General | MathCityMap

Our MathCityMap team in Slovakia, led by Janka Medová and Silvia Haringová from the University of Nitra, once again impressively proved that outdoor mathematics not only works in winter, but can also be used just as well as in the rest of the year.

Silvia travelled to Krakow for a one-week scholarship at the local Pedagogical University, where she developed tasks and trails on the topic of functions together with PhD students from Košice.

Janka and Silvia attended the conference Dva dny s didaktikou matematiky (Two Days of Mathematics Education) in Prague together shortly afterwards, where they gave a presentation on Mathtrails in teacher education. In particular, they spoke there about their collaboration with primary and secondary teachers in designing and implementing the teaching trails.

Lysá nad Labem was Janka and Silvia’s next stop. A group of local maths and reading enthusiasts, in cooperation with Antonín Jančařík from the Department of Mathematics and Didactics of Mathematics at the Faculty of Education of Charles University, was preparing an outdoor maths experience for visitors to three Czech towns: Benátky nad Jizerou, Milovice and Lysá nad Labem. Each of these towns had its own tasks and a Mathtrail, where visitors had to solve mathematical and literary tasks in addition to exploring the beauty and history of the towns. Janka and Silvia helped to create some sample tasks here and familiarised group members with the MathCityMap application.

Also in Athens, the capital of Greece, Janka and Silvia were able to present their research on classroom research online with the support of MathCityMap at the National and Kapodastrian University.

In the course Development of Specific Mathematical Thinking for students of the Pre-school and Primary Education programme at the University of Nitra, Mathtrails were thematised and tried out as a central part of the content. The students then developed their own tasks with a focus on combinatorics and probability, which they uploaded to the MathCityMap system.

PhD student Katka Laššová created a mathtrail focusing on the spatial skills of vocational students with a technical focus. The trail was carried out with students from the technical secondary school for mechanical engineering in Bánovce nad Bebravou. She also visited the primary school Duklianska 1 in Bánovce nad Bebravou. The school management had the idea to organise a mathtrail with future first graders during the open day. Katka helped the teachers develop the trail and the tasks.

Under the leadership of Janka Medova, Veronika Bočková and Kitti Páleníková, a workshop on mathtrails was held for pre-service teachers. They solved tasks in the atrium of the Nitra University campus and were then introduced to the creation of mathtrails and finally designed a task themselves on the campus in the MathCityMap system. Many of the teachers went on to develop mathtrails at their schools and use them in the classroom.

It has been one and a half years since a trail took the title of the mathtrail with the most downloads in the MathCityMap app worldwide. With 569 downloads, Yunas Chandra’s trail Banteng Berhitung in Jakarta slipped to the top of our download charts.

Now, however, Corinne Stephan from Buchy in France has succeeded in generating 1163 downloads within a few weeks with her Trail Rallye dans Buchy.

Corinne Stephan got to know MathCityMap through the French textbook series Sésamath and she has been using the application for several years, as she tells us in a short interview.

“I developed the “Rally through Buchy” trail for my Year 6 students (age 11) to help them realise that mathematics surrounds us and that we can use it on a daily basis. Maths is not just in books. You just have to lift your eyes to see that we use it every day without even realising it.”

Congratulations to the new record holder on your great trail and we are excited to see when we will set this new record!

Less than 10 months ago, we already had 40,000 tasks on the MathCityMap web portal. Now the MathCityMap team is celebrating over 60,000 tasks and has reached another milestone on the way to making outdoor mathematics and mathtrails an experience throughout Europe.

Our anniversary tasks, which cracked the 60,000 mark, was created by Teresa Vinal Gómez in Orihuela a city in southeastern Spain ans asks about the characteristics of Gothic architecture at Orihuela Cathedral. Click here to go to the task.

We are looking forward to many more MatchCityMap tasks and we are curious when we will reach the next mark of 70,000 tasks!

MathCityMap was planned from the very beginning as a sustainable and long-term project with a perspective for the future, and in order to continue to do justice to this basic principle, some of the project partners from all over Europe met in Frankfurt at the end of January to develop new ideas.

