Philipp Larmann | MathCityMap

MathCityMap on Begabungslotse

The MathCityMap web portal and app is now also featured in the online portal of Bildung & Begabung (Education & Talent), the Begabungslotse (Talent Guide). The “Begabungslotse” is a web portal which has made it its task to provide quality-assured information on the topics of individual support, talent development and the promotion of giftedness for […]

The MathCityMap web portal and app is now also featured in the online portal of Bildung & Begabung (Education & Talent), the Begabungslotse (Talent Guide).

The “Begabungslotse” is a web portal which has made it its task to provide quality-assured information on the topics of individual support, talent development and the promotion of giftedness for interested parents, teachers, students and non-school education practitioners, thus contributing to equal opportunities in education.

There are now over 5,500 entries in the Talent Guides portal and the service is additionally enriched with podcasts, videos and downloads.

The MathCityMap entries are available for the web portal here, and for the app here.

MathCityMap wishes you a Merry Christmas!

Dear MathCityMap users, at the end of the year 2022, we would like to take a brief look back at the many great events and developments that the past months have offered MathCityMap, as we do every year: Over 20,000 new tasks were created in the system this year, so that we now count a […]

Dear MathCityMap users,

at the end of the year 2022, we would like to take a brief look back at the many great events and developments that the past months have offered MathCityMap, as we do every year:

Over 20,000 new tasks were created in the system this year, so that we now count a total of over 50,000 tasks in the MathCityMap portal, of which approx. 15,200 tasks have been published. There has never been such a strong increase in tasks in a single MathCityMap year!
A total of 45,000 mathtrails were downloaded in 2022. In addition, 2,700 digital classrooms were conducted with a total of approximately 12,400 participants and almost 1,700 badges were awarded to MCM authors.
We also saw a record increase in the number of registered users: Approximately 8,000 new MathCityMap users have registered in the system, bringing the MCM community to over 18,000 members, almost doubling in size within a year.
We also had a new addition to our team. Patrick André Müller has been supporting us since this year and, together with our technical team, ensures that MathCityMap continues to function smoothly for you.
Our Erasmus+ project MaSCE³ (Math Trails in School, Curriculum and Educational Environments of Europe) has been successfully completed. We would like to thank our European partners from Portugal, France, Estonia and Spain in particular for the fantastic cooperation during the project and we are already very excited to see how cooperation can develop in the future.
Of course, MCM was not to be missed at international events. We and our partners presented the system and its latest developments at the CERME conference and at the Tomorrow Summit in Porto. In addition, there were again numerous workshops and activities that brought MathCityMap closer to researchers, teachers and students.
The partner school programme launched as part of the MaSCE³ project has also been widely expanded. There are now 30 official MathCityMap partner schools in a total of 8 countries that have successfully completed the application process and we are already looking forward to many more applications from all over the world.
The e-learning tool ASYMPTOTE, which was introduced in last year’s annual review and has its roots in MCM@Home, is now fully usable for adaptive and synchronous distance learning and we are already excited about how positive the initial feedback has been.

We are once again blown away by the fantastic and exciting developments in the MCM system, not to mention the community. Thank you for your joy and willingness to experience mathematics in a new way and to give learners a unique view of this great subject and their environment. You fill MathCityMap with life, new tasks and trails and thus make a decisive contribution to constantly rethinking and improving mathematics learning and the functions of MathCityMap.

We wish you and your families a Merry Christmas and a Happy New Year 2023. We are already looking forward to welcoming many new members to the MCM community and discovering new, exciting tasks all over the world.

Your MathCityMap Team

Trail of the month: Exploring the other side of Opuwo

This month we would like to present you a trail from a country that has hardly been visible in the MathCityMap community so far. The Mathtrail of the month December “Exploring the other side of Opuwo” comes from the city of Opuwo in Namibia, where there is a growing enthusiasm for MathCityMap as well. The […]

This month we would like to present you a trail from a country that has hardly been visible in the MathCityMap community so far. The Mathtrail of the month December “Exploring the other side of Opuwo” comes from the city of Opuwo in Namibia, where there is a growing enthusiasm for MathCityMap as well. The trail can be accessed in the MCM app under the code 5612172 and can also be found in the web portal.

The trail consists of a total of 5 tasks, which are thematically located primarily in the topics of areas and volume calculation and are suitable in their complexity especially for the 9th and 10th grade level. Often the tasks also have a relation to crafts, which makes the relevance for the everyday world particularly clear.

