processes were expressed as moments of disharmony; and spatial movement with percussion instruments—starting at the corners of a room and gradually converging toward the centre—was used to sonify the distinction between surface area and volume in a rectangular prism.

In written reflections and recorded interviews, students described the project as a meaningful for their understanding of both mathematics and pedagogy. Translating mathematical learning into musical representation, using digital recording and editing tools alongside simple percussion and melodic instruments, encouraged them to reimagine mathematics instruction as both a communicative and creative practice.

The rapid advancements in artificial intelligence (AI) present new opportunities for professional development, particularly in STEM education. While much research has focused on AI’s role in student learning, less attention has been given to its potential for personalizing professional development for teachers. This study investigates AI design principles aimed at enhancing the professional development of geometry teachers in Israel. Specifically, these principles focus on content knowledge (CK), which plays a critical role in the quality of geometry instruction.

Geometry, a cornerstone of mathematics education, fosters critical reasoning and problem-solving skills. However, in Israel, many middle school teachers are not adequately trained to teach geometry effectively, leading to gaps in student learning. Traditional professional development programs tend to be overly standardized and fail to address the individualized needs of educators. To bridge this gap, this study proposes an AI-driven system that assesses and enhances teachers' CK by offering personalized learning pathways tailored to their specific needs.

The proposed system is grounded in the Van Hiele theory of geometric understanding, which categorizes geometric thought into five levels, from basic shape recognition to abstract reasoning. The AI system will diagnose each teacher’s current level and provide adaptive learning experiences to support their progression to higher levels. It is designed to help teachers develop their understanding at their own pace, receiving targeted support and feedback.

This study employs a design-based research approach involving multiple iterative cycles to develop and implement an AI-based professional development system for middle school teachers in Israel. At the conference, we will present the design principles that guided the development of the system and share findings from the first implementation cycle. These findings will illustrate the impact of the system on teachers’ development of content knowledge in geometry and highlight the effectiveness of AI-driven professional development in geometry education.

This paper explores how prospective teachers integrate mathematics and other disciplines in the design of STEAM activity plans as part of a transdisciplinary teacher training program developed through a design-based research approach. Conducted over three academic years at a Romanian university, the program engaged over 700 students from diverse specializations in collaboratively creating and sharing STEAM activity plans on a dedicated blog platform. These plans were intended for pre-university learners and emphasized hands-on, technology-enhanced, and interdisciplinary learning experiences.
Focusing on the final study in the broader doctoral research, this contribution investigates the nature of curriculum integration, particularly the roles mathematics plays in conjunction with science, technology, arts, and engineering. Using a combination of semantic analysis and manual coding of 140 blog posts, the study identifies patterns in how mathematical content is contextualized, its didactic roles, and the degree of disciplinary coherence achieved across subjects. The findings reveal that while mathematics is frequently present, its integration varies by student specialization and confidence in transdisciplinary thinking. Prospective teachers specializing in mathematics tend to embed more explicit and conceptually sound content, while others often resort to surface-level mathematical references. Technology is commonly used to support visualization, modeling, or interactive learning, but deeper integration remains inconsistent.
This research contributes to the discourse on curriculum design by highlighting the pedagogical and cognitive dimensions of interdisciplinary planning in teacher education. It suggests that fostering authentic integration of mathematics requires not only cross-disciplinary collaboration but also explicit scaffolding in teacher preparation. The insights inform future directions for designing STEAM curricula that are both conceptually rigorous and accessible, positioning mathematics as a central, connecting discipline within transdisciplinary educational experiences.

Inquiry-Based Learning (IBL) in mathematics is a pedagogical approach that positions students as active participants in the learning process. Rather than passively receiving knowledge, students explore, question, hypothesise, and reason through mathematical ideas. In parallel, digital technologies have become increasingly embedded in mathematics classrooms, offering a wide range of possibilities to support inquiry (Hinostroza et al., 2024).

Despite these affordances, integrating digital tools in IBL environments remains complex. Teaching with technology requires careful orchestration, particularly when balancing open-ended inquiry with structured guidance necessary for deep learning. Teachers need to make strategic decisions about when and how to use tools in ways that align with learning goals, student needs, and pedagogical intentions (Clark-Wilson, Robutti & Thomas, 2020). Consequently, a key challenge arises: How can digital technologies be orchestrated to support both students and teachers throughout the phases of inquiry?

We address this through two complementary frameworks: Theory of Didactical Situations (TDS) and Instrumental Orchestration (IO). TDS structures inquiry into phases—Devolution, Action, Presentation, Validation, and Institutionalisation (Brousseau, 1997). IO (Drijvers et al., 2010) describes how teachers orchestrate digital tools to guide learning. Combining TDS’s structure with IO’s practical adaptability, we design and analyse technology-rich IBL lessons.

Our guiding question is: How can we design and implement an inquiry-based mathematics lesson in a technology-rich classroom? Specifically, we aim to: explore how TDS informs task sequencing within IBL lessons; examine how IO guides purposeful orchestration of digital tools; and investigate how technology supports students’ mathematical thinking.

We conduct a qualitative case study at a secondary school in the Netherlands. The lesson integrates diverse digital tools (e.g., GeoGebra, Padlet, and designed simulations). A key challenge is creating coherence among tools currently functioning in isolation. To address this, we investigate orchestration strategies that support continuity across inquiry phases and smooth transitions between TDS phases.

This presentation shares key insights from organizing the First Function Art Competition, an invitational pilot initiative involving six schools in the Philippines selected for their prior engagement in the Function Art project. The competition aimed to deepen students’ understanding of mathematical functions through the creation of original artworks using GeoGebra. Participants—either individually or in pairs—submitted applets featuring at least 15 mathematical functions, with artworks inspired by Philippine culture, history, or art.

Entries were evaluated using the Function Art Creativity Evaluation Rubric (FACER), a scoring system developed by the author and adapted from the Torrance Tests of Creative Thinking (TTCT) to assess mathematical structure and function diversity. A separate panel of judges scored the artworks based on aesthetics, originality, cultural relevance, and technical execution.

While the competition highlighted the creative and analytical capabilities of students, it also revealed logistical and technical challenges. Some artworks contained an excessive number of functions, leading to slow-loading applets and making the Algebra View difficult to navigate. Processing outputs—such as capturing screenshots for evaluation—was time-intensive. Additionally, since the competition was scheduled near the end of the school year, participation was affected despite strong prior engagement in related classroom activities.

These findings offer valuable guidance for scaling future editions of the competition across the Philippines and Southeast Asia. The presentation will reflect on rubric design, judging coordination, and implementation strategies for educators interested in blending mathematics, culture, and digital art.

One challenge for technology use in mathematics education is the integration of tools in the classroom. In the EJEME project (E-textbooks for Japanese and English Mathematics Education) we first analysed secondary data from the Programme for International Student Assessment (PISA) to explore predictors of effective technology use in mathematics education, and then co-designed a digital mathematics book for Japan and England. Two researchers, one from England and one from Japan, worked with three mathematics teachers in a secondary school in Japan. The aim was to co-design a book around one task on ‘patterns’ from PISA that both English and Japanese students find challenging. We co-designed the books in three steps. In the first step we discussed the topic of ‘patterns’ through analysing the PISA task and other mathematical ‘pattern’ tasks. We asked the teachers to then bring pattern tasks a few days later, which we then discussed in-depth, so the research team had an understanding of the intended aims. The first author then designed a first version of a digital mathematics book with the teachers’ tasks, which was presented a week after that. The feedback that was given then led to a new version of the book. During the co-design process, we did not just converge on the content of the book, but also on design principles for the books, which included sequencing, interactivity, and feedback. In this presentation, we report on both the PISA data analysis, as well as the co-design process.

Computer Algebra based test and assessment systems (from here on: Computer Assisted Assessment) have become more and more prevalent in the last three decades, but even though these tools are more powerful than ever, some simple features of ‘traditional’ education are still often missing. One such feature is partial grading of erroneous work.

Complex problems, in which success of later steps are dependent on results of earlier ones, are common in STEM subjects. These problems can be interpreted as dependent multi-part (DMP) questions. Computer Assisted Assessment has long been criticised for its inability of flexibly evaluating erroneous work in a DMP question, meaning that mistakes in calculation need to be revised manually, which might take even longer on the computer than in a pen-and-paper setting. Using linked response areas in a DMP question, automating partial grading of these flawed student works is made possible.

The technical implementation of DMP questions is called Adaptive Question in the Möbius Test and Assessment System (formerly Maple TA). Adaptive Questions can utilize the error carried forward principle: the computer can evaluate whether the logical steps taken by the student are correct, regardless of the numerical value of their answer; thus mimicking the traditional in-person didactical situation. Modelling teacher guidance, these questions allow students to concentrate on problem solving rather than technical (computational) details – the part of mental work not easily outsourced to AI.

This talk will demonstrate how DMP questions are used in teaching Mathematics to Computer Science Engineer students at the University of Pécs. Since utilizing Maple-based grading and the Adaptive Question options, partial scores, retries or even wrong answer penalties can be applied automatically, Computer Assisted Assessment has never looked so much like a red pen!

This study explores the effectiveness of integrating Augmented Reality (AR) technology and the Edpuzzle platform into teaching the topic "Distance in Space" within the secondary school mathematics curriculum. AR technology enhances the visualization of abstract mathematical concepts, while Edpuzzle facilitates formative assessment through interactive video-based learning. The study employs an experimental method, including both a control group and an experimental group, to measure improvements in students' academic performance, engagement, and conceptual understanding. The findings indicate that this combination not only improves students' ability to solve spatial geometry problems but also fosters critical thinking and active participation. The paper also discusses the potential for applying this integrated teaching model to other complex mathematical topics.

Mathematical activity has gone from requiring pencil, paper and wastepaper basket for its development, to viewing the computer as its greatest collaborator, as well as conceiving programming and specialized software not only as an instrument, but as the origin of its mathematical activity; let's say, its own laboratory. The curricula of the undergraduate studies in Applied Mathematics at Nebrija University has developed an innovation project for the integration of logical/formal thinking with during the first 3 years of its implementation (2022-2025).

One of the focuses of this implementation has been to encourage the development of computational or algorithmic thinking in students, rather than simply learning programming languages (Wing, 2006). To this end, the computer has been integrated, in a coordinated manner, in different subjects and for different purposes, confronting students with the scientific text compilation language Latex, mathematical computing environments (such as Maple or Desmos), programming languages (such as Python or R) and generative artificial intelligence (such as ChatGPT).

The aim of this proposal is to present how this integration between programming and mathematics has been planned from the first course to its extension to successive courses and to comment on some partial results and proposals for improvement.

References

J. M. Wing (2006) Computational Thinking. Communications of the ACM, Vol. 49, No. 3. Retrieved April 1 2025 from https://www.cs.cmu.edu/~15110-s13/Wing06-ct.pdf

N. S. Borweing, V. Jungic (2025) A survey of Experimental Mathematics for Education. Maple Transactions, Vol. 5, No. 1, 22378. Retrieved April 1 2025 from https://mapletransactions.org/index.php/maple/issue/view/1998

Generative AI technologies such as ChatGPT offer new opportunities for teacher education by enabling the creation of responsive, interactive environments. While recent discussions highlight how these tools personalize student learning and enhance learner agency (Pepin et al., 2025), our work explores how AI technologies can assist teacher education. Drawing on a sociocultural perspective in which technologies act as agents in the learning process (Borba & Villarreal, 2005), we report on the design of simulated student agents developed to support preservice mathematics teachers’ professional practices.

Our focus is creating three custom GPTs within ChatGPT, each simulating a secondary student who exhibits a common misconception about the equal sign. Each AI agent was paired with a carefully selected task and a short video illustrating the student’s incorrect reasoning. The simulated students were designed to engage in realistic, plausible conversations, allowing preservice teachers to develop their professional skills in a controlled environment.

The development process involved iterative prompt engineering, expert feedback, and cross-linguistic testing. Initial prompt design and review were conducted in English, followed by testing in German with preservice mathematics teachers in Austria, Spanish with in-service mathematics teachers in Uruguay, and Turkish with mathematics educators in Türkiye. Across these stages, the process was shaped not only by our instructional goals but also by the capabilities and constraints of the AI itself.

This work contributes to current conversations about the role of AI in mathematics education by showing how designing with generative technologies involves a dynamic interplay between human intention and technological agency, shaping new spaces for professional learning.

The rapid evolution of digital tools in education demands closer alignment between educational technology (EdTech) developers and pedagogical needs. Many EdTech developers often focus more on technological or market-driven aspects rather than grounding their designs in pedagogical principles and evidence-based learning research (McGrath & Åkerfeldt, 2020). This lack of integration between technological innovation and educational expertise can result in tools that do not adequately support effective learning.

This study proposes a measurement tool to assess EdTech companies’ needs for better pedagogical alignment across six dimensions: (1) General company profiles, (2) Goals and challenges, (3) Product technology, (4) Pedagogical alignment, (5) Market strategy, and (6) Collaboration opportunities. Needs assessments are foundational for aligning interventions with stakeholder priorities as a critical bridge between strategic planning and evaluative practice (Altschuld & Watkins, 2014). Yet, few studies apply this methodology to EdTech development.

Our work adapts Kaufman's (2000) Organisational Elements Model to evaluate EdTech companies across these six dimensions. This structure mirrors established needs assessment phases: identifying gaps, prioritising solutions, and fostering partnerships (Witkin & Altschuld, 1995). The assessment follows a structured three-phase process for mentoring, ensuring alignment from problem exploration to solution implementation:

• Phase 1: Discover "What is?" The initial phase emphasizes comprehending the company's current situation through a semi-structured survey and exploratory discussions.

• Phase 2: Data gathering & analysis. Based on the findings from Phase 1, this phase includes thorough validation through face-to-face meetings and targeted assessments, specifically focusing on identifying gaps in pedagogical alignment and exploring collaboration opportunities.

• Phase 3: Decision-making. The third phase translates insights into actionable plans, co-developing implementation roadmaps with key performance indicators to address identified challenges. It ensures solutions balance pedagogical needs (micro-level) with market strategy (macro-level) and societal impact (mega-level) per Kaufman's model.

Future steps include validating the measurement tool with edtech companies, expanding its application.

Combining games with mathematics education offers strong potential for deep and sustainable learning. The playful setting not only increases learners’ motivation but also enables them to engage with mathematical content through action, experimentation, and discovery. Games foster communication and cooperation, stimulate reflection, and offer opportunities for practicing mathematical skills in a motivating way. They help make mathematical concepts tangible and support diverse approaches and ways of thinking.

Digital applets such as those developed in GeoGebra offer particular added value: they are easily accessible, interactive, customisable, and allow for differentiated learning scenarios. At the same time, their use supports the curriculum objective of fostering digital literacy and critical reflection on digital tools. GeoGebra applets thus go beyond being mere digital game tools—they offer a meaningful, didactically grounded extension to traditional instruction.

In addition, the GeoGebra games support discovery-based learning in mathematics lessons: learners can develop their own hypotheses, recognise patterns and connections, and explore mathematical structures independently through active experimentation, visual feedback, and variable game situations. The applets enable a dynamic engagement with mathematical content, in which explorative action and productive practice are intertwined—a central component of modern, skills-oriented mathematics didactics.

