Tuesday, 06.05.2025, 4 p.m. c.t., Mathematics Laboratory, Building I Room 1.08
Modelling-aware stochastics teaching at upper secondary level
Prof. Dr. Rolf Biehler, University of Paderborn
Stochastics teaching at upper secondary level requires more conscious modelling than was previously the case. Tasks often contain implicit assumptions and artificial contexts and questions. For example, uniform distribution, stochastic independence or constancy of probability are tacitly assumed without critically questioning their validity. Random samples are unrealistically drawn from fictitious populations, relative frequencies are hastily interpreted as probabilities, etc. In this lecture, examples will be presented in which a reflective approach to stochastic models can be achieved through the choice of authentic contexts and a conscious examination of the model assumptions. By consciously addressing idealizations and assumptions, students should be sensitized to the modeling aspects of stochastics. The examples address - with the inclusion of real data - the law of large numbers, the binomial distribution, tasks relating to Bayes' theorem and evaluative statistics.

Tuesday, 20.05.2025, 4 p.m. c.t., conference room, building C1, first floor, room CI 1

Prof. Dr. Henning Sievert, University of Hildesheim, Mathematics Didactics and Computer Science Didactics

Tuesday, 07.01.2025, 4 p.m. c.t., digital in building I room 1.08

Arguing in mathematical play situations in kindergarten

Dr. Julia Böhringer, PH- Weingarten

Early mathematical education focuses on research into play-based learning opportunities. One key to knowledge construction in mathematical learning is verbal and non-verbal interactions and the associated argumentation. This is the focus of the lecture. After a theoretical and methodological insight into my qualitative study on argumentation in mathematical play situations in kindergarten, the focus will be on the model developed to describe interaction and argumentation processes. This can be used to record children's argumentation skills. Exemplary selected video sequences of a rules game illustrate different forms of mathematical argumentation in children. Finally, I will summarize the key findings of my study and provide an outlook for further research perspectives.

Tuesday, 14.01.2025, 4 p.m. c.t., conference room, building C1, first floor

Hans-Jürgen Elschenbroich & Wilfried Dutkowski

Successful mathematics teaching with the computer

25 years ago, Volker Hole published his book "Erfolgreicher Mathematikunterricht mit dem Computer - Methodische und didaktische Grundfragen in der Sekundarstufe I", which reflected the state of didactics at the time. In addition to numerous concrete examples with a variety of programs, we owe Hole in particular the didactic idea of combining Bruner's three forms of knowledge acquisition E-I-S (Enactive, Iconic, Symbolic) with the computer to form the C-E-I-S model.

In the meantime, a lot has happened at the level of software, hardware and didactics.
We focus here on didactics and formulate basic didactic principles for the organization of teaching with digital mathematics tools (genetic principle, operative principle, spiral principle, diversity of forms of representation, dynamic visualization, systematic variation) as well as the C-E-I-S model and then look at typical examples for lower and upper secondary schools.
We will show you in concrete terms how you can successfully approach teaching with digital tools using today's technical and didactic standards and then we will be happy to discuss this with you.

You can also experience the examples yourself online using a tablet or laptop. Our examples are available in a GeoGebra book summarized.

Tuesday, 28.1.2025, 4 p.m. c.t., Mathematics Lab, Building I, first floor, Room I 1.08

Dr. Wolfgang Riemer, Pulheim

A common thread through stochastics

If one refrains from understanding probabilities as objectively - independently of humans - existing quantities and instead consistently interprets them as uncertain and revisable determinations that arise as models by turning experiences into expectations, didactic problems that have remained unsolved for decades disappear.
The classical (LAPLACE), frequentist (V. MISES), subjectivist (BAYES) and axiomatic (KOLMOGOROFF) concepts of probability (a further development of the hypothetical-prognostic) merge into a single unit under the umbrella of DUBUFFET's* concept of probability. With its help, a common thread runs through stochastics, merging probability theory with descriptive and evaluative statistics from elementary school to Abitur ... and beyond ... into a single unit. Of course, bridges are built to hypothesis tests, prediction and confidence intervals.
It is possible that the change of perspective in this experimental lecture will expand your stochastic view of the world, perhaps even constructively shake it, at least a little.
As provisions for the way home, there are teaching materials "ready to use" - also for the next teaching rehearsal.

*) JEAN DUBUFFET (1901-1985) created the artwork "unsichere Festlegungen" in 1965. Because this title sums up how (not only) children experience probabilities, we have made him the namesake of the new concept of probability.

Tuesday, 04.02.2025, 4 p.m. c.t., Mathematics Laboratory, Building I, first floor, Room I 1.08

Prof. Dr. Jörg Lampe, Rhenish University of Applied Sciences Cologne

Green hydrogen from solar energy at 1000 degrees

Efficient production of green hydrogen is a fundamental component of the energy transition. Hydrogen is called green if it comes from renewable energy sources. An established process consists of a system of photovoltaics and downstream water electrolysis. However, this results in high losses, particularly when converting solar energy into electrical energy. A promising alternative option is the direct production of hydrogen from solar energy by means of so-called solar-thermochemical water splitting. In this process, solar radiation is reflected and bundled with mirrors to generate heat of up to 1400 degrees. The water vapor is then converted directly into hydrogen in a circular process at around 1000 degrees.

In the lecture, Prof. Lampe will present the process and the most automated prototype reactor in Jülich to date. Current results of the prototype plant, findings achieved and open technical challenges will be presented. Project in cooperation with the German Aerospace Center (DLR) and Stausberg & Vosding

Tuesday, 7.5.2024, 4 p.m. c.t., Mathematics Lab "Math is more", Building I, ground floor, Room 1.08

Prof. Dr. Lena Wessel, University of Paderborn

Teacher professionalization for analytical geometry and linear algebra

A better understanding of the knowledge and orientations of mathematics teachers for teaching analytical geometry and linear algebra in the upper secondary level, together with the empirically based development of further training materials, is an overarching goal of the development research project within the QuaMath framework(www.quamath.de). Based on the overarching QuaMath principles, the presentation will show how the principles of understanding orientation and consistency are particularly focused on the content area of analytical geometry. Using the example of the processes of algebraizing and geometrizing as well as selected content focal points ("mirroring on planes" and "scalar product"), initial results on tested training activities and visible knowledge activations and orientations will be presented and discussed.

Tuesday, 2.7.2024, 4 p.m. c.t., Building C I 1, large meeting room

Prof. Dr. Silke Ruwisch, Leuphana, University of Lüneburg

Support point concepts as the core of understanding quantities and the basis of estimation

Quantities play a special role in everyday life and in elementary school mathematics lessons. However, more importance is still attached to calculating with quantities than to building up concepts.

The lecture will first present a model for understanding quantities, in which comparison, measurement and estimation activities have been integrated. The respective requirements will be highlighted by way of example and linked to empirical findings. In this way, the model not only focuses more strongly on ideas, but also proves to be a planning alternative to the didactic sequence of stages.

The estimation of quantities is then discussed in more depth and the question of which estimation situations can be distinguished and how estimation results can be evaluated and assessed is discussed.

Tuesday, 9.7.2024, 4 p.m. c.t., Mathematics Lab "Math is more", Building I, ground floor, Room 1.08

Prof. Dr. Jan Filo, Institute of Applied Mathematics, Bratislava, Slovakia

Power-like nonlinear diffusion equations in a two-component domain

We consider a system of two doubly nonlinear diffusion equations defined on two different components in the plane connected by a nonlinear contact condition. The system of two equations for a porous medium on two different components of the real axis connected by a nonlinear contact condition has already been studied in [FP] J. Filo and V. Pluschke, "The porous medium equation in a two-component domain, J. Differential Equations 247 (2009) 2455-2484".

In the first part of my talk, I will introduce a class of explicit solutions of the power-like nonlinear diffusion equations, known as Barenblatt solutions, and show their qualitative properties. Then I will talk about the results of [FP] and their generalizations to two space dimensions and to more general diffusion equations.

English Version: Power-like nonlinear diffusion equations in a two-component domain

Let us consider a system of two double nonlinear diffusion equations defined on two different components in the plane, that are connected by a nonlinear contact condition. The system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition has already been studied in [FP] J. Filo and V. Pluschke, The porous medium equation in a two-component domain, J. Differential Equations 247 (2009) 2455-2484.

In the first part of my presentation, I am going to present a class of explicit solutions of the power-like nonlinear diffusion equations that are known as Barenblatt's solutions and to show their qualitative properties. Afterwards I shall speak about the results of [FP] and their generalizations to two space dimensions and to more general diffusion equations.

Tuesday, 16.7.2024, 4 p.m. c.t., Mathematics Lab "Math is more", Building I, ground floor, Room 1.08

Prof. Dr. Alexander Salle, University of Bielefeld

On the derivation of basic concepts
Theory-based procedural framework and exemplary application

Basic concepts provide possible guidelines for the design of learning processes and for structured research into mental representations of mathematical content. How the derivation of basic concepts can be carried out is described differently in the literature or only partially explicated. In the lecture, a procedural framework for such a derivation will be presented and exemplified using the concept of sine.

