Transition from in-class to outdoor learning with real-world mathematical modelling: PhD research project 2015-2021

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 ▲]

GeoGebraTAO: Geometry Learning using a Dynamic Adaptive ICT-Enhanced Environment to Promote String Differentiation of Children's Individual Pathways

Scientific Conference (2020, November 12)

In our project, we investigate the scientific validity of a specific self-built Adaptive Learning Tool in the field of dynamic geometry with a particular focus on the individual learning pathways of a ... [more ▼]

In our project, we investigate the scientific validity of a specific self-built Adaptive Learning Tool in the field of dynamic geometry with a particular focus on the individual learning pathways of a highly diverse student population. 164 children of Luxembourg elementary schools, aged between 10 and 13 years, acted as test-group and explored elementary geometric concepts in a sequence of learning assignments, created with the dynamic mathematics system GeoGebra integrated into the computer-assisted testing framework TAO. They actively built new knowledge in an autonomous way and at their own pace with only minor support interventions of their teacher. Based on easily exploitable data, collected within a sequence of exploratory learning assignments, the GeoGebraTAO tool analyses the answers provided by the child and performs a diagnostic of the child’s competencies in geometry. With respect to this outcome, the tool manages to identify children struggling with geometry concepts and subsequently proposes a differentiated individual pathway through scaffolding and feedback practices. Short videoclips aim at helping the children to better understand any task in case of need and can be watched voluntarily. Furthermore, a spaced repetition feature is another highly useful component. Pre- and post-test results show that the test-group, working with GeoGebraTAO, and a parallel working control-group, following a traditional paper-and-pencil geometry course, increased their geometry skills and knowledge through the training program; the test-group performed even better in items related to dynamic geometry. In addition, a more precise analysis within clusters, based on similar performances in both pre- and post-tests and the child’s progress within GeoGebraTAO activities, provides evidence of some common ways of working with our dynamic geometry tool, leading to overall improvement at an individualized level. [less ▲]

Fostering process skills with the educational technology software MathemaTIC in elementary schools

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 17)

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 ▲]

Connecting the real world to mathematical models in elementary schools in Luxemburg

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 ▲]

PIAF: Developing Computational and Algorithmic Thinking in Fundamental Education

in Proceedings of EdMedia + Innovate Learning (2020, June 23), 2020(1), 315-322

In this article, we present the objectives and first achievements of the PIAF project supported by the European Union and aiming at developing computational and algorithmic thinking in basic education ... [more ▼]

In this article, we present the objectives and first achievements of the PIAF project supported by the European Union and aiming at developing computational and algorithmic thinking in basic education. This project brings together researchers in educational sciences and computer science from four countries (Belgium, France, Germany and Luxembourg) around the theme of teacher training. More concretely, the aim is to define a framework (competency framework, pedagogical scenarios) enabling teachers to (i) appropriate the concept of computational and algorithmic thinking and (ii) implement learning activities that promote the development of this kind of thinking in children. [less ▲]

Discovering Everyday Mathematical Situations Outside the Classroom with MathCityMap and GeoGebra 3D

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 ▲]

Fostering process related skills in mathematics though educational technology in elementary schools

Scientific Conference (2020, January 17)

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 ... [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. [less ▲]

Dynamische Mathematik mit GeoGebra – Evaluation

Speeches/Talks (2019)

Die Bildungsstandards Mathematik für die Klassen begünstigen einen entdeckenden, problemorientierten Unterricht. Dynamische Mathematiksysteme (DMS) wie GeoGebra erlauben den Schülern/-innen, sich mit ... [more ▼]

Die Bildungsstandards Mathematik für die Klassen begünstigen einen entdeckenden, problemorientierten Unterricht. Dynamische Mathematiksysteme (DMS) wie GeoGebra erlauben den Schülern/-innen, sich mit Fragestellungen auseinanderzusetzen und Hypothesen aufzustellen. Damit die Lehrer/-innen hierbei möglichst entlastet sind und sich den Fragen einiger Schüler/-innen widmen können, ist es von Vorteil, digitale Arbeitsblätter zu nutzen, die eine (Auto-)Evaluation erlauben. [less ▲]

Dynamische Mathematik und computergestützte Tests: GeoGebra in TAO

in Ladel, Silke; Knopf, Julia; Weinberger, Armin (Eds.) Digitalisierung und Bildung (2018)

In diesem Beitrag stellen wir die Integration der Dynamischen-Mathematik-Software GeoGebra in die technologiebasierte Assessment-Plattform TAO vor. Diese Kombination von Anwendungen schafft neue Lern- und ... [more ▼]

In diesem Beitrag stellen wir die Integration der Dynamischen-Mathematik-Software GeoGebra in die technologiebasierte Assessment-Plattform TAO vor. Diese Kombination von Anwendungen schafft neue Lern- und Beurteilungsmöglichkeiten in einem modernen Unterricht: die Lernerfolge im Geometrieunterricht werden, im Vergleich zu einem klassischen Unterricht, gefördert und eventuelle Hindernisse beim Kompetenzerwerb können präzise identifiziert werden. Außerdem wird die Studie im Rahmen des Forschungsprojektes GeoGebraPrim beschrieben, wobei die Versuchsgruppe der 9-jährigen Kinder während ihres Lernprozesses Zugang zur Technologie haben, um mathematische Eigenschaften anhand von dynamischer Geometrie zu entdecken. Im Pre-Test unterscheiden sich die Versuchs- und Kontrollgruppe kaum. Die Versuchsgruppe erlangt allerdings signifikant bessere Resultate in den beiden Post-Tests sowie erstklassige Resultate in dem TBA-Test. [less ▲]

Dynamische Mathematik mit GeoGebra – 3D-Grafikfenster

Speeches/Talks (2017)

Die Bildungsstandards Mathematik für die Klassen begünstigen einen entdeckenden, problemorientierten Unterricht. Dynamische Mathematiksysteme (DMS) wie GeoGebra erlauben den Schüler/-innen, sich mit ... [more ▼]

Die Bildungsstandards Mathematik für die Klassen begünstigen einen entdeckenden, problemorientierten Unterricht. Dynamische Mathematiksysteme (DMS) wie GeoGebra erlauben den Schüler/-innen, sich mit Fragestellungen auseinanderzusetzen und Hypothesen aufzustellen. Anschließend müssen diese natürlich noch immer mathematisch bewiesen werden; diese Beweise lehnen sich aber oft an den durchlaufenen Prozess der Schüler/-innen an und sind somit leichter verständlich. [less ▲]