Abstracts

Designing Batik Stamp model with 3d printer.

Putro - Yunianto

Solo is well known for its batik products. Our school is located in Solo, and we want our students to contribute to preserving their local culture, batik. Making batik involves painting or stamping the material with a unique wax. One of the things we can do with our students is make batik stamps. With the new innovation of 3D printers, we would like students to preserve culture through STEAM learning by utilizing 3D printers. We incorporated GeoGebra to make the 2D design and exported it to ThinkerCad. From the activity, we learned that students could creatively design the pattern of the stamp.

Opportunities for geometric and morphological analysis in the reverse modeling process for 3d printing.

Picchio - Fu - Martinelli - Galasso - La Placa

This study follows the application of an experimental workflow in the field of digitization of elements for 3D printing as an education opportunity for students in engineering and architecture faculties. The entire reverse modeling process offers students several opportunities of knowledge and understanding of geometric shapes at different scales and complexities such as: the recognition of pure geometries in architecture, the comparison between numerical (mesh based) and mathematical (NURBS based) 3D modeling, the rigorous perspective reconstruction in an SfM process (Structure from Motion). Therefore, in this conceptual research, a class of students in the course of Survey of Architecture of the University of Pavia, Department of Civil Enginnering and Architecture, was led to carry a deep study for the description of architectural detail of the facade of the Certosa di Pavia. Thanks to a photogrammetric survey conducted with UAVs, and then digitally processed, the reality based model offers a solid base for the didactic purpose, with respect to the LoD (Level of Detail). The conversion of the model and the planning of a 3D print (scaling, cutting, identification of critical areas) therefore appear as expedients for the critical evaluation of the entire workflow process, and let them understand the possibilities of alternative fruition, tactile, VR and Ar, of a complex heritage.

Enhancing pre-service teachers’ knowledge through 3DMP task design.

Tejera - Ulbrich - Lavicza

3D Modelling and Printing (3DMP) presents a novel method for producing educational materials (Ng, 2017) and integrating them into the training of pre-service mathematics teachers (PMTs). However, there is a need for more research on how the integration of this technology affects the knowledge of PTMs (Ford & Minshall, 2019).

This study delves into the integration of 3DMP within mathematics teacher education, guided by the research question: Which specific knowledge is mobilised by PMTs when creating tasks incorporating 3DMP? It not only aims to examine the variety and depth of knowledge that PMTs engage with and develop when designing tasks with 3DMP technology but also to contribute to the refinement of our 3DMP course. Identifying the specific knowledge areas used in task creation helps refine course content, pedagogical strategies, and the integration of other digital technologies.

Beyond the Classroom: 3d modelling activities and student’s self-esteem. 

Hosic - Kreis - Lavicza

In recent decades, the utilization of 3D modeling in STEAM learning activities has gained significant traction. Such activities involving 3D modeling typically fall into two categories: those where students function as users and those where they serve as creators. This research focuses specifically on students as 3d modelling creators, within the context of the maker movement. The study delves into the examination of students' self-esteem throughout their engagement in 3D modeling activities conducted in the classroom. Two distinct activities were undertaken: the creation of 3D models based on museum collections and the construction of flower diagrams. Diverging from conventional approaches reliant on quantitative methods and questionnaires, this study adopts a qualitative approach, employing interviews with students to assess their self-esteem. The findings from these interviews were subsequently thematically analyzed to identify the factors associated with students' self-esteem within the context of this study.

Keywords: 3D modeling, students, self-esteem

3D printed jewelry inspired by mathematics.

Budinski - Lavicza

 We discuss the possibilities of 3D printing in mathematical lessons in the process of developing artistic ornaments inspired by mathematics such as jewelry. The paper describes      how to approach students in the field of 3D printing to explore possibilities of artistic expressions based on mathematics and new technologies. The activity has several parts. The first part is exploring mathematical concepts that could be used as an artistic inspiration and the second part is an introduction to 3D printing. The final activity is presentation of results and discussion.

