Matthias Ludwig

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• Professor
• Professor (Full) at Goethe University Frankfurt

We present the continuation of a study on an international MOOC for the training of mathematics teachers who were introduced to the methodology of outdoor mathematics through MathCityMap. Previously, we presented the immediate learning and professional development outcomes achieved by teachers who participated in the MOOC. Here, using the theoretic...

Im Beitrag wird die Auswirkung digitalen Feedbacks auf den Bearbeitungserfolg bei Modellierungsaufgaben untersucht. Exemplarisch wird hierbei die MathCityMap-App in den Blick genommen. Die Untersuchung zeigt erstens, dass die Nutzung von Feedbackfunktionen den Bearbeitungserfolg bei Modellierungsaufgaben signifikant steigern kann. Dies steht im Ei...

The DIM²ENSION project aims to provide digital support for mathematical modeling from the perspective of the United Nations Sustainable Development Goals (SDGs) (2015). This goal results in four specific objectives: (1) Development of a digital tool, consisting of a web portal and a mobile app, to support mathematical modeling, (2) Create an open...

Die mathedidaktische Problemlöseforschung hat lange Tradition – bereits so lange und von intensiver Forschung begleitet, dass sich die wesentlich jüngere Disziplin der Informatikdidaktik zumeist mathematisch erprobter Problemlösemodelle bedient. Allen voran ist hier George Polyas Vier-Phasen-Modell zu nennen. Allerdings findet die Nutzung dieses fa...

Instructional mathematics videos that can be found e.g. on YouTube are very popular with students as support for doing homework or learning for an exam. However, from a didactical point of view, these videos can often be criticised for only conveying the superficial use of procedures and for leaving students as passive recipients of knowledge. In a...

In this study, six high school students used the app to build target 3D-structures out of cubes using a block-based language. The app provides an AR view to examine the current state of the built 3D-structure. We analysed how the app and its AR view are used by the students to evaluate and test their code. The observed processes showed signs of inc...

Im außerschulischen Enrichmentprogramm Junge Mathe-Adler Frankfurt konnten begabte Schüler:innen 3DModelle fiktiver und echter Bauwerke digital modellieren. Der offene Ansatz ist auch im Regelunterricht realisierbar und fördert Strukturierung, Kreativität und räumliches Vorstellungsvermögen.

Mathematikunterricht kann ins Freie verlagert werden: Bei sogenannten Mathtrails bearbeiten die Lernenden draußen – unterstützt durch die MathCityMap-App – mathematische Aufgaben zu real existierenden Objekten. Im Beitrag wird die Motivation von Lernenden bei einer Mathtrail-Bearbeitung untersucht. Es zeigt sich, dass die Motivation von der Bearbei...

Möglichst kurz, aber dennoch didaktisch wertvoll-Können mathematische Erklärvideos dem Spannungsfeld beider Ansprüche gerecht werden? In den letzten Jahren sind viele Kriterienkataloge zur Gestaltung "guter" (mathe-matischer) Erklärvideos entwickelt worden. Die Fülle an Anforderungen steht je-doch oft im Widerspruch zum Wunsch nach einer möglichst...

Mathematical modelling allows students to experience mathematics in different ways: There are unique artifacts in many places which might be a site of interest, such as landmarks, roadways, or areas where mathematics can be experienced in a real-life context. To stay up with current mobile technological breakthroughs, this connection of reality and...

Instructional videos are popular with students as they offer short summaries of topics e.g. related to high school mathematics. However, these videos are often criticised for forcing students into a passive role not actively constructing knowledge. There are some strategies, however, that can make the learning process more active such as taking not...

Mathematical modelling aims to investigate and explore real-world situations. It can be supported by digital tools in various ways, for example by the provision of communication and feedback functionalities. Since these functionalities are provided by most learning platforms, one might expect that these tools facilitate mathematical modelling teach...

In this poster proposal, we report on first experiences concerning students creating their own modelling tasks. The study is part of the project MATRIX and therefore contributes to the context of mobile outdoor mathematics education. The poster contains a compilation of task design criteria for this particular task setting and reports the students'...

This chapter explores instrumental orchestrations with three kinds of digital technology for teaching mathematics: embodied mathematics learning technolo-gies, augmented reality technology, and geolocation mobile technologies. Our basic assumption was that emerging digital technology might shape teacher practices. To shed light on how the use of em...

Mathematical modelling cannot only be performed inside the classroom, but also outdoors: working on so-called math trails, students solve mathematical tasks directly at real-world objects. These modelling activities can be supported by mobile apps like MathCityMap, which provides hints, app feedback, and a sample solution. Even though recent studie...