In this interactive workshop, we will explore which mathematical concepts can be particularly well supported through digital games, which cognitive processes are stimulated in learners, and how interactive tools can enhance problem-solving skills. As part of a hands-on phase, participants will try out selected GeoGebra applets. With the help of guiding questions, they will analyse how mathematical thinking is stimulated through play and discuss the didactical potential of the games in classroom contexts.

The workshop is aimed at researchers, teachers, teacher educators, and developers of interactive learning materials interested in playful and digitally supported mathematics education across educational levels.

This study investigates how preservice mathematics teachers (PMTs) engage in instructional design using digital tasks in the Illustrative Mathematics (IM) curriculum accessible through GeoGebra. Within the context of a computer-assisted mathematics education course, teachers were guided through a structured design process that included curriculum alignment, task analysis, identification of prerequisite knowledge and misconceptions, and lesson planning with digital integration.

Instead of working independently, PMTs followed a scaffolded design template provided by the instructor (first author). This framework required them to select a learning objective from the national middle school mathematics curriculum, divide lessons into three phases (introduction, development, conclusion), and justify pedagogical choices. Special emphasis was placed on anticipating student thinking and adapting digital tasks to local classroom contexts.

Five representative lesson plans were selected for analysis across all submitted studies. These plans targeted a variety of grade levels (5–8) and geometry-related topics (e.g., angles, area, volume, triangles, and the Pythagorean Theorem). While working within the same scaffold, teachers demonstrated a variety of strategies in task adaptation and the use of digital tools.

The analysis revealed that PMTs frequently modified the original IM tasks to simplify language, increase visual support, or sequence activities more gradually. GeoGebra applications were used not only for visualization but also as questioning and formative assessment tools. Although the pedagogical structure was externally imposed, teachers engaged meaningfully in the process and made instructional decisions that reflected increased awareness of the curriculum, technology, and student needs.

The study suggests that when targeted scaffolding is provided, PMTs can move beyond superficial use of digital resources and begin to act as reflective instructional designers. It also highlights the potential of internationally developed materials such as IM to support mathematics teacher education when carefully adapted to local contexts.

Project-based learning is increasingly used in mathematics within an integrated STEM (Science, Technology, Engineering, and Mathematics) approach. However, teachers often struggle to identify meaningful contexts in which mathematics can be naturally explored (Diego-Mantecón et al., 2021). Artificial intelligence (AI), particularly Generative Pretrained Transformers (GPT), may offer new opportunities for finding and designing such contexts, as it can simulate users’ language structure by processing large volumes of text to generate responses (Pepin et al., 2025). Consequently, in this study, we evaluate the effectiveness of ChatGPT-4o in helping pre-service secondary mathematics teachers design tasks for a STEM project on ‘relationships and functions’ for 15-year-old students. Specifically, we examine prompt techniques, task alignment with the Spanish curriculum, and integration with other STEM disciplines. Data from 15 participants were collected through the generated task, ChatGPT interaction histories and interviews and analyzed using a mixed-methods approach. Concerning prompt techniques, preliminary results reveal that most participants initially copied the instructions exactly as they were given, adding only information about their role as teachers or curricular details. Most of the designed tasks were either unsuitable for 15-year-old students or unrelated to ‘Relationships and Functions’. Many tasks neither integrated knowledge from other STEM disciplines nor provided appropriate learning context. These findings suggest that users need training to generate effective mathematical tasks within a STEM project using AI. In some cases, ineffective prompting or insufficient task analysis hindered the expected results.

Acknowledgment

This study is part of R&D&I project Grant PID2021-122326OB-I00 funded by MCIN/AEI/ 10.13039/ 501100011033.

References

Diego-Mantecon, J.M., Prodromou, T., Lavicza, Z., Blanco, T.F., & Ortiz-Laso, Z. (2021). An attempt to evaluate STEAM project-based instruction from a school mathematics perspective. ZDM–Mathematics Education, 53(5), 1137-1148.

Pepin, B., Buchholtz, N., & Salinas-Hernández, U. (2025). A scoping survey of ChatGPT in mathematics education. Digital Experiences in Mathematics Education, 11, 9-41.

This study aims to evaluate the 3D Drawing Understanding Scale (3DUS) within the context of technology and vocational education training (TVET) in indonesian higher education, specifically in relation to 3D modeling for engineering drawing. The developed 3DUS scale is designed to assess essential 3D drawing competencies relevant to technical and engineering-related instruction in TVET settings. The 3D modelling workshop was conducted in hybrid learning environments focused on 3D modeling in engineering drawing before data collection. A total of 278 respondents, consisting of pre-service and in-service vocational education teachers across Indonesia, participated in this study. The 3DUS consisting five questionnaire items. The results show that all items meet the fit validity criteria, with average infit and outfit MNSQ values of 0.99 (SD = 0.11) and 0.91 (SD = 0.09), respectively. The 3DUS also demonstrated high reliability (0.956), exceeding the acceptable threshold of 0.67. The Wright Map indicates that most respondents possess moderate to high ability in 3D drawing understanding, with person measures concentrated between logits 0 and +11. In contrast, item difficulties range from approximately 0 to -2 logits, suggesting that the items are relatively easy to understand by participants. Although this reflects a successful learning outcome, it also suggests a slight improvement for target participants; future versions of the scale may benefit from more challenging items to better target higher-ability individuals. Additionally, none of the five 3dUS items exhibited significant DIF based on pre-service and in-service vocational teachers. All DIF contrasts are below absolute 0.43 logits, indicating negligible (Category A) and confirming no significance based on teacher group. These results suggest that the scale measures 3D drawing understanding fairly and consistently across both teacher groups, with no evidence of item bias.

The Bertrand paradox (Joseph Bertrand, 1889) on the length of chords of a circle is one of the most well-known paradoxes in probability theory and it is frequently mentioned as a thought-provoking problem. Despite that, there seem to be very few studies/presentations that go deeper into the understanding of the differences between the three base models of the paradox than just the usual midpoint/chord distribution diagrams and calculation of the Bertrand probability.

In our research, we first investigated how the three base models can be described by different sorts of probability distribution functions and explored the connections between those distributions. We ran simulations, visualized the generated data and compared it to the theoretical description.

Second, we extended the set of models by some new ones that either generate random chords in a natural-looking way or fill some gaps in the theoretical framework. We generalized the previously introduced probability distribution functions to all possible models, giving general formulae for changing between different representations. Some of the new models are fascinating in their own right.

Finally, we characterized scale-invariant models and uncovered some interesting connections between different elements of the theory. In the end, we summarized the different statistics computed for each model in a table.

There are still plenty of questions left open in this topic that are worthy of further investigation.

Computational and visualization capabilities of computer algebra systems have been of great help in our research and simulation tests, while their demonstrative power greatly helps to make the topic understandable to the audience.

The development of digital technologies has significantly impacted teaching and learning environments across various subjects, including mathematics (e.g., Pepin et al., 2024). Among these technologies, generative and communicative artificial intelligence (AI) agents—such as ChatGPT—have recently garnered significant attention in education. ChatGPT is a highly advanced language model with self-improving capabilities, designed to provide personalized responses in real time (Farrokhnia et al., 2024). Its vast potential to assist educators has been well documented, particularly in reducing workload in teaching (e.g., writing lesson plans and learning objectives), assessment (e.g., creating student progress reports and grading rubrics), and supporting student learning (e.g., generating study guides, posing word problems, and drafting sample texts for students to critique) (Trust et al., 2023, p. 4).

This study investigates the potential applications of a generative and communicative AI agent—ChatGPT-4o—in designing mathematical tasks, with a particular focus on derivatives, a fundamental topic in calculus. Drawing on the tenets of the Anthropological Theory of the Didactic (ATD), particularly the concept of paradidactic praxeology (Winsløw et al., 2018), ChatGPT-4o is employed to assist in designing two types of tasks that are central to mathematics education: mathematical modeling and problem-posing tasks.

To analyze the tasks proposed by ChatGPT, a reference model grounded in the literature on task design for mathematical modeling (e.g., Borromeo Ferri, 2018) and problem posing (e.g., Radmehr & Vos, 2020) is constructed and used to evaluate the outputs of the AI agent. The findings reveal both opportunities and limitations in using ChatGPT for task design, offering insights that could inform the professional development of upper secondary and university mathematics teachers aiming to incorporate this tool into their task design practice.

In contemporary mathematics education, there is an increasing use of digital technology, particularly screens, to provide individualized learning experiences. However, there is a need to balance digital technologies and analog approaches to make mathematics tangible for students, such as physical manipulatives in mathematics education. However, integrating manipulatives in mathematics classrooms is not without challenges, and there is a need for tailored materials. Digital fabrication (DF), such as 3D-printers and laser-cutters, can enable teachers to create tailor-made manipulatives. DF combines the benefits of digital technologies, such as fabrication accuracy and sharing DF-files, with hands-on experience of tactile manipulatives in K -12 education.
To explore the potential of DF for making manipulatives, we conducted eight full-day workshops with teachers over one year. In the workshops, we collaborated with teachers to explore how DF can be utilized to make manipulatives that facilitate more practical, inquiry-based mathematics teaching. In this talk, we present a novel DF-created manipulative, an empty number line (ENL) the teachers created using a 2D sketch program to model and laser-cutter to produce. This example demonstrates how teachers reflect on mathematics and mathematics teaching when making manipulatives using DF.
Our preliminary results show that: 1) ENL allows pupils to work with and represent mathematical concepts in various ways. 2) ENL facilitates differentiated teaching because the manipulative is flexible, and all pupils can work with the same manipulative at different difficulty levels. 3) The teachers collaborate and are critically aligned regarding the ENL, expressed when they reflect on different iterations and variants they have made using DF.
This study underscores teachers’ changing role when expanding their repertoire of digital technologies for creating tactile manipulatives, enabling hands-on and practical teaching methods. This research offers valuable insights into the design of learning environments by documenting how DF technologies can inspire teachers’ creativity and contribute to mathematics education.

Technology-aided instruction in mathematics higher education has been a topic of significant discussion over the past 30 years. Research has covered various mathematical disciplines, including calculus, algebra, statistics, and geometry. However, there is a notable gap in the literature regarding the utilization of technology to facilitate inductive, experimental approaches in mathematics education, in which learners comprehend abstract ideas, rediscover mathematical facts, analyze examples, formulate conjectures, and get hints for formal rigorous reasoning. My presentation aims to describe a technology enhanced, and inquiry-based learning activity that relates the Butterfly theorem to locus problems in the Gaussian plane. Among the outcomes of that activity: the technology-aided construction of new knowledge, the application of prior knowledge in novel situations, the development of a deeper understanding of the theorem's limitations, and the exposure of interdisciplinary bridging between various branches of mathematics. The purpose of planning this activity was to introduce young learners to a theorem that was likely unfamiliar to them. By incorporating a technological component and providing new forms of representation—particularly interactive ones—I aimed to create an opportunity for students to explore the theorem within a scientific laboratory setting. Through hands-on engagement and dynamic examples, students could better grasp and experience the core concepts of the theorem. This approach also encouraged the discovery of new insights and supported the development of formal reasoning by distinguishing between various cases. Notably, the exploration led to unexpected conclusions and generalizations, revealing a surprising connection between the Butterfly Theorem and Möbius transformations.

This study investigates how mathematics teachers use Gen-AI to generate math problems for middle and high school students. While recent studies have highlighted the potential of generative AI in educational content generation, few have examined the authentic process through which teachers interact with these tools—how they iteratively generate, modify, and evaluate AI-suggested tasks until arriving at a final version suitable for their classroom. This study aims to fill that gap by exploring the reasons behind teachers’ use of Gen-AI, the ways in which they adapt its outputs, and the pedagogical considerations that underlie their decisions. The research also explores the characteristics of the tasks the teachers produced and the pedagogical benefits and challenges associated with their integration.

Gen-AI holds significant potential to support teachers in content generation, particularly in producing a wide range of math problems aligned with various instructional goals. Traditionally, adapting such tasks to fit specific classroom needs has required considerable effort, pedagogical insight, and deep content knowledge on the part of the teacher. Gen-AI may reduce this burden by streamlining the task generation process, though effective and responsible use still requires critical review and careful pedagogical adaptation of the outputs.
At the conference, I will present examples from teacher–AI interaction logs and share preliminary findings that illustrate the types of tasks teachers generated, the modifications they made, and the reasoning behind their decisions. These examples reveal common patterns, practical challenges, and emerging strategies for integrating Gen-AI effectively into mathematics instruction.

As the use of technology in schools continues to advance rapidly, new teaching and learning methods and tools have emerged. One of these advances in learning with technology is adaptive learning (AL) through digital mathematics learning materials. AL describes an approach where elements, such as instructions, content, difficulty, or feedback, within digital learning materials are tailored to the individual learner. In doing so, AL moves away from the one-size-fits-all approach and provides an individualised learning experience to address heterogeneity among learners in the classroom. Although this approach has been shown to be beneficial for learners and teachers in several empirical studies, little research has been done on teachers’ perceptions of AL and their implementation in mathematics classrooms. This gap is critical because teachers serve as the primary decision-makers regarding the adoption of educational resources such as adaptive learning materials; without their decision to integrate AL materials, the potential advantages of AL cannot be realised. Therefore, there is a clear need to understand teachers’ needs and perceptions of AL in order to promote its use and reap its benefits in mathematics teaching and learning. Hence, the underlying study aims to uncover teachers’ needs and perceptions of AL in digital mathematics learning materials and their implementation in secondary mathematics classrooms. To achieve this goal, we employ a qualitative research approach using semi-structured interviews with mathematics teachers. We utilise reflexive thematic analysis to analyse teachers’ perceptions and implementation strategies of AL in mathematics classrooms. The findings provide valuable insights into the needs and perceptions of mathematics teachers regarding AL. By shedding light on these very needs, we will be able to provide fruitful information for researchers, educational stakeholders, and material developers on how to foster the implementation of AL in digital mathematics learning materials.

This paper presents a comparative analysis of four AI chatbots with potential applications in the fields of mathematics education, namely ChatGPT, Gemini, DeepSeek, and Claude. Previous research has highlighted that ChatGPT can serve as a useful tool to mentor students in enhancing computational thinking, particularly in algorithms and debugging facets. The main objective of this paper is to compare the functionalities, educational affordances and limitations of these generative AI tools in constructing geometrical objects in GeoGebra using only commands. This comparison focuses on how these tools can support the development of computational thinking in mathematics education. By examining their potential, this study aims to offer insights into the classroom implementation of AI chatbots to enhance student learning. For this purpose, we designed a common task that involves constructing an inscribed regular 15-sided polygon in a circle using command-based input in GeoGebra. Data were collected from the researchers’ exploration and a pilot study with high school students. By attempting the same task using different AI chatbots, we compare the resulting command sets (executability and mathematical concepts involved) and the ways in which computational thinking facets emerge. We will highlight both the capabilities and limitations of each AI chatbot in facilitating this process. By examining their strengths and weaknesses, this study aims to offer insights into the effective selection and classroom implementation of AI chatbots to enhance student learning. Further research is encouraged to investigate deeper on how AI can be utilized effectively for learning mathematics.