Highschool teacher Given Kahale Matengu , to whom we owe our new Trail of the Month, already created several other math trails with MathCityMap in the past years. In a short interview he tells us about his experiences with MCM so far. Have fun reading!

How did you come across the MathCityMap project?

I was introduced to the MathCityMap project in 2017 during my M. Ed studies at Rhodes University, South Africa. In one of the contact sessions my supervisor Professor Marc Schäfer invited Professor Matthias Ludwig to Namibia (my home country where we sometimes use to attend contact sessions). It was this time that I learned the operations of the MCM project by creating my tasks through the help and guidance of Professor Matthias Ludwig.

Where is your trail located? What is special about your trail?

“Exploring the other side of Opuwo” math trail is one of the many trails that I have created with my teacher participants around the town of Opuwo. The trail is located at the southwest side of the town and contains five tasks based on the topics of length, area, volume and proportion. This trail is best walked when it is not the rainy season as most of the spots where the tasks are located are prone to flooding.

How do you use MCM and why?

I use the MCM app as a mobile tool to analyse how teachers can use authentic tasks to conceptually teach the topics of length, area, volume, ratio and proportion to grade 9 learners. With a group of nine secondary school teachers, we create tasks within school environments, the town centre as well as the nearby surroundings of the town of Opuwo, and then teachers use these tasks to teach outdoors. The aim is to popularise mathematics within the community and at the same time campaign against policies that prohibit the use of smartphones in teaching and learning contexts in the region and the country at large.

Describe your favorite task on the trail. How can it be solved?

My favourite task in this trail is the “painting wall Task” which asks learners to calculate the quantity of paint in millilitres that is needed to cover the exterior frontside of a building in a situation where a litre of paint covers a surface area of 6 square meters. This task can be solved by first calculating the area of the wall and then subtracting the area of the two rectangular windows. The next step is then to use a ratio of 1 liter : 6 square meters to determine the needed paint.

First, in this task learners get to understand that even in reality, when working outside you need mathematical concepts and modelling skills to calculate the surface that needs to be painted. Secondly, the solving of this task involves measurements, so when solving the task learners can learn how to use a tape measure, how to convert between units as well as learning how to round off to the nearest whole number. Thirdly, this task teaches learners that for one to paint the wall, it would be necessary to have an idea of how much paint to use, hence an informed decision of how much paint to buy. Buying too much paint is a waste of money and buying too little paint can become a total headache, so whoever needs to paint the wall would want to ensure that the estimate is accurate.

MathCityMap at the “Tomorrow Summit”

On November 10 and 11, the 5th edition of the “Tomorrow Summit” took place in Porto. It was an event on technology and innovation organized by the Academic Federation of Porto. This year, the program was planned in special connection with the European Year of Youth. The aim of this event was to lead the […]

On November 10 and 11, the 5th edition of the “Tomorrow Summit” took place in Porto. It was an event on technology and innovation organized by the Academic Federation of Porto. This year, the program was planned in special connection with the European Year of Youth. The aim of this event was to lead the discussion for “Tomorrow”. At the Tomorrow Summit, participants found a wide range of innovation, research and technology that attracted many visitors.

The MathCityMap and ASYMPTOTE projects were represented at this event to display innovative ideas for teaching mathematics and mathematics education in general.

Portugal’s 6th partner school

We are very pleased to welcome the sixth Portuguese partner school, Escola Secundária de Caldas das Taipas, to our partner school network. A report about the work with MathCityMap so far and the further plans and application possibilities of Mathtrails was written by the math teacher Arminda Machado, who initiated the application process: “At ESCT […]

We are very pleased to welcome the sixth Portuguese partner school, Escola Secundária de Caldas das Taipas, to our partner school network. A report about the work with MathCityMap so far and the further plans and application possibilities of Mathtrails was written by the math teacher Arminda Machado, who initiated the application process:

“At ESCT (Secondary School of Caldas das Taipas), the MathCityMap application was used to create Mathtrails, an activity that contributed to the valorization of information and communication technologies and to the development of specific skills in mathematics among the students, namely logical thinking and problem solving.

This school year, the students at our school integrated the Erasmus+ project Maths&Art with the International Mathematics Day, which is celebrated on March 14. As part of this, a great challenge was launched for all ESCT math students, which consisted of forming teams of three members representing each class to participate in a Mathtrail with MathCityMap, put together by themselves and implemented on the school campus. The students accepted this invitation with enthusiasm and the initiative, in which the entire educational community participated, was a success.

