Presentations by Ben Haas
European Association for Practitioner Research on Improving Learning (EAPRIL) 2015 Conference, Nov 25, 2015
The personlized and multilingual mathematical learning environment MathemaTIC is one of the flags... more The personlized and multilingual mathematical learning environment MathemaTIC is one of the flagship projects of the Digital (4) Education strategy of the Luxemburgish Ministry of National Education, Children and Youth incorporated in the concept Digital Luxembourg of the Luxemburgish government. It is based on the national curriculum, allows different pedagogical objectives (differentiation, individualization, remidiation and certification) and offers 4 languages (German, French, Portuguese and English) to the user. The development is done in partnership with the teachers who can follow in real-time the learning progress of their students working in class or autonomously at home.
During the workshop the (unexperienced) participants will - after a brief presentation - explore the environment, discuss the different pedagogical objectives and usage scenarios this tool offers for teaching and learning mathematics.
CADGME Online Gathering 2021, Jun 24, 2021
Designing Innovations in STEAM Education Conference, May 27, 2021
While we examined mathematical modelling of architectures with CAD software during the last years... 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.
ISEP Seminars On Novel Teaching Methodologies, Jul 4, 2021
During the past year, technology has started enabling new forms of teaching and learning in highe... more During the past year, technology has started enabling new forms of teaching and learning in higher education in Luxemburg. Thus, to be able to work more closely with elementary school pre-service teachers, we shifted our mathematics education course during the past years to flipped classroom approaches and worked with synchronous and asynchronous teaching on- and off-campus modes. Furthermore, due to the restrictions of the COVID-19 pandemic, we decided to shift our teaching to entirely online flipped classroom approaches together with outdoor mathematical trails with STEAM integrated assessments. This final shift to a fully online flipped classroom, with self-paced, student-centred teachings and learnings, showed strong positive effects on pre-service elementary school teachers in mathematics teaching. In this presentation, we will outline results of this transition period and describe results from different studies.
Regular Course on Integrating ICT in Mathematics Education for Junior High School Mathematics Teachers, Apr 1, 2021
Intensive training school in qualitative research design and research methods in mathematics education, Mar 25, 2021
Early-Career Researchers in STEAM Education Conference, Mar 19, 2021
3D printing in STEAM Education seminar, Feb 17, 2021
Asian Technology Conference in Mathematics (ACTM), Dec 15, 2020
In elementary schools in Luxemburg, sciences and mathematics are generally taught in class based ... 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.
PhD Proposal feedback, Dec 10, 2020
In this PhD outline, I will present highlights from my PhD research project on mathematical mode... 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.
LuxERA (Semi-)Virtual Conference 2020, Nov 12, 2020
During the confinement of COVID-19, many efforts were made by teachers in elementary school to sw... more During the confinement of COVID-19, many efforts were made by teachers in elementary school to switch from in-school to schooling at home (Kreis et al., 2020). The use of educational technology in early childhood (cycle 1), however, is not yet a common practice in elementary schools in Luxemburg. Participation in online video conferences or the use of educational technologies relied in early childhood in significant parts on the disponibility and skills of parents. Younger students were experiencing difficulties in following-up courses requests in schooling at home. From previous research (Haas et al., In Preparation), we designed a conceptual framework on parent assisted remote teaching. Hence, we used these findings to work with 12 early childhood students (ages 4-6), their teachers and parents in schooling at home. Based on the four basic principles of Dienes’s theory of mathematics in physical and digital modelling (Lieban, 2019), we created mathematical modelling tasks with TinkerCad. During two weeks, we collected data through chat responses, web meetings and observations. In this presentation, we will explain insights and how further tasks in schooling at home in early childhood could benefit from this experience.
New Researcher's Day Conference (BSRLM), Jul 3, 2020
When we address the learning of mathematics in elementary school, we imagine pupils doing experim... 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.
