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See detailIntegrated STEAM Approach in Outdoor Trails with Elementary School Pre-service Teachers in Luxemburg
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

in Journal of Educational Technology and Society (in press), 24(4),

Due to the COVID-19 pandemic it was impossible to carry out on-campus teaching and examinations as planned for the first-year elementary school Bachelor’s degree teacher training courses during the summer ... [more ▼]

Due to the COVID-19 pandemic it was impossible to carry out on-campus teaching and examinations as planned for the first-year elementary school Bachelor’s degree teacher training courses during the summer term of 2019/2020. Therefore, we moved our on-campus STEAM (Science, Technology, Engineering, Arts and Mathematics) related courses to schooling at home. For their course examination, students designed outdoor trails in groups with the educational technology MathCityMap based on an integrated STEAM approach. Hence, they combined STEAM with real-world situations (e.g., monuments, marketplaces, playgrounds). The tasks within the trails required the use of technologies such as augmented reality (AR), digital modelling (e.g., GeoGebra 3D Graphing Calculator), and GPS. Analogue measuring tools (e.g., triangle ruler) were also used in the task designs. We collected data from 21 trails with 259 tasks from 49 pre-service teachers to analyse the effects on professional growth in STEAM education. Through hierarchical cluster analysis we identified three different clusters with patterns regarding STEAM in outdoor trails. This paper will describe a pedagogical framework for the integrated STEAM approach to designing and evaluating outdoor trails. Furthermore, we will explain patterns pre-service teachers developed during this professional development. [less ▲]

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See detailCase study on augmented reality, digital and physical modelling with mathematical learning disabilities students in an elementary school in Luxemburg
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

in International Journal for Technology in Mathematics Education (in press), 28(3),

This paper reports on a case study of two elementary school students with mathematical learning disabilities (MLD) (ages 10 and 11) using augmented reality (AR), digital and physical modelling in ... [more ▼]

This paper reports on a case study of two elementary school students with mathematical learning disabilities (MLD) (ages 10 and 11) using augmented reality (AR), digital and physical modelling in mathematics class. MLD students worked on modelling geometric shapes (cubes, cuboids, squared pyramids, and octahedrons) and forms (polygons) by combining real-world objects with AR and creating a copy of geometric shapes or missing parts with a 3D printing device. The study focused on the development of process skills and mathematical concepts, tried to identify changes in the visual-spatial memory, and documented the learning behaviour in class. Further, we collected data through task-based interviews with both students. Based on our findings, we present settings and manipulatives which are likely to foster process skills and mathematical concepts in geometry tasks suitable for MLD elementary school students. [less ▲]

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See detaileJMT Problem Corner: June 2021
Kreis, Yves UL; Haas, Ben; Lavicza, Zsolt

in The Electronic Journal of Mathematics & Technology (2021)

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See detailFirst results of the iterative STEAM design process in 3D modelling and printing with pre-service teachers
Kreis, Yves UL; Haas, Ben; Lavicza, Zsolt

Scientific Conference (2021, May 28)

While we examined mathematical modelling of architectures with CAD software during the last years, we intended in our higher education courses in pre-service elementary school teachers' initial training ... [more ▼]

While we examined mathematical modelling of architectures with CAD software during the last years, we intended in our higher education courses in pre-service elementary school teachers' initial training to expand the complexity of the modelling tasks. In addition, our previous research results indicated a high difference between the quality and functionality of designs by students. Therefore, we investigated the design process in 3D modelling and printing. Based on the industrial iterative design process (e.g., design of a pen), we became aware of the importance of iterative process milestones, quality controls, discussions and peer evaluations. Therefore, we created a remote teaching course for pre-service teachers to design complex objects (e.g., functionality) and create learning settings and tasks based on an iterative design process concept. We will present the first results and reflections at this conference. [less ▲]

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See detailThe STEAM skilled child: How children can learn to apply STEAM skills to their living environment
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

Scientific Conference (2021, April 01)

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See detailMixed-methods research in STEAM outdoor trails in elementary school pre-service teacher training
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

Scientific Conference (2021, March 25)