Tuesday, 05.12.2023, 4 p.m. c.t., Mathematics Lab "Math is more", Building I, ground floor, Room 1.08

Prof. Dr. Sebastian Bauer, Karlsruhe Institute of Technology (KIT)

The representation of the main theorem of differential and integral calculus in textbooks in the field of tension between technical correctness, "intellectually honest simplification" and falsification

Mathematics lessons in the upper secondary school level pursue the overarching goals of scientific propaedeutics and in-depth general education. On the one hand, the knowledge imparted must be valid and compatible with university knowledge; on the other hand, it is probably not possible, nor is it sufficient in terms of an in-depth general education, to design the lesson content in the form of a reduced image of the university approach. In this area of tension, various concepts of "simplifying without falsifying" and emphasizing central ideas, which focus on different basic concepts of derivation and integrals, have been developed since the 1970s in relation to the introduction of the integral concept and the treatment of the main theorem.

In this lecture, on the basis of a technical clarification, possible teaching approaches with the associated simplifications and points and the associated presentation and justification of the main theorem will be presented based on literature. In the second part of the lecture, representations of the main theorem in various current textbooks will be classified and evaluated under this theoretical lens.

Tuesday, 16.01.2024, 4 p.m. c.t., Building I, ground floor, Room 1.08

Prof. Dr. Christine Streit, University of Teacher Education FHNW

Promoting understanding of operations in the classroom

Operational understanding is said to play a central role in the development of mathematical knowledge in arithmetic and algebra. The ability to link situations, actions, images etc. with mathematical-symbolic notations is considered an important indicator of operational understanding. The study presented in the lecture investigated whether a lesson-integrated promotion of operational understanding in the second school year is associated with an effect on the pupils' general mathematics performance. To this end, specific teaching materials to promote understanding of operations were developed and used in the classroom. Contrary to expectations, the effectiveness of the intervention could not be proven, which may be due to the restrictions imposed by the Covid-19 pandemic, but could also be related to the way it was implemented by the teachers, as the analyses of implementation fidelity make clear.

Tuesday, 18.07.2023, 4 p.m. c.t., Mathematics Lab "Math is more", Building I, ground floor, Room 1.08

Jennifer Rothe, University of Leipzig

Flipped classroom in mathematics lessons at secondary level I
using the example of the Pythagorean theorem group

The flipped classroom method has received increased attention during the coronavirus pandemic. Students work on learning content at home with the help of a short learning video so that face-to-face lessons can be used for practice, application and consolidation. While the flipped classroom and its effects in mathematics at universities have already been examined in a large number of research studies, there are hardly any empirical findings in relation to learning at school. In particular, subject-specific design considerations and their influence on the assessment of the effects of the flipped classroom method have received little attention. The aim of the doctoral project is therefore to specify the concept of the flipped classroom for mathematics lessons more precisely using the example of the learning content of the Pythagorean theorem group with regard to which design variants related to subject content prove to be particularly suitable and which effects are shown with regard to learning success and motivation. The lecture will present the procedure and results of the associated mixed methods study, which was carried out in several ninth grade classes at grammar schools in Saxony. Implications for the design of flipped mathematics lessons will be derived.

Tuesday, 09.05.2023, 6 p.m. c.t., Building CIV 266

Prof. Dr. Engelbert Niehaus and Dr. Christian Fahse, at RPTU Kaiserslautern - Landau

AI as a turning point? - Info for everyone who wants to know more about AI

The speakers informed the 12th and 13th grades at a grammar school in Neustadt about AI. Most of the presentations are about the social impact of artificial intelligence on society. In one part, an attempt is also made to introduce neural networks in a completely non-mathematical way and without computer science. The aim was to identify the dangers and opportunities of AI - every citizen should be informed about it! Almost nobody is. Why should you come? Because you can expand your knowledge of AI, even if you have no knowledge of computer science. Or because you are interested in how this topic can be dealt with at school - from any subject! Or because you are looking forward to an exciting discussion. Because it is difficult to assess the situation, but facts and sober argumentation will help.

Tuesday, 02.05.2023, 4 p.m. c.t., conference room (building CI, first floor)

Prof. Dr. Daniel Walter, University of Bremen

Digital media - opportunity or obstacle Opportunity or obstacle for insightful mathematics learning at school and university?

The use of digital media is currently a key topic in education policy that is the subject of controversial debate - especially in the mathematics didactics community in primary schools. In my presentation, I will address opportunities and obstacles for insightful mathematics learning on two levels:

In relation to the use of digital media at university, insights will be given into the FALEDIA project, in which a learning platform to increase prospective teachers' diagnostic skills was developed and researched. The conceptual background of the learning platform and empirical findings regarding the diagnostic skills of students will be discussed.

With regard to learning mathematics at school, the results of the MAppsa project will be presented, in which an inventory analysis of currently available mathematics software for primary schools was carried out. The analysis of a total of 227 apps shows the curricular objectives for which digital learning opportunities are available in the app stores, the extent to which the mathematics didactic potential of digital media is implemented in software for primary schools - and where there is still a need for development.

Monday, 30.01.2023, 4 pm c.t., conference room (building CI, first floor)

Prof. Dr. Stefan Ufer & Timo Kosiol, LMU Munich

DigitUS project: Professional learning communities for learning mathematics with digital media - concept, materials and first results

Abstract:
Teachers are required more than ever to use digital media in their lessons in order to teach learners digital skills and to support subject teaching with digital media in a way that is effective for learning (e.g. KM Bayern, 2022). Studies on the state of Digitalization show that digital media are not used across the board in the classroom and that subject-specific tools in particular are used comparatively rarely (e.g. Lorenz et al., 2022). However, these in particular are seen as conducive to learning (Hillmayr et al., 2020). Establishing and working in professional learning communities is proposed as a way of developing teaching (Rolff, 2014) to address this issue. The aim is for teachers to intensify and continuously reflect on the use of digital media in mathematics lessons.

We present the DigitUS (Digitalization of Teaching in Schools) project funded by the Federal Ministry of Education and Research. The project analyzes the conditions for successful mathematics and science lessons using digital media. In a waiting control group design, teachers are supported by multipliers in forming and working together in professional learning communities. The aim of these learning communities is to reflect on the quality of their own teaching with a particular focus on digital media and to encourage them to work together on their own teaching activities and concepts using digital media. An overview of the background model and design of the studies in DigitUS will be presented.

The presentation will focus on how the multipliers in the project were supported in their work in the professional learning communities. One focus is on the materials developed for the work in the learning communities and on the training of the multipliers. The first results of a pilot study on the conditions for success and obstacles to the establishment of professional learning communities in schools will be presented.

References

• Hillmayr, D., Ziernwald, L., Reinhold, F., Hofer, S. I., & Reiss, K. M. (2020). The Potential of Digital Tools to Enhance Mathematics and Science Learning in Secondary Schools: A Context-Specific Meta-Analysis. Computers & Education, 153, 103897.
• Lorenz, R., Yotyodying S., Eickelmann B. and Endberg M. (2022). Schule digital - der Länderindikator 2021. Teaching and learning with digital media at lower secondary level in Germany in a federal state comparison and in trend since 2017. Waxmann.
• Rolff, Hans-Günter. 2014. Professional learning communities as the ideal way to develop teaching. In H.-G. Rolff (ed.): Handbook of lesson development, 564-575.

Monday, 19.12.2022, 4 p.m. c.t., conference room (Building CI, first floor)

Prof. Dr. Christina Surulescu, TU Kaiserslautern

Multiscale models of glioma invasion.

Abstract:
Malignant gliomas account for about half of all primary brain tumors in adults. These fast-growing tumors are characterized by direct invasion of adjacent brain tissue and occur in all age groups, but predominantly in late adulthood. Due to the high proliferation rate and diffuse tumor infiltration, a microscopically complete resection is generally impossible, which leads to considerable clinical challenges and high mortality of the affected patients. Mathematical models use the incomplete information from medical imaging about individual tumors to make predictions about their spread in healthy brain tissue with the help of simulations. They therefore have the potential to make a decisive contribution to improving diagnosis and treatment. The lecture addresses the multi-scale modeling of such tumors with the aim of enabling more precise contours for patient-specific radiotherapy. Some mathematical challenges related to the developed model(s) will also be mentioned.

Monday, 28.11.2022, 4 p.m. c.t., conference room (building CI, first floor)

Junior Prof. Dr. Amru Hussein, TU Kaiserslautern

If time were a graph...

Abstract:
I would like to invite you to a thought experiment: Let's assume that time is not just an interval or a straight line, but a network with branches and circles. This invites us to speculate about the representation of science fiction scenarios as graphs or networks, to look at the "non-straight" time courses of space-time in popular science terms, and finally to rigorously examine mathematically evolution equations on time graphs.

The lecture is based on a collaboration with Delio Mugnolo from the FernUniversität in Hagen (see link.springer.com/article/10.1007/s00028-021-00672-8).

Tuesday, 15.11.2022, 4 pm c.t., conference room (CI, ground floor)

Prof. Dr. Marita Friesen, Heidelberg University of Education

How can subject-specific didactic teacher noticing be developed and recorded with vignettes?

Abstract:
Being able to identify learning-relevant situational aspects in complex teaching situations and to interpret them on the basis of professional knowledge is considered an expert characteristic of teachers. For mathematics teachers, it has been shown that such analytical competence or teacher noticing is predictive of the quality of teaching and the academic performance of students. The use of vignettes as specifically selected or constructed representations of teaching practice plays a central role in both the development of teacher noticing and its assessment. The article uses various studies to show how didactic noticing (e.g. for dealing with diverse representations) can be promoted and recorded on the basis of vignettes. Test instruments and learning environments are presented in which, in addition to text and video vignettes, teaching cartoons are also used in the training and further education of mathematics teachers.