3DMP projects chosen by maths teachers: equally supporting creativity?

Ulbrich - Schmid - Tejera - Sabitzer - Lavicza

Using technology can be challenging for teachers and using it meaningfully is important for successfully providing good STEAM educational settings to students. Technologies such as 3D modelling and 3D printing (3DMP) gain popularity for STEAM education and can offer opportunities to support developing the four C’s of the 21st century. However, the presumption, female teachers would be engaging with technology less or with different intensity than male teachers and the rising numbers of female teachers in maths education could create learning scenarios not offering the same learning opportunities to everyone. We therefore looked at more than 100 3DMP project documentations from pre-service mathematics teachers attending a 3DMP beginners course searching for similarities or differences regarding fostering the four C’s. We found that female pre-service mathematics teachers are highly engaged in a course offering insight into technology since they attended the course overproportionally (female students slightly more than male students becoming mathematics teachers and two third of the participants of the course being female).

Conic sections and spirographs with 3d printing. A proposal for pre-service secondary teachers. 

Fernández-López - Blanco - Castiñeira 

In recent years, the use of 3D printing as a didactic tool is increasingly present (Ford, S., & Minshall, T., 2019). This document presents a proposal carried out with preservice secondary teachers in which the learning processes of conic sections, hypotrochoids, epitrochoids and three-dimensional bodies are combined with 3D printing. The sample is made up of 15 students, 1 woman and 14 men. The project is structured in four phases: (I) Introduction to Tinkercad through conic sections, (II) Creation of spirographs, (III) 3D printing of the results and (IV) Debate on possible didactic applications. The data collection instruments used were notebook and students creations. The results shown unexpected limitations in spatial vision skills, problem solving application of mathematical knowledge and interest. This results, and some comments recorded during phase III, lead to infer, in relation to students, an excessively abstract thought (that will hinder their teaching practice, especially in relation to the lower courses of secondary education) and worrying predilection for traditional methodological orientations. On the other hand, a good digital competence and some witty final products stands out. More studies will be necessary to obtain conclusive results.

The experiences of pre-service mathematics teachers with a model-eliciting activity using a digital tool and 3d printing.

Aydınyer - Bautista - Tejera - Lavicza

Pre-service mathematics teachers need to be provided with opportunities to experience activities using digital tools and 3D printing technology so that they understand the possibilities, limitations, and general pedagogical nature of these tools. Model-eliciting activities are open-ended and realistic problems that involve the development or design of mathematical model(s) collaboratively with the groupmates. Therefore, by combining these perspectives, the present study has two aims: (i) to design, implement, and evaluate a model-eliciting activity that involves mathematical modeling using a digital tool, 3D printing technology, and two-dimensional geometry concepts and (ii) to reveal the experiences (e.g., difficulties) of the pre-service mathematics teachers with the activity. For these purposes, the activity was conducted on 19 pre-service teachers and the qualitative data (classroom observations, interviews, responses to the reflection questions) were obtained. It is thought that the findings of the present study can offer different perspectives on mathematics education and teacher education. The topic chosen from the list is “3D printing and STEAM education with a focus on mathematics”. 

How can we integrate 3d printing technology into teacher noticing?

Hatice - Lavicza

Recognition of the crucial role of teacher noticing in professional competence has grown. Given the significance of technology in our daily lives, particularly in the realm of mathematics education, there is an increasing need to incorporate technology into teacher noticing practices. In the literature on teacher noticing, technology is predominantly characterized as a tool, as seen in the use of videos to identify and enhance teachers' noticing skills. As technology becomes more integrated into classroom settings, it becomes clear that it will be a key factor where teachers observe and assess student thinking. Consequently, there is a need for environments where technology goes beyond being a mere tool for teacher noticing. 