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See detail3D Modelling in online learning for pre-service elementary school teachers at the University of Luxembourg
Kreis, Yves UL; Haas, Ben; Lavicza, Zsolt

Scientific Conference (2021, March 19)

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See detailOutdoor STEAM integrated framework in elementary schools in Luxembourg using MathCityMap and GeoGebra 3D Calculator
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

Scientific Conference (2020, December 15)

In elementary schools in Luxemburg, sciences and mathematics are generally taught in class based essentially on textbooks. However, the findings of multiple studies on understanding and applying skills in ... [more ▼]

In elementary schools in Luxemburg, sciences and mathematics are generally taught in class based essentially on textbooks. However, the findings of multiple studies on understanding and applying skills in STEAM (Science, Technology, Engineering, Arts and Mathematics) report that students need hands-on activities on real-world objects. Furthermore, in times of the COVID-19 pandemic, where numerous restrictions and risks dominate teaching inside the classroom, outdoor learning is safer and offers many opportunities. Hence, we created outdoor mathematical trails with a STEAM integrated approach for elementary schools using the free educational software MathCityMap and the dynamic mathematics software GeoGebra 3D. In these outdoor trails, students used a set of promising technologies, i.e. AR (Augmented Reality) or GPS, to support STEAM education. Based on results from our first study on outdoor mathematical trails in June 2020 (in review), we developed and evaluated a framework on outdoor STEAM integrated teaching. This framework was used for further outdoor task and trail creations in elementary schools, which we investigated by conducting semi-structured interviews with students and teachers. Hence, we will present how this framework was used in elementary schools to create outdoor mathematical trails and describe how it affected the students' learning. [less ▲]

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See detailTransition from in-class to outdoor learning with real-world mathematical modelling: PhD research project 2015-2021
Haas, Ben; Lavicza, Zsolt; Dana-Picard, Thierry (Noah) et al

Presentation (2020, December 10)

In this PhD outline, I will present highlights from my PhD research project on mathematical modelling with real-world information in the classroom, remote teaching and outdoor learning in Luxemburg ... [more ▼]

In this PhD outline, I will present highlights from my PhD research project on mathematical modelling with real-world information in the classroom, remote teaching and outdoor learning in Luxemburg. Through design-based explanatory studies, I investigated different technology enhanced tasks, learning and teaching settings that could likely engage students in understanding and transferring mathematical modelling to their living environments. The selected design-based research methodology and its characteristics, allowed to adapt task designs, settings and methods during my PhD research project. Hence, firstly, I investigated process skills learning (e.g.: mathematical modelling) with an automated tutoring system (the educational technology software MathemaTIC) within an international project. Although findings were promising, I redesigned my interventions to connect further students mathematical modelling learning to real-world information. Thus, secondly, I performed mathematical modelling tasks with augmented reality on real-world objects in remote teaching and in special needs educations. Utilising findings of these studies and a redesign of the intervention based on outdoor mathematical trails, thirdly, I undertook my final study. In pre-service teacher higher education, I explored outdoor mathematical modelling with an integrated STEAM (Science, technology, engineering, arts, and mathematics) approach. With the aim of such holistic approach, I collected data on education-related perceptions from different stakeholders of elementary school education (students, parents, in-service, and pre service teachers) and developed conceptual frameworks on task creation, mathematical modelling, and stakeholders' roles. In my PhD research project, I aspired to contribute and explain how in-class learning and teaching could be connected and transferred to mathematical modelling within students living environments. Although there are many crucial moments, method choices and findings within these studies, in this report, I will offer highlights of my PhD work and results. [less ▲]

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See detailFostering process skills with the educational technology software MathemaTIC in elementary schools
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

in Donevska-Todorova, Ana; Faggiano, Eleonora; Trgalova, Jana (Eds.) et al Proceedings of the 10th ERME TOPIC CONFERENCE (ETC10) on Mathematics Education in the Digital Age (MEDA) (2020, September 07)

This study reports the use of automated tutoring and scaffolding implemented in the module “arithmetic word problem” in the educational technology software MathemaTIC in grade 3 (age 8 to 10). We examined ... [more ▼]