Monday, 16.05.2022, 3 p.m. c.t., Conference room (CI, ground floor)

Prof. Dr. Peter Bender, University of Paderborn

Mathematics and common sense

Abstract
Mathematics, as it is used in society and should be learned in school, is closely linked to common sense throughout. However, it is often used differently than desired when solving problems. In the lecture, its possible use will be illustrated using topics from all school levels (the phenomenon of mirroring, counting quantities, infinity). Examples will be presented of how people with and without common sense do mathematics, from small children who do not obey Piaget's theories with their common sense to economics professors who produce absurd studies while neglecting common sense.

Tuesday, 17.05.2022, 4 p.m. c.t., conference room (CI, ground floor)

Prof. Dr. Rudolf vom Hofe, University of Bielefeld

Basic ideas - the basis for substantive thinking

Lecture video

Abstract
Mathematical problem-solving processes are always associated with intuitive ideas and accompanying assumptions that more or less influence the solution path. In favorable cases, these can develop into viable basic ideas that form a basis for substantive mathematical thinking. However, intuitive assumptions can also be misleading if they solidify into unconsciously effective misconceptions.

The question therefore arises as to how to deal with this area, for example, whether to assume that adequate ideas will emerge by themselves or whether to consciously support and promote the development of basic ideas. The lecture will present theoretical and practical perspectives on the concept of basic ideas. In particular, the role that basic concepts play in the area of individual diagnosis and support will be discussed.

Tuesday, 05.07.2022, 4 p.m. c.t., conference room (CI, ground floor)

Prof. Dr. Jessica Hoth, Goethe University, Frankfurt am Main

Estimating lengths in elementary school

Abstract
Estimating lengths is a central competence in everyday life and is therefore also anchored internationally in the curricula of mathematics lessons. In this presentation, results on the estimation competence of children in 3rd and 4th grade in an international comparison between Germany and Taiwan will be presented and discussed against the background of the respective educational traditions in the two countries. Furthermore, it will be discussed how the structure of estimation competence is formed, with which mathematical abilities the children's estimation competence is connected and what significance the choice of strategy has.

Tuesday, February 8, 2022, 4 p.m. c.t., video conference

Dr. Ralf Weigel, Johannes Gutenberg University Mainz, Institute of Atmospheric Physics

Aerosols of extra-terrestrial origin in the middle atmosphere (Aerosols of extra-terrestrial origin the middle atmosphere)

Abstract below
The amount of cosmic dust particles entering the Earth's upper atmosphere worldwide is still uncertain. Estimates of cosmic input vary by two orders of magnitude from about 3 to 300 tons/day [Plane, 2012]. The reasons for this uncertainty and the current findings on the occurrence, chemical composition and physical nature of meteoritic smoke particles (MSP) are summarized in Kremser et al. 2016.

Recent chemical analyses of airborne aerosol particles in the stratosphere of the Arctic winter vortex (Ebert et al. ACP 2016) and further airborne measurements in the lowermost stratosphere over Central Europe and over the Indian subcontinent (Schneider at al. ACP, 2021) strongly suggest that MSPs are ubiquitous in the middle atmosphere. These new findings were obtained using online laser ablation aerosol mass spectrometry during three independent aircraft missions over central Europe at altitudes of up to 14 km and 20 km, respectively, and over the Indian subcontinent at altitudes of up to 20 km.

Due to their ubiquitous occurrence, MSPs most likely play an important role in the formation of high-altitude clouds (e.g. non-visible cirrus clouds) and in heterogeneous chemistry, as they provide surfaces for condensation and chemical reactions. However, the abundance of MSP in the stratosphere of the winter vortex over the polar regions could have a particular influence on the formation of polar stratospheric clouds and thus on the denitrification of the polar stratosphere. Further up, at an altitude of about 85 km in the mesosphere, it is assumed that the MSP support the formation of noctilucent clouds (nacreous clouds).

The presentation summarizes the background and state of knowledge on the origin and presence of extraterrestrial aerosols. We present the latest results from airborne measurements and a project idea to gain further insights into the possible role of MSP in cloud formation. Finally, we give an overview of the current status of numerical flow simulations and technical development within the joint project.

The presentation will primarily be held in German, but can also be held in English if required.

Abstract:

The amount of cosmic dust particles that globally enters the Earth`s upper atmosphere is still uncertain. Estimates concerning the cosmic input vary by two orders of magnitude from about 3 to 300 tons/day [Plane, 2012]. Reasons for this uncertainty as well as the current knowledge concerning the occurrence, the chemical composition, and the physical habit of Meteoric Smoke Particles (MSPs) is summarized in Kremseret al. 2016.

Most recent chemical analyses of airborne sampled aerosol particles in the arctic winter vortex stratosphere(Ebert et al. ACP 2016) and further airborne measurements in the lowermost stratosphere over Central Europe and over the Indian Subcontinent(Schneider at al. ACP, 2021) strongly indicate that MSPs are ubiquitously present in the middle atmosphere. These new findings by means of online laser ablation aerosol mass spectrometry were performed during three independent aircraft missions, over Central Europe at altitudes of up to 14 km and 20 km, respectively, and the measurements over the Indian Subcontinent reached up to 20 km.

Due to their ubiquitous presence the MSPs very likely play a significant role in the high-altitude cloud formation (e.g., sub-visible cirrus) and heterogeneous chemistry by providing surfaces for condensation and chemical reactions. However, the abundance of MSPs within the winter vortex stratosphere over polar regions may particularly impact the formation of Polar Stratospheric Clouds (PSC) and, thus, the denitrification of the polar stratosphere. Further aloft, at about 85 km altitude in the mesosphere, MSPs are assumed to support the formation of noctilucent clouds (mother-of-pearl clouds).

We compile the background and state of knowledge on the origin and presence of extra-terrestrial aerosols. We present the latest findings from airborne measurements and a project idea to gain further insight into the possible role of MSP in cloud formation. Finally, we give an overview of the current status of numerical flow simulations and technical development within the joint project

Tuesday, 18.01.2022, 4 p.m. c.t., video conference

Prof. Dr. Elke Söbbeke, University of Wuppertal, Working Group Didactics & History of Mathematics

On the interplay of communication, argumentation and conceptual understanding - Understanding and productively using interpretative occasions with visual aids

Abstract
It is fundamental for mathematical thinking to grasp the structure of numbers and to understand structural relationships between numbers or equations (e.g. in the form of arithmetic laws). With this in mind, from the beginning of the first school year, children are offered activities to recognize and use patterns that are intended to promote such an understanding of structure. In such learning settings, visual aids no longer (only) serve as aids for solving the task, but take on the role of a means of communication and argumentation as well as an epistemological tool.
To do this, however, children have to interpret patterns and structural relationships in the visual aids and symbolic representations. Current studies show that it is by no means trivial for children to differentiate between surface features and the deep mathematical structure of a representation. The lecture will present findings from two current research projects, which show that it is necessary to sensitize children to this divergence in order to be able to argue and understand concepts.

Tuesday, Dec. 14, 16 c.t., video conference:

Antonius Warmeling, MUED e.V.

Debunking fake news - sometimes math helps ...

Abstract
MUED is an association of committed math teachers who believe that teaching should follow the principle of action and application orientation. Not always, but more and more often. Such mathematics teaching provides orientation for decisions and actions, both for the development and change of private life situations and for the development and change of social practice.

In this sense, learners must also be prepared for dealing with fake news, especially in mathematics lessons. Using examples, you can learn about strategies used in the production of fake news. And they can develop procedures that are suitable for debunking such fake news. A bit of intermediate level mathematics is enough for some of this. It is often a matter of finding time series and data sets and preparing them with a view to the fake news under investigation.

In this presentation, I will use suitable examples from the areas of "man-made climate change" and the "corona pandemic" to show how this can be achieved in mathematics lessons at both lower and upper secondary level.

Tuesday, 18.05.2021, 4 p.m. c.t., video conference

Prof. Dr. Julia Rausenberger, University of Applied Sciences Northwestern Switzerland

Math meets eduScrum - Experiences with a new, field-tested teaching concept

Abstract
How can a beginners' mathematics lecture in the life sciences take into account the heterogeneity of students in terms of their basic mathematical knowledge and their learning speed while at the same time combining the achievement of learning objectives with elements of agile working, such as self-organization in heterogeneous teams or the promotion of creativity and motivation?

The eduScrum framework, which transfers the ideas of agile working methods to the education sector, provides an innovative approach to this and is already being used at various educational institutions around the world. eduScrum is an active form of teaching in which learning teams work on topics and tasks within a predefined structure. The students plan and determine their own work steps. The lecturers set the learning objectives and support the teams as coaches and experts. This way of working creates more freedom for the students: They can design their own learning processes within a specific framework and with predefined learning objectives.

At the beginning of 2019, a course concept was developed at the FHNW using a human-centered design approach. Since HS 2019, eduScrum has been used alongside the traditional teaching format in a beginners' mathematics lecture at the FHNW School of Life Sciences and its acceptance and effectiveness have been examined and evaluated. eduScrum promotes students' sense of achievement and competence. The continuous development of knowledge within the learning teams in combination with regular reflection of the level of knowledge promotes sustainable learning. Due to the open way of working, eduScrum requires more self-discipline, but leads to students taking greater responsibility for their own learning process. The inclusion of elements of distance teaching & learning as well as the collaborative group work inherent in eduScrum enabled an (almost) smooth transfer of the teaching setting to virtual face-to-face teaching last year.