This study examines the interaction between high school students and Gen-AI in the context of mathematics education, focusing on how students formulate prompts and validate AI-generated responses while learning the concept of the derivative. Previous studies have addressed various prompt engineering techniques and emphasized the importance of clarity, relevance, and context in prompt construction. Others have focused on the need to critically evaluate AI-generated content due to its probabilistic nature and occasional inaccuracies. However, few studies have explored how these processes unfold in real classrooms, during live interactions that involve teacher guidance and classroom dialogue. This study aims to address that gap by investigating how teachers’ guidance and discussion shape students’ prompt construction and response validation when engaging with AI.

While generative AI increasingly offers significant potential to support mathematical reasoning and critical inquiry, its effectiveness largely depends on how it is used, and how teachers mediate its use. This study argues that prompt writing and answer validation are not merely technical skills, but educational processes that require guidance, practice, and reflection. By analyzing in-class interactions, the research seeks to understand how students can be supported to use AI not just efficiently but critically and meaningfully.

The study adopts Activity Theory as a theoretical framework. This theory enables a systemic view of classroom interactions, examining how student-AI engagement is shaped by teacher interventions and broader school-based contexts. I will present findings from classroom observations and AI interaction logs at the conference. These findings will demonstrate how teachers’ guidance affects the quality of student-generated prompts and validation strategies and will offer practical suggestions for improving mathematics instruction in classrooms that integrate AI.

This study explores how the introduction of digital tools reshapes the role of the teacher in primary mathematics classrooms, drawing on data from a Grade 4 Marathi-medium school in India. Forty-five students were divided into two groups: one engaged with an arithmetic learning application designed for individual interaction, while the other used a socially interactive application encouraging peer collaboration. Through video recordings, focus group discussions with students, field notes, and computer log data, we conducted an interaction and discourse analysis to understand how these differing digital contexts influenced teaching practices.

In the individual-use setting, the teacher’s role largely mirrored traditional classroom norms- monitoring progress, offering direct instruction, and providing corrective feedback. However, in the socially interactive setting, the teacher's authority was distributed. Students frequently turned to their peers for help, validation, and explanation, positioning the teacher less as the sole source of knowledge and more as a facilitator of collaborative learning. These findings suggest that the impact of digital technology on the teacher’s role is not uniform but is shaped by the features of the digital tools, the classroom norms that emerge, and the broader school culture.

Our analysis highlights that technology integration alone does not redefine teaching roles. Rather, the design of digital tools and the ways in which they support or constrain social interaction significantly mediate pedagogical dynamics. The findings carry important implications for the design of digital learning environments, especially in multilingual and resource-constrained contexts. We argue for context-sensitive design that takes into account local classroom cultures, tool-specific affordances, and evolving teacher-student relationships. There is no universal model- tools must be adapted to the cultural and pedagogical realities in which they are deployed.

Mathematics plays a pivotal role in numerous academic disciplines; however, recent
research indicates a concerning decline in undergraduates’ proficiency in traditional
mathematical areas, such as symbolic calculations. A German study highlighted this
issue, showing that while students often struggle with routine symbolic tasks, they
demonstrate strength in broader mathematical competencies such as reasoning, modeling,
and the use of multiple representations. These findings suggest that curriculum reforms
prioritizing process-oriented skills could provide a more effective path forward, even as
traditional procedural fluency wanes. The MATH-DIGGER – Mathematical Digital Escape
Rooms project explores the use of digital escape rooms as an innovative educational
strategy to support the development of both content knowledge and essential mathematical
process skills. Digital escape rooms offer a dynamic and interactive environment where
students are motivated to apply mathematical reasoning under time constraints to solve a
series of interconnected puzzles. Their potential lies in fostering engagement while aligning
game mechanics with pedagogical goals, creating meaningful and memorable learning
experiences [1].
In this paper, we present the conceptual framework and educational rationale behind MATHDIGGER. We detail the mathematical competencies that guide the design and
implementation of the digital escape room, describe the development process, and analyze
sample tasks tailored to enhance key areas such as problem-solving, logical reasoning, and
mathematical communication. Finally, we discuss the expected learning outcomes and the
potential of this approach to complement and enrich traditional mathematics instruction.
[1] C. M. Pinto, C. Nikolopoulos, M. Cruz, R. Queiros, and K. Petridis, “Empowering
engineering students’ math literacy with digital escape rooms,” in 2024 IEEE World
Engineering Education Conference (EDUNINE), 2024, pp. 1–6.

This study analyzed the performance of ChatGPT-4 in solving three Mathematical Analysis in IR (MA1) exams in Portuguese higher education, covering most of the traditional topics of the discipline. The results demonstrated remarkable performance, with accuracy rates of 96%, 91% and 100%. In most questions, the model presented correct, precise and detailed answers, structured in steps that facilitate students' understanding. Although, in some cases he did not use the simplest method, he still managed to solve the problems. However, specific difficulties were identified, namely in determining codomains and calculating areas by integrals, where inconsistencies were revealed, failing in a more complex question, but correctly answering a simpler one. With an accuracy rate of over 90%, ChatGPT-4 is proving to be a promising tool for teaching and learning Mathematical Analysis, both to help students with independent study and for classroom support, and the creation of teaching materials. However, its use still requires critical review by teachers and students. This study provides relevant insights for MA1 teachers, identifying the topics in which the model presents the greatest weaknesses.

In line with areas of emergent interest, this proposal inquiries on "How do Mathematics Teacher Educators (MTE) use technology in their work with mathematics teachers?". This study is set in the Chilean context, where new initial teacher education standards recently came into force. These updated regulations emphasize technology integration, particularly for the training of prospective secondary school mathematics teachers.

During the first semester of 2025, MTEs of a mathematics pedagogy program emphasizing technology integration as one of its hallmarks will meet monthly to discuss this topic. This initiative aims to build a consensus understanding of the purposes, potential benefits, and limitations of integrating technology into mathematics education.

1. The first session aimed to diagnose teaching practices associated with integrating digital technologies in teaching itself. The SQD framework (Tondeur et al., 2025) was used during this session.

2. The second session was devoted to unpacking the potential benefits of a dynamic applet in addressing the recurring problem of distinguishing between the sum of squares and the square of the sum in secondary education.

3. The third session will be devoted to discussing the impact that promoting the conceptualization of the media as a point of balance can have on students' understanding, and the role of technology in achieving this objective.

4. The fourth session aims to analyze the proposals for technology-enhanced didactic teaching activities that each member has planned for their subject course program and to receive feedback from the group.

5. The fifth session will be devoted to examining the results of the technology-enhanced classes implemented during the first semester. We will include testimonies from prospective teachers regarding their experiences of using digital technologies in the different courses.

Conclusions and projections from this initiative will be presented for further discussion in the future.

Geometry is traditionally taught according to the definition-theorem-proof sequence, and the pictures were stilled figures. The introduction of digital tools has transformed its teaching and learning into an experimental field, using Dynamic Geometry and Computer Algebra Systems. Networking between different kinds of software, together with websurfing and the usage of databases devoted to geometry and algebraic geometry, offers large possibilities to broaden horizons.

We will present examples of activities being an extension of the curriculum, which have been proposed for pre-service and in-service teachers, the last learning towards an advanced degree.These students discovered a STEAM approach to Mathematics, with emphasis on T, A and M.. Together with their technological literacy, the students developed also new algebraic skills. Among the topics:

• Construction of geometric loci beyond the elementary examples (such as perpendicular bisectors): Euler line, pedal curves, hyperbolisms of plane curves, etc.
• Exploration of offsets of plane curves.
• In some cases, the study of singular points.
• Models of trajectories in space
• Models of archtectural items and creation

For the Dynamic Geometry aspects, we use GeoGebra, and its companion GeoGebra-Discovery (GD) which provides both symbolic versions of commands offered by the regular GeoGebra (with numerical algorithms). The commands for the determination of geometric loci are used extensively. For singular points, the command Plot2D available only in GD is very efficient.

Finally, we will present some outputs and (enthusiastic) feedbacks by students.

References

1. Th. Dana-Picard, M. Tejera and E. Ulbrich (2024): 3D space trajectories and beyond: abstract art creation with 3D printing, Electronic Proceedings in Theoretical Computer Science EPTCS 398, 142–152, https://doi.org/10.4204/EPTCS.398.17

2. Th. Dana-Picard (2025). Dynamic constructions of hyperbolisms of plane curves, Electronic Journal of Technology in Mathematics 19(1). Online: https://ejmt.mathandtech.org/Contents/eJMT_v19n1p4.pdf

3. Th. Dana-Picard (2025): Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more. arXiv: http://arxiv.org/abs/2503.15135

The Poly-Universe education game family enhances geometric and artistic competences, as well as soft skills, through its ‘scale-shifting’ symmetry inherent in its geometric forms and a universal color combination system. The main objective of the game is to develop a new visual system for mathematics education.

The EARLY-POLY (Preschool and Lower Primary STEAM Education with Poly-Universe) project’s objective is to introduce the Poly-Universe game family to preschool and primary students, respectively to preschool and primary school teacher students and to familiarize participants with the game's basic shapes, sizes, colors, and various applications. Research and experience indicate that exposing children to STEAM subjects at an early age can foster their interest, creativity, and problem-solving skills. Our project aims to strengthen STEAM education in preschools and primary schools by integrating the Poly-Universe tool and incorporating a STEAM-focused approach into the curriculum.

A needs analysis and survey conducted with 101 educators across four European countries revealed that teachers predominantly use manipulatives with children aged 3-10. Our results indicated a need for a methodological teaching tool suitable for both kindergarten and lower elementary school settings. No significant gender differences were found in preferences for manipulative tools or in attitudes and abilities related to STEAM education. Educators reported that the use of such tools facilitates the transition from kindergarten to primary school and that both formal and non-formal educational contexts are equally relevant for this age group. The importance of art in STEAM education was emphasized, with educators expressing a need for additional practical resources for the application of manipulatives. The problem-solving activities conducted by us with the Poly-Universe games demonstrated a significant positive shift in students' attitudes toward mathematics. The games fostered creative thinking through hands-on tasks, thereby enhancing engagement and confidence in learning among students of various ages.

Generative artificial intelligence offers the opportunity to promote 21st century skills in general and mathematical competencies in particular among secondary school students. Thus, a smart chatbot can provide individual learning support and offer differentiated feedback. One condition for this is that students have appropriate basic mathematical knowledge and language skills to be able to communicate “mathematically” with the AI. For evaluating its output, they must also be able to think critically and reflect because AI is not a guarantee of reliable answers.

Roland Fischer's model (2012), which describes the communication between laypersons and experts, is an established concept in mathematics education, that can be applied to learning with AI: Accordingly, students primarily need basic knowledge and reflection skills because they can leave the actual operating to the AI. Communication and reflection in mathematics lessons — an important factor of citizen empowerment through mathematical education — must be addressed even more considering AI.

In this poster, we present constructive examples of how students can learn geometric and arithmetic topics with the help of AI. The first educational objective is to enable students to produce questions and practice needs in writing. They should then be capable of processing the AI’s answers and tasks in order to finally engage in a critical reflection on the solutions and statements. The learning material was designed as part of a mathematics lesson in which students used a chatbot to follow up individual questions and practice according to their interests. Our first conclusions show that the listed competencies are necessary for learning with AI to be effective and motivating. We also discuss how the use of AI in the classroom changes the workload of teaching and diagnostics for teachers.

This paper presents physical electronic stationery on electronic paper, with a particular focus on the physical electronic digital compass tools (digital compass). E-learning has become widespread in recent years, even for mathematical drawing, but the problem-solving steps are limited to the operation of a single task, like the mouse-based GUI. Very often a stationery item is selected from a menu, displayed somewhere on the screen, adjusted with the mouse or keyboard, moved to an appropriate place and executed. Actions that involve using both hands, such as using multiple stationery items, are broken down into single-handed operations and serialized. These steps are so different from physical stationery. On the other hand, we are working on a pen-based environment for answering all questions by handwriting with a pen as on paper. We use an electronic paper named IoT Paper, which combines an electronic paper display (EPD) and a tablet. The IoT Paper is equipped with a pen and an eraser, each of which samples time series of pen tip coordinates at 480 points/sec. We have added the digital compass to the IoT Paper to allow learners to answer for drawing questions. This digital compass physically has a needle and a stylus and can draw an arc by placing the needle on the EPD, opening the digital compass, or in reverse order, and moving the stylus. This is exactly the same as a normal compass tool. In addition, the needle and the stylus positions are sampled chronologically as a pair. While the needle position information may be difficult to find on ordinary paper, it is clearly recorded with this digital compass. The sampled position data can be used to replay the drawing steps, and to analyze the user’s problem-solving process. We analyze some cases where the problem solving-processes are so different.

Introduction: This study investigates the connection between the use of digital tools and learning outcomes, attitudes, understanding, algebraic skills, instrumentation, and creativity among students in the Mathematical Modelling and Data Analysis (MMAD) program at Gdansk University.

Methods: Data were collected through surveys of MMAD students, focusing on their use of digital tools, study habits, and academic performance.

Findings: Digital tools such as YouTube, ChatGPT, and educational websites were widely used by students, enhancing their understanding of complex concepts and improving algebraic skills. Students generally had positive attitudes towards these tools, appreciating their role in creative problem-solving and practical applications. However, challenges such as information overload and dependence on digital tools were noted.

Conclusion: Digital tools significantly enhance learning outcomes for MMAD students at Gdansk University. A balanced approach combining digital resources with traditional methods is recommended to maximize educational effectiveness.

Bibliography:

1. Pozo, J.-I., Cabellos, B., & Pérez Echeverría, M. d. P. (2024). Has the educational use of digital technologies changed after the pandemic? A longitudinal study. PLOS ONE. https://doi.org/10.1371/journal.pone.0311695
2. Tai, B. T., & Son, N. T. (2023). The Survey of Digital Transformation in Education: A Systematic Review. International Journal of Technology in Education. https://doi.org/10.54855/ijte.23343
3. Eaton, S. E. (2025). Global Trends in Education: Artificial Intelligence, Postplagiarism, and the Future of Learning. Education Integrity. https://doi.org/10.1007/s40979-025-00187-6

Many undergraduate students struggle with writing mathematical proofs (Stylianides et al., 2017). One major contributing factor is limited knowledge and control over formal definitions of mathematical concepts (Moore, 1994). Students often rely on their intuitive "concept image"—which may be incorrect—even when they can accurately recall the formal definition (Edwards & Ward, 2004).

This study explores the relationship between three variables: (1) students' ability to recall definitions, (2) their ability to analyze and reason about definitions, and (3) their success in an undergraduate mathematics course.

For the purpose of this study, we define:

• Knowledge of a definition as the ability to accurately state a formal definition of a given mathematical concept.
• Understanding of a definition as the ability to distinguish between equivalent and non-equivalent formulations of a definition, to construct counterexamples to incorrect formulations, and to justify equivalence of alternative correct formulations.
• Success in the course as the student’s final grade on the course exam.

The first stage involves designing mixed-format questionnaires (open-ended and multiple-choice) on definitions from a first-year calculus course. A small sample of students will complete the questionnaires and their performance will be compared to their final exam scores. Based on this initial analysis, a set of closed-format assessment tools will be developed to examine the same relationships on a larger scale.