This study reports the use of automated tutoring and scaffolding implemented in the module “arithmetic word problem” in the educational technology software MathemaTIC in grade 3 (age 8 to 10). We examined 246 students with access to MathemaTIC and receiving tutoring and scaffolding through a one-to-one learning setting with this technology. The control group (n=226) had access to the same learning tasks and worked with paper-and-pencil without MathemaTIC but with their teachers. Results showed that the experimental group finished with higher outcome scores than the control group. This paper will outline the study and attempts to explain these results. [less ▲]

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See detailSTEAM Education in elementary schools: A holistic investigation on technology enhanced teaching and learning
Haas, Ben; Lavicza, Zsolt; Kreis, Yves UL

Scientific Conference (2020, July 03)

When we address the learning of mathematics in elementary school, we imagine pupils doing experiments, discoveries, and combining the different elements from arithmetics to geometry. Pupils interact with ... [more ▼]

When we address the learning of mathematics in elementary school, we imagine pupils doing experiments, discoveries, and combining the different elements from arithmetics to geometry. Pupils interact with their environment and try to use their learned skills to get a deeper understanding of the world. They engage in a mathematical thinking process and try to interact with their environment. However, when you visit a classroom, you find a rather old fashioned teaching based on a deductive approach where imitations of technics play an essential role. Based on our observations, pupils learn mainly through to repetitions in textbooks. Experimentation, if any, comes as additional work, it is seen as a ludic activity rather than as real learning activity. In our research, we inquired about different ways to engage pupils in an experimental approach. We used digital and physical modulation, augmented reality, and various educational technologies. In one of our first studies, we designed a tutoring system to foster process-related skills in mathematics within the educational software MathemaTIC . We collected data on pupils in assessments on transferring mathematical thinking from instructional technology to the everyday classroom teaching. In a second study, we worked with pupils from elementary schools, kindergarten, and from the special needs section to go beyond two-dimensional representations and discover how mathematics operates in three-dimensional settings. Pupils worked on designing software and three-dimensional printing. We collected data on how pupils and parents perceived the learning and teaching and how this influences the further thinking in mathematics. In a holistic approach, we aimed to identify how pupils, teachers and parents perceive the learning through these new technologies and how it affects the learning and teaching. Our research happened in onsite and remote teaching. In this conference, we will present results from the different studies, give insights into our research, and present future experimental investigations. [less ▲]

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See detailConnecting the real world to mathematical models in elementary schools in Luxemburg
Haas, Ben; Kreis, Yves UL; Lavicza, Zsolt

in Proceedings of the British Society for Research into Learning Mathematics (2020, July), 40(2), 1-6

In the Luxemburgish national curriculum for elementary schools (MENFP, 2011) experimentations and discoveries of mathematics concepts in courses are strongly recommended. Elementary school teachers should ... [more ▼]

In the Luxemburgish national curriculum for elementary schools (MENFP, 2011) experimentations and discoveries of mathematics concepts in courses are strongly recommended. Elementary school teachers should engage students in active mathematical modelling approaches, where they can develop processes and content skills through discoveries. Moreover, learned skills should be connected to real-world problems and situations to foster a better understanding of students’ living environments. Nevertheless, this teaching culture in mathematics is unusual in elementary schools and teachers tend to teach based on textbooks. Students mostly learn mathematics by imitation and repetition rather than through modelling mathematics with real-world problems and situations. Thus, to develop new methodologies in teaching mathematics and to meet the requirements of the national curriculum, we designed different technology-enhanced teaching and learning methods to engage students in experimental approaches within and outside classrooms. Moreover, we conducted three studies with digital and physical modelling, augmented reality, and a tutoring system in elementary school mathematics courses. Based on our collected data, we identified settings and tasks likely to support active mathematical modelling approaches. [less ▲]

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See detailSTEAM in special needs education in an elementary school in Luxemburg
Haas, Ben; Lavicza, Zsolt; Kreis, Yves UL

Scientific Conference (2020, June 25)