Representatives from Spain, Portugal, Italy, Estonia, Austria, Slovakia and Germany spent the day engaged in many activities and working groups to identify features and opportunities that MathCityMap can develop, based on feedback from the community, teachers and academics, to provide an even more effective and comprehensive tool and learning environment for the classroom.

We are very excited to be able to present the new ideas and the focus of the development of MathCityMap to you in near future! Stay tuned…

All good things come in threes! With the successful application of the Istituto Comprensivo “Commenda”, there are now three official MathCityMap partner schools in Italy. Maths teacher Manuela Saponaro created two trails in the vicinity of the school in Brindisi and tried them out with her students.

She told us about the trails she created and her experience with her class as follows:

“Both Math trail cross well-known places in the city and through tasks suitable for different school levels test students on various areas from numerical to geometric, trying to develop in them the ability to problem solving and encouraging creativity.

The trails were tested both with pupils of the school and with a group of Polish students and teachers during an Erasmus + project. The students were also provided with the paper file in addition to the use of the app, in order to then reflect on their task resolution methods.

The students initially seemed disoriented since the approach to the problem of Mathematics was different from what they had been accustomed to until then. After the initial surprise and further clarification on the use of the app, the dominant feeling was the excitement and the desire to win the challenge.

Elements of strength were certainly the playful approach and the collaboration between the boys. These felt free to make their contribution without fear of error, while we noticed hesitation in wanting to use the tips in order not to lose points … they wanted to make it on their own even at the risk of ending the chances of attempting.

A critical element that we observed was time management and the inability to adequately use measuring instruments. Moreover, thanks to this activity, gaps have clearly emerged on the contents that will be recovered and enhanced.

The course gave the opportunity to enhance the attention on some details of their city on which the students had never dwelt and become aware of how much mathematics was around them.

Even the Polish colleagues and the Italian teachers involved were enthusiastic and understood how this way of doing mathematics is highly engaging and inclusive and gives the possibility to solve real problems of reality.

The totality of the participants following a questionnaire administered to them expressed the desire to include the use of Math City Map within the curricular activities or as an in-depth tool during the guided tours.”

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

Matematica tra parchi e piazze (5710839)
Dal centro al Casale … passeggiata matematica (6910838)

In addition to the experiences Manuela Saponaro shared with us, she wrote an article for the 36° Convegno nazionale Incontri con la matematica, an important national conference on mathematics didactics in Italy, in collaboration with other mathematics teachers, Lucia Del Chiaro, Giovanna Zito and Eugenia Taranto. Here, the teachers reported on their previous activities with MathCityMap under the title “Matematica in città”.

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

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

With the Trail of the Month for January, we would like to introduce you to a special mathtrail created as part of the ERASMUS+ project LECLIC “Living in the Era of Climate Change”, which uses innovative trends in the STEAM curriculum and cloud computing to raise awareness about environmental issues and climate change.

The students and teachers participating in the project will be encouraged to reflect on the need for behavioural change in their families’ lifestyles to mitigate climate change by analysing the bi-directional relationship between lifestyle and climate change, analysing the current lifestyle and quality of life in their European region and suggesting how they can change their habits on a large scale.

The project is organised in the form of four LECLIC conferences on climate change, where students from Portugal, Spain, Italy and Greece analyse the similarities and differences of climate change in each region. It is very important to get to know the different localities, which is why the use of MathCityMap has become an important tool in the project.

This month’s mathtrail “A LECLIL trail” is located in the Spanish city of Puerto Real and is available in the MCM app under the code 3812670 and on the MathCityMap web portal here.

The trail is made up of five tasks, all of which relate to the city and the impacts Puerto Real could be affected by if climate change continues to progress.

Ana Serradó Bayés, the creator of the trail, gives us a short interview below about her work with MathCityMap and her trail. Enjoy reading!

How did you come across the MathCityMap project?