Tuesday, 15.06.2021, 4 p.m. c.t., video conference

Dr. Frank Reinhold, University of Education Freiburg, Institute for Mathematical Education (IMBF)

Fractions teaching with and without digital media: Insights into mathematics learning in a world shaped by Digitalization

Video recording
Lecture by Dr. Frank Reinhold

Abstract
An understanding of the concept of fractions is considered an essential learning objective in the content area of number and an indicator of later mathematical performance. However, many pupils face great difficulties in this respect. In addition to insights into the didactics of fractions, digital support measures in the form of tools or learning environments can also appear promising here. The successful use of digital media is one of the main challenges of today's mathematics lessons, which has not only been demonstrated by the current situation surrounding the COVID-19 pandemic. The presentation will use the example of a study on fractions to show how digital tools can be implemented in regular lessons and what benefits can be expected for the teaching and learning of mathematics. Furthermore, on the basis of a research synthesis, success factors for the use of digital media will be shown and the current challenges of research on the digitalization of mathematics teaching with regard to teaching practice will be presented.

Tuesday, 24.11.2020, 4 p.m. s.t., video conference

Students of the Landau campus, University of Koblenz-Landau

Corona squared: Immunological modeling under immunological conditions in digital semester with students.

Abstract
Last summer semester, as a result of the first wave of the corona pandemic, universities remained closed and lecturers and students suddenly had to switch to digital formats. On this occasion, a Master's module of the mathematics teaching degree program at the Landau campus was dedicated to mathematical models of the dynamics and spatial spread of the COVID 19 disease, see the digital learning resource https://de.wikiversity.org/wiki/Kurs:Räumliche_Modellbildung.

In this contribution, the students of this course present the discrete and continuous epidemiological models used, describe their digital working methods and cooperation platforms and present the results of their modeling with a local geographical reference.

Tuesday, 15.12.2020, 4 p.m. c.t., video conference: bbb.rlp.net/b/hun-sbk-wvn-0tr

Prof. Dr. Christine Bescherer, Ludwigsburg University of Education, Institute of Mathematics and Computer Science

Programming in mathematics lessons

Abstract
When learning through discovery in mathematics lessons, students need suitable tools and materials with which they can work. These tools must be able to provide direct feedback as to whether the reasoning is correct or not. Programming environments are particularly well suited to this if they are designed to be learner-friendly. Various models for designing such environments will be discussed in the lecture and illustrated with examples. The concept of 'computational thinking' will also be discussed.

Tuesday, 15.12.2020, 4 p.m. c.t., video conference:

Prof. Dr. Christine Bescherer, Ludwigsburg University of Education, Institute of Mathematics and Computer Science

Programming in mathematics lessons

Abstract
When learning through discovery in mathematics lessons, students need suitable tools and materials to work with. These tools must be able to provide direct feedback as to whether the reasoning is correct or not. Programming environments are particularly well suited to this if they are designed to be learner-friendly. Various models for designing such environments will be discussed in the lecture and illustrated with examples. The concept of 'computational thinking' will also be discussed.

Tuesday, 04.06.2019, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Günter Krauthausen, University of Hamburg

APPsicht - Experiences and classifications of tablet use in elementary school mathematics lessons. Experiences and classifications

Abstract
A project 'Digital Learning Primary School', funded by the Telekom Foundation and recently completed, focused primarily on ways of promoting subject-related learning. Geometric learning environments were developed and tested in the Hamburg sub-project APPsicht.

The presentation will introduce and discuss the overarching project and selected findings from APPsicht. An attempt will also be made to place the project in the context of the now almost 30-year-old discussion on the use of 'new media'.

According to this, elementary school currently seem to need to remain calm. On the one hand, this means openness towards the potential of digital media under the primacy of didactics, and on the other hand, reflected scepticism towards the promises of a 'digitalization hype' (including educational policy promises).

Tuesday, 25.06.2019, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Tina Seufert, University of Ulm

Multimedia learning - a challenge for learners and teachers

Abstract
In times of digital change, the use of digital media and thus also multimedia presentations in the learning context is constantly increasing. The use of different media formats does indeed have many advantages for supporting learning processes, such as promoting motivation. But can learners really benefit from the variety of information presented? Are they able to focus their attention on the important information, decide how to select information or link the various presentations and thus actually exploit their potential? Numerous studies have shown that cognitive processing and self-regulation in multimedia learning represent a challenge for many learners. Teachers are therefore required to precisely understand possible deficits of learners and to design learning materials or tasks in such a way that they stimulate in-depth learning processes. In my talk, I will present various studies that shed light on both the learning processes in multimedia learning and the effectiveness of various instructional measures on the part of the teacher.

Tuesday, 15.01.2019, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Antje Ehlert, University of Potsdam

A theory-based approach to understanding, diagnosing and supporting mathematical learning difficulties

Abstract
The acquisition of basic arithmetic concepts at pre-school and primary school age (age range 4 to 8 years) is described using a cognitive-developmental psychological model with 6 levels. Building on this, various cross-sectional and longitudinal studies are presented that investigate the testing of the model. Corresponding research questions pursue the extent to which there is conceptual growth in a longitudinal view, the conceptual foundations at the end of the 1st school year can predict curriculum-based competencies at the end of the 2nd school year, but also the extent to which performance-related differences exist for this predictability and the developmental model is valid for non-German children and for children with a learning disability. The results should show the importance of basic arithmetic concepts for mathematical learning at school with corresponding consequences for the targeted support of children with mathematical difficulties. Finally, examples of areas of application will be given.

Thursday, 24.01.2019, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Miriam M. Lüken, University of Bielefeld

"I see greens and yellows. They change." - On the development of early mathematical pattern skills in children's map children

Abstract
Mathematics is often referred to as the science of patterns. It is therefore not surprising that current studies consistently confirm the importance of (early) pattern skills for children's mathematical learning. What is surprising, however, is the fact that we know very little about the development of mathematical patterning skills - especially in early childhood. The presentation will provide insight into an ongoing study that observes and interviews kindergarten children during activities with repetitive pattern sequences. It shows that even young children have different perspectives on patterns and use different strategies to continue a pattern sequence, for example. In addition, the lecture will discuss initial findings on the development of pre-school pattern and structure skills.

Wednesday, 30.01.2019, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Mária Lukácová-Medvidová, University of Mainz

Numerical modeling of atmospheric flows (Numerical simulation of atmospheric flow)

Abstract
In this talk we will present asymptotic preserving methods for numerical simulations of atmospheric flows. The methods are uniformly consistent and stable in a singular limit as the Mach number approaches zero. Furthermore, we show the results of uncertainty quantification for a cloud model. This will allow us to quantify the propagation of small-scale stochastic errors initiated at cloud scales to macroscopic scales of flow dynamics.

The lecture will be held in English, the subsequent discussion in German.

Tuesday, 29.05.2018, 4 p.m. c.t., Room C III 240 (green staircase):

Prof. Dr. Rolfdieter Frank, University of Koblenz-Landau, Koblenz Campus

The perspective images of a quadrilateral

Abstract
Every plane quadrilateral is a perspective image of a square. This theorem was recently reported in the article "The Image of a Square" in the journal "American Mathematical Monthly". It remained open whether every plane quadrilateral is a perspective image of the unit square. In the lecture I will present a necessary and sufficient criterion for a quadrilateral to be the image of a given quadrilateral. According to this criterion, for example, the rectangle with side lengths 2 and 3 is not an image of the unit square. To prove this criterion, you need results from projective geometry and 5 different relations in the set of all quadrilaterals of a plane.

Tuesday, June 26, 2018, 4 p.m. c.t., Room I 1.08 (Mathematics Lab):

Dr. Jan Wörler, University of Würzburg

Concrete art in mathematics lessons: A training ground for mathematical modeling and problem solving

Abstract
'Classical' modeling is based on everyday problems or environmental situations. However, they are often so complex that major simplifications have to be made - or a lot of time is required. The search for mathematical construction principles in works of art is very similar to modeling and can be done authentically in everyday lessons, but - as art theory demands - is much easier to accomplish than the usual modeling variant. Does the modeling of works of art therefore represent an introduction to or a training ground for classical modeling?

The lecture will discuss the modeling of artworks using various examples. The role of simulation in the context of modeling will also be highlighted. The results of a field study on modeling and simulating works of art will be presented, from which the relationship to mathematical problem solving can also be derived.

Tuesday, 28.11.2017, 4 p.m. c.t., Room C I 208 (blue staircase)

Prof. Dr. Birgit Werner, PH Heidelberg

Inclusive mathematics didactics?! Mathematics didactics and special educational considerations for the design of differentiated educational programs in lower secondary education

Abstract
(Inclusive) mathematics teaching at secondary level is caught between the conflicting priorities of completion and follow-up orientation. This applies in particular to the integration of differentiated educational programs in the special needs areas of 'learning' and 'intellectual development'. Didactic and special educational considerations are outlined as examples for the learning support focus, which also include the design of target group-specific examination formats. The concepts are framed by the educational standards of the KMK (2004) and the criteria for the design of authentic mathematical tasks (Palm 2007).