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See detailDiscovering Everyday Mathematical Situations Outside the Classroom with MathCityMap and GeoGebra 3D
Lavicza, Zsolt; Haas, Ben; Kreis, Yves UL

in Ludwig, Matthias; Jablonski, Simone; Caldeira, Amélia (Eds.) et al Research on Outdoor STEM Education in the digiTal Age: Proceedings of the ROSETA Online Conference in June 2020 (2020, June 10)

In elementary school, teaching and learning activities aim to develop, among others, students’ skills to acquire deeper understanding of their living environments. There are numerous opportunities for ... [more ▼]

In elementary school, teaching and learning activities aim to develop, among others, students’ skills to acquire deeper understanding of their living environments. There are numerous opportunities for students to recognize forms, shapes, and mathematical connections in everyday situations. These everyday situations can be simulated in classrooms; however, educational technologies offer new approaches to extend classroom activities, teachers can simulate and design shapes through Augmented Reality and 3D printing within or beyond the classroom. To stimulate students’ everyday mathematical connections utilizing these technologies could assist in developing activities outside the classroom in urban or in natural environments. Through this approach students could utilize or enhance their mathematical and technical skills within their usual living environments. Utilising educational software such as MathCityMap, GeoGebra 3D Calculator, and other 3D modelling software we developed examples of tasks that could offer easy transitions from in- to out-side of classrooms. In this paper, we will describe learning and teaching aims of these tasks and outline further research and development directions to broaden opportunities to develop students’ mathematical, design and modelling skills. [less ▲]

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See detailEstablishing a Professional Development Network in England around Dynamic Mathematics Software
Lavicza, Zsolt; Hohenwarter, Markus; Jones, Keith et al

Poster (2011, February 10)

The principal aim of this project was to conduct research on GeoGebra-related professional development materials and approaches. The study was conducted through tight collaboration of educational ... [more ▼]

The principal aim of this project was to conduct research on GeoGebra-related professional development materials and approaches. The study was conducted through tight collaboration of educational researchers and mathematics teachers in England utilising frameworks of communities of inquiry (Jaworski, 2006) and collaborative design (Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003). By joint collaboration and design we aimed to establish a core group of GeoGebra experts in England who can offer professional development and support for teachers. We also wanted to explore the ways in which GeoGebra can be used to enhance the teaching and learning of mathematics within the English curriculum. [less ▲]

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See detailFirst International GeoGebra Conference 2009
Chrysanthou, Irene; Hohenwarter, Judith; Hohenwarter, Markus et al

Report (2010)

The principal aim of the First International GeoGebra Conference 2009 was to discuss the direction and vision the GeoGebra community should take in the future. On July 14th and 15th, 2009, a group of 114 ... [more ▼]

The principal aim of the First International GeoGebra Conference 2009 was to discuss the direction and vision the GeoGebra community should take in the future. On July 14th and 15th, 2009, a group of 114 people from 35 countries met for the First International GeoGebra Conference in Hagenberg, Austria at the RISC institute of the Johannes Kepler University Linz. During these two days researchers, developers, and teachers discussed and shared their experiences and ideas concerning GeoGebra in five working groups: Software Development and Online Systems; Teaching Experiences in Primary and Secondary Schools; Creation of Instructional Materials; GeoGebra at Universities and in Teacher Education; GeoGebra Institutes and Research. This report summarizes the GeoGebra related experiences of the conference participants as well as outcomes of the working group discussions and future plans for the development of GeoGebra and its user community. [less ▲]

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See detailInternational GeoGebra Institute: nurturing a community to assist the integration of the open-source mathematics software GeoGebra into mathematics teaching
Kreis, Yves UL; Lavicza, Zsolt

Scientific Conference (2009, July 06)

GeoGebra is a free open-source dynamic mathematics software that is a versatile tool for visualizing mathematical concepts from elementary through university level. Without any promotion and organised ... [more ▼]