The courses were conducted outside the classroom and in a real-world context, focusing on hands-on and experimental work, which increased the students’ motivation to learn. Students walked in small groups and in constant collaboration along trails guided by the MathCityMap application previously installed on their mobile devices, solving a series of mathematical problems related to objects or constructions present in the outdoor areas of the school. In this way, they mobilized the fundamental knowledge acquired in class. In certain situations, students used measuring tools such as the tape measure and protractor to address the practical side of the subject and the importance of its application in everyday life. The fact that students have the opportunity to develop various skills such as independence, critical thinking, creativity, collaboration, and communication while completing these tasks makes the use of this tool even more important. After completing the Mathtrails, students could analyze and discuss the solutions and results of each task in class with the math teacher. This type of activity adds a new dynamic to the classroom that is very attractive to students and promotes educational success.

For the next school year, a math trail is planned in the city of Guimarães, connected with mathematical problems related to monuments of the historical center, to be carried out by students of partner schools from Spain, Finland, Italy and Turkey during the student exchange planned in ESCT in the framework of the Erasmus+ project Maths&Art. In addition to broadening knowledge in the field of mathematics and information and communication technologies, this trail aims to develop intercultural and language skills.”

The package with the official partner school plaque and the MCM measuring tools is already on its way to Portugal and we are very much looking forward to receiving further applications from all over the world.

All further information about the partner school program and the requirements for the application can be found in the article about the first MCM partner school as well as on the homepage of our project MaSCE³.

Task of the week: Mainbank

The mathematics teacher Henrike Homann, recently created the task “Mainbank” in Gemünden, a town located east of Frankfurt directly on the Main River, which we would like to present to you as the task of the week. The aim of the task is to determine the ratio in which the position of the town of […]

The mathematics teacher Henrike Homann, recently created the task “Mainbank” in Gemünden, a town located east of Frankfurt directly on the Main River, which we would like to present to you as the task of the week. The aim of the task is to determine the ratio in which the position of the town of Gemünden divides the total length of the Main and thus of the bank reproducing the course of the Main. In the following interview Henkrike Hohmann talks about her experiences with MathCityMap so far and about the idea for her task.

How did you come across the MathCityMap project? How do you use MCM?

Many years ago, I attended a training course at the University of Würzburg in which Prof. Ludwig presented some of his projects in mathematics teaching. I liked the ideas so much that I kept looking for new projects by Prof. Ludwig. Thereby I came across the MathCityMap application. In an advanced training course, I was able to get to know the app from a student’s point of view and create the first tasks myself. Right from the start, I liked the fact that with the help of the app, the students experience the relationship of “dry” mathematics to reality and discover mathematical objects everywhere in their environment. In the process, they encounter completely new problems that don’t arise in the usual textbook tasks: How do I measure correctly? What quantities do I actually need to solve the problem? What accuracy is appropriate? Last but not least, the handling of the cell phone and the new learning location outside is motivating for the students.

Based on MCM, I created trails for the city of Gemünden together with the students of a project seminar. These have already been used with pleasure by students of our school on project days or on other special occasions. But also tourists can borrow the necessary materials at the tourist information and go on a mathematical scavenger hunt. A few trails have already been created on the school grounds as well. I have noticed that the effect is even greater for the students when they create tasks for their classmates themselves.

What can learners take away from working on the task?

The rather easy task Mainbank is part of a trail revised for the Tourist Info, which leads families coming to Gemünden to various mostly also historical buildings in the city and links information about the city with small mathematical tasks. At the task “Mainbank”, which should be solved without a calculator, you can not only repeat mathematical content such as distance ratios, common divisors, shortening and estimating, but you also have to bring some geographical knowledge about the location of the cities on the Main.

A new Spanish partner school

In Spain, too, there are more and more official MathCityMap partner schools. The fourth Spanish school that has successfully applied to the partner school program is IES Santa Eulalia, in the city of Mérida. As part of the application, which was initiated by math teacher María Bravo Conde, a total of three math trails were […]

In Spain, too, there are more and more official MathCityMap partner schools. The fourth Spanish school that has successfully applied to the partner school program is IES Santa Eulalia, in the city of Mérida. As part of the application, which was initiated by math teacher María Bravo Conde, a total of three math trails were created and tested with students from the school.

Regarding the motivation to integrate MathCityMap into the teaching, the school’s team wrote as follows:

“Using MathCityMap allows us to bring math closer to a real and everyday environment, and our students have to work together in groups, make independent and critical decisions, take initiative, and evaluate different options to find solutions.”

The first trail is located directly at the school, the second trail is located on an island in the Guadiana River, which flows through Mérida, and the third trail is located in a park that the students of the school can easily reach by bus.