Tuesday, December 5, 2017, 4 p.m. c.t., Room W 1.02 (Westring 2)

Ms. Andrea Wullschleger, University of Zurich

Individual-adaptive learning support in the play-integrated promotion of quantity-number skills in kindergarten

Abstract
Children between the ages of four and six already have considerable mathematical knowledge and skills. However, the inter-individual differences are very large. Because early quantity-number skills are important predictors of math performance in elementary school, targeted support during the preschool years is important. The presentation will introduce a play-integrated support concept and discuss how early childhood educators can support children's learning in play situations in an individually adaptive way. Results from the projects "Spielintegrierte mathematische Frühförderung (SpiF und SpimaF)" and "Wir lernen Mathematik (WILMA)" will be presented.

Tuesday, 16.01.2018, 4 p.m. c.t., Room CI 1 (conference room)

Prof. Dr. Bärbel Barzel, University of Duisburg-Essen

Functional thinking in the classroom - competences. Media. Promotion.

Abstract
Functional thinking was emphasized as a central concern of mathematics teaching in the Meran Reform. This is more valid today than ever. What exactly is behind it and what do pupils need to learn in order to develop functional thinking and be able to apply it flexibly?

This question will be addressed in the lecture. Based on current research and development projects, conceptual ideas on the structure of functional thinking will be presented and specific findings on individual elements will be discussed in detail. This includes, for example, the question of the competencies of pupils at the end of lower secondary level, the comparison of dynamic, media-based visualizations and ways to become diagnostically and promotionally active in the subject area.

Tuesday, 30.01.2018, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Dr. Markus Ruppert, Siebold-Gymnasium Würzburg

Ways of forming analogies

Abstract
There is a broad scientific consensus on the particular importance of analogy formation processes in learning in general and in learning mathematics in particular. It therefore stands to reason that mathematics teaching that is conducive to learning should be developed with an awareness of this importance - that it should, on the one hand, identify analogies and make use of them when teaching mathematics, but that it should also offer learners opportunities to recognize and develop analogies. In short: the ability to form analogies should be specifically promoted through teaching.

In order to meet this requirement, sufficient knowledge must be available about how analogy-building processes take place when learning mathematics and solving mathematical tasks, what characterizes successful analogy-building processes and where difficulties may arise.

In the presentation, a research project will be presented that shows how processes of analogy formation can be initiated, observed, described and interpreted when solving mathematical tasks in order to identify starting points for suitable support measures, to assess existing ideas for promoting analogy formation skills and to develop new ideas. Ways of analogy formation are traced and examined that are based on the interweaving of two dimensions of analogy formation within the framework of the underlying theoretical model. In this way, different approaches can be contrasted as well as critical points in the course of an analogy-building process. This results in teaching suggestions that build on the ideas of example-based learning.

Monday, May 8, 2017, 4 p.m. c.t., Room CI 1 (meeting room)

Prof. Dr. Karin Richter and Jenny Kurow, University of Halle-Wittenberg

Discovering mathematics individually in open learning situations - approaches to stimulate individual problem-solving processes

Abstract
Opening up learning situations to mathematical problems can be done in different ways. Both the degree to which the prepared problem definition as such is sharpened and the (implementation in the) formulation of the task and support through the provision of suitably selected materials for enactive exploration are starting points for this, which will be highlighted in the presentation. The focus of the discussion will be on linking them with the aim of enabling differentiated problem solving according to the individual learning requirements and opportunities of the pupils. The main focus will be on the initiation of learning processes in the area of mathematics for pupils in the lower classes of the Realschule and the grammar school entry level. These considerations are underpinned by concrete examples from the work of an extracurricular mathematics learning center in the areas of geometry and arithmetic.

Tuesday, 04.07.2017, 4 p.m. c.t., Westring 2, 1st floor, room 1.02

Dr. Julia Bruns, University of Osnabrück

Development of math-related competencies of elementary education professionals through further training

Abstract
Due to empirical findings on the importance of the quality of mathematical learning environments in elementary education for children's later mathematics performance (Lehr, Kluczniok & Rossbach, 2016), the professional competencies of elementary education specialists in the field of mathematics are coming into focus (Anders & Rossbach, 2015; Dunekacke, Jenßen & Blömeke, 2015a). The German Center for Mathematics Teacher Education (DZLM) would like to support elementary education specialists in developing these skills and has developed the intensive training course "EmMa - Erzieherinnen und Erzieher machen Mathematik" for this purpose. The article provides an insight into the objectives as well as the didactic design and implementation of the training course. In addition, the accompanying research to investigate the effectiveness of the training and initial results are presented.

Tuesday, 29.11.2016, 4 p.m. c.t., Room I 1.08 (Mathematics Lab)

Prof. Dr. Stephan Hußmann, TU Dortmund University

'Anyone can do math' - challenges and opportunities in supporting low-achieving students in mathematics lessons

Abstract
Using the example of place value comprehension and the transition to decimals, the lecture will address the difficulties that students with poor numeracy skills have at secondary level 1 and the concepts that can be used to respond appropriately. Various approaches to diagnosis and support and their use in lessons will be presented and discussed using examples.

Tuesday, 13.12.2016, 4 p.m. c.t., Room CI 1 (meeting room)

Dr. Claudia Hildenbrand, Institute for Educational Monitoring and Quality Development (IFBQ), Hamburg

Concepts and effectiveness of early mathematical support

Abstract
In recent years, more and more programs and materials have been developed to promote early mathematical skills. A distinction can be made between training programs and support integrated into everyday life as basic conceptual approaches. The effectiveness of these two support concepts was examined as part of a comparative intervention study, the principles, implementation and key results of which will be presented.

Tuesday, 24.01.2017, 4 p.m. c.t., Room C I 1 (meeting room)

Dr. Charlotte Rechtsteiner, PH Ludwigsburg

Developing numeracy - promoting flexibility

Abstract
Over the last twenty years, moving away from counting and developing flexible numeracy skills in all children has become a central goal of elementary school mathematics teaching. Accordingly, both aspects have become the focus of national and international research, which is reflected in the increasing number of publications. With regard to learning arithmetic and the development of flexibility, two key questions need to be clarified:
- How can we succeed in specifically promoting detachment from counting arithmetic in all children and thus support them in the crucial step of learning arithmetic?
- What does flexible arithmetic mean and how can it be developed?
The presentation will provide an overview of current research findings and, building on this, will present approaches that can support the development of flexible numeracy skills. The concept of numeracy training will be discussed in more detail.

Tuesday, May 24, 2016, 4 p.m. c.t., Room I 1.08 (Mathematics Lab):

Dr. Andrea Hoffkamp, HU Berlin

Mathematics lessons in highly heterogeneous classes - a practical project for school and lesson development

Abstract
The lecture will present a long-term project on school and teaching development at a community school in Berlin-Kreuzberg. Subject teaching there takes place in highly heterogeneous classes with a large number of children with special educational needs, but also children at grammar school level. This presents teachers with complex problems when it comes to designing mathematics lessons. A teaching concept was developed in close cooperation with the teaching staff as part of a participatory action research project. Since teaching in highly heterogeneous classes is primarily a pedagogical task, an approach is required that combines learning and subject-specificity with the education of the children in a special way. The lecture will present this approach and take a closer look at individual developments, their effort, effectiveness and opportunities.

Tuesday, 14.06.2016, 4 p.m. c.t., Room C I 1 (meeting room):

Prof. Dr. Silvia Wessolowski, PH Ludwigsburg

Supporting children with learning difficulties in mathematics - a learning opportunity for students with close links between theory and practice

Abstract
Domain-specific skills in the area of diagnosis and support are indispensable for teachers in their daily teaching practice. This area should therefore be given a central role in the professional training of mathematics teachers. In order to provide student teachers with more than just theoretical insights into the subject, they are involved in the work of the "Advice Center for Primary School Pupils with Learning Difficulties in Mathematics" set up at the Ludwigsburg University of Education. The basis for this is a teaching concept that closely interlinks theory and practice and enables students to develop skills in the areas of diagnosis and support in a special way.
The lecture will present this teaching concept and its framework conditions and discuss possibilities for linking it with research and teacher training.

Tuesday, 21.06.2016, 4 p.m. c.t., C I 1 (meeting room):

Dr. Christoph Neugebauer, Westfälische Wilhelms-Universität Münster

When studying becomes the norm - support services for first-year students of mathematics at the University of Münster

Abstract
The transition from school to university is associated with major hurdles, especially in degree programs with a high proportion of mathematics. The introductory phase is not only a major challenge for many students, they also have to find their way in a new environment and learn a different way of working.
The universities offer various programs to counteract this development. For example, preliminary or bridging courses or special events are offered, e.g. for students studying to become teachers. Online self-assessments are also used to identify any weaknesses at an early stage and eliminate them through special support.
Heublein et al. (2013) report that the drop-out rate in Bachelor's degree courses at universities for the subject group mathematics/science is 39%. Increasingly, internal factors (mental/physical stability, performance, motivation, etc.) must also be taken into account as determining factors for dropping out (e.g. Heublein et al., 2013; Dieter 2012). Around a fifth more students now seek mental health counseling than before the switch from Diplom to Bachelor's and Master's degree programs.
The lecture will present various services for first-year mathematics students at the University of Münster. In addition to specialist support in the context of preliminary courses or the preparatory course, there has been close cooperation with the Psychotherapy Outpatient Clinic for some time on topics such as procrastination, self-management and motivation.
In addition, the Learning Center offers students the opportunity to resolve any difficulties that arise, for example together with trained tutors.

Tuesday, 01.12.2015, 4 p.m. c.t.