At ICME-14, the Topic Study Group (TSG) on the teaching and learning of geometry at the secondary school level, TSG-9, enabled participants from around the world to share research results, research projects, new developments, and updates on ongoing projects concerning geometry education at the secondary school level. The TSG embraced the four theme...

Instructional mathematics videos are very popular with students. However, they are often criticised for only conveying procedural knowledge instead of fostering comprehension. We report first results from a pilot study suggesting that interactive tasks in an instructional video may aid students in also acquiring conceptual knowledge.

Mathematical modelling addresses numerous demands of modern mathematics education: The learning of mathematics is directly linked to reality and students learn what they can use mathematics for. We focus on the link between architecture and geometry and observe the modelling steps of students in recreating Frankfurt's fair tower-a 257 meters' tall...

Die Digitalisierung im Mathematikunterricht bietet sowohl Potenziale als auch Herausforderungen für das Lehren und Lernen. Die Bandbreite der verwendeten digitalen Medien und Werkzeugen ist dabei in den letzten Jahren extrem gewachsen und geht von 3D-Druckern über Lego-Roboter bis hin zu Erklärvideos. Bei der zweiten Vernetzungstagung zum Thema „Ma...

Die Digitalisierung im Mathematikunterricht bietet sowohl Potenziale als auch Herausforderungen für das Lehren und Lernen. Die Bandbreite der verwendeten digitalen Medien und Werkzeugen ist dabei in den letzten Jahren extrem gewachsen und geht von 3D-Druckern über Lego-Roboter bis hin zu Erklärvideos. Bei der zweiten Vernetzungstagung zum Thema „Ma...

Die Digitalisierung im Mathematikunterricht bietet sowohl Potenziale als auch Herausforderungen für das Lehren und Lernen. Die Bandbreite der verwendeten digitalen Medien und Werkzeugen ist dabei in den letzten Jahren extrem gewachsen und geht von 3D-Druckern über Lego-Roboter bis hin zu Erklärvideos. Bei der zweiten Vernetzungstagung zum Thema „Ma...

Algorithms play a key role in everyday life. Virtually every student is exposed to applications and modern digital artifacts that use them. With that, a need to address Computational Thinking and through that, Algorithmic Thinking is inherent. In the project < colette/> , we create material and resources to foster Computational Thinking in European...

Interest and self-efficacy are seen as important requirements for students’ performance. Two approaches that can promote students’ affective attitudes towards mathematics are mobile learning as well as outdoor learning. The latter one can be realised in mathematics education by so-called math trails, which connect math tasks to real outdoor objects...

This paper focuses on a professional development programme delivered via MOOC in order to introduce future and in-service mathematics teachers to the ASYMPTOTE system. It is a twocomponent system (web portal and app) designed to enable teachers to provide synchronous and adaptive mathematics lessons online. Since (future) teachers are involved in a...

In this paper, we present a qualitative pilot study that approaches the thinking of teachers about students with exceptional difficulties in learning mathematics in a knowledge and belief integrating approach via the theoretical construct of subjective theories according to Groeben and Scheele (2000). For this we will discuss the theoretical fit of...

Mathematical modelling addresses numerous demands of modern mathematics education: The learning of mathematics is directly linked to reality and hence to real objects. At the same time, these tasks are very challenging for students, especially when their own solution process needs to be validated and refined. Studies even show that some students do...

Geometry is part of the core of mathematics. It has been relevant ever since people have interacted with nature and its phenomena. Geometry’s relevance to the teaching and learning of mathematics can be emphasized, too. Nevertheless, a current potential shift in the topics of mathematics education to the detriment of geometry might be emerging. Tha...

3D modelling and printing (3DMP) is a suitable context for education. With it, own manipulatives for mathematics education can be created, which was not possible easily before. We develop a seminar at Goethe University, in which use 3DMP to teach mathematics student teachers about mathematics, pedagogy, and technology. In this paper, we present the...

Block-based coding is a way to teach Computer Science (CS) concepts and Computational Thinking (CT) skills to K-12 students. Nowadays, there are more and more educational applications (learning apps) to teach programming in STEM subjects, but detailed studies on which and how these can be used successfully in Biology classes are still lacking, beca...

Schulmathematik in der eigenen Umwelt zu entdecken, ist ein Ziel sogenannter Mathtrails. Diese bestehen aus mehreren standortgebundenen Aufgaben, bei welchen Lernende interessante Objekte in ihrer Umwelt mathematisch untersuchen (Shoaf et al., 2004). Die Aufgaben im Freien werden von den Schüler*innen in Kleingruppen bearbeitet. Somit weist diese M...