The trails are available under the following names and codes in the MathCityMap system:

Ruta matemática por el IES Santa Eulalia (079113)
La isla de Mérida (256425)
El parque de las Siete Sillas (786348)

The package with the official partner school plaque and the MCM measuring instruments is already on its way to Spain and we are very much looking forward to receiving further applications from all over the world.

The MathCityMap Summer in Slovakia

In the summer of 2022, several events, such as conferences and so-called summer schools for young scientists, took place all over Europe on the topics of development of mathematics education and research in the field of mathematics education. Several of them were attended by the staff of the Department of Mathematics of the Faculty of […]

In the summer of 2022, several events, such as conferences and so-called summer schools for young scientists, took place all over Europe on the topics of development of mathematics education and research in the field of mathematics education. Several of them were attended by the staff of the Department of Mathematics of the Faculty of Mathematics of the University of Constantine the Philosopher in Nitra, as well as by teachers and students of various disciplines of the University of Constantine the Philosopher in Nitra. The aim of the visit was, among other things, to make MathCityMap better known in Europe and to present the latest findings on the use of MathCityMap in the classroom.

In the following report, Janka Medová, Veronika Bočková, Soňa Čeretková and Silvia Haringová present the activities of the Slovak MathCityMap Summer:

The first of the summer schools, Socio-scientific Issues in Mathematics and Science Initial Teachers Education: Join a unique intercultural experience preparing you for the future classroom! was held on 15-24 June 2022 at the Faculty of Education, Charles University in Prague, Czech Republic. Soňa Čeretková prepared and facilitated a workshop including MathCityMap trails named Preparation of teaching with the use of innovative teaching methods and outdoor teaching with the support of digital technologies. The summer school was organised within the Erasmus+ ENSITE project (https://icse.eu/ensite/), as was the summer school Dealing with environmental issues in science education – Deepening future science and maths teachers’ learning by teaching. A two-day workshop on MCM trails as a tool for developing awareness of environmental issues was prepared in Varna by Janka Medová and Veronika Bočková. The summer school took place in Varna, Bulgaria, 31 July-11 August 2022 and was organised by the Institute of Mathematics and Computer Science of the Bulgarian Academy of Sciences.

At the summer school for graduate students and early career researchers Intensive training school in qualitative research design and research methods in mathematics education supported by European Society for Research in Mathematics Education (ERME), held in Nitra on 29 June – 1 July Silvia Haringová referred about her work with teacher in co-designing and teaching the MCM trails.

During the two-day Summer School of Didactics of Mathematics, which took place on 6-7 July 2022 at the Pavol Jozef Šafárik University in Košice, Slovakia, primary and secondary school teachers solved a mathematical trail using the MathCityMap application in the city centre. The seminar led by Silvia Haringova continued after solving all the tasks in the premises of the university. During the seminar, participants learned how to create a trail on the portal and received manuals for creating math trails in MathCityMap.

A workshop on MCM trails was conducted by Janka Medová and Veronika Bočková in the centre of Utrecht, the Netherlands, as part of Utrecht Summer School: Mathematics Education held on 15-25 August 2022. The implementation of the summer school was also supported by the ICSE Academy project, in which researchers from several departments of Constantine the Philosopher University in Nitra collaborate with the Freudenthal Institute of the University of Utrecht to design and implement professional development programmes for teachers of mathematics, science and engineering (STEM) with a European dimension.

Janka Medová went also to Usti nad Labem in the Czech Republic, where she attended an event called the Summer School of Didactics of Science STEM Subjects, consisting of several accredited programmes for teachers of mathematics and science. As a lecturer, she collaborated in the implementation of the programme Didactic Principles in STEM subjects with colleagues from the J.E. Purkyně University, Ústí nad Labem and Charles University in Prague. The proposed professional development programme included MCM trails and is based on a joint book of 16 authors, didacticians of various subjects, entitled Didactic principles in science education: methodological guide for teachers of biology, chemistry, physics, geography, informatics, mathematics and lecturers of environmental education. The book was officially invited on Thursday, 18 August 2022, with the participation of the Dean of the Faculty of Science of UJEP and the Faculty of Education of Charles University.

From 22 to 26 August 2022, the prestigious summer school for doctoral students and young researchers called YESS (YERME Summer School) organized with the support of ERME at Johannes Kepler University in Linz, Austria, was attended by a doctoral student of the Department of Mathematics, a student of the study programme Theory of Mathematics Education, Mgr. Silvia Haringová. In TWG 1: Mathematics teacher expertise, practice, and professional development, led by Alf Coles from the University of Bristol (UK), she presented partial results and proposed methodology of her PhD thesis on Collaboration as a means of professional growth of mathematics teachers where she collaborates with mathematics teachers in development of MCM trails.