GeoGebra is a free open-source dynamic mathematics software that is a versatile tool for visualizing mathematical concepts from elementary through university level. Without any promotion and organised training GeoGebra has been discovered and used by tens of thousands of enthusiastic teachers and researchers around the world. In the past four years, an extensive self-supporting user community was formed by users of GeoGebra and they share interactive teaching materials on the GeoGebraWiki and support fellow users through the GeoGebraForum. Volunteers from this community have also translated GeoGebra to 42 languages offering great opportunity to use the software in local languages and in multicultural environments. To be able to support such extensive user community, we established the International GeoGebra Institute (IGI). The principle aims of IGI are to develop a platform to offer training and support for teachers and to coordinate research in relation to GeoGebra. During the past year, eight local GeoGebra institutes were established. In this talk, we will share our ideas about IGI and outline the current developments of this project. We hope to nurture a network of people who can contribute to any aspects of GeoGebra based on their interests. [less ▲]

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See detailGeoGebra – free dynamic mathematics software
Hohenwarter, Markus; Hohenwarter, Judith; Kreis, Yves UL et al

Scientific Conference (2008, July 09)

GeoGebra is free, multi-platform, open-source dynamic mathematics software with rapidly growing worldwide popularity. The basic idea of the software is to join dynamic geometry, algebra, and calculus ... [more ▼]

GeoGebra is free, multi-platform, open-source dynamic mathematics software with rapidly growing worldwide popularity. The basic idea of the software is to join dynamic geometry, algebra, and calculus, which other packages treat separately, into a single easy-to-use package for learning and teaching mathematics from elementary through university level. Participants of this workshop will be introduced to the versatile possibilities of GeoGebra in hands-on activities in geometry, algebra, and calculus. They will learn how to use GeoGebra as a visualization tool for teaching and to create student-engaging interactive online materials. Free software and materials will be provided. No special computer experience is required. [less ▲]

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See detailMathematics teacher development and technology: towards an International GeoGebra Institute
Hohenwarter, Markus; Hohenwarter, Judith; Kreis, Yves UL et al

Poster (2008, July 09)

Research indicates that despite the numerous benefits of using technology in mathematics education, the process of embedding technology in classrooms is slow and complex. Most teachers need more than just ... [more ▼]

Research indicates that despite the numerous benefits of using technology in mathematics education, the process of embedding technology in classrooms is slow and complex. Most teachers need more than just being provided with technology if the benefits of technology are to be substantially realized. It has been suggested that adequate training and collegial support boost teachers' willingness to integrate technology into their teaching and to develop successful technology-assisted teaching practices. GeoGebra is free open-source dynamic software for mathematics teaching and learning that offers geometry and algebra features in a fully connected software environment. Its pool of free interactive materials and user forum are examples of online collaboration of a world-wide community of mathematics educators. In this poster presentation, we will outline the emergence of the software GeoGebra and its recent developments as well as the first steps towards (using present tense to show that work has already been done) International GeoGebra Institute to be able to offer structured training and support for teachers who are ready to integrate GeoGebra into their classrooms. In addition, we will organize and coordinate research projects in relation to GeoGebra to enhance the development of training and support materials. While our initial plan is to establish an IGI site at Florida Atlantic University (USA), in the long run our goal is to collaborate with colleagues and set up other institutes in various locations around the world. [less ▲]

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See detailGeoGebra – free software for dynamic geometry, algebra and calculus
Hohenwarter, Markus; Hohenwarter, Judith; Kreis, Yves UL et al

Poster (2008, July 09)

GeoGebra (www.geogebra.org) is free, multi-platform, open-source dynamic mathematics software with rapidly growing worldwide popularity. The basic idea of the software is to join dynamic geometry, algebra ... [more ▼]

GeoGebra (www.geogebra.org) is free, multi-platform, open-source dynamic mathematics software with rapidly growing worldwide popularity. The basic idea of the software is to join dynamic geometry, algebra, and calculus, which other packages treat separately, into a single easy-to-use package for learning and teaching mathematics from elementary through university level. GeoGebra offers the powerful opportunity for teachers to create interactive online learning environments which have led many teachers to foster experimental and discovery learning for their students. An extensive self-supporting user community shares free interactive teaching materials on the GeoGebraWiki, supports fellow users through a user forum, and has translated GeoGebra to 36 languages. In this poster presentation, we will both present applications of the software and plans for its future development, as well as raise some of the implications of technological developments such as GeoGebra for the pre-service education and inservice professional development of teachers of mathematics. [less ▲]

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