As 3D printing technology becomes increasingly present in math classrooms, teachers' understanding of this technology alone may not suffice to grasp the nature of their students' mathematical thinking while utilizing it. Our objective is to explore how 3D printing and /or other technologies can be integrated into the noticing skills of mathematics teachers. To reveal and/or enhance teachers' noticing abilities we envision presenting classroom scenarios where students use 3D printing and/or other technologies. We think that we can create scenarios or problem-solving tasks that require students to apply mathematical principles through these technologies and prepare tasks for teachers by observing how students approach and solve these challenges, focusing on the integration of the technology. However, we welcome any suggestions on this matter.

Demands for the representation transformations throughout 3d modelling with Geogebra: Construction of Taj Mahal.

Galiç - Tejera - Urhan - Arkün Kocadere - Lavicza

Duval emphasizes that using at least two representation registers and performing a transformation within and/or between registers in geometry tasks is required to reach the aim. The performance to transform one representation register into another is a crucial threshold for learning geometrical concepts. In math classes, students should be given learning opportunities to use multiple representations and perform transformations while building knowledge structures in geometry tasks. 3D modelling provides such opportunities in math classes, promoting the construction and transformation of multiple representations. Before implementing modelling tasks in math classes, it is required to determine the cognitive demand for the use of the representation register. Hence, it becomes possible to identify the cognitive effort that is expected from students during 3D modelling and take the necessary measures. This paper aimed to examine the demands for constructing and transforming representation registers throughout the 3D modelling of a real object using mathematical concepts and GeoGebra tools based on Duval's theory of semiotic representations. For this aim, the 3D modelling of the Taj Mahal via the semiotic mediator of GeoGebra performed by an expert was examined and demands for performing cognitive processes. The findings would elucidate to determine the requirements of the task for the students to perform productive modelling based on the construction and transformation of representations. Furthermore, the findings would be useful to lead the discursive process to turn into productive argumentations and to prepare a rubric to assess students implementing this task in math classes.

Use of 3D modeling and printing technologies in solving mathematical problems and its reflections on learners’ computational thinking.

Köroğlu - Ertan - Arkün Kocadere

3D modeling and printing technologies play a crucial role in helping learners embody mathematical concepts. Research indicates that these technologies contribute to the development of 21st-century skills such as critical thinking, creativity, technological literacy, and problem-solving (Cheng & Cheng, 2022; Turst & Maloy, 2017). Moreover, these technologies provide students with the opportunity to develop their Computational Thinking (CT) skills such as algorithmic thinking, abstraction, and data analysis by encouraging CT, which lies at the center of 21st-century skills (Kordaki & Kakavas, 2017; Shute, Sun, & Asbell-Clarke, 2017). In this context, this study aims to investigate the implications of using 3D modeling and printing technologies in mathematical problem-solving processes on learners' Computational Thinking skills. For this purpose, a learning activity that involves the integration of 3D modeling and printing in solving a mathematical problem that we developed is used. 

The activity is presented to five 7th-grade students through worksheets containing a scenario about ratio and proportion. Data on the learners’ computational skills and experiences during the problem-solving task were collected through worksheets, and observations which include the think-aloud method. In addition, semi-structured interviews will be conducted in order to determine learners’ experiences regarding the use of 3D modeling and printing technologies in mathematics. The data gathered from observations, think-aloud processes and students’ responses to interview questions will be analyzed through content analysis. In order to analyze learners’ responses on the worksheets Computational Thinking Skills Evaluation Rubric will be used. It is expected that this study will contribute to concretizing abstract mathematical concepts by providing an example of supporting Computational Thinking in the mathematical problem-solving process through the use of 3D modeling and printing technologies.

Role of 3D printing object in visualization.

Rafiepour

In this presentation we focus on rotation of 3D object and visualization of each side of that object with using concrete object. This type of activities can foster students capability in solving different geometrical problems. 

Renewable energy and 3D printing.