In the last days before the start of the lecture period, 7-9 September 2022, the Faculty of Natural Sciences and Informatics of the Constantine the Philosopher University in Nitra, Slovakia hosted the thirteenth ERME Topic Conference 13 (ETC13) entitled MEDA 3 Mathematics Education in the Digital Age. The MEDA3 conference follows the MEDA conferences organized at the Department of Mathematical Sciences, University of Copenhagen, Denmark in 2018 and Linz School of Education, Johannes Kepler University, Austria in 2020. During the conference Silvia Haringova presented a contribution Identification of domains of mathematics teachers’ knowledge addressed in reflection on technology-supported mathematical trails, co-authored with Janka Medova. The presented model of PD for mathematics teachers and the MCM trails evoked rich discussion.

A week later, on 13-16 September 2022, Janka Medova presented another contribution of the team Haringova-Medova, titled Factors affecting collaboration in designing and enacting MathCityMap trails by in-service teachers at the conference TiMER Trends in Mathematics Education Research held in Krakow, Poland. Event was supported by European Society for Research in Mathematics Education (ERME) within the call Initiatives for Supporting Emerging Communities for Mathematics Education Research in Eastern Europe.

And, since the school year in Slovakia has already started, we are again visiting the schools where we develop and enact the new MCM trails in collaboration with mathematics teachers.

Mathtrails with MCM – A Seminar at the University of Paderborn

In the summer semester of 2022, Dr. Susanne Podoworny offered a seminar on MathCityMap for master students of elementary school teaching at the University of Paderborn. We would like to present a report about the implementation of this great seminar idea in this article. The goal of the seminar was to create and implement a […]

In the summer semester of 2022, Dr. Susanne Podoworny offered a seminar on MathCityMap for master students of elementary school teaching at the University of Paderborn. We would like to present a report about the implementation of this great seminar idea in this article.

The goal of the seminar was to create and implement a mathematical trail using the MCM app with elementary school children on a suitable theoretical basis.

In the area around Paderborn, two elementary schools could be won over, which agreed to carry out a mathematical trail with five first and two second classes later on.

After a few sessions in which the students explored theoretical backgrounds on learning in out-of-school places, learning with digital media, and of course MathCityMap, four student groups formed to create four mathematical walking paths with MCM. The students found it particularly challenging to create appropriate tasks for the still very young target group. One student wrote in this regard “It’s very difficult to formulate tasks for first grade when the kids can barely read.”

The implementation then took place in a double lesson at each of the two elementary schools. The trails were designed along the schoolyards and often referred to the playground equipment. Overall, the student teachers reported that the students involved, as well as the teachers, greatly appreciated this different mathematics lesson. A questionnaire was distributed to the students by the students and 145 children completed it. Some results can be seen in the following diagram.

As a hint from the implementation, the recommendation to integrate a read-aloud function into the MathCityMap app arose, which we gladly take up for the further development of our system.

The seminar was well attended with 24 students. On the one hand, the students appreciated the freedom offered by the seminar design and, on the other hand, the real-life work with elementary school children, which gave everyone a lot of pleasure. Due to the positive response from the students, this seminar will be offered again in the winter semester.

Math on Campus!

Even in autumn, there are still plenty of opportunities to experience mathematics outdoors! Following this motto, an exchange school program of the Heinrich-Heine-Schule in Dreiech visited the MathCityMap team Frankfurt on the campus of the Goethe University. The group consisting of 18 Spanish students and 13 German students as well as two Spanish and two […]

Even in autumn, there are still plenty of opportunities to experience mathematics outdoors! Following this motto, an exchange school program of the Heinrich-Heine-Schule in Dreiech visited the MathCityMap team Frankfurt on the campus of the Goethe University. The group consisting of 18 Spanish students and 13 German students as well as two Spanish and two German teachers had the opportunity to get to know the idea and the functionality of MathCityMap in a short presentation and afterwards to try out a math trail directly on the campus.

The special feature of the trail was that it consisted of tasks in German, English and Spanish, which made cooperation between the students of the partner schools indispensable.

The MathCityMap team in Frankfurt was very happy about this visit on campus and is always available for inquiries for small trips into the world of mathtrails with MathCityMap at our address info@mathcitymap.eu!