Supporting education through digital technology becomes increasingly important. Especially in the light of the Covid-19 pandemic, online teaching and learning has been increased massively. In these precarious times, multiple approaches have been developed to enable the delivery of online education. But also for the regular classroom setting, more a...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

This poster is about my research regarding the phases of 3DMP and their relation to TPACK. It briefly shows the seminar in which the research is situated.

In recent years, numerous applications (apps) for mobile devices have been developed for STEM education, but there is a lack of suitable educational apps that support teachers in promoting computational thinking (CT) in mathematics and computer science (CS) lessons. In this position paper, two types of CT tasks, Building Cubes and Draw-o-Bot, of th...

Mikrocontroller bieten Schüler/inne/n die Möglichkeit, eigene Ideen für relevante, sie selbst betreffende Anwendungen zu entwickeln. Die daraus entstehenden authentischen Lerngelegenheiten können dann besonders im Informatik-und Technik-unterricht aufgegriffen werden. Im Kooperationsprojekt Digitechnikum setzen Schüler/innenteams mithilfe von Mikro...

Introduction One of the most important goals of mathematics at all levels of learning is to understand the thinking involved in teaching, learning and doing mathematics, in an effort to enhance and improve access to knowledge. Studies have shown that the learning and practice of mathematics are not purely and solely intellectual activities isolated...

The purpose of this study is to explore how MathCityMap training for teachers can be designed and implemented in a hybrid setting. Design research has been carried out involving teachers from 34 provinces in Indonesia. A four-day model training program for indoor and outdoor activities in a hybrid setting has been designed. The core concept of desi...

3D printing has been used in classes by teachers previously in several studies. In Germany, a lot of schools lack the funds or opportunities to use 3D printing in classes on a broad scale. Therefore, a seminar is in development and in the second iteration at Goethe University to train student teachers (educators) to create their own manipulatives f...

Discovering mathematics in one's own environment inspires students. Numerous everyday objects offer potentials for posing interesting and motivating measuring tasks. To organize the mathematics lesson outdoors, teachers can create so-called math trails in their environment using the MathCityMap system: a web portal and a smartphone app are availabl...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

How can STEM education be enriched by means of digital technology? This key question was addressed by the “Research On STEM Education in the Digital Age” conference (ROSEDA). It took place in Porto from February 23 to 25, 2023, and focused on teaching and learning of science, technology, engineering, and mathematics with digital technology. During...

Mathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no connection, whereas other models consider the formul...

Archaeological sites offer valuable insights into the past. Without a good presentation, however, it is difficult to communicate this knowledge to the general public. The newly developed ArchaeoTrail App does just this and offers the opportunity for visitors to discover the archaeological sites on their own.

Was bleibt von den temporären Schulschließungen im Zuge der COVID-19-Pandemie? Welche Konsequenzen ergeben sich für den Mathematikunterricht der Primarstufe? Im Beitrag wird auf Basis der Lehr- und Lernsituation im Frühjahr 2020 das MathCityMap@home-Konzept zur Umsetzung des mathematischen Distanzlernens vorgestellt. Nach Vorstellung von MathCityMa...

Distance teaching and learning due to the Covid-19 pandemic was perceived as a major challenge by both, teachers and students. Emerged ways of instruction-summarized in the term Emergency Remote Teaching (ERT)-could not fully meet the needs of online teaching and learning in Spring 2020. With a particular focus on reported challenges of mathematics...

In the workshop, the participants are introduced to the MCM@home system which has been developed for synchronous distance learning due to COVID-19 pandemic. To participate in a lesson conducted with MCM@home, only a smartphone with active internet connection and the free MathCityMap app is required on student’s side.

Teaching and learning in Europe have undergone massive changes due to the Covid-19 pandemic. Based on challenges of distance education, we derive the following criteria for the design of distance learning environments: enabling synchronous lessons, facilitating communication despite spatial separation, fostering individual support and assessment, a...

Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context,...

The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online le...

Das Zentrum für Lehrerbildung der Westfälischen Wilhelms-Universität Münster war vom 8. bis 10. September 2021 Gastgeber der Onlinetagung Diversität Digital Denken – The Wider View. Eine Vielzahl der Tagungsbeiträge ist in diesem Band dokumentiert. Nach der durch die SARS-CoV-2-Pandemie schnellen und teils überstürzten Digitalisierung wird die Frag...