Prof. Dr. Sebastian Wartha, PH Karlsruhe

Diagnosis, prevention and support for special difficulties in arithmetic

Abstract
Based on case studies (video sequences and student documents), symptoms of particular difficulties in learning arithmetic will be developed. The content and methodological principles of diagnosis and support aimed at specific problems in learning mathematics are then considered.
Particular hurdles are the detachment from counting arithmetic, the development of a sustainable understanding of place value and the development of basic concepts of numbers, arithmetic operations and strategies.
On the basis of these considerations, concrete measures for support and preventative teaching are highlighted. The focus here is on the interaction between diagnosis (error analyses, reconstruction of processing strategies on material and in the mind) and the possibilities for support tailored to this. The targeted use of material and suitable means of presentation as well as supporting the development of mental tools play a central role.

Tuesday, 15.12.2015, 4 p.m. c.t.:

Prof. Dr. Susanne Prediger, TU Dortmund University

Subject didactic development research - A research program for linking design and theory development

Abstract
For some years now, the systematic linking of design (of teaching-learning arrangements) and empirical research (with the aim of theory formation) has been gaining increasing importance in subject didactics, especially when the focus is on the processes of teaching and learning.
The lecture will discuss the strengths and quality requirements of the research program using an example from mathematics didactics.

Tuesday, 12.01.2016, 4 p.m. c.t.:

Dr. Sebastian Krusekamp, Westfälische Wilhelms-Universität Münster

What can they actually do? - Diagnostic mathematical online tests in the introductory phase of studies

Abstract
The transition from school to university poses major challenges for students and teachers alike.

The former are first and foremost confronted with the question of which subject - and whether they want to study it at all. In addition to personal interests, a realistic assessment of one's own abilities is of course also essential. At the same time, it is of interest to the teaching staff at (technical) universities to be able to gain an early impression of the knowledge and skills of first-year students.

Given the ubiquity and availability of digital media today, it makes sense to use digital test procedures to diagnose the level of knowledge and skills of (future) students with as much precision and as little effort as possible. Be it to give students helpful feedback or to provide teachers with suggestions for possible focal points of their introductory courses.

After an overview of existing online (self-)assessments and an analysis of their strengths and weaknesses, this presentation will deal with the theory, concepts and implementation possibilities of so-called diagnostic online tests. Among others, the projects MaStEr ("Mathematik Studieren mit Erfolg", WWU Münster) and DOT ("Digitale Online-Tests", WWU Münster, ILIAS open source e-Learning e.V.) will be presented.

Monday, April 27, 2015, 4 p.m. c.t., Room: CI 1, ground floor (meeting room)

Dr. Imke Toborg, University of Koblenz-Landau, Campus Landau

Finite groups

Abstract
We call a set G together with an associative link *:GxG->G a group if and only if G has an element 1 such that for all elements g of G g*1=g, and for each element g of G there exists an element ^g-1 such that ^g*g-1=1. If the set G is finite, the group (G, *) is also called finite.
There are many examples of finite groups. If we consider a finite set M and the set G of all bijective mappings from M to M, then G together with the consecutive execution forms a finite group, the symmetric group on M. Furthermore, every finite group can be found in a suitable symmetric group.
What does it mean that a finite group can be found in another group? Is it sufficient to understand bijective mappings of a finite set into itself in order to understand finite groups?
In this lecture I would like to address the above questions. In particular, I would like to give the audience an insight into the so-called local analysis of finite groups, which I dealt with in my dissertation.
We will see that the finite simple groups are not so easy to understand and that the classification of these is actually only the beginning and not the end of group theory.
No prior knowledge of group theory is necessary, but it is assumed that the audience is familiar with the concepts of bijective mapping and the successive execution of mappings.

Monday, June 15, 2015, 4 p.m. c.t., Room: CIV 060 UG

Prof. Dr. Wilfried Herget, Martin Luther University Halle-Wittenberg

What a coincidence - luckily there's math ...

Abstract
"Even chance is not unfathomable, it has its laws" (Novalis) - these laws can be playfully explored and appropriately analyzed in secondary school mathematics lessons, but also in elementary school.

"Data and chance" is very present in everyday life - and yet somehow different. But extremely exciting!

Teaching ideas will be presented and can be "experienced" and discussed from different perspectives - in the interplay of conscious observation and model-building reflection.

Monday, 20.07.2015, 4 p.m. c.t., Room: CI 1, ground floor (meeting room)

Prof. Dr. Timo Leuders, PH Freiburg

Higher algebra for the teaching profession - interactive, genetic and visual approaches

Abstract
Groups, rings and solids as mathematical operational structures are also covered in teacher training courses as part of so-called "higher", "modern" or "abstract" algebra. However, the courses offered are often designed with a "forward-looking" approach, i.e. they aim to provide universal mathematical concepts and tools that students can use as future researchers or users of mathematics. Future teachers, however, need to "look back": they need to recognize how the abstract mathematical structures represent the unifying concepts for school mathematics and from which problems and questions they have emerged. The lecture presents a teaching concept in which student teachers actively, genetically and interactively develop the central concepts of algebra with computer-aided explorations.

Leuders, T. (2015). Algebra experience - for active discovery and independent development. Heidelberg: Springer

Monday, 17.11.2014, 4 p.m. c.t.

Prof. Dr. Torsten Fritzlar, Martin Luther University Halle-Wittenberg

Mathematical exploration problems - Promising support programs for interested and gifted primary school children

Abstract
For the development of mathematical interests and talents, I believe it is important to provide long-term, subject-specific and conceptually continuous support from an early age. Anyone who wants to make this commitment must also look for suitable content for support programs.

An important element could be so-called exploratory problems. These will be presented as examples in the lecture and their potential will also be discussed on the basis of documented student work processes and results. In addition, they will be integrated into more general conceptual considerations for the long-term support of mathematically gifted pupils.

Monday, 08.12.2014, 4 p.m. c.t.

Prof. Dr. Andreas Filler, Humboldt University Berlin

Key issues in the didactics of analytic geometry: the concept of vectors and parameter representations

Abstract
The teaching of analytic geometry/linear algebra at upper secondary level is often dominated by calculus-based work and the applications considered often appear contrived. However, analytical geometry has many interesting applications and links with other areas are possible and worth striving for. In addition, the content area plays an important university propaedeutic role in the initiation of a structural understanding of mathematics as a "world of its own". The lecture therefore focuses on two areas:

• Using the concept of vectors, ways are shown how structural commonalities (arithmetic laws) can be "crystallized" based on geometric as well as application-related arithmetic approaches and how students can gain initial insights into ways of thinking in mathematics that are important in many university courses.
• Parameter representations should not only be understood as "descriptions of static objects" but also include their functional aspect. They are therefore suitable for describing motion processes and form the mathematical basis for creating computer animations. In addition, there are links between analytical geometry and functional theory as well as possibilities for describing and generating interesting curves.
  

Lecture slides

Monday, 19.01.2015, 4 p.m. c.t.

Prof. Dr. Katja Lengnink, University of Giessen

Forming ideas and concepts in mathematics lessons - a reflection on teaching and learning processes

Abstract
Mathematical ideas and concepts are central to learning mathematics. How can they be formed? Which processes help and which processes are more of a hindrance? What role does the use of materials play in this? What effect does the heterogeneity of the learning group have?

The lecture will discuss approaches to the formation of ideas and concepts using teaching topics from the secondary level (such as the basics of geometry, ray theorems, elementary algebra). Learning environments, student products and video sequences of students' working processes are presented and reflected on in relation to the development of basic concepts and the design of concept formation processes. In particular, questions of dealing with heterogeneity and the targeted use of materials are discussed.

The teaching and learning situations under consideration were carried out and videotaped by students with pupils in the mathematics learning workshop at the University of Giessen.

Monday, 23.06.2014, 4 p.m. c.t.

Junior Professor Dr. Kathrin Winter, Westfälische Wilhelms-Universität Münster

Diagnosing and promoting students' mathematical proof skills

Abstract
Mathematical proofs play an important role in various teacher training courses (with and without mathematics as a major subject) - at the same time, there are only a few students who break out in an optimistic good mood at the keyword "proof". It seems undisputed that proof skills are particularly important for prospective teachers. But what proof skills do students need, how can they be described in concrete terms and, above all, how can students' difficulties be individually diagnosed and support measures developed? With this in mind, the lecture will discuss typical mistakes made by students on the basis of empirical findings. In addition, concrete ideas for the development of diagnostically meaningful online self-assessments and e-exams (eProofs) will be presented.

Monday, June 30, 2014, 4 p.m. c.t.:

Mr. Joachim Jakobs, Freelance Journalist

What does the Internet of (infected) Things do to the profiles of people and objects?

Abstract
The "Internet of Things" creates detailed profiles of people and the things they surround themselves with every day, such as phones, cars, buildings and milk cartons. The profiles of people and objects can then interact with each other - which is already making our lives easier in many ways. However, it turns out that not all people are able to use this capability in a meaningful way.
In his lecture, journalist Joachim Jakobs explains how these profiles are created, who has an interest in such profiles and what risks and side effects they can have for individuals and society. He uses examples to show how a person's unprotected data can be remotely controlled in the information society.