Bekesi - Ulbrich - Hourhton - Lavicza

The presentation aims to show a case study on using 3D printing while discussing various solutions to how wind power could be used at home. The students learned about 3D printing, where and for what it is used, looked for printable models and designed some using Tinkercad, experimented with small vertical axes wind turbines, compared them, and some designed new models for private use. While printing, the students implemented tiling the models to use as little support as possible. The study involved students from three lower secondary school classes aged between 13 and 14. The activities stretched over two months and took place in regular physics and mathematics lessons. Data were collected from questionnaires, focus groups and observations. We aimed to study how students’ motivation changed during the activity and the reasons for this change. We hypothesized that implementing technology and discussing sustainability, a topic that seems to interest especially the young generation, would both contribute to the change in students’ motivation. The activity was part of a bigger project titled “Sun, Water and Wind” allowing students plenty of room for creativity, for instance, to work on topics such as renewable energy, using watercolours or blindness.

AI Supported 3D Modeling: Innovations in Mathematics Education through ChatGPT-Assisted 3D Print Creation.

Köroğlu - Yıldız

This research explores the integration of artificial intelligence and 3D printing technologies to transform mathematics education, with a focus on leveraging ChatGPT to generate instructional materials in the form of STL files. Mathematics is crucial for developing conceptual understanding and problem-solving skills, yet it is often perceived as challenging by students. 3D printing offers a significant tool to overcome this challenge by enabling students to visualize and physically interact with mathematical concepts and objects. However, to fully exploit the educational potential of this technology, teachers and educators need access to high-quality instructional materials that are easily customizable. ChatGPT addresses this need by assisting teachers and educators in creating customized 3D printing models for mathematics lessons. This research details how ChatGPT can be utilized, outlining the steps involved in the development and implementation of teaching materials. The methodology primarily focuses on the selection of mathematical concepts and their transformation into 3D models. It then examines how these models are prepared in STL file format and optimized for 3D printing. In the application section, activities and projects conducted by teachers and students using these models are introduced. Additionally, the impact of this technology on student engagement, motivation, and understanding of mathematical concepts is evaluated. Findings indicate that 3D printing materials prepared with ChatGPT significantly contribute to students' ability to concretize and comprehend mathematical concepts. In conclusion, the research underscores how the integration of artificial intelligence and 3D printing technology in education, especially in challenging subjects like mathematics, can enrich learning experiences. It also offers practical suggestions for educators to integrate these technologies into their lessons. This study aims to lay a foundation for the future development of educational technologies, contributing to the continuous evolution of teaching methods.

Making manipulatives in mathematics education.

Stigberg - Stigberg

While digital fabrication and 3d printing have been closely linked to narratives of STEAM education and design thinking, it can provide a gateway to reimagining mathematical teaching and deepening the understanding of both mathematical content and pedagogy. In our presentation, we will describe our efforts to create a digital fabrication curriculum module for mathematics teacher education, that engages teacher students in making manipulatives which we assumed would inform their mathematical teaching.

Manipulatives are tangible objects reifying mathematical concepts and one type of representation used in K-12 mathematics education to teach concepts such as number, fraction, or geometry. Manipulatives are often mass-produced, and teachers are usually encouraged to think like consumers when it comes to how these materials can support understanding, learning, and teaching of mathematics. We see an opportunity for teachers to create their own manipulatives using digital fabrication to open for new learning experiences and customized mathematical teaching.

We conducted two workshop series including pre-service teachers and in-service teachers introducing 3D printers, laser cutters, and vinyl cutters to make manipulatives for mathematics teaching. The presentation will highlight our key insights from integrating these technologies within a mathematical context, combining technology, didactics, and mathematics. We will present selected manipulatives created by the workshop participants and share their reflections on using 3D printers and laser cutters as innovative tools for making manipulatives. We look forward discussing our work and getting inspired by other projects and research in the field. 

Teachers using 3d modelling and 3d printing (3DMP) in STEAM education in Montenegro and Austria and suggestions on how to support them.