Der Distanzunterricht im Zuge der Covid-19-Pandemie führte im Frühjahr 2020 zu einer raschen Neuorganisation des Lernens: Innerhalb kürzester Zeit musste der Unterricht vom gemeinsamen Lernort Schule in die Kinderzimmer verlagert werden. Jener rapide Wechsel vom Präsenz- zum Distanzlernen wird als Emergency Remote Teaching (ERT) (Hodges et al. 2020...

Der Beitrag zum Aufbau von Grundvorstellungen zum Messen ist erschienen in: Fördermagazin Sekundarstufe 01/2022

Das Zentrum für Lehrerbildung der Westfälischen Wilhelms-Universität Münster war vom 8. bis 10. September 2021 Gastgeber der Onlinetagung Diversität Digital Denken – The Wider View. Eine Vielzahl der Tagungsbeiträge ist in diesem Band dokumentiert. Nach der durch die SARS-CoV-2-Pandemie schnellen und teils überstürzten Digitalisierung wird die Frag...

Mathematical modelling needs to be taught in realistic contexts. In this paper, we examine the potential of outdoor tasks that are solved by means of the digital tool MathCityMap to learn mathematical modelling stepwise. From a theoretical perspective, it can be assumed that the tasks have the potential to force the “Simplifying/Structuring” and “M...

In this paper, we present the MathCityMap system which aims at bringing the idea of mathematics trails into an educational context. To facilitate the preparation and conduct from both, teacher's and students' perspective, the system provides two components: a web portal to create outdoor tasks and a smartphone app to guide students to discover math...

Als frei zugängliche und stets verfügbare Open Educational Resource bieten mathematische Erklärvideos auf YouTube viel Potenzial zur Nutzung im Zusammenhang mit dem Mathematikunterricht, insbesondere in Zeiten von Corona und dem damit einhergehenden Distanzlernen. Dies wirft für viele Lehrkräfte die Frage auf, wie sie dieses Medium nutzen und in ih...

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished u...

Im Frühjahr 2020 stellten die coronabedingten Schulschließungen Lernende und Lehrende vor eine völlig neue Herausforderung: Den Distanzunterricht. Jener Situation begegneten Lehrkräfte zunächst hauptsächlich durch asynchrone Unterrichtsformate. Im Beitrag wird mit MCM@home eine Möglichkeit für die Durchführung von synchronem Distanzunterricht vorg...

During a math trail, students discover authentic mathematics problems in their environment. Studies have shown that this method has several advantages for learning outcomes. Nevertheless, it is a rarely used way to teach mathematics. By means of a Massive Open Online Course (MOOC), it is the aim of the MaSCE³ project to educate teachers in designin...

In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children’s homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper,...

Due to the Corona Pandemic, the importance of digital learning tools got reemphasised. However, already before, online instructional videos targeting school content had been very popular among students. While teachers in many countries might see the Corona Pandemic as an incentive to engage more with this particular medium, many students already wa...

Mathematical reasoning shows relevance for the support of mathematical giftedness. In order to combine both aspects from elementary school age, knowledge on two aspects is required: firstly, on changes in mathematical reasoning and secondly on possible connections between mathematical reasoning and the mathematical giftedness profile. This article...

The digital transformation has affected us and our daily lives in the last years in ways we could not have imagined. Although the generation of digital natives is exposed to modern technology excessively and often uses it, they do not automatically develop sophisticated digital competencies. However, as a consequence of the digital transformation,...

The school lockdown due to the Corona pandemic is perceived as a major challenge by teachers, students and parents. The shift of teaching from the classroom to the children's rooms results in a massive change in the organization of learning. With a view to the Corona situation in Germany and based on empirical studies on the German school situation...

The JIMplus study [1] shows that teaching and learning in Germany at secondary level during the Corona pandemic was conducted mostly asynchronously regarding time and location. Besides reported technical issues by using digital tools for distance education [2], the learning at home has inherit social and organizational challenges: Distance learning...

Dieser neue ISTRON-Band für die Lehrerbildung beschäftigt sich mit der Konzeption, Organisation und Betreuung von Modellierungsprojekten für Schülerinnen und Schüler. Hierbei handelt es sich um offene Fragestellungen – in vielen Fällen eingebettet in ein interdisziplinäres Umfeld – bei denen es in der Bearbeitung einen großen Freiraum gibt, sowohl...

Outdoor mathematics education can be organized by using the math trail method. A math trail is a walk where students work on realistic mathematical tasks outside (Gurjanow et al. 2019). As students discover the world by using mathematics while running a math trail and are thereby highly motivated (ibid.), the repeated use of the math trail method c...