Panel discussion
Following the lecture, Mr. Jakobs will moderate a panel discussion with, among others

• Thorsten Kornmann, Director of Communications, Sparkasse Südliche Weinstraße
• Dr. Joachim Riess. Group Data Protection Officer, Daimler AG
• Prof. Dr. Jürgen Roth, Institute of Mathematics, University of Koblenz-Landau
• Uwe K. Schneider, Lawyer, Vogel & Partner Rechtsanwälte mbB, Karlsruhe
• Patrick Ungeheuer, security consultant and pentester

Joachim Jakobs is the initiator of a further education initiative with which he wants to get freelancers and small companies interested in the topic of "security". He believes that such awareness is necessary for anyone who develops, implements or uses software to control industrial systems or process personal data. With his monthly column SicherKMU, he wants to help medium-sized companies achieve secure business operations.

Note: The event is sponsored by Ungeheuer-IT from Rülzheim. We would like to thank the sponsor and ask for your kind attention.

Tuesday, 29.10.2013, 4 p.m. c.t.:

Prof. Dr. Thomas Götz, University of Koblenz-Landau, Koblenz Campus

Is mathematics contagious? Mathematics and epidemiology

Abstract
Winter semester = flu season and the health authorities are preparing vaccination campaigns again this year. In contrast to our flu, many tropical diseases such as malaria, dengue, etc. are much more dangerous. Great efforts are therefore being made to predict the spread of such diseases. In order to plan possible countermeasures efficiently, attempts are also being made to simulate the success of vaccinations or the control of vectors. The lecture will give an insight into the mathematical models used to simulate the spread of diseases. The tools of mathematical optimization allow the control of efficient countermeasures.

Monday, 11.11.2013, 4 p.m. c.t.

Mr. Michael Besser, University of Kassel and University of Lüneburg
Prof. Dr. Werner Blum, University of Kassel

How can we diagnose student performance in mathematics lessons and provide feedback that promotes learning? Results from theCo²CAproject

Abstract
The idea of performance assessment as a natural part of everyday teaching, which differs in particular from grade-based assessment situations, represents a promising basis for diagnosing and promoting student performance. Pedagogical-psychological studies as well as some didactic studies show the great potential of formative assessment with regard to the targeted promotion of student performance in comparison to more conventional, summative performance assessment. However, especially with regard to competence-oriented mathematics teaching, it is by no means clear under which framework conditions formative assessment can be successfully implemented and what demands such mathematics teaching places on the professional competence of teachers. The DFG research project Co²CA ("Conditionsand Consequencesof ClassroomAssessment"; headed by E. Klieme, K. Rakoczy, W. Blum & D. Leiß) has been addressing these questions since 2007. The lecture will present the results of individual sub-studies of Co²CA on the possibilities and limitations of competence-oriented diagnostics and feedback of student performance using the example of mathematical modeling and discuss implications for the teaching and learning of mathematics.

Monday, 02.12.2013, 4 p.m. c.t.:

Prof. Dr. Susanne Prediger, Dortmund University of Technology

Linguistic challenges in mathematics lessons - subject didactic development research and teaching consequences

Abstract
Not only because of the increasing number of multilingual pupils, language challenges are becoming an increasingly important topic for mathematics lessons. Large-scale performance studies have shown that linguistically disadvantaged learners also perform less well in mathematics. However, learners with poor language skills also need targeted support in order to be able to cope with the linguistic and conceptual demands of lessons and examinations. In the Dortmund MuM project, the background to these difficulties in performance and learning situations is being investigated, language-promoting teaching and learning arrangements are being developed and their effects on the learning process are being researched in in-depth analyses.

In the lecture, approaches and selected results are presented and teaching consequences are shown.

Link to the publication

Monday, 13.01.2014, 4 p.m. c.t.

Mr. StD Henning Körner, Studienseminar Oldenburg/Graf-Anton-Günther Schule Oldenburg

From inventory to change and back - An understanding-oriented concept for analysis

Abstract
What can a calculus lesson look like that productively takes up the focus on "change" and "reconstruction from change", which is also given by the educational standards, instead of "slope" and "area" and implements it in lessons in an understanding-oriented way? How can a variety of age-appropriate student activities be made possible and how can the difficulties of concept formation not be swept under the carpet in an intellectually honest way? The lecture attempts to answer these questions. A concept will be presented that places applications, clarity and consideration of intuitions, but also reflections on misconceptions and concept formation, at the center of teaching rather than a canonical
structure based on subject-specific science. (New) technologies (GTR, CAS, TK) are not troublemakers but important helpers and dialog partners. The concept has been tried and tested in the classroom.

Monday, 29.04.2013, 4 p.m. c.t.

Prof. Dr. Reinhard Oldenburg, Goethe University Frankfurt am Main

Algebra

Abstract:
Algebra is still a central component of school mathematics at lower secondary level, it is to a certain extent the gateway to higher mathematics. Unfortunately, in many classroom situations, from modeling to calculus, it becomes apparent that students have problems with the algebraic basics. In order to ultimately obtain suggestions for better algebra teaching, attempts have been made in recent years to understand the structure of algebraic competence more precisely, i.e. to determine which skills are central and should therefore be developed with particular care. Some results from this research program will be presented and initial conclusions drawn for school practice.

Monday, 13.05.2013, 4 p.m. c.t.:

Prof. Dr. Hans-Wolfgang Henn, Technical University of Dortmund

"The education of the habit of functional thinking."

Abstract:
As early as the Merano Conference in 1905, which was strongly influenced by Felix Klein, the education of functional thinking was called for as an important task of mathematics education. The educational standards for the intermediate school-leaving certificate published in 2003 list guiding ideas for mathematics teaching, one of which is the functional context. In the lecture, suggestions are made as to how "education for functional thinking" can take place in concrete terms. Among other things, the function box of the math case offers suggestions.

Monday, 24.06.2013, 4 p.m. c.t.:

Prof. Dr. Stefan Ruzika, University of Koblenz-Landau, Koblenz Campus

Save yourself who can! Models for evacuation planning

Abstract:
Evacuation is understood to mean the short-term evacuation of a building or region on the one hand, and the medium or long-term relocation of the center of life of people on the other. Both types of evacuation are usually triggered by an event that endangers the life and limb of people and - fortunately - we experience both types of evacuation relatively rarely. However, if an emergency does occur, the consequences are often tragic and far-reaching, as the accident in Fukushima or the disaster during the Love Parade in Duisburg show.
Mathematical and information technology models can help to prepare evacuations in a wide variety of scenarios and improve the necessary planning in advance. Questions about (minimum) evacuation times, good evacuation routes or the critical points of an evacuation can be answered. These models are dynamic and transferable, i.e. they can be adapted to a changed situation and with their help, those responsible can quickly and cost-effectively run through a whole series of "what-if" questions on the computer. In this way, virtual experience can be gained where a real wealth of experience can hardly be acquired due to the rarity, size or diversity of corresponding events.
The lecture will outline the current state of research in the field of evacuation modeling and present its potential as an interdisciplinary field of research, but also discuss its limitations and opportunities.

Monday, 05.11.2012, 4 p.m. c.t.:

Prof. Dr. Matthias Ludwig, Goethe University Frankfurt am Main

Mathematics in sport

Abstract:
All learning must be motivated, according to Thorndike's first law of learning. It is therefore clear to everyone that this should also apply to mathematics lessons. But how do you motivate students? One way is to bring the world into the classroom. This demand is not new, but it has to be repeated again and again because it is laborious and has to be rethought again and again. The lecture will present examples from the subject area of sport for all year groups and some empirical results relating to dealing with such open tasks.

Monday, 10.12.2012, 4 p.m. c.t.:

Prof. Dr. Elisabeth Rathgeb-Schnierer, PH Weingarten

Diagnosis and support as a central component of mathematics teacher training at primary level - Insights into the teaching concept of the "Counseling Center for Learning Difficulties in Mathematics"

Abstract:
In the current discussion about competencies and standards in teacher training, the promotion of diagnostic competencies is of great importance. In order to enable future teachers to adequately develop domain-specific diagnostic and support skills, a "Counseling Center for Children with Learning Difficulties in Mathematics" was established at the Weingarten University of Teacher Education. As part of this advice center, students of mathematics have the opportunity to support a child with learning difficulties over the course of a semester. This support is preceded by an intensive theoretical examination of the didactic background as well as diagnostic and support concepts. Parallel to the support, the students receive ongoing support in a supervision seminar.

The aims and content of the teaching concept, which was awarded the State Teaching Prize of the Ministry of Science, Research and the Arts in Baden Württemberg in 2010, will be presented in the lecture. In addition, there will be a brief insight into two other areas of the Counseling Center's work, which relate to services and research.

Monday, 21.01.2013, 4 p.m. c.t.:

Prof. Dr. Bernhard Burgeth, Saarland University

"Image processing: Seeing how (elementary) mathematics works"

Abstract:
Image impressions from the environment are processed in the human visual system, i.e. filtered, supplemented and segmented in the broadest sense. Computers now make it possible to imitate this processing with mathematical algorithms. To this end, the lecture will present elementary background concepts of image processing, such as

- the representation of digital images in the computer by means of discretization and quantization.

- Point transformations of images for the manipulation of images

- Local transformations for denoising, eroding, dilating and segmenting images.

In terms of mathematical principles, knowledge and techniques from arithmetic (maximum/minimum), analysis (concatenation of functions, differentiation), numerics (finite differences), geometry (edges as curves) and probability theory (histograms) are combined. Pen and paper are also sufficient to implement these image/signal processing methods.

Monday, 23.04.2012, 4 p.m. c.t.