INSTEAD VI - Workshop on Innovative Teaching Methodologies for Math Courses on Engineering Degrees, Jun 25, 2020
CADGME Online Gathering 2020, Jun 23, 2020
Pedagogical Innovations in STEAM Education Conference, Jan 17, 2020
The Teaching in elementary school is mostly based on paper-pencil approaches and does not yet rel... more The Teaching in elementary school is mostly based on paper-pencil approaches and does not yet rely primary on educational technologies. But educational technology has found its way into the elementary schools, this based on various numbers of governmental initiatives launched during the last years in Luxemburg. The aims of these initiatives were to support students in mathematics and foremost render improvements on both skill settings, content and process. However using educational technology in mathematics does not jointly mean teaching and learning process skills. There are many different types of educational technology in mathematics, from tutoring systems to dynamic mathematical software and drill and practice software, only to name those as examples. We want to identify educational technologies and methodologies which are most likely to foster process skills (problem solving, modeling, argumenting, representing and communicating) in mathematics. Therefore we would work on a set of educational technologies offered to the students in elementary school in Luxemburg and evaluate their impacts on the fostering of process skills in mathematics.
13th International Congress on Mathematical Education, Jul 29, 2016
The personalized and multilingual mathematical learning environment MathemaTIC is one of the flag... more The personalized and multilingual mathematical learning environment MathemaTIC is one of the flagship projects of the Digital (4) Education strategy of the Luxemburgish Ministry of National Education, Children and Youth incorporated in the concept Digital Luxembourg of the Luxemburgish government. It is based on the national curriculum, allows different pedagogical objectives (differentiation, individualization, remediation and certification) and offers 4 languages (German, French, Portuguese and English) to the user. The development is done in partnership with the teachers who can follow in real-time the learning progress of their students working in class or autonomously at home. The project is coordinated by the Agency for the Development of Quality in Schools of the Luxemburgish Ministry of National Education, Children and Youth.
Doctoral Students' Conference: Tradition, Development & Innovation in Didactics - Early Career Researchers Conference (TDID - ERC), Dec 16, 2022
Symbols are used to visualise and understand abstract mathematical concepts. According to Duval (... more Symbols are used to visualise and understand abstract mathematical concepts. According to Duval (1999), visualisations are the core of understanding mathematics and creating a visualisation involves reasoning and construction. This is also common in culture, for example, in religions where internalisation and externalisation are used for reflection (Vicini, 2017) that might be a visualisation such as geometric art.
We want to create learning situations for problem based learning useful for various subjects (i.e., mathematics, history, culture, arts) in primary school based on geometrical shapes.
Geometrical shapes are among symbols used in human beliefs (e.g., the cross in Christianity, the star of David in Judaism or the wheel of law in Buddhism) and can be found on buildings and several school books. Visualisations, e.g. in Islam, can be based on polygons, stars or rosettas (Abdullahi & Embi, 2013).
Lesson plans combining cultural subjects such as history or art with mathematics are not common, but we believe there is a visible connection with geometric art. Therefore, we aim to find out whether teachers from subjects with a cultural background are interested in such lesson plans and which attributes they should have to combine the subject, geometry and technology in a maker-centred learning experience (Michael & Jones, 2020).
We plan on a qualitative approach, first introducing an activity and then interviewing primary school children and their teachers for their perceptions and learnings. For a first orientation of attributes and teacher needs, we created an activity to develop bookmarks in 2D and 3D using chequered paper and the 3D modelling software TinkerCAD for over 50 primary school students. The lesson plan and comments of the student's teachers hinting towards attributes will be presented, and future steps will be discussed.
International Symposium on Augmented and Virtual Reality in Mathematics Education, Oct 6, 2022
Although there are manifold connections between mathematics, foremost geometry, and the real-worl... more Although there are manifold connections between mathematics, foremost geometry, and the real-world (e.g., architecture, arts, functional objects), integration seldom happens in daily learning lessons in mathematics primary education. Learning three-dimensional geometric shapes, for example, is mainly done in a two-dimensional setting using textbooks instead of three-dimensional settings using technology or didactical material. This circumstance, however, makes it far more difficult for students with learning difficulties in mathematics to understand mathematical properties, recognize shapes in the real world, and understand the possibilities of modulating shapes.
Students with learning difficulties learn efficient strategies to apply mathematics to their environment when shapes and connections are visualized with Augmented Reality within the real world. Based on several experiences and studies, we will present and discuss learning mathematics with Augmented Reality in primary education for students with learning difficulties.