Findings may offer insights into how students’ understanding of definitions contributes to learning and achievement in advanced mathematics. We will draw on the work of Lew et al. (2022), who investigated how lecturers model the learning of new definitions through examples, counterexamples, and classroom discourse. The study suggests ways to integrate digital tools that help students explore definitions through dynamic examples, feedback, and interactive tasks.

The rapid development and availability of chatbots have raised the question of how to use them in teaching mathematics to support students’ thinking and creativity rather than replace them. A study was conducted with teacher-training students (n=19), in which we attempted to direct the chatbot ChatGPT to guide learners step by step in solving word problems related to quadratic functions. Each student entered a detailed prompt into ChatGPT, prepared by the authors of this article, instructing the chatbot to guide the learner step by step, considering the learner’s prior knowledge. The students solved the problems throughout one lesson and submitted a link to their ChatGPT conversation for analysis. In addition, they shared their opinions on the positive and negative aspects of ChatGPT as a tutor. The results show that ChatGPT generally performed well in solving the tasks. Its explanations were thorough. However, in an attempt to engage the learner, it mostly posed closed-ended questions, often checking understanding with yes/no answers. During the conversation, the chatbot frequently asked several questions at once. Although the instructions specified that the chatbot should not solve the problem for the student, it sometimes did so without involving the learner. Furthermore, ChatGPT explanations contained linguistic inaccuracies (in Estonian), obscure terminology, excessive information, instances of accepting incorrect answers given by learners as correct, and errors in the solution steps —all of which could mislead or confuse students. Understanding the strengths and limitations of chatbots as a student tutor helps teachers decide where and how to integrate ChatGPT into mathematics teaching so that it supports learning.

The poster presentation provides an overview of a study that examines the implementation of a digitally supported team-based learning (TBL) approach in the course Elements of Discrete Mathematics, taken by STEM students at the University of Tartu. As the new generation of students grows up immersed in digital environments, traditional teaching methods often struggle to meet their learning preferences and needs. Discrete mathematics, with its abstract concepts and logical rigor, has become increasingly challenging for students when taught through passive or lecture-based instruction.

In response to these challenges, TBL—a collaborative active learning pedagogy—was adopted to increase student engagement, encourage peer instruction, and support deeper conceptual understanding. The structure of the course was deliberately adapted to leverage the affordances of the Moodle learning management system, which has long been in use by instructors at the university. This integration created a blended learning environment that combines the pedagogical strengths of TBL with the flexibility and structure provided by digital tools.

The study investigates how this blended approach supports independent learning and fosters collaborative problem-solving, especially among digital native students. Based on student reflections collected through surveys and open-ended responses, the analysis focuses on how the new learning experience influenced their attitudes toward mathematics, their perceptions of the course, and their intentions to retain and apply the adopted learning strategies in future studies. Given the unique course design and long-standing institutional experience with Moodle, this case offers valuable insights for colleagues interested in adapting active learning in digitally supported environments.

The present study aimed to investigate the impact of the dynamic geometry program GeoGebra on seventh-grade students’ learning outcomes in functions, as well as their attitudes toward using GeoGebra. In the experimental group (n = 128), linear functions and inverse variation were studied using GeoGebra. The control group (n = 84) did not use computers; their learning took place traditionally using a textbook, paper, and pencil. In the experimental classes, students used GeoGebra for 3–4 of the 19 allocated lessons and were guided to explore relationships among different representations of functions. No statistically significant differences were found between the experimental and control groups in the pre-tests (before studying functions) or the post-tests (after studying functions). However, 42% of respondents in the experimental group indicated that using computers improved their attitude toward mathematics. Four reasons emerged from those whose attitudes had improved: (1) computers helped them understand the content better, making learning easier; (2) using computers was more convenient and interesting, thus boosting their interest in mathematics; (3) they enjoyed that there was less manual writing required; and (4) some simply liked working with computers.

“Bridging Linguistic and Technological Challenges: Russian-Speaking Primary Mathematics Teachers' Experiences with ChatGPT in Estonian-Language Instruction”

Parandatud ja täiendatud abstrakt:
This article focuses on Russian-speaking primary school mathematics teachers in Estonia who are required to transition to teaching in the Estonian language. The study explores their readiness and experiences in using ChatGPT as a technological aid for generating educational tasks in which both mathematical content and accurate use of the Estonian language are equally important, particularly when the tasks involve extended textual components. The primary aim is to investigate whether and how ChatGPT can support the formulation of text-based mathematical problems and to identify the perceived challenges and advantages related to linguistic barriers stemming from the language shift.

To address the research questions, data were collected through surveys and logged conversations between teachers and ChatGPT. These sources provide insights into teachers’ experiences and readiness to implement AI tools in their instructional design. The findings help to illuminate how artificial intelligence can facilitate the development of didactic materials under conditions of both linguistic and disciplinary complexity.

Importantly, the study aligns with national education policy developments: beginning in the academic year 2025/26, the Estonian state mandates the integration of AI tools into classroom practice. This policy context lends additional relevance to the study, making it both timely and multidimensional. The outcomes offer valuable implications for education policymakers and practitioners, providing practical recommendations for the pedagogically effective and linguistically sensitive integration of AI into everyday teaching.

The INCOLTS framework (Innovative Cooperative Open-Learning in Technology-Enhanced Science Education) is a newly developed model designed to reimagine science education by integrating emerging educational technologies (EdTech) with a strong foundation in neurodidactical and constructivist principles. By aligning teaching strategies with how the brain learns best—through multimodal, active, and collaborative experiences—INCOLTS enhances both cognitive and emotional learning processes, fostering deeper understanding and long-term retention. The framework emphasizes inclusivity and adaptability, addressing diverse learning needs and breaking down barriers to high-quality educational resources. INCOLTS equips students with critical 21st-century skills, such as creativity, problem-solving, computational thinking, and collaboration, which are essential for navigating an increasingly digital and interdisciplinary world. At the same time, it empowers teachers to integrate EdTech effectively and sustainably into their classrooms. By leveraging cutting-edge tools like Artificial Intelligence (AI), Augmented Reality (AR), Virtual Reality (VR), and Block-Based Programming (BBP), INCOLTS creates immersive, engaging, and learner-centered environments that make complex scientific concepts more accessible and memorable. To ensure its long-term success, INCOLTS provides tailored professional development opportunities for teachers, including workshops, webinars, and ongoing mentoring. These training programs are designed to meet the specific needs of educators, equipping them with the skills and confidence to use EdTech as a transformative tool in their teaching practices. While initial testing has demonstrated the potential of INCOLTS to enhance both teacher and student engagement, the framework is still in its early stages. Further testing, refinement, and scaling are required to optimize its impact and applicability across diverse educational settings. As a work in progress, INCOLTS aims to bridge the gap between science education and technology, ensuring that both teachers and students are prepared for the challenges and opportunities of the 21st century.

The aim of this talk is to explore the past, present and future use of educational technology in mathematics education. I will first reflect on the past CADGME papers published in the International Journal for Technology in Mathematics Education (IJTME). IJTME has published papers presented at CADGME conferences. I will review these papers and summarize what has been discussed and reported in past CADGME conferences and papers. I will then discuss my own experience and research in the use of technological tools. In particular, I will discuss examples of the use of Lean, the Interactive Theorem Prover, and generative AI to create educational resources for teaching proofs to undergraduate mathematics students. Reflecting on the CADGME papers and the use of Lean, I will conclude my talk with a discussion of how technological tools should be used in the teaching of mathematics in the future.

This paper presents findings from an action research study focused on the integration of mobile technologies—specifically tablets—and artificial intelligence (AI) tools into mathematics instruction for students aged 12 to 14. Conducted in a constructivist learning environment, the study centered on geometry topics and combined the use of digital tools such as GeoGebra with hands-on, manipulative activities and electronic testing (e-tests). AI served as a support tool for teachers, primarily assisting in the generation of test questions and the structuring of formative assessments. Interactive applications like Kahoot were used to provide instant feedback, foster classroom engagement, and motivate students. The paper includes examples of e-tests, their implementation during lessons, and an evaluation of their contribution to student learning. Results highlight increased interest in mathematics, more active participation, and improved understanding of geometric concepts. The study also identifies key challenges and provides recommendations for effectively incorporating digital technologies and AI into everyday mathematics instruction. These findings underscore the potential of technology-enhanced learning to support and enrich geometry education in alignment with contemporary pedagogical approaches.

This study analyzes the use of digital tools by University of Tartu students taking math courses during their first semester in 2024. The analysis is based on data collected from three mathematics subjects taken by students in seven specializations: biology and biodiversity conservation, gene technology, physics, chemistry, material science, computer engineering, and computer science. The research aims to identify students’ preferred types of digital applications, their usage strategies, and the perceived impact of these tools on independent problem-solving and learning.

The data was collected through an end-of-semester questionnaire, which included closed and open-ended responses and was filled out by 367 students. Quantitative methods (descriptive statistics, significance tests, and correlation analysis) were used alongside qualitative analysis of students' comments.

The results reveal the most frequently used tools and how preferences vary by specialization and academic performance. We also examine students' common difficulties (e.g., over-reliance on AI, misunderstandings due to incorrect output, distractions) and what kind of support or improvements they expect.

We analyze how students searched for additional information using various online resources, including search engines, artificial intelligence tools, and educational platforms. We also investigate whether specific student groups used certain types of tools more commonly. Finally, the study explores learning strategies by analyzing students’ preferences for working independently or collaboratively with coursemates as well as the connection between these strategies and using digital tools.

Our findings contribute to understanding how digital resources are integrated into university-level mathematics learning and offer practical recommendations for supporting their effective and critical use in this context.

The potentialities of Large Language Models (LLMs) are at the centre of attention even in research in Mathematics Education, but their meaningful integration into teaching practices is still an area to be explored. For instance, LLMs could have a significant role in fostering students’ critical mathematical thinking. Indeed, the idea of rationality—understood in a Habermasian sense as the capacity for argumentation, mutual understanding, and meaning-making through discourse—is often neglected in real classrooms. Yet, it is essential for prompting students’ ability to engage with mathematics as a communicative and reflective practice.

This research project investigates how ChatGPT, one of the most used and advanced examples of LLMs, could be seen as a voice that enriches a mathematical classroom discussion. This contribution presents the lesson plan implemented in an Italian 9th-grade classroom to reflect on mathematical proofs.

Students were invited to discover the features of the quadrilateral obtained by connecting the midpoints of a generic quadrilateral (i.e., a parallelogram according to the Varignon theorem). Such exploration was conducted in small groups, first with pen-and-paper, then with the support of GeoGebra. While elaborating mathematical conjectures, students were requested to keep track of their observations and strategies in a Padlet. Eventually, students interrogated ChatGPT to better understand the validity of their conjectures and to obtain a proof in the context of Euclidean geometry. The teaching sequence concluded with a classroom discussion on the features of a valid mathematical proof and their interactions with ChatGPT.

The qualitative analysis of the collected data is currently at an early stage. However, our goal is to carry out a focused examination of the answers ChatGPT provided to students, using the three components of Habermas’s theory of rationality—epistemic, teleological, and communicative—as an analytical lens. We aim to identify how AI’s responses have supported students in developing critical thinking.

As the Estonian education system transitions towards digital examinations, growing attention must be paid not only to the availability of technological solutions but also to students’ readiness to adopt them. The implementation of computer-aided assessment tools in mathematics requires that students become comfortable solving tasks in digital environments. It is crucial that such tools support and enhance learning rather than create additional cognitive or procedural burden.

STACK (System for Teaching and Assessment using a Computer algebra Kernel), integrated into the Moodle learning management system, is a robust digital platform designed specifically for the assessment and instruction of mathematics. It enables the creation of dynamic and variable tasks, automatic grading, and individualized feedback. Moreover, it supports adaptive learning and student engagement through interactive assessments. Despite challenges in question authoring and the demand for teacher training, STACK offers significant pedagogical value through personalization and improved learning outcomes.

In this study, we examine how upper secondary students preparing for their national final mathematics exams perceive STACK-based assignments. The focus is twofold: first, on students’ subjective evaluations regarding the usefulness of STACK tasks in their learning process; and second, on the analysis of their actual input and solution behavior in the system. Special attention is given to how students navigate the technical aspects of answer entry, a factor which can influence the perceived usability and effectiveness of digital assessments.

Finally, we discuss proposals for integrating STACK into everyday teaching practices in a way that aligns with teachers’ existing routines and pedagogical aims. By bridging the gap between traditional instruction and digital assessment, we seek to ensure that all stakeholders—students, teachers, and institutions—can benefit from the transition toward more flexible, responsive, and student-centered learning environments.

In today’s digital learning ecosystem enhanced by artificial intelligence, there is an increasing need for a common technological and pedagogical framework that describes student-driven adaptive learning and learner-centered instructional scenarios in a machine-readable and interoperable manner. Previous studies indicate that Intelligent Tutoring Systems (ITS) have a potential for personalizing and adapting learning based on students' cognitive and affective needs within the context of mathematics education but at the same time point out the weak connection to pedagogical and domain models in ITS (Niño-Rojas et al., 2024). Furthermore, the role of the student is often limited in the individual interaction with the system, as are student’s choices in adaptive learning. Meanwhile, a combination of personalized instructional trajectory and meaningful options could improve learning outcomes and student’s emotional state ‘when students can exercise their self-determination through choice’ (Clément et al., 2025). This paper proposes a conceptual model and software tool for designing flexible instructional trajectories that facilitate human-AI shared regulation of student-driven adaptive learning in a technology-rich mathematics education environment and examines what support the student may need in order to make informed choices for effective learning.

For this purpose, using iterative cycles of design-based research, there has been developed and validated a prototype of the conceptual model of flexible instructional trajectories and corresponding software tool for designing instructional trajectory for 9th grade algebra. Initial instructional trajectory has been tested with 159 students from 5 schools. Based on this study, this paper examines students' performance solving tasks of varying complexity in order to offer a more detailed description of previously defined student profiles for implementing more appropriate scaffolding for students. Also, this paper summarises the results from our participatory design research and follow-up validation of the updated conceptual model and software prototype through heuristic evaluation by a panel of experts.

A deep understanding of mathematical concepts and definitions is a cornerstone of undergraduate mathematics learning, particularly in proof-based courses. Definitions are used not only in constructing proofs but also in applied parts of the course, requiring students to grasp their meaning with precision.

However, many students struggle to recognize whether a given statement is logically equivalent to a formal definition or to identify incorrect formulations, and to provide supporting or refuting examples or explaining when equivalent. In many courses, there are currently no tools that offer students immediate feedback on misconceptions regarding fundamental concepts, which may negatively impact their success as the course progresses.

The goal of this study is to develop an AI-based tool capable of automatically analyzing students' open-ended responses to questions about definitions in a first-year calculus course, classifying them into common error categories, and providing targeted, immediate feedback.

In the first phase of the study, a dataset of open-ended responses will be collected, in which students are asked to evaluate whether a given formulation is equivalent to a formal definition and to justify their reasoning. This dataset will serve as the basis for identifying and defining error categories. At this stage, responses will be manually classified by instructors and mathematicians to support the definition of categories and the training of the AI model.

In the second phase, an AI-based tool will be developed to classify new responses according to the learned categories and to provide students with tailored feedback, including guidance for correction. The tool’s effectiveness will be evaluated by comparing its analysis to that of expert human raters on new student responses.