Wie wurde der Mathematikunterricht im coronabedingten Lockdown durchgeführt? Welche Tools wurden verwendet, um Aufgaben zu verteilen und zu besprechen? Welche Probleme wurden identifiziert und was sind die Konsequenzen? Im Beitrag werden diese Fragen auf Basis einer Online-Umfrage mit 171 deutschen Mathematiklehrkräften thematisiert. Mit Rückbezug...

Outdoor learning offers a wide range of opportunities for (mathematics) classes. One of these options are so-called math trails. During a math trail, mathematical tasks are discussed and solved in small groups in the environment related to real objects. Within the two-component system "MathCityMap", this method is supported by a web portal and an a...

"Digitechnikum" is an extracurricular enrichment programme originating in Frankfurt, Germany, in which students work in groups on a computer science project over the course of one school year. The projects are meant to solve real world problems in areas such as healthcare or secure traffic. The term 2019/2020 served as a pilot year and first conclu...

We describe, how Drones and Algorithms can be used to teach the topic of vectors in a different approach, combining elements of Computational Thinking together with new technology.

Der Beitrag befasst sich mit mathematischen Lernvideos auf YouTube. Zunächst werden exemplarisch drei Videos der erfolgreichsten deutschsprachigen Kanäle analysiert und verglichen. Hierbei zeigt sich die Schwierigkeit einheitliche Bewertungskriterien zu definieren, da diese abhängig von der Zielsetzung der Lernvideos sind. In einer 2019 durchgeführ...

Führt Matheunterricht im Freien zu einem nachhaltigeren Lernen? Im Rahmen einer Interventionsstudie (zweites Halbjahr des Schuljahres 2020/21) soll untersucht werden, wie sich die regelmäßige Nutzung von MathCityMap-Mathtrails langfristig auf den mathematischen Lernerfolg von Schülerinnen und Schülern der 8. gymnasialen Jahrgangsstufe auswirkt. Li...

We introduce the math trail method as an opportunity to teach math outdoors with digital tools. Regardless of proven positive effects on motivation and learning, math trails are so far rarely used to teach a specific math topic. In order to promote the use of math trails as part of regular math lessons and to meet the requirements of outdoor learni...

Due to its links to computer science (CS), teaching computational thinking (CT) often involves the handling of algorithms in activities, such as their implementation or analysis. Although there already exists a wide variety of different tasks for various learning environments in the area of computer science, there is less material available for CT....

For already over 40 years mathematics trails have been used in order to improve the attitude towards mathematics. With the availability of mobile devices, a new approach came into sight for mathematics trails and thus the MathCityMap project was founded. The projects started by reconstructing the workflow to create and walk a maths trail but then m...

Homeschooling in der Corona-Krise stellt Lehrende und Lernende vor neue Herausforderungen. Insbesondere die Unterstützung der Lernenden durch Hilfestellungen und die Überprüfung von Lösungen und Lösungswegen scheinen besonders herausfordernd. Ursprünglich als Lernumgebung für außerschulische Lernorte entlang mathematischer Wanderwege konzipiert, ka...

The changes and development of argumentative skills in the context of a deeper mathematical understanding are important aspects of mathematical teaching and learning, and especially in the support of gifted children. Various characteristics of primary school children's arguments could have been worked out, but so far, they have not been observed ov...

Although many countries have not yet included Computational Thinking (CT) into their national school curricula, CT is an integral skill to obtain for young people in the 21st century. Key aspects of CT encompass – but are not limited to – abstraction, algorithmic thinking, debugging and generalization. In countries where teaching CT is not mandator...

Both, mobile learning and extracurricular learning, offer great potentials for mathematics education. An interesting approach which combines those two concepts is the math trail idea: Students work outside on mathematical problems related to real-existing objects. Thereby, the mathematical learning progress can be structured by the MathCityMap app....

Mathematics trails offer students the possibility to apply their knowledge in authentic outdoor contexts. Organizing and carrying out such an activity is a challenge for teachers. The MathCityMap project digitizes the math trail idea and consists of a smartphone app for students to run math trails and a web portal for teachers to create math trails...

Within the Erasmus+ project Mobile Math Trails in Europe MoMaTrE, a two-week Intensive Study Programme was conducted in March 2019. 30 university students from the field of mathematics education from Germany, France, Portugal and Slovakia got to know outdoor education and the MathCityMap system for creating mobile math trails from a student's and t...