Prof. Dr. Bernd Wollring, University of Kassel

Action-guiding diagnostics for teaching mathematics in elementary school

Abstract:
Based on the analysis according to E. Moser-Opitz (2010), we explain the training concept for subject-didactic diagnostics, which is used to train elementary school teacher training students in the compulsory subject of mathematics in Kassel. We distinguish between localizing diagnostics and action-guiding diagnostics. Tools for localized diagnostics include the DEMAT, the ZAREKI and the OTZ. An example of action-guiding diagnostics is the EMBI, an interview-based procedure that is to be carried out by teachers themselves and aims to support the development of lessons and individual support. The ambivalence of the distinction becomes clear in the discussion of the nationwide obligatory VERA, which aims to combine situational diagnostics for decision-makers and action-guiding diagnostics for teachers.

Monday, May 14, 2012, 4 p.m. c.t.:

Prof. Dr. Hans-Georg Weigand, University of Würzburg

Five theses on the use of digital technologies in future mathematics teaching

Abstract:
Advantages and disadvantages of the use of digital technologies and especially the use of Computer Algebra Systems (CAS) in mathematics education are controversially discussed worldwide. In this lecture, the question of what significance digital technologies will or could have in the coming years and decades will be explored. In particular, it will be asked which current findings can be used as a basis for a forward-looking answer and, finally, the question of a vision for future developments will also be posed.

On the one hand, developments in the use of digital technologies since the middle of the last century will be analyzed and explained using examples from the M3 project in Bavaria. This project "Model project for the use of media in mathematics lessons" involves the use of pocket computers from the 10th grade onwards at Bavarian grammar schools. The author's personal experiences lead to (probably) five theses on the use of digital technologies in future mathematics lessons.

Monday, 02.07.2012, 4 p.m. c.t.:

Prof. Dr. Hans-Stefan Siller, University of Koblenz-Landau

(Mathematical) modeling as a central idea - using the example of block processing

Abstract:
For some time now, mathematical modeling has enjoyed great popularity in mathematics lessons at Austrian schools. The didactics of the subject is also intensively concerned with it and is developing proposals for practical implementation in schools. In the lecture, the importance of mathematical modeling as a central idea for mathematics teaching will be elaborated and explained using a (tried and tested) real-life problem - block processing. A (possible) use of technology as well as different approaches within the problem will be discussed. This results in deeper mathematical reflections and insights, such as suitable calculation methods, the gradual improvement of modeling and the reflection of the solutions achieved.

Wednesday, 26.10.2011, 12.30 p.m.

Dr. Roland Gunesch, University of Koblenz-Landau, Campus Landau

"Chaos, entropy and the solution to all problems"

Abstract:
This lecture contains a generally understandable explanation of the terms dynamic systems, chaos, information and entropy. In particular, the following topics are covered:

• Is the motion of our planet regular or are we being hurled into space?
• How well can the weather be predicted?
• Other open questions, in particular about the universe, life and all the rest.

Monday, 28.11.2011, 4 p.m. c.t.

Prof. Dr. Gerald Wittmann, University of Education Freiburg

"On the question of the consistency of error patterns in fractions - linking quantitative and qualitative research methods in mathematics didactics"

Abstract:
All common error patterns in fractions are now well known and extensively documented in the relevant literature. However, it remains unclear whether these error patterns are also consistent at the level of individual students and what factors influence the solution process (and thus also the occurrence of error patterns). A current study, which will be presented in the lecture, can provide answers to both questions. This study is an example of how quantitative and qualitative research methods complement each other and where their respective strengths and limitations lie.

Monday, 12.12.2011, 4 p.m. c.t.:

Prof. Dr. Anselm Lambert, Saarland University

"On the practical relevance of mathematics didactics research"

Abstract:
Mathematics didactics is a science that has been developing in the field of tension of its related sciences (pedagogy, psychology, sociology, history ... and not least mathematics) for several decades and seeks to answer a variety of questions about mathematics education using appropriate methods. It is an empirical, descriptive science about teaching, a theoretical, normative science behind teaching and a constructive, prescriptive science for teaching. An examination of the question of its practical relevance presupposes an answer to the question of what is meant by practice. The field of practice to be considered is broad. It ranges from the practice of concrete teaching-learning situations in mathematics lessons, to the institutional practice of the school system with its subsystems, to the practice of good research - the latter requires "memory and design" (Lyotard). Mathematics didactics can actively and relevantly drive development in these fields of practice. In doing so, it should not lose sight of the mutual relationship between these fields and carefully weigh up the positive and negative effects of its contributions. The lecture will discuss the practical relevance of selected examples on a map of the situation.

Monday, 16.01.2012, 4 p.m. c.t.:

Prof. Dr. Regina Bruder, Technical University of Darmstadt

"Competence modeling in the area of changing forms of representation of functional relationships - methods and results of the HEUREKO project"

Abstract:
In the DFG-funded HEUREKO project in cooperation with the PH Freiburg, the 5 competence dimensions favored in theory when switching between forms of representation of functional relationships in grades 7-9 were empirically demonstrated. The theoretical background and the methodological approach of this competence modeling as well as prospects for the didactic usability of the results are reported. The focus here is on learning environments for diagnostics and the promotion of the corresponding competence facets.

Presentation slides

Thursday, 05.05.2011, 4 p.m. c.t.

Prof. Dr. Dr. h.c. Erich Ch. Wittmann, University of Dortmund

"Rules and leeway in mathematics and in learning mathematics"

Celebratory colloquium on the occasion of the birthday of Prof. Dr. Rasch

Monday, 06.06.2011, 4 p.m. c.t.

Prof. Dr. Hedwig Gasteiger, University of Munich

"Competence-oriented promotion of mathematical development in everyday life at daycare centers"

Abstract:
For a long time, mathematical education was not a priority in day-care centers. With the publication of the first results of international comparative studies, it became the focus of interest. As a result, numerous programmatic or more open proposals for mathematical learning in daycare centers were published, some of which differed significantly. Based on empirical findings from various scientific disciplines on the topic of 'early mathematical education', the lecture will present a concept that supports children based on their individual prerequisites so that they can acquire basic mathematical skills.

Monday, 04.07.2011, 4 p.m. c.t.

Prof. Dr. Reinhard Schugmann, Rosenheim University of Applied Sciences

"Ecological and economic aspects of logistics - conflict between the competing goals of short-term and long-term use of resources"

Abstract:
In more and more sectors, manufacturing value chains are taking place in global networks. In most cases, the cost reductions resulting from low-cost production sources clearly outweigh the relatively low transportation costs of goods.
There is a clear imbalance between the impact on the environment and the economic costs of global logistics activities. Transport volumes are even predicted to have high growth potential. The current logistics situation will be examined from both perspectives. A number of technical and organizational solutions for attempting to reconcile ecological requirements with today's economic demands will be presented and discussed.

Monday, 15.11.2010, 4 p.m. c.t., meeting room (Building CI, ground floor)

Prof. Dr. Ulrich Kortenkamp, PH Karlsruhe

"Computers and mathematics teaching - ideas and possibilities for using a creative potential"

Abstract:
The use of computers in mathematics lessons is often limited to facilitating routine work. There are various reasons for this: On the one hand, the development of virtual materials is a creative process that requires a lot of time, and their use in MU must be well-considered and didactically sound in terms of its objectives and implementation. On the other hand, software and technology are developing at a rapid pace and it is not easy for teachers in particular to keep up to date.

At CERMAT in Karlsruhe, some highly topical new ideas and technological possibilities on the subject of computers and MU are currently being developed and tested in various research and development projects. In my presentation, I will show how the potential of the computer can be exploited both in the development of new teaching and learning materials and in their creative use in the classroom.

In doing so, I will show that the inevitable introduction of the computer into the classroom requires a rethinking of it, based on the paradigm shift that our society is currently experiencing through the penetration of information technology.

Monday, 31.01.2011, 4 p.m. c.t., Mathematics Laboratory (Building I, ground floor, 1.08)

PD Dr. Rita Borromeo Ferri, University of Hamburg

"Mathematical modeling in the classroom - insights into the behavior of learners and teachers"

Abstract:
The cognitive perspective in relation to modeling processes has so far led a shadowy existence in the national and international didactic discussion on modeling. Analyzing learners and teachers in a reality-based mathematics classroom, addressing micro-processes of individuals, keeping student groups in mind during the modeling process, and at the same time considering the role of the teacher, therefore seemed suitable for advancing the current modeling discussion. In the presentation, central results of a study will be presented that provide insights into the inner world of mathematical modeling of teachers and students from grade 10.

Monday, April 26, 2010, 4 p.m. c.t:

Dr. Michael Johann, University of Koblenz-Landau, Campus Landau

Is ...9992⁼ 1 ?

Abstract:
In general, it is considered a mistake when students perform written subtraction as in the adjacent calculation.

On the other hand, such results can be used for further calculations: Addition and subtraction are child's play, multiplication is a bit tedious - but also works - and things get really interesting with division.

Mathematically speaking, these are Hensel's numbers - and a computer calculates with them in the binary system, just as we do with negative numbers (in the tens system). Hensel's decadic numbers are nevertheless peculiar: namely in the irrational range.

Monday, June 07, 2010, 4 p.m. c.t.:

Prof. Dr. Gilbert Greefrath, University of Cologne

Tasks with references to reality in secondary education

Abstract:
In recent years, special attention has been paid to tasks with references to reality, as they are of particular importance in the acquisition of higher-level competencies. The presentation will first give an overview of different types of reality-based tasks. Subsequently, an investigation of a special form of open tasks with reality references will be presented and the results of these detailed case studies will be reported.