This research contributes to the integration of technology in learning abstract mathematical concepts and to the development of personalized feedback systems for undergraduate mathematics education at multiple stages of the course.

The concept of a plane curve being a conchoid of another curve is well established and widely discussed in the scientific literature. For instance, Lockwood (2007) mentions focal conchoids of conics, briefly explaining how their shape depends on the type of conic and the relationship between the fixed distance, known as the conchoid parameter, and the conic's latus rectum. He also encourages visual exploration of these curves. Among the well-documented focal conchoids is the pretzel curve of a parabola (Hašek, 2017). In this article, we delve deeper into the conchoidal properties of this and other focal conchoids, focusing on their dependence on the type of conic and the magnitude of the parameter. Using dynamic geometry software and computer algebra tools, we demonstrate their properties and potential applications in university courses on the geometry of conics and other plane curves.

References
Lockwood, E. H. (2007). Book of Curves (Reprint of the 1961 edition). Cambridge University Press, Cambridge.
Hašek, R. (2017). A Remarkable Quartic Pretzel Curve. Journal for Geometry and Graphics, 21(1), 37–44. https://www.heldermann.de/JGG/JGG21/jgg21.htm

In the proposed talk, I present findings from recent joint research with Isabel Floor on using the Augmented Reality (AR) Sandbox as a digital tool to support the learning of vector geometry in secondary mathematics education [2]. This project is a follow-up from work with Doorman, Drijvers, and Shvarts [1]. The AR Sandbox, originally designed for geoscience, enables real-time projection of height lines or coordinate systems onto a manipulable sand surface. Our study reimagines this system as an embodied learning environment for mathematics, emphasizing action with artifacts, symbolic feedback, and collaborative exploration.

To this end, we developed software that projects a coordinate system onto the sand and registers the position of a color-marked stick within this system. Then it provides symbolic feedback based on students’ manipulations of the stick. A sequence of tasks was designed to explore fundamental vector concepts—including direction, magnitude, vector representations and dot product. The design allowed students to test hypotheses through actionst, use gestures to communicate mathematical thinking, and connect intuitive understanding with abstract symbolism.

A case study with two high school students revealed how the sandbox fostered productive mathematical reasoning. Students engaged in perception-action loops with the stick, marked reference points in the sand, and developed ways of communicating their ideas through gestures and actions; the stick-position registration and symbolic feedback playing a central role.

This work contributes to the growing body of research on embodied and AR-supported mathematics education. It offers insights into how interactive dynamic geometry can move from 2-dimensional screens into 3-dimensional AR-“sandscapes”.

[1] Bos, R., Doorman, M., Drijvers, P., & Shvarts, A. (2022). Embodied design using augmented reality: the case of the gradient. Teaching Mathematics and its Applications, 41(2), 125-141.

[2] Floor, I. (2025). Building sandcastles in AR: How playing with sand can help students learn mathematics. Master thesis, Utrecht University.

The integration of generative Artificial Intelligence (AI) tools, such as ChatGPT, in education opened new perspectives for fostering students’ metacognitive skills. In this study, ChatGPT was trained as an educational tutor: to guide problem solving without directly providing answers; to personalize questions based on students’ responses; to use open-ended questions to stimulate critical thinking; to enhance students’ efforts even when mistakes occurred; to encourage metacognitive activities (Meijer, 2006), that is, orientating, planning, execution, monitoring, evaluation, and elaboration.

The aim of this study is to analyze the impact of students’ interactions with ChatGPT, trained as described above, on the development of metacognitive processes during problem-solving activities. In particular, the aim is to investigate to what extent the interaction with ChatGPT facilitates students’ metacognitive activities in solving mathematical problems.

The study involved 41 high school students. We analyzed their interactions with ChatGPT during math problem-solving activities from both quantitative and qualitative perspectives. Preliminary findings, in agreement with previous studies (Cusi, 2024), seem to show that not all metacognitive activities are activated. In particular, the results seems to show an effectiveness of interactions in activating monitoring and evaluation activities, but difficulty by students in activating planning and elaboration. The results of this study provided insights to improve the interaction patterns between students and generative AI. From this perspective, this work could contribute to the literature on the development of metacognitive skills in problem solving within generative AI environments.

References

Cusi, A., Contel, F. (2024). Investigating the Role of ChatGPT in Supporting Metacognitive Processes During Problem‑Solving Activities. Digital Experiences in Mathematics Education.

Meijer, J., Veenman, M., & van Hout-Wolters, B. (2006). Metacognitive activities in text-studying and problem-solving: Development of a taxonomy. Educational Research and Evaluation, 12(3), 209–237.

This action research study explores the integration of Computational Thinking (CT) and GeoGebra to enhance secondary school students’ ability to recognize and generalize patterns in number sequences, a critical skill for algebraic reasoning. Addressing the common challenge of abstract pattern identification in mathematics, this study adopts a participatory, cyclical framework involving three iterative action research cycles (planning, acting, observing, reflecting) with 45 students and three mathematics teachers at a public secondary school. The intervention design embedded CT components—decomposition (breaking sequences into terms), pattern recognition (identifying arithmetic/geometric relationships), abstraction (formulating rules), and algorithm design (creating solving steps)—into GeoGebra-supported activities. Teachers collaboratively developed dynamic learning modules.

Data collection included pre-/post-tests on sequence mastery, student reflective journals, classroom observations, and focus group interviews with teachers. Quantitative analysis revealed a 35% improvement in students’ ability to solve non-routine sequence problems (p < 0.05), with notable gains in algorithmic fluency. Qualitative findings highlighted increased student agency in hypothesizing patterns and teachers’ enhanced capacity to scaffold CT through technology. The reflective cycles also uncovered pedagogical insights, such as the need for phased scaffolding in algorithm design and the role of visual feedback in reducing cognitive load.

This study demonstrates that action research, combined with CT and GeoGebra, fosters a transformative learning environment where iterative reflection and technology integration empower both students and teachers. The results advocate for context-sensitive, teacher-led curricular innovations to bridge theoretical mathematics and computational problem-solving.

Keywords: Computational Thinking, Sequences, GeoGebra, Action Research, Pattern Recognition, Reflective Practice.

3D printing technology has emerged as a transformative tool in education, particularly in STEM fields, by bridging theoretical knowledge and practical application. This study explores the integration of 3D printing into a STEM lesson titled ‘Designing a Mini 3D Projector,’ where students engage in model creation using design software and 3D printing techniques. Through a mixed-methods approach combining classroom observations, student feedback, and competency assessments, we demonstrate how this hands-on activity enhances students’ understanding, creativity, and technical skills. Results indicate that the process of designing and manufacturing tangible products fosters key competencies such as problem-solving, collaboration, and digital literacy. Additionally, the project’s interdisciplinary nature (combining physics, engineering, and art) increases student engagement and real-world relevance. The paper concludes with practical recommendations for educators to adopt 3D printing in STEM curricula, addressing challenges such as resource limitations and pedagogical strategies. This case study contributes to the growing body of research on innovative technologies in education, highlighting 3D printing’s potential to revolutionize experiential learning.

Recent studies are showing the need to include 3D modelling and printing (3DMP) technology into teacher training programs, as well as the importance of developing and testing integrated hands-on experiences at schools (Tejera et al., 2025). Following this direction, in this communication we present a STEAM experience in which students were involved in the collaborative design and construction of a classroom. They used Tinkercad, a free online 3D modelling tool, to create models of different elements and furniture of a real or ideal classroom, which were then fabricated using 3D printing technology.

The experience was carried out with two different groups of participants—21 prospective Primary school teachers enrolled in a Master’s Degree in Educational Innovation at the Universidad Autónoma de Madrid (Spain), and 18 Secondary school students from the Balearic Islands (Spain)—both engaged in a shared modelling challenge. While the pre-service teachers designed various classrooms to examine alternative uses of educational space within a mathematics education context, the secondary students modelled their actual classrooms based on real measurements. The objective was to engage students in an interdisciplinary design project involving geometry, measurement, and scale, enhanced by 3DMP technology.

In both experiences, the aim was to analyse students’ modelling processes, explore their ability to connect mathematical concepts with spatial design, and evaluate the acceptance and motivational impact of this methodology.

From the results obtained in both experiences, we highlight the development of students’ spatial reasoning skills, improved engagement with mathematical content, and a positive attitude toward collaborative and technological tasks, reinforcing the support for the inclusion of 3DMP activities in initial teacher training and secondary education.

Tejera, M., Galić, S., & Lavicza, Z. (2025). 3D Modelling and Printing in Teacher Education: A Systematic Literature Review. Journal for STEM Education Research, 1–32.

Geometrical demonstrations play an important role in Mathematics education, serving as an effective means of developing students' logical and critical thinking. In this context, Dynamic Geometry Systems (DGS) have been used in secondary education for many years now. They enable an easy construction of geometric configurations, where relationships between elements can be explored dynamically. By manipulating free elements, students can investigate geometric properties, make conjectures, and expand their mathematical understanding. However, while DGS facilitate exploration, they do not provide formal proofs, even with tools like Cinderella’s randomised theorem checker, Cabri Géomètre’s
algebraic oracle, or GeoGebra’s Relation tool. For this purpose, a Geometry Automated Theorem Prover (GATP) is required, like GCLC and GeoGebra Discovery.

Java Geometry Expert (JGEx) integrates a DGS with multiple GATP methods, allowing for interactive and visual proofs. Its key features include user-friendly interface, multiple provers, readable proofs and dynamic proof visualisations.

The Geometry Deductive Database method in JGEx is particularly promising for educational purposes. It employs forward reasoning, applying inference rules to derive conclusions from geometric axioms. This
results in visually supported, step-by-step proofs, reinforcing students’ logical and deductive skills.

This study aims to examine the role of geometrical demonstrations in secondary education using JGEx in a context of a master in mathematical education (pre-service teachers). It explores mathematical argumentation and synthetic geometry through interactive tools. The research will be conducted in two phases: (1) explore software-provided examples relevant to curricula; (2) use JGEx’s tools to introduce and formulate new problems. We will use Mathematical Olympiads geometry problems as a test
case.

By integrating JGEx, students can visualise and construct proofs interactively, fostering confidence, logical reasoning, and a deeper understanding of geometric principles.

This paper describes the tasks with applets. Probabilities, conditional probabilities, the total probability theorem, and Bayes' formula are the contents of the topic of Probabilities, including Mathematics Applied to Social Sciences (MACS of the 11th grade, 16 years old), which were selected in this research. This research has the ontosemiotic approach as its theoretical framework, OSA. This paper presents the tasks using the applets, providing students with a different experience in the classes of this topic. Those tasks were included because students struggle and make errors when learning probabilities – semiotic conflicts in OSA. Having detected the semiotic conflicts in those probability topics in a prior work, a set of tasks was developed to overcome them. In this paper, we present the planning of a didactic intervention using tasks outlined based on the semiotic conflicts detected in Portuguese students of MACS (11th grade) and Mathematics (12th grade). The students' opinions in each group of classes are also presented, as well as the pre and pos tests results. The students liked the technological approach with the applets. Some conflicts seem to be fixed, but the need to accompany their scholar journey to check it was felt.

Our talk presents two examples of the possibilities that arise for STEAM education when considering the automated reasoning tools of GeoGebra Discovery. It focuses on some works of two Dutch artists, Theo van Doesburg (Arithmetic Composition I) and Theo Jansen (Strandbeest).

Concerning van Doesburg work, our proposal for students begins with the construction in GeoGebra of the squares represented in his painting Arithmetic Composition (see https://en.m.wikipedia.org/wiki/File:Theo_van_Doesburg_study_for_Arithmetic_Composition.jpg), observing the geometric properties that appear in the painting (the symmetry of the squares with respect to one of the diagonals, and how the squares reduce the size of their sides by half). Added to this analysis are the automated reasoning capabilities of GeoGebra Discovery to verify different conjectures that arise from the construction. For example, if we inscribe a quadrilateral in the isosceles triangle drawn in the painting, must it be verified that the side of the quadrilateral is 1/3 of the hypotenuse? Is this the square with the biggest area that can be inscribed in the triangle?

The second example of our proposal focuses on Theo Jansen’s Strandbeest sculptures (see https://espacio.fundaciontelefonica.com/theojansen/strandbeest-como-funcionan/). Here, students will be asked to create some models of the Strandbeest legs, and will explore different variations of the parameters in the design process (see for example the applet https://www.geogebra.org/m/fmhzvxfc), giving rise to Jansen's holy numbers and to discuss why the artist considered those legs to be more efficient.

In conclusion, we will present Arithmetic Composition I and the Strandbeest as two examples where the use of automatic reasoning and dynamic geometry creates rich interdisciplinary STEAM learning contexts.

Nitrogen overfertilization is a significant environmental issue in agriculture, influenced by political, economic, and social factors (Krautzberger & Ehlers 2020, p. 31). Therefore, a solution is needed that does justice to this multi-perspective system. Digital tools enable educators to tackle complex issues like nitrogen overfertilisation through interdisciplinary, action-focused classroom approaches. This utilises the educational potential of the subject and at the same time it promotes the integrative education goals, such as the promotion of Education for Sustainable Development (ESD), democratic values, and digital literacy.

A learning environment is presented that uses the dynamic geometry software GeoGebra to enable mathematical modeling and the analysis aof a multi-perspective system. Dynamic visualisations and interactive features through GeoGebra applets foster process-oriented mathematical competencies. The analysis of functions under variable parameters, such as fertiliser prices, fostered by this approach enhances the ability to effectively use digital tools. This in turn supports the creation of mathematical models and their critical reflection within real-world contexts.

The learning environment integrates the STEAM disciplines of mathematics and biology, as well as political science and economics, thereby addressing the interdisciplinary nature of ESD tasks and enabling authentic modelling (cf. Maaß 2010). Students simulate a democratic negotiation process through a panel discussion, weighing arguments using previously acquired biological knowledge and mathematical methods.

The environment accessible via the GeoGebra website is based on the requirements of the curriculum for vocational education and training specialising in business and administration in North Rhine-Westphalia (MSW NRW 2008). It combines the established ESD framework Recognise - Evaluate - Act (Schreiber & Siege 2016, p. 90) with the concept of complete action to design action-oriented teaching in vocational education (Hermes et al. 2012, p. 22; Riedl 2004, p. 123).

We look forward to discussing the learning environment with you and receiving your valuable feedback on our approach.

Mathematics education is evolving rapidly with the increasing integration of online environments and digital tools. These can complement regular in-person teaching sessions, offering potentially different opportunities for student learning. This shift calls for further understanding of how digital environments and tools can support students’ mathematical development, particularly in terms of how communication and interaction are shaped compared to traditional classroom settings.

In the ongoing project FallAha! for engineering students, we explore how a digital community offering a discussion platform, online study sessions and on-demand online tutoring for mathematics university courses can serve as an alternative to conventional in-person study sessions. The platform provides engineering students with continuous mathematics support on the courses given at their university, available 24/7 throughout the entire year, both beyond regular class hours and after the course has concluded, including preparation for re-examinations. It was developed in response to the challenges engineering students encounter when transitioning to university-level mathematics, such as increased workload, stress, lack of consistent support, and difficulties with self-directed learning. In the first phase of the project, we collect data from both classroom-based and online tutor-student interactions complemented with tutor interviews to identify key similarities, differences, and the constraints and affordances of the digital environment.