In May 2020, when Spanish inhabitants were confined at home due to COVID19 pandemia I participated in the elearning training “Education School of Miguel of Guzman”. During the school, Claudia Lazaro of the Spanish Federation of Maths Teachers’ Association (FESPM) and one of the MathCityMap partners presented us with this ERASMUS+ project. One of the activities was to construct a trail. At that moment, it was difficult to construct a trail because we were only able to walk 1km far from home. But, from the terrace of my home I was able to admire the “Porvenir gardens”. I walked through them taking photos, making measurements, while I was willing to return to normality and prepare a trail for my students, who would be able to learn mathematics outside their homes. The name of that trail is “Cuidemos los Jardines del Porvenir” (Take care of the Porvenir Gardens, 012984).

Please describe your trail?

A LECLIC Trail is a STEAM tour to analyze how climate change affects Puerto Real city in South Spain. It consists of five tasks with a total length of 1.5 km and a duration of 1 hour and 20 minutes. Junior secondary students are asked to solve five STEAM problems and infer on the consequences climate change can have in five iconic locations of the city. Students participating in it investigate, analyze, calculate accessible and inaccessible lengths and develop stochastical thinking. And, infer about how Puerto Real could be affected by the climate change concerning to the drinkable water, the flooding of its beach, the destruction due to high waves of the 19th century fortified quay, the experience of a “wind drought” and the change in the sea level height.

How do you use MCM and why?

At our school, the students of Colegio La Salle-Buen Consejo use tablets at school and mobiles outside the school. In particular, the MCM is useful for them to understand the integration of two independent technologies: online maps and quizzes. As a member of the STEM department, I am involved in the development of activities that help students to understand the transdisciplinary approach of STEAM. In particular we are involved in many ERASMUS+ projects that use innovative technologies that help the integration of the other subjects.

I consider that these kinds of trials help students to develop the four global competences of communication, collaboration, critical thinking and creativity. Communication and collaboration because students are asked to solve it in a team, due to the fact that most of the measurements to be done on site need more than one person to do it. Secondly, because some of them have a high complexity that needs a discussion on the creation of strategies on how to solve the problem, to value its accuracy, developing their critical thinking, and finally decide which is the solution. The fact that MCM puts math tasks outside the classroom in a real context can extend the problem solving process to a geometrical or algebraic modelling process.

The possibility of introducing hints in the MCT tasks is very useful because then it is open to attend the diversity of our schools and provide students with the theoretical principles that they can use to solve the situation. When returning at school the analysis of the math trail is also an opportunity to deepen their learning and formalize the modelling process developed.

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

I think that all five tasks of the trail are interesting because the students need to infer about how climate change could affect their city and this kind of reflection is of pressing topical interest. But, if I have to choose one, my favorite task is “The wind rose in Sant Telmo Square”. San Telmo is a new square in the old city that most of the students of Puerto Real did not know about their existence. Even more about the wind rose oriented in the center of the square. Admiring the tiles of the wind rose and their symmetry is an artistic and mathematical activity by itself. Nevertheless, the fact that the students need to analyse the direction and speed of the wind transforms it into a scientific and engineering design activity. The comprensension of the stochastic nature of the wind speed is essential to answer the task. But, also this process of thought helps students to understand the difference between using a deterministic model for the speed and the stochastic and chaotic nature of the wind.

Autumn was busy with training and implementation of MathCityMap trails across Slovakia.

At the end of September, the Primary and Lower-Secondary School in Nábrežná street in Nové Zámky held a project day, which was attended by all 9th grade pupils. They explored the town centre, the surroundings of the school and also the villages of Branovo and Dvory nad Žitavou by solving MCM trails. The Department of Mathematics of the Charles University in Zámov participated in this beautiful project.

Silvia Haringová, a PhD student from Constantine the Philosopher University in Nitra, taught three groups of full-time and one group of part-time pre-service teachers for primary education students how to create and implement mathematical trails during the workshops. Sona Čeretková did the same activity for future secondary mathematics teachers.