CADGME 2022 Conference, Sep 12, 2022
Visualising abstract concepts such as for example geometrical objects in mathematics can be a val... more Visualising abstract concepts such as for example geometrical objects in mathematics can be a valuable support for learners. Visualisation, however, is a process involving several steps that influence each other. Duval (1998) uses steps connecting reasoning by an explanation or proof to a construction step involving tools creating a visualisation to a production of a visual representation leading to new insights about a geometrical object. Vágová (2020) argues that visualising geometrical objects needs the ability to create, manipulate, and transform mental images by an internal and an external representation which both require information about the spatial arrangement. 3D modelled and then visualised geometrical objects can support the development and train visualisation skills.
Steps of visualisation processes require visuospatial competencies and are also important for other subjects in Science, Technology, Engineering, Arts and Mathematics (STEAM) education (Ng 2017). Being able to understand representations and their spatial rotations, transitions between 2D and 3D and being able to manipulate representations are valuable for STEAM related subjects (Kok 2020). Martin-Dorta et al. (2008) says that spatial abilities can be improved using real and computer-aided models. 3D printing can therefore be an interesting activity as it also combines the mentioned steps in a mathematical modelling way. This approach was used in a beginners course for pre-service mathematics teachers and some of them chose to create mathematical proofs as visualisation. We will look at 3D printed objects, which concepts they visualise and what teachers' ideas behind visualisations were.
Articles by Ben Haas
In this paper we propose STEAM practices that would foster mathematics learning through modelling... more In this paper we propose STEAM practices that would foster mathematics learning through modelling architecture while connecting to culture and history. The architectural modelling process is applied by the teachers as participants of these practices from different countries allowing a broad
cultural and historical connection to mathematics education. The modelling is implemented in GeoGebra platform as it is an open-source platform to allow teachers to model on a mathematics basis. The architectural modelling process does not provide participants with steps to follow but rather allows them to explore the architectural models’ components and construct them with various approaches which may foster problem solving techniques. We aim to investigate how different phases of this approach (such as motivation, modeling, and printing process) reflect on opportunities of learning in STEAM education, with a particular lens in mathematical development from open tasks. This paper will show two use cases that took place in Upper Austria and the MENA region.
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Presentations by Ben Haas
During the workshop the (unexperienced) participants will - after a brief presentation - explore the environment, discuss the different pedagogical objectives and usage scenarios this tool offers for teaching and learning mathematics.
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.
We want to create learning situations for problem based learning useful for various subjects (i.e., mathematics, history, culture, arts) in primary school based on geometrical shapes.
Geometrical shapes are among symbols used in human beliefs (e.g., the cross in Christianity, the star of David in Judaism or the wheel of law in Buddhism) and can be found on buildings and several school books. Visualisations, e.g. in Islam, can be based on polygons, stars or rosettas (Abdullahi & Embi, 2013).
Lesson plans combining cultural subjects such as history or art with mathematics are not common, but we believe there is a visible connection with geometric art. Therefore, we aim to find out whether teachers from subjects with a cultural background are interested in such lesson plans and which attributes they should have to combine the subject, geometry and technology in a maker-centred learning experience (Michael & Jones, 2020).
We plan on a qualitative approach, first introducing an activity and then interviewing primary school children and their teachers for their perceptions and learnings. For a first orientation of attributes and teacher needs, we created an activity to develop bookmarks in 2D and 3D using chequered paper and the 3D modelling software TinkerCAD for over 50 primary school students. The lesson plan and comments of the student's teachers hinting towards attributes will be presented, and future steps will be discussed.
Students with learning difficulties learn efficient strategies to apply mathematics to their environment when shapes and connections are visualized with Augmented Reality within the real world. Based on several experiences and studies, we will present and discuss learning mathematics with Augmented Reality in primary education for students with learning difficulties.
Steps of visualisation processes require visuospatial competencies and are also important for other subjects in Science, Technology, Engineering, Arts and Mathematics (STEAM) education (Ng 2017). Being able to understand representations and their spatial rotations, transitions between 2D and 3D and being able to manipulate representations are valuable for STEAM related subjects (Kok 2020). Martin-Dorta et al. (2008) says that spatial abilities can be improved using real and computer-aided models. 3D printing can therefore be an interesting activity as it also combines the mentioned steps in a mathematical modelling way. This approach was used in a beginners course for pre-service mathematics teachers and some of them chose to create mathematical proofs as visualisation. We will look at 3D printed objects, which concepts they visualise and what teachers' ideas behind visualisations were.