This presentation shares preliminary findings from our initial round of analysis, focusing on communication and interaction in digital tutoring environments, contrasted with in-person study sessions. We examine aspects such as responsiveness, use of tools, and the nature of mathematical discourse. These early results provide insights into how digital environments shape not only the structure of interaction but also the opportunities students have to engage with mathematical ideas.

Our findings contribute to the ongoing discussion about effective online mathematics education and offer input for the design of future digital learning environments.

In linear algebra courses for first-year engineering students, instructional improvements have been pursued due to the highly abstract nature of the content. Specifically, anticipating that preliminary study of abstract concepts could reduce students' cognitive load, video materials aimed at flipped learning have been developed since 2015. Additionally, during the COVID-19 pandemic, online exercises designed for formative assessment and grading were primarily created using STACK. STACK is a Moodle question plugin that employs Maxima for automated grading, random problem generation, and feedback tailored to student responses. The author developed these exercises as "cheating-resistant," requiring conceptual thinking beyond mere computation by software or computer algebra systems (CAS). These materials have been actively used from 2020, during the pandemic-induced online instruction, through the gradual shift back to face-to-face classes by 2024. Students primarily completed these online tasks as home assignments, and analysis of their completion rates, online quiz results, and paper-based final examination outcomes confirmed a moderate effectiveness. However, a significant number of students remain reluctant to consistently complete online assignments, highlighting the need for further careful review of the quantity and content of tasks. Moreover, the meaning of "cheating-resistance" has notably evolved in the current AI-driven era, necessitating consideration of tasks designed not merely to resist cheating but also to be effective educationally despite the possibility of cheating. This presentation will provide concrete examples from the extensive STACK-based problem sets developed and discuss their future use through the lens of APOS theory.

Augmented Reality (AR) is increasingly entering mathematics education, and recent research has found AR to be effective in improving spatial geometric thinking and understanding. Most of these studies have used quantitative methods using questionnaires to evaluate the spatial thinking of students. In fact, AR provides an interactive learning experience by transforming abstract geometric concepts into visually and physically engaging forms, enabling students to explore geometry in both an intellectually and tangibly accessible way. However, the embodied affordances of AR, which may be central to how cognition emerges through sensorimotor engagement, have not been explored extensively. Our study investigates how a purposefully designed AR environment enables students to enact the transition from two-dimensional nets to three-dimensional solids through embodied interaction.

The study employs a case study methodology, focusing on two fifth-grade students (aged 11), an age when foundational concepts of 3D geometry begin to emerge. A case study approach enables an in-depth analysis of the enactment transitions students engage when using AR to develop their geometric reasoning.

The findings suggest that through embodied interaction with AR, students shifted from relying solely on internal visualizations—such as mentally folding nets—toward more enacted, sensorimotor strategies that involved actively exploring spatial relationships between net components and their corresponding 3D structures. This shift indicates that AR supports deeper mathematical understanding by grounding abstract reasoning in embodied experience and physical engagement.

The significance of this study lies in its contribution to understanding how AR facilitates the embodied development of geometric understanding by engaging students in sensorimotor interactions that support the enactment of spatial and analytical reasoning. By illustrating how AR grounds abstract geometric concepts in physical and perceptual experience, the study highlights how students cultivate deeper insight into the relationship between nets and solids through embodied activity.

An important feature of a text is its readability. Readability is the ease with which a reader can understand a written text. The readability of a text is determined by many factors and plays an important role in many areas of interest.

A mathematical text is composed of many elements: descriptions in natural language, formulas and diagrams; thus, it is much more difficult to quantify its readability through formulas, then in the case of regular text. Even more complex is the problem of the readability of mathematical proofs produced by automatic provers that are often presented in a form that can only be read by experts.

In my talk I will introduce both a language to formulate readability criteria for formal proofs produced by automated theorem provers for geometry, based on the area method and also a novel criterion based on our modernisation of Lemoine’s Geometrography.

Research in mathematics education claims that encouraging students’ covariational reasoning is beneficial for the development of mathematical concepts (Bagossi, 2024; Thompson & Carlson, 2017). Moreover, changing theory, exploring the meaning of a concept within each mathematical theory, makes richer the semiotic representations set and stronger its understanding. Just think about the use of Taxicab geometry to deeply understand a Euclidean geometry concept (Kemp & Vidakovic, 2023).

The simultaneous variation of two representations (quantities, relationships, etc.) within distinct theories is said to be theoretical covariation (Miranda & Saliceto, 2025).

At the university level, theoretical covariational reasoning processes can help in understanding and manipulating more advanced mathematical concepts. In the experiment I’m going to discuss, undergraduate mathematics students were required to explore the definition of homeomorphism in the domain of topology. Each group was required to reason with respect to two different metrics supported by GeoGebra. The digital environment helped them to enhance reasoning about spatial figures, verifying if the graphical representation of the object corresponds to what is visualised in the mind. But what happens from a mathematical point of view? They discover that a homeomorphism with respect to a given metric is not necessarily one with respect to another metric, even in the case where the metrics are topologically equivalent. In particular, the study focuses on stereographic projection, which is a widely used application in the STEAM fields. The theoretical covariation between the Taxicab-Euclidean stereographic projections helps them visualise and reflect on the reason for which the Taxicab-stereographic projection is not a homeomorphism. The data are analysed through the lens of the IK-MWS theoretical model (Miranda et al., 2025). The results are promising: the use of the digital tool in synergy with the change in geometry refines the visualisation and construction processes and thereby the discursive processes within the theories.

When students interpret and conceptualize real phenomena through dynamic simulations, they might engage in covariational reasoning. First-order covariational reasoning concerns conceptualizing how two quantities vary simultaneously, whereas second-order covariational reasoning concerns how that two-quantity relationship co-varies with a third quantity acting as parameter. While first-order covariational reasoning has been widely studied, second-order covariational reasoning has only recently gained attention, and the interplay between these two orders of reasoning remains unclear.

This talk shares preliminary findings from a larger project that, by using eye-tracking technology, investigates learners’ strategies when reasoning at the second order of covariation, and the connections between the first and second order of covariational reasoning. Eye-tracking has already been applied in Mathematics Education research to identify students’ strategies when reading contextual graphs and engaging in first-order covariation. Our project expands on these insights by examining the conceptualization of second-order covariation while students connect various representations. Such investigation is conducted by adopting a multimodal perspective on learning.

Here, we discuss a case study involving a 10th grade student engaging with two tasks about a ball rolling down an inclined plane. In the descriptive task, the student was asked to describe the dependence of time and distance by referring to a provided graph. In the drawing task, he was asked to sketch additional distance-time graphs while varying the plane’s incline (with the plane length fixed) and to explain the resulting graphs’ shapes. Both tasks were performed while using monitor-based eye-tracking, followed by a stimulated recalled interview. The data from the recordings of the session and eye-tracking have been qualitatively analyzed by triangulating all the multimodal resources involved (speech, gestures, gazes, representations). Preliminary findings offer new insights into how first-order covariational reasoning relates to second-order covariational reasoning.

As technology becomes increasingly integral to mathematics instruction, teacher education programs face the pressing challenge of equipping pre-service mathematics teachers (PMTs) with the knowledge and skills necessary to use digital tools effectively in the classroom. Learning to integrate technology meaningfully involves more than technical proficiency; it requires PMTs to develop a deep understanding of how digital tools can support students' mathematical thinking, foster engagement, and enhance conceptual understanding. This study examines one PMT’s use of dynamic geometry software—specifically GeoGebra—through designing and implementing a technology-based task focused on the area formula of the trapezoid, exploring how such a task supports goals related to students’ mathematical thinking. Adopting a qualitative case study design, the research was conducted in the context of a practicum course in a 4-year mathematics teacher education programme in Türkiye. To guide the analysis, the study adopted the Interactive Geometry Software (IGS) framework as its conceptual foundation. The data comprised the PMT’s lesson plan for a technology-based task, audio recordings of pre- and post-lesson interviews, and a video recording of his classroom teaching during a school placement. The findings revealed that he designed at a high level technology-based task as a reorganizer, enabling students to engage in generalizing the area formula of a trapezoid. However, he could not manage to conduct his lesson as planned in real classroom teaching. The possible reasons why he was unable to successfully implement his plan will be discussed in this presentation.

This paper introduces a unique educational approach to teaching both mathematical and biological concepts through the use of the MathCityMap learning app, which combines biological exploration with mathematical learning pathways in a single, interdisciplinary framework. The app allows students to navigate mathematical trails centered around tree and plant identification in natural settings, such as forests, meadows, and tree-lined avenues. Through hands-on activities, such as tree species identification in the Schlosspark of Steyr, Austria, students solve mathematical tasks like calculations, estimations, and problem-solving exercises directly related to the biological context. This innovative STEAM+ (Science, Technology, Engineering, Arts, and Mathematics) learning experience is structured according to the INCOLTS framework (Innovative Cooperative Open Learning in Technology-Enhanced Science Education). The workshop, targeted at secondary school students aged 11–13, emphasizes cooperative and open learning while integrating educational technology (EdTech) into scientific education. The MathCityMap app, certified in Austria, is used to create an interactive and cross-disciplinary learning environment, making this workshop an innovative example of a creative and holistic approach to EdTech education. The session provides material for educators seeking to foster student engagement and support interdisciplinary learning in mathematics and technology-enhaced science education.

This contribution explores the use of the digital learning platform MathemTIC as an innovative solution for student remediation in secondary mathematics education. Traditional remediation often relies on time-consuming, repetitive handwritten assignments that overwhelm students and fail to address their individual learning needs. This can lead to disengagement and increased frustration toward mathematics, particularly among struggling learners.

MathemaTIC offers interactive, adaptive modules with real-time feedback, allowing to create personalized learning paths tailored to each student. Such targeted remediation can foster greater engagement and improve learning outcomes. The goal is to provide students with an effective, student-friendly tool to review key concepts at their own pace, close knowledge gaps and build confidence for the next academic year. This digital learning platform may also reduce dependence on private tutoring, thereby promoting education equity.

The integration of MathemaTIC illustrates the potential of digital tools to modernize remediation practices and create more inclusive and effective learning environments in contemporary education.

Understanding common errors and misconceptions is key to improving student learning in algebra. Students often struggle with interpreting variables correctly—some may think that a variable can represent multiple values simultaneously, or that different variables must always represent different values. Others confuse variables with alphabetical order, interpreting ‘b’ as 2, for example.

To address such misconceptions, the SMART (“Specific Mathematics Assessments that Reveal Thinking”) project developed the 'Values for Letters' test, an online diagnostic tool. After administering the test, teachers receive automated feedback that includes an analysis of student responses along with targeted teaching suggestions. This feedback is designed to inform instruction and support students in developing a more accurate understanding of variables.

In this talk, we want to investigate how we can create automated feedback for teachers that guide their following lessons. In our study, 103 teachers across six German federal states administered the SMART test twice—once early in their instructional sequence on variables, and again four weeks later. Only teachers in two of the three groups had access to the full automated diagnosis, including feedback on misconceptions and teaching suggestions. A third group received only a basic overview of right and wrong answers. Altogether, 2220 students completed both tests.

Using Latent Transition Analysis, we explore the response patterns and how they evolved over time. By linking these transitions to the type of feedback teachers received and used, we examine how targeted information and suggestions in an online tool can guide teachers to adapt instruction in ways that promote student learning and conceptual development.

Through the STEAM Connect Project (ERASMUS+), we aimed to inspire secondary school teachers to emphasize key concepts in mathematics, physics, music, biology, visual arts, and electronics through innovative hands-on learning activities. At the center of these activities was the Circuit Playground Express board, developed by Adafruit Industries—an open-source hardware company. Equipped with various sensors, it enables the creation of sound effects using its MEMS microphone, light-based interactions through its phototransistor, motion detection via its built-in accelerometer, and temperature measurements via its thermistor. As an all-in-one tool, it empowers teachers at all levels—not just in secondary education—to design dynamic, interactive lessons that engage diverse learners and promote inclusive understanding across multiple disciplines.

Building on this foundation, the present study adopts a multidisciplinary approach to teaching mathematics—primarily in primary education—through a STEAM pedagogical strategy. The focus is on developing logical and mathematical reasoning while simultaneously encouraging creative expression through the arts and music. It explores the use of the Circuit Playground as a pedagogical tool, with particular attention to strategies that foster active participation, scaffold conceptual understanding, and respond to the diverse needs of young learners.

This presentation includes a Skateboard Challenge—a learning activity in which children balance on a wooden board placed over a PVC pipe to generate and reproduce pre-programmed songs. By adjusting the board’s angles and positions, they engage with core mathematical concepts while developing coordination, rhythm, tempo, and timing—skills essential for musical interpretation. This integration of mathematics into a physical task strengthens their spatial reasoning, problem-solving abilities, and physical awareness.

By showcasing this activity, we aim to demonstrate how mathematics can serve as an important element in a multidisciplinary learning experience—interacting meaningfully with creative expression in art and music, as well as with scientific thinking across the natural and human sciences.

This contribution explores the integration of Artificial Intelligence (AI) and 3D modeling and printing technologies within STEAM (Science, Technology, Engineering, Arts, Mathematics) education, focusing on their transformative potential for pre-service teacher training. The paper highlights two distinct yet interconnected roles of AI-supported 3D modeling and printing in the educational context. First, AI enables teachers to design and fabricate customized teaching aids tailored to the specific learning needs and instructional approaches of their classrooms. These resources, often unavailable commercially, can be efficiently created through AI-assisted modeling, empowering educators to enrich their pedagogical strategies and support personalized learning experiences. Second, the teacher takes on the role of facilitator in constructivist-oriented learning environments. AI-supported 3D modeling encourages students at the primary level to actively engage in designing and printing tangible objects. These objects become integral components of inquiry-based learning, fostering creativity, problem-solving, and a deeper understanding of STEAM concepts. The paper also presents findings from action research conducted with pre-service primary education teachers. These results provide insights into the practical implementation of AI-assisted 3D modeling and printing in educational settings. Through real-life examples, we demonstrate how these technologies can transform traditional teaching into interactive, student-centered learning experiences, while underlining the importance of digital competence in modern teacher education. Furthermore, the contribution highlights the need to develop a coherent theoretical framework for STEAM education in teacher training programs. This framework should emphasize key 21st-century skills such as critical thinking, creativity, problem-solving, and digital literacy, including the ability to effectively use AI tools. Preparing future primary school teachers to integrate these competencies into their practice is essential for fostering meaningful and future-ready STEAM learning environments.

Despite extensive investment in professional development, many teachers struggle to sustain the use of technology-enhanced learning (TEL) methods over time. This study explores the long-term adoption of TEL practices among mathematics teachers who participated in schoolyear-long innovation lab trainings held over the past five years. While initial evaluations showed strong uptake and intention to apply new methods, it remains unclear which factors influence teachers’ ability to maintain these practices years later.

Grounded in the Expectancy-Value-Cost (EVC) theory and Situated Learning Theory, this longitudinal mixed-methods study investigates how teachers’ motivational beliefs and contextual experiences shape the sustainability of TEL adoption. We combine earlier data - collected pre- and post-training on self-efficacy, pedagogical beliefs, and intended use of TEL - with new follow-up data gathered two to four years after training. The follow-up includes survey items measuring expectancy (confidence in applying learned methods), perceived value, and cost (effort and stress), along with self-reported long-term TEL use. Open-ended responses enrich the findings with teachers’ reflections on classroom practice, challenges, and support mechanisms.