Ulbrich - Cruz - Anđić - Tejera - Dana-Picard - Lavicza

Integrating 3D-modelling and -printing (3DMP) in STEAM education presents opportunities and challenges for teachers, particularly in some European countries where its adoption in schools still needs to be improved. This paper presents findings from a cross-cultural examination of 3DMP in STEAM education, showing results from teachers in Montenegro and Austria. The study aimed to gather insights into teachers' perceptions of 3DMP, ideas for its implementation, and the challenges they face. Data was collected through questionnaires, interviews, and examples of 3DMP use were analysed to identify similarities and differences in the impressions and use of the technology. The findings indicate that teachers in both Montenegro and Austria expressed interest in using 3DMP for STEAM teaching purposes and saw potential for connecting to subjects such as digital literacy. However, they also identified software-related challenges, time constraints, training, and financial difficulties when adopting 3DMP. The slow adaptation of 3DMP in schools suggests that teachers should be better supported in using this technology, considering external and internal influences such as teacher training, local culture, and availability of technology. Furthermore, the study highlights the need for suitable measures for teacher training and ensuring access to technologies necessary for 3DMP.

The Use of 3D printing in visualisation mathematics classroom: A systematic literature review.

Saimon - Tejera - Ulbrich - Anđić - Lavicza

Facilitating the increasing use of 3D printing technology for visualisation in mathematics classrooms requires informed practices and policies. Nevertheless, there is a lack of systematic literature review in this area. As a result, the present aimed at filling this gap by conducting a systematic literature review on the use of 3D printing technology in visualisation for the visualisation mathematics classrooms. The data used were drawn from 7 articles published from 2014 to 2024, accessed from Scopus and Web of Science.  Data were analysed through content analysis. The study focused on answering questions about learning context, learning content, pedagogical aspects, assessment strategies, outcomes and modelling technologies. Findings show that 3D printing technology is integrated into both regular and irregular curriculum contexts. The learning content includes volume, STEAM-related and geometry; the pedagogical approach includes lecture and project-based learning; the assessment strategies include survey and observation; the learning outcomes include spatial and problem-solving skills; and CAD is the most used modelling technology. However, the present research evidence is drawn from research with limited global coverage, which limits the contribution to policies and practices in a global context. 

Exploring geometric understanding through 3D printing: The oloid experience.

Rotger - Ribera

In this communication, we delve into the innovative intersection of mathematical education and 3D printing technology, focusing on the practical application and educational benefits of modeling the geometric figure known as the oloid. Drawing from the Educational Mathematics Realistic (EMR) perspective, which emphasizes the importance of connecting mathematical teaching to real-life and socially relevant elements, this study aligns with the interdisciplinary approach of STEAM education to foster integrative and meaningful learning experiences. The primary objective of this study is to explore the potential of 3D printing in enhancing the understanding and application of geometric concepts within STEAM education, using the oloid as a case study. Employing a qualitative research approach, this study integrates the use of 3D modeling software (TinkerCAD and BlocksCAD) for the design and creation of the oloid, followed by its physical realization through 3D printing. This process is complemented by a series of educational activities designed to engage students in hands-on learning, from conceptual understanding to practical application. The findings reveal that the 3D printing of the oloid enhances students' spatial visualization skills, understanding of geometric properties, and interest in mathematics. Furthermore, the study highlights the interdisciplinary potential of this approach, as students apply mathematical concepts in practical projects, thereby appreciating the real-world relevance of their learning. The integration of 3D printing into STEAM education, exemplified through the oloid experience, represents a transformative synergy that enhances interdisciplinary learning and the practical application of mathematical knowledge.

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Lieban - Galiç - Tejera - Lavicza

Genius Square is a strategy game, composed of a board in the shape of a square, 9 pieces (like TETRIS pieces) in different colors, and 7 black cylinders, which are used to block some spots defined by coordinates (A1 to F6). In this work, we will present some possibilities to explore the use of the game either by modeling purposes or to develop competencies regarding spatial reasoning and combinatorics by working with this funny game.