Articles by Ben Haas
cultural and historical connection to mathematics education. The modelling is implemented in GeoGebra platform as it is an open-source platform to allow teachers to model on a mathematics basis. The architectural modelling process does not provide participants with steps to follow but rather allows them to explore the architectural models’ components and construct them with various approaches which may foster problem solving techniques. We aim to investigate how different phases of this approach (such as motivation, modeling, and printing process) reflect on opportunities of learning in STEAM education, with a particular lens in mathematical development from open tasks. This paper will show two use cases that took place in Upper Austria and the MENA region.
During the workshop the (unexperienced) participants will - after a brief presentation - explore the environment, discuss the different pedagogical objectives and usage scenarios this tool offers for teaching and learning mathematics.
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.
We want to create learning situations for problem based learning useful for various subjects (i.e., mathematics, history, culture, arts) in primary school based on geometrical shapes.
Geometrical shapes are among symbols used in human beliefs (e.g., the cross in Christianity, the star of David in Judaism or the wheel of law in Buddhism) and can be found on buildings and several school books. Visualisations, e.g. in Islam, can be based on polygons, stars or rosettas (Abdullahi & Embi, 2013).
Lesson plans combining cultural subjects such as history or art with mathematics are not common, but we believe there is a visible connection with geometric art. Therefore, we aim to find out whether teachers from subjects with a cultural background are interested in such lesson plans and which attributes they should have to combine the subject, geometry and technology in a maker-centred learning experience (Michael & Jones, 2020).
We plan on a qualitative approach, first introducing an activity and then interviewing primary school children and their teachers for their perceptions and learnings. For a first orientation of attributes and teacher needs, we created an activity to develop bookmarks in 2D and 3D using chequered paper and the 3D modelling software TinkerCAD for over 50 primary school students. The lesson plan and comments of the student's teachers hinting towards attributes will be presented, and future steps will be discussed.
Students with learning difficulties learn efficient strategies to apply mathematics to their environment when shapes and connections are visualized with Augmented Reality within the real world. Based on several experiences and studies, we will present and discuss learning mathematics with Augmented Reality in primary education for students with learning difficulties.
Steps of visualisation processes require visuospatial competencies and are also important for other subjects in Science, Technology, Engineering, Arts and Mathematics (STEAM) education (Ng 2017). Being able to understand representations and their spatial rotations, transitions between 2D and 3D and being able to manipulate representations are valuable for STEAM related subjects (Kok 2020). Martin-Dorta et al. (2008) says that spatial abilities can be improved using real and computer-aided models. 3D printing can therefore be an interesting activity as it also combines the mentioned steps in a mathematical modelling way. This approach was used in a beginners course for pre-service mathematics teachers and some of them chose to create mathematical proofs as visualisation. We will look at 3D printed objects, which concepts they visualise and what teachers' ideas behind visualisations were.
cultural and historical connection to mathematics education. The modelling is implemented in GeoGebra platform as it is an open-source platform to allow teachers to model on a mathematics basis. The architectural modelling process does not provide participants with steps to follow but rather allows them to explore the architectural models’ components and construct them with various approaches which may foster problem solving techniques. We aim to investigate how different phases of this approach (such as motivation, modeling, and printing process) reflect on opportunities of learning in STEAM education, with a particular lens in mathematical development from open tasks. This paper will show two use cases that took place in Upper Austria and the MENA region.
At the beginning of grade 3 in the fundamental schools in Luxembourg, students begin to delve into the skills needed to solve arithmetic wording problems. That students encounter more barriers to perform highly in the resolution of arithmetic wording problems than in those problems presented in a numeric form is however a well-known fact (Reusser 1990). The needed skills are not only mathematical, but well-developed skills in reading the language are needed, to solve an arithmetic wording problem (LeBlanc & Weber-Russel 1996). Both conditions do not allow the low performing students, who also perform less well in Ep.Stan, to succeed.
The purpose of this PhD study will be to measure the impact on the test results from Ep. Stan of the grade 3 students by letting students learn on wording problems that require intuitive strategies at first, up to those needing a more arithmetic strategy through interactive animated items in the digital learning environment MathemaTIC.