The study focuses specifically on the long-term use of digital tools in mathematics education, such as H5P and Teacher Desmos, which were introduced during training to promote students´ cognitive engagement and conceptual understanding. Quantitative analyses examine associations between EVC components measured years after training and teachers’ long-term adoption of TEL practices. Qualitative data provide insight into the professional and contextual conditions -as well as into teachers’ pedagogical practices - that support or hinder the long-term integration of digital tools.

By highlighting both motivational and situational factors, this study contributes to a deeper understanding of why some teachers sustain TEL innovations while others abandon them. The results offer guidance for designing professional development that not only initiates change but also supports teachers in continuing to use digital tools effectively in mathematics classrooms.

A didactic situation was designed that connects knowledge of 2D and 3D geometry. The situation deals with the intersection of spheres in three stages using different artifacts. Stage one, with the use of manipulative material (oranges) for a first intuitive approach. Then, a second stage, of contrasting and validation of information with Chat GPT generative AI, and a third stage, of mathematical validation, by means of the elaboration of mathematical models in GeoGebra.

The situation was approached by 24 mathematics teachers in initial training belonging to two Chilean universities, who worked in pairs, making written, audiovisual and screen recordings. The data analysis was carried out from the Mathematical Working Space Theory (MWS) (Kuzniak et al. 2022), characterizing their personal MWS, from a semiotic, instrumental and discursive dimension.

The results show that future teachers identified that the intersection of two spheres is a circumference or a point of tangency in space, determining the conditions for such an intersection to exist. In particular, the relevance of gestures and corporeality was evidenced when approaching 3D geometry tasks, as well as the mathematical work is modified when incorporating the use of generative AI Chat GPT, where epistemic vigilance is required before the information it provides, which was observed in a deficient manner in the future teachers.

Finally, the construction of mathematical models with tools that have relative epistemic validity, such as GeoGebra, allowed the future teachers to coordinate algebraic and graphic information in a spiral process that leads them to the elaboration of new models, validating or refuting their own conjectures, a process in which it was fundamental to resort to their own theoretical referential.

Kuzniak, A., Richard, P. y Montoya-Delgadillo, E. (2022). Mathematical Work in Educational Context. En A. Kuzniak, E. Montoya-Delgadillo y P. Richard (eds.), Springer International Publishing. https://doi.org/10.1007/978-3-030-90850-8

This study presents an innovative method for teaching axial and central symmetry in natural contexts by leveraging GeoGebra and artificial intelligence (AI). Symmetry—manifested in biological structures, crystalline formations, and fractal patterns—is a key concept in mathematics and science, yet students often struggle to grasp its abstract principles. This paper introduces a technology-enhanced learning framework where GeoGebra’s dynamic geometric tools and AI-based image analysis enable students to interactively explore and classify symmetric patterns in nature (e.g., butterfly wings, snowflakes). A mixed-methods approach was employed, assessing both quantitative improvements in student performance and qualitative feedback from classroom implementations. Results demonstrate that integrating digital visualization and AI-assisted pattern recognition enhances students' understanding of symmetry transformations, particularly in distinguishing between axial (reflectional) and central (rotational) symmetry. The findings suggest that such an approach not only improves conceptual learning but also fosters interdisciplinary connections between mathematics and biology.

To integrate digital tools in mathematics classrooms, teachers require various competencies, as outlined in several theories: Mathematics Digital Task Design Knowledge, Mathematical Digital Competencies for Teaching, or Mathematical Digital Knowledge for Teaching, just to name a few. These theories detail the necessary competencies for teaching mathematics with digital technologies. This diversity of theories suggests multiple perspectives for investigating the use of digital technologies in mathematics lessons.

Our research focuses on understanding mathematics teachers’ motivations concerning the use of digital technologies as well as exploring the digital-enhanced activities mathematics teachers wish to incorporate into their lessons. To achieve this, we employ mixed-methods research, combining large-scale quantitative and small-scale qualitative approaches.

We employ a modified version of the Unified Theory of Acceptance and Use of Technology, based on Venkatesh et al. (2003), to examine how internal, external, and technological factors influence teachers’ expectations and usage of digital technologies. For understanding how teachers use these technologies, we refer to Chi and Wylie’s (2014) Interactive, Constructive, Active, and Passive (ICAP) Theory, which categorises cognitive engagement modes hierarchically, and the ICAP Technology Scale, which is derived from this theory and aims to measure technology integration in educational settings.

To investigate teachers’ needs regarding technology use and its impact on their epistemological beliefs about teaching mathematics, we conduct interviews with experienced teachers. We focus on teachers' convictions regarding the nature of mathematics and the acquisition of mathematical knowledge.

By exploring the motivations and methods of mathematics teachers in employing digital technologies, we provide a comprehensive view of teaching mathematics in the digital era.

Chi, M. T., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist, 49(4), 219–243.

Venkatesh, V., et al. (2003). User acceptance of information technology: Toward a unified view. MIS Quarterly, 425–478.

Squaring a figure is the challenge of constructing a square equivalent to a given figure by using only ruler and compass. The problem of squaring figures was already known in ancient Greece. Greek mathematicians were able to square polygons but also some “rounded-shaped” figure, as Hippocrates’ lunes. They also tried to square the circle. The problem remained unsolved for about 2000 years, and, in the end, and only with the aid of algebraic tools, it was proved that it was not possible to square a circle.

In this contribution we present a mathematical didactic proposal aimed at high school students on “squaring plane figures”. The activity challenges students with squaring triangles, rectangles, parallelograms, quadrilateral with perpendicular diagonals, polygon circumscribed to a circumference, and then, any polygon and even particular figures with round shapes. The whole activity is based on the use of technology (GeoGebra) and of a laboratorial approach where students can find their own role and give their contribution. The whole activity has been planned taking into account the role of technology, the role of pedagogy with respect to the introduced content. The activity has been tested with high school students (grade 10-11) and with university students (future teachers). The result of the experimentation with university students will be presented. In particular, we discuss the role of the artifact GeoGebra in the active construction by students: constructions by hands can be difficult for students, and can distract the student, too busy in drawing figures to be focused enough in the mathematical reasoning.

Digital technologies and embodied interaction are increasingly recognized as powerful mediators of mathematical learning. This study presents a teaching experiment conducted in an Italian upper-secondary classroom that merges an embodied perspective with an emergent extension of GeoGebra, GeoGebra Plus (GGB+). Developed by David Hornsby (JKU Linz, Austria), within the Widera-Horizion project TransEET, GGB+ recognizes key body points in human figures via webcam, depicting an avatar in GeoGebra’s graphic environment, enabling learners to control it through body movements. By letting students “step inside” this environment, GGB+ affords direct interaction with mathematical objects and delivers immediate feedback. A sequence of GGB+ applets for linear functions was designed within an inquiry-oriented laboratory setting, in the TransEET context. The learning trajectory comprised three consecutive phases: (1) open exploration, where students freely experimented with corporeal interaction to discern affordances of the technology; (2) guided exploration, focused on identifying how changes in bodily posture modify the coefficients that define the function; and (3) production, where students attempted to match given target graphs by refining their movements and reasoning aloud. Throughout the activity in class, the researcher – with the role of teacher – orchestrated collective discussions to connect kinaesthetic experiences with formal representations. Preliminary observations indicate that the feedback-rich environment fostered peer collaboration: while taking turns in front of the webcam, students negotiated strategies, verbalised their reasoning aloud, and collectively refined the avatar’s trajectory, building shared mathematical meanings from gestures. Guided by the research question Which design principles most effectively support learning about linear functions through embodied interaction in GGB+? the study identifies principles such as visible parameter trace, explicit object–motion mapping, low-threshold/high-ceiling tasks, and roles variation during the activity. These principles are accompanied by reflections on technical constraints and opportunities and followed by directions for future research on embodied digital tools in secondary mathematics education.

Motivating students has always been one of the most important and difficult tasks of mathematics teachers. Over the last decades, a new approach to facilitate student motivation has been developed: gamification, i.e. the use of game elements in non-game environments. Although many studies highlight the proficiency of gamification to facilitate student motivation, the design of gamified learning environments often remains unexplored. Using a taxonomy of game elements and a gamification design framework, this study gamifies preexisting materials using GeoGebra. The preexisting material that was gamified for this study was initially produced in a project for open educational resources in Austria, which aims to ensure high-quality learning materials. After modifying the preexisting materials employing five different gamification strategies, derived from the used gamification taxonomy, we conduct semi-structured interviews with experts in the field to analyse their opinions on the different variants. The expert status of the participants is constituted by different areas of expertise: participants are either designers of educational learning materials, game-designers, or researchers of gameful learning. The semi-structured interviews that were conducted in this study follow an interview protocol that was developed leaning on the attention, relevance, confidence, and satisfaction (ARCS) framework, as well as the taxonomy of game elements that informed the development of the different gamification variations. With this study, we aim to facilitate a broader understanding of how experts attribute motivational potential to different gamification strategies and what experts in the field deem specifically viable to motivate users of learning environments. The findings of this study should inform future gamification design for randomized mathematics learning environments, as different gamification dimensions impact very different aspects of student motivation. Results of this study, therefore, could also be used in future research for personalized gamification strategies, as associations between gamification design strategies and motivational impact are being discussed.

Since at least the 1970s, computers have been used to solve mathematical research problems (e.g., the four-color theorem). Around the same time, portable calculators became commonplace in schools. However, these tools were not very useful for solving non-routine problems in school mathematics. This changed in the 1980s with the introduction of dynamic geometry software, at least for non-routine problems in geometry. Recent developments in artificial intelligence will revolutionize the handling of text-based problems. In this talk, I will summarize studies on problem solving with digital technology and reflect on the changes that will occur due to chatbots such as ChatGPT.

Geometry plays an essential role in developing mathematical thinking, offering learners opportunities to engage with reasoning, abstraction, and spatial intuition. However, one persistent challenge in its learning lies in grasping formal definitions and visualising geometric elements before students engage with proofs and derivations (Burger & Shaughnessy, 1986). Over the past few decades, dynamic geometry software has emerged as a valuable tool for visualising and exploring complex geometric phenomena. The interactive features and construction tools offered by platforms such as GeoGebra enable richer, more exploratory experiences compared to static resources (Sinclair et al., 2016).

However, as with many technological tools designed to facilitate learning, these platforms may inadvertently obscure essential mathematical processes. This paradox—where a tool intended to enhance mathematical understanding may diminish it—raises the question of demathematisation: the loss or dilution of mathematical experience through over-reliance on automation (Jablonka & Gellert, 2007). This study investigates how dynamic geometry software, despite its potential, can lead to such demathematisation.

The research is motivated by classroom observations of university students who, while adept at plotting linear and quadratic functions using GeoGebra, struggled to perform the same tasks manually on graph paper. Interestingly, students who used physical tools demonstrated a deeper understanding of the properties and behaviours of linear equations. Using the framework of embodied cognition (Abrahamson et al., 2020), this study seeks to theorise which experiential elements might be absent in digital environments and to re-evaluate the educational possibilities and limitations of dynamic geometry tools in light of demathematisation.

The use of digital technologies (DTs) in education is rapidly expanding worldwide, with a wide range of devices and software now available for classroom use. In mathematics education, subject-specific DT tools—such as computer algebra systems (CAS), dynamic geometry software (DGS), data analysis tools, and programming environments—are particularly well developed.

However, the use of DTs in mathematics classrooms remains largely confined to traditional teaching practices, primarily serving as presentation tools such as interactive whiteboards. Consequently, DTs have had only a limited impact on how mathematics is taught, learned, and practised. In other words, their more transformative potential—to support inquiry-based learning and collaboration—has yet to be fully realised.

In our previous study, we developed computer-based testing (CBT) items for mathematics that incorporated dynamic objects for summative assessment. We concluded that these items were effective when used in conjunction with learning activities that also employed DTs.

With this in mind, this study focuses on the use of DTs in various “mathematical activities” and describes the development of digital tasks for upper secondary mathematics that foster conceptual understanding, reasoning, and problem-solving. In particular, we have utilised features such as dynamic representations and 2D/3D visualisation. In this presentation, we will report on several case studies related to this development. Finally, we offer a categorisation of the roles played by different DTs within the established taxonomy of "doing mathematics", "learning mathematics", and "teaching mathematics". We also discuss how interaction data collected through these DTs can be used to enhance the effectiveness and efficiency of formative assessment.

This presentation shares insights from an ongoing study that explores first-year university students' perceptions when working with Calculus tasks in the computer-aided assessment (CAA) system STACK. The students, who are new to digital learning platforms, also engage with several types of formative feedback, including immediate automated feedback from STACK and visual feedback from GeoGebra. Data were collected through a survey, which captured students' attitudes, experiences, and challenges related to these digital assessment tools. The preliminary findings reveal that students generally appreciate the immediacy and interactivity of CAA, especially the feedback provided by GeoGebra’s visualizations, which help clarify mathematical concepts. However, there are students that express difficulties in interpreting and applying the feedback effectively, particularly in the context of transitioning from traditional, paper-based assessments. The study highlights the importance of understanding students' perceptions in designing effective CAA systems, particularly for those new to digital platforms, and provides insights into how formative feedback can be better tailored to support student learning in this transition.

The use of generative AI in mathematics lessons can open new possibilities for developing subject-specific and interdisciplinary mathematical skills for secondary school students. The use of chatbots can provide individualised learning support and differentiated feedback. In order to make the most of this potential, students need to have basic mathematical and linguistic skills for interacting appropriately with AI. In addition, the ability to critically evaluate the results provided by the AI is crucial, as its answers are not always accurate.

The model developed by Roland Fischer, which describes the communication between laypersons and experts, can be transferred to learning with AI as a mathematics-didactic background. The ability to reflect is substantial, while the technical handling of the AI plays a subordinate role. So, the promotion of 21st century skills (e.g. the ability to communicate and reflect) thus becomes more relevant in the context of AI-supported learning environments.

As part of a project, learning materials have been developed that enable students to deal with geometric and arithmetic questions using a chatbot. The aim is to enable learners to formulate their own mathematical tasks, analyse and critically question the answers generated by the AI. The materials have been designed in such a way that they encourage individual and interest-driven processing of mathematical content.

First trials of this approach took place in a 5th grade class. The presentation will report on the first results. Based on these, possible conditions for the success of the mentioned goals will be outlined. At the same time, this approach also has an impact on the organisation and implementation of teaching, which — in the best case — facilitates the work of teachers.

The emergence of generative artificial intelligence (AI) in mathematics teaching and learning is a relatively new and rapidly expanding pedagogical phenomenon. In our research, we examined whether Hungarian students in grades 11–12 preferred the correct solution to certain tasks from intermediate-level mathematics examinations in a blind test, provided either by a human or by generative AI, and what indicators in the preferred solution influenced their choice. We selected three tasks from three different mathematical topics (trigonometry, arithmetic sequences, and probability). Although human-generated solutions were preferred significantly more than AI solutions, a more detailed analysis of the choices indicates that the preference was influenced by whether the human solution was authored by a novice or experienced teacher, as well as by the type of task. One possible explanation for our results is that human solutions may reflect a pedagogical sensitivity that students appreciate more, such as the gradual development of the reasoning process, an empathetic tone, or the proactive handling of common mistakes, which are related to the pedagogical content knowledge of teachers. There is limited empirical research on student preferences between generative AI-generated and human-generated solutions. Existing studies vary in their experimental designs but often yield similar outcomes, highlighting nuanced patterns of trust and preference. Thus, our research contributes to a deeper understanding of this emerging educational phenomenon.