Janka Medová and Silvia Haringová visited Primary and Lower-Secondary School in Duklianska street in Bánovce nad Bebravou, where they conducted training on mathematical trails. A teacher from Primary and Lower-Secondary School in Gorazdova street in Bánovce nad Bebravou prepared a mathematical trail in the footsteps of Sherlock Holmes for his 6.A pupils in the school building. Doctoral students Katka Laššová and Silvia Haringová came to help him with the implementation of the trail with his pupils.

Pre-service mathematics teachers Michal Fojtík and Peter Košt’ál prepared trails for pupils from grades 4, 5 and 9 in the primary and lower-secondary school in Slatina nad Bebravou. Janka Medová, Katka Laššová, Silvia Haringová and Peter Košt’ál came to Slatina nad Bebravou to implement the trail.

Another trail took place at the United Catholic School in Nemšová, where the pupils of three classes of grade 5 solved tasks prepared for them by their teachers Veronika Meščánková and Majka Šimáková. The trail included both indoor and outdoor tasks. Janka and Silvia could not miss the realization again.

In the beautiful surroundings of Zaježovské Lazy, a workshop on mathematical trails was held for teachers from all over Slovakia, to whom the creation and implementation of MCM trails was presented by Silvia.

The webinar was another event to promote the trails among teachers from all over Slovakia. It was led by Silvia together with Veronika Bočková. It was attended by more than 150 participants.

Silvia also travelled with the trails to Skalica to Primary and Lower-Secondary School in Vajanského street, where she came to help the teacher Zuzka Chytilova and the 9th grade pupils prepare a trail for the 5th grade pupils.

At the end of October Silvia conducted a training on MathCityMap trails in Stara Ľubovňa for teachers from the primary and lower-secondary school on Komenského street. Together with the teacher Libuše Hnátová, they prepared a trail around the school for the training.

In November, the Science and Technology Week took place in Slovakia. During this Silvia visited St. Mark’s Primary and Lower-Secondary School in Nitra and Silvia helped the teacher Kika Hazuchova, who had prepared the tasks in advance, to upload them to the MathCityMap portal. A few days later, they enacted the trail together with the pupils of 6th and 7th grade. Silvia also visited the grammar school Gymnasium of Ivan Kupec in Hlohovec, where she prepared and implemented a mathematical trail in the main square of Hlohovec for the pupils. During the Week of Science and Technology, Veronika Bočková carried out a home trail aimed at revising natural numbers at the Pribina Primary and Lower-Secondary School in Nitra with all 5th grade pupils.

As part of the course focused on mathematical problem solving, a former student of the Constantine the Philosopher University in Nitra, now a teacher, Kristína Čierniková from the Primary and Lower-Secondary School of Pavol Demitra in Dubnica nad Váhom, came to talk to the future primary teachers about the activities she does with her pupils. She also shared with them her experiences with the implementation of mathematical trails, whether outdoors or indoors with the primary pupils, even with the pupils of the first grade.

The mathematical trail focused on fractions, situated in the main building of the University, was attended by pupils from the out-of-school science and mathematics activity, which is supported by national project funded by the Agency for Research and Development APVV-20-0599 Intervention Programme in Natural Sciences and Mathematics.

The last MCM trail so far in this calendar year was tackled by pupils who came to the Open Day at the Faculty of Science and Informatics.

There were also other mathematical trails in this autumn period. We are aware that some were carried out in the Primary and Lower-Secondary School in Kanianka, the grammar school M.R.Štefánik Gymnasium in Nové Mesto nad Váhom, the Private Primary and Lower-Secondary School in Nová Dubnica, the St. Joseph’s United School in Nové Mesto nad Váhom and the Kukučínova Primary School in Detva.

We are delighted with the interest of teachers and schools in MathCityMap and look forward to continuing this great trend in our slovakian community in 2023.

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.

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

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.

Category: General

MathCityMap in winter? Of course!

A trail breaks all records!

60.000 MathCityMap-Tasks

A meeting for the future

A third partner school in Italy

Trail of the month: A LECLIC trail

A busy MCM-autumn in Slovakia

MathCityMap on Begabungslotse

MathCityMap wishes you a Merry Christmas!

Trail of the month: Exploring the other side of Opuwo