The foundation program at Qatar University prepares first-year students in mathematics and the English language. The mathematics department offers two courses for students: Elementary Algebra (EA) and pre-calculus (PC). There are many challenges for students and instructors teaching these courses, such as students' low study skills, error repetition, and shallow learning. We have used Socrative software as a formative assessment followed by a graded assessment. We follow four stages in this intervention. In the first stage, students are asked to answer formative questions, either one question at a time followed by immediate feedback, or they answer the whole assessment. Then, the teacher discusses the results with the class based on the students' answers. The second stage is re-teaching or more practice, especially on the problematic items. Third stage a graded assessment is done and after that discussion of the results with the whole class. The fourth stage is a follow-up based on students' mistakes, and students can get some bonus grades. Results showed students focused more in class, had better study skills, and had less error repetition.

In our contribution we focus on a recent feature of GeoGebra Discovery, the ShowProof that algorithmically finds (using G-Basis computations) the expression of the NormalForm of 1 (i.e. 0) as a combination of the equations of hypotheses and the negation of the thesis , that is: , a proof by contradiction of the geometric statement. And ranks its ``interest'' or ``difficulty'' by computing the highest degree of the polynomials

As a toy example of this approach, let us consider a right triangle A(a₁, a₂), B(b₁, b₂), C(c₁ ,c₂), with a right angle at vertex A. This fact is expressed by means of this single hypothesis: h:=(c₁-a₁) (b₁-a₁)+(c₂-a₂) (b₂-a₂)=0. Now Pythagoras theorem involves the square of the lengths of the catheti AC:= (c₁-a₁)²+(c₂-a₂)² and AB:=(b₁-a₁)²+(b₂-a₂)², and of the hypothenuse BC:=(c₁-b₁)²+(c₂-b₂)². Is easy to verify that the thesis t:=AC+AB-BC=0, is two times h, that is, t=2h, so we can say that the complexity of the statement is the degree of the constant 2, i.e. 0. Or, if we consider instead a proof by contradiction, we see that the combination of the negation of the thesis zt-1=0, with a dumb variable z, and the hypothesis, yields the expression 1=2zh - (zt-1), so the “difficulty” will be 1 (the degree of the polynomial 2z).

The analysis of the behavior of this measure of interest/complexity/difficulty is an on-going project, and our communication intends to present some initial results, analyzing the output of an experience that we have developed, comparing the ``difficulty'' measure assigned by ShowProof to a variety of well-known, elementary geometric statements, and the performance (i.e. correctness, clarity, and detailed answer), regarding the same statements, of ChatGPT, having in mind the potential cooperation of symbolic vs generative AI, i.e. GeoGebra Discovery/ChatGPT, that can be considered as the general framework of our contribution.

This study explores the experiences and perceptions of mathematics teachers and school principals regarding the integration of GeoGebra and ChatGPT as constructivist teaching tools to enhance numeracy learning in junior secondary schools in Indonesia. Grounded in constructivist learning theory, the research investigates how digital technologies, particularly dynamic mathematics software and AI-based dialog systems, can support student engagement, conceptual understanding, and problem-solving skills. A qualitative research design was employed, with data collected through semi-structured interviews involving five mathematics teachers and five school principals from four regions in North Sumatra Province (Karo District, South Nias District, Binjai City, and Medan City). The findings revealed that teachers face ongoing challenges in teaching numeracy, particularly in statistical topics that require the integration of local cultural contexts. Many teachers have expressed uncertainty about designing culturally relevant instruction and have reported limited pedagogical strategies to address these topics. While participants had some experience using ICT tools such as GeoGebra, their ability to apply the software effectively in numeracy instruction was constrained by a lack of advanced technical skills. GeoGebra has been viewed as a potentially powerful visualization tool; however, many teachers have struggled to utilize its statistical and algebraic features. In terms of AI integration, teachers primarily used ChatGPT as a supplementary resource for instructional materials rather than as an interactive tool to facilitate learning. Although ChatGPT’s potential to support personalized learning and dialogic instruction has been acknowledged, its pedagogical use in the classroom remains underdeveloped. This study highlights both the opportunities and limitations of incorporating digital tools into culturally responsive student-centered mathematics instruction. This underscores the need for targeted professional development to strengthen teachers’ competencies in technology-enhanced numeracy education and offers implications for curriculum innovation and teacher preparation in diverse educational contexts.

Binary system is at the root of the power of electronic devices. Every piece of information can be coded in numbers. We are used to decimal numbers yet, its learning, especially decimal fractions, show particularly devious, leaving aside many students, with robust misconceptions, still visible in upper secondary courses. Taking a step aside, let's dive into numeral systems, and not only for the fad for computational thinking, mistake for thinking like an AI, let's study the binary system and some didactical situations that we experimented over the years. We will open up with ternary and Fibonacci numeral systems.

Because of its reactive and adaptive nature, Generative Artificial Intelligence (GenAI) has the potential to provide users with a range of personalised strategies tailored to their needs. At the same time, chatbots possess conversational features that make them unique in terms of agency, offering a new set of affordances and constraints with respect to their use in mathematics teaching and learning. These aspects highlight that GenAI constitute a class of artefacts very different from the digital educational technologies to which the instrumental genesis framework is usually applied and suggest the need for a theoretical reconceptualisation of human-GenAI interaction. In a previous study, we presented the first draft of a model that aims at this reconceptualisation by identifying the factors that influence the processes of instrumentation and instrumentalisation in the context of human-GenAI interaction. This model takes into account both the artefactual/instrumental and affective factors that influence human-GenAI interaction. The aim of this study is to deepen the analysis of the role of affective factors. In particular, we focus on students' views and beliefs about mathematics and its learning, and on students' anthropomorphisation of the chatbot's actions as factors affecting students' interpretation of the processes of instrumentation and instrumentalisation and, consequently, the instrumental genesis process itself. This study is part of a broader ongoing research aimed at exploring upper secondary students' perspectives on the role that GPT-4o could play in scaffolding their self-assessment processes in the context of conjecturing and proving activities using algebraic language. Data were collected through semi-structured interviews developed before, during and after the students' interaction with GPT-4o. The data analysis, developed using IPA methodology, highlights the complex interplay between the affective factors highlighted by our model and the students' interpretation of the support received by GPT-4o.

Common teaching approaches to teaching function transformations often emphasize the transformation of parent functions, promoting object-like conceptions of graphs. While this approach can enhance students’ fluency in applying function transformations, researchers argue that it may not fully support students’ understanding of what they are transforming, i.e. representations of covarying quantities. This study explores an alternative approach through tasks that promote emergent graphical shape thinking (EGST). EGST involves conceiving graphs dynamically, as traces of moving points constrained by two varying quantities.

The study reports a case study of two preservice teachers completing a two-part digital task sequence. In the first task, they constructed a graph of temperature anomalies using the 1981–2020 temperature average as the baseline. In the second task, they were provided with a graph based on the 1981–2020 baseline and asked to sketch a new graph using the 1951–1980 baseline, knowing that the earlier mean temperature was 0.6°C lower.

Initially, the students demonstrated difficulty interpreting the shift in the baseline and sketched a slightly lower graph. After revisiting the meaning of temperature anomaly and its dependence on the baseline, they reasoned that each point in the new graph must increase by 0.6°C, resulting in a graph translated vertically upward and corresponding to the function T₂(x) = T(x) + 0.6. This case illustrates how EGST can support preservice teachers’ construction of vertical translation meanings, both graphically and algebraically, through authentic, climate-based modelling tasks. These findings suggest that fostering EGST can support students in constructing meanings for relationships between functions, such as those involved in vertical translation, by helping them attend to how one function emerges from another. This approach has the potential to be extended to other types of transformations, function operations, and composition, as they share a similar underlying structure.

This study explores the potential of GeoGebra 3D modelling as a digital tool for enhancing mathematics learning and promoting student engagement in STEM fields within African educational contexts. Thirteen high school students in Tanzania participated in a training workshop focused on using GeoGebra for dynamic 3D modelling. Data were collected through reflection journals, focus group discussions, and analysis of student-created applets. Thematic analysis revealed that students perceived GeoGebra as a powerful educational tool that makes abstract mathematical concepts more concrete, promotes joyful and visual learning, fosters interdisciplinary thinking, and attracts students to mathematics. Student projects included a 3D model simulating planetary revolution and a visualisation of a ship, illustrating creativity and applied understanding. These findings highlight GeoGebra’s potential as a game-changing digital tool for transforming mathematics education and increasing student motivation in low-resource contexts. The study offers insights into scalable practices for digital integration in STEM education across Africa.

In mathematics learning, students often write their ideas and answers, which are difficult to express using standard input devices such as a keyboard and mouse. While computer-based learning environments have become widespread, most learning management systems (LMSs), including Moodle, lack effective support for handwriting input.

To address this gap, we introduce Handwritten Answer Input, Management, and Recognition (HAIMR), a comprehensive plugin designed to integrate handwritten input into Moodle-based assessment workflows. HAIMR enables students to submit handwritten answers directly within Moodle using a stylus or touchscreen device. These handwritten answers are directly stored in the Moodle database, allowing teachers to manage, view, and evaluate them efficiently.

A key feature of HAIMR is its ability to preserve the original handwritten input, enabling educators to observe not only the final response but also the actual strokes and writing process—crucial for understanding how students think and solve problems.

The toolkit supports integration with handwriting recognition engines and manual marking, enabling semi-automated or fully automated scoring. HAIMR is multidisciplinary by design, supporting applications not only in mathematics but also in chemistry and language learning—particularly beneficial for beginner-level learners. For example, we implemented chemical formula recognition by adapting techniques used in mathematical formula recognition. Furthermore, it provides an open infrastructure for developing activities that assess logical thinking and problem-solving skills.

We are currently conducting a feasibility study involving users across various subjects and device types. Preliminary observations suggest that the plugin is easy to use, promotes student engagement, and shows promise in supporting handwriting-based interaction. These early findings highlight HAIMR’s potential as a digital tool for enabling more natural, expressive, and analyzable input in education, contributing to the advancement of digital tools in teaching and assessment.

As part of the "Digitalization Project in Steyr," the Ozobot initiative engages over 1,000 Austrian primary and secondary school students and 200 compulsory school teachers. This large-scale educational robotics project leverages analog and block-based coding with Ozobots to facilitate interdisciplinary learning in STEAM+ subjects. Targeting primarily Austrian primary school students, the project aims to enhance digital skills and foster an integrated understanding of science, technology, engineering, arts, and mathematics (STEAM+). This talk will present an overview of the project's scope, objectives, and implementation strategies. A key focus will be placed on the application of Ozobots in mathematics education, showcasing how students interact with fundamental concepts such as multiplication tables, addition, subtraction, division, and general arithmetic through hands-on, interactive learning experiences. The project follows a mixed-methods, design-based research approach, with empirical data collected from tested materials and real classroom settings. Observations from the classroom, including student engagement and learning outcomes, will be shared, providing valuable insights into how robotics can be integrated into everyday teaching practices.Case studies and classroom-tested teaching materials will be presented, offering educators practical tools for incorporating Ozobots into their curricula to effectively support the development of both mathematical and STEAM+ competencies.

Checkbox grading is a digital assessment method in which a group of teachers define a set of criteria—formulated as checkboxes—each linked to descriptive feedback and partial grades. This approach was initially implemented during a large-scale mathematics state exam, where assessors reported improved clarity and usability (Moons et al.,2025),and students responded enthusiastically to the transparency of the feedback (Moons et al.,2024).

To explore checkbox grading beyond large-scale assessment contexts, we investigated its potential for fostering student learning through self-assessment. In a pre-posttest experiment, 68 secondary students were randomly assigned to one of three groups during a one-hour intervention on the difference quotient (five tasks). The control group received solution keys after each task. The second group received solution keys supplemented with checkbox grading schemes. The third group received the same as the second group but were actively encouraged to revise their solutions using their checked checkboxes. Two isomorphic test versions were randomly assigned as pre- or post-test to control for test effects. Learning gains were analyzed, controlling for mathematical attitude and efficacy.

Preliminary results suggest that checkbox-based self-assessment does not enhance learning outcomes. In fact, students in the checkbox group performed worse on the post-test compared to peers in other groups, despite being randomly assigned and similar at baseline. This points to a lack of transfer between checkbox grading and understanding. The findings challenge the assumption that effective assessment tools necessarily support learning in a self-assessment setting. While checkbox grading aids teachers in delivering structured feedback in large-scale settings, it may constrain students' reflections when repurposed for self-assessment.

References

• Moons, F.,Vandervieren, E.,&Colpaert, J.(2025).Checkbox grading of large-scale mathematics exams with multiple assessors:Field study on assessors’ inter-rater reliability,time investment and usage experience.SEE.https://doi.org/10.1016/j.stueduc.2024.101443
• Moons, F.,Iannone,P.,&Vandervieren, E.(2024).Checkbox grading of handwritten mathematics exams with multiple assessors:How do students react to the resulting atomic feedback?A mixed-method study.ZDM.https://doi.org/10.1007/s11858-024-01550-6

This workshop builds on the presentation "Innovative STEAM Pathways: Centering Mathematics, Supporting Equity, and Leveraging Other Disciplines Primarily as Tools—Through an Electronic Platform", which emerged from the STEAM Connect Project (ERASMUS+). In this practical session, participants—including primary and lower-secondary school teachers, as well as researchers—will engage in hands-on, multidisciplinary STEAM activities that integrate mathematics, physics, music, movement, biology, visual arts, and technology using the Circuit Playground Express board. Developed by Adafruit Industries, this all-in-one microcontroller is equipped with sensors that enable playful and creative experimentation with sound, light, motion, and temperature.

Participants will experience the Skateboard Challenge from a learner’s perspective by balancing on a wooden board placed over a PVC pipe to reproduce pre-programmed songs. This physical and musical activity engages children with key mathematical concepts such as angles, measurement, and spatial reasoning, while also enhancing coordination, rhythm, tempo, and timing—skills essential for both musical expression and physical development. Participants will also be guided through basic modifications to the underlying Python code, allowing them to experiment with the musical output and explore how programming can support and enrich engaging, creative, mathematics-based learning environments.

Throughout the workshop, we will reflect on the pedagogical foundations of this approach, highlighting strategies that promote active participation, scaffold conceptual understanding, and respond to the diverse needs of all learners. Alongside the Skateboard Challenge activity, participants will be introduced to and experiment with additional hands-on learning tasks that showcase the versatility of the Circuit Playground across various STEAM contexts. By the end of the session, they will gain practical insights and resources for integrating these activities into their own teaching or research, and for using the Circuit Playground as a powerful tool for inclusive, equity-driven, creative, and meaningful instruction—especially in mathematics, enriched through artistic and musical expression.