General | MathCityMap

As in previous years, it was a special pleasure for our team in Frankfurt to present the ideas and potential of MathCityMap at the recent annual conference of the Gesellschaft für Didaktik der Mathematik (Society for Didactics of Mathematics).

As the largest conference for didactics of mathematics in the German-speaking countries, the GDM annual conference not only offers us the opportunity to discuss current research on MathCityMap and the idea of app-supported mathematical walking paths with the scientific community and to generate new ideas for the further development of the MathCityMap system. In addition, we were able to promote the enthusiasm and understanding for the concept of making mathematics experienceable and learnable outdoors with a workshop for teachers on MathCityMap and an information desk on the conference grounds.

We were again able to gain some new impulses for our work and are already looking forward to the appearance of the many contributions on MathCityMap in the conference proceedings of the GDM, which we will of course also link for you on this website.

We are once again in a European capital for the “visit” of the Trail of the Month September. The trail “Mathematics outdoors” is located in a city that bears the same name as the state, Luxembourg. This mathematical walk was created by Claude Reuter as part of the initiative “Mir gi raus” of the SCRIPT, a coordination center for educational and technological research and innovation.

The trail consists of a total of 11 tasks covering a wide range of topics such as geometry, stochastics and arithmetic and is located in the central district of Clausen directly on the Alzette River. The trail is available in the MCM app under the code 4710757 and in the MathCityMap web portal here.

Claude Reuter describes his experience and work with MathCityMap in the following interview. Enjoy reading!

How did you come across the MathCityMap project?

I came across MathCityMap while researching on the internet about applications that help in creating GPS-based trails.

Please describe your trail?

The MathTrail is intended as an example trail. It is designed to show teachers how mathematics can be experienced in a playful way using simple means in the immediate environment of the school (in this case the schoolyard). Mathematics is everywhere and should therefore not only be dealt with in the classroom.

How do you use MCM and why?

MCM is designed to help people experience mathematics. Although mathematics is an exact science, we often work with estimates in everyday life. With MCM, mathematical content can be connected to the real context.

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

My favorite task from the trail is the task to determine the flow velocity of the Alzette River. In this task, the focus is not on the result, but on the process. The result cannot be determined unambiguously. To solve the task, students must come up with possible procedures on their own and then check them for feasibility.

We are very happy to welcome the first MathCityMap partner school in Estonia. The “Saue Kool” (Saue School) in the Estonian city of Saue near Tallinn has successfully applied and has created seven trails and tested them with their students.

Ave Mitt, a math teacher at Saue Kool, initiated the application process and reported his experience with MathCityMap as follows:

My experience with trails in terms of creation is that the MathCityMap website is very easy to use. I like creating these types of different exercises that give me the opportunity to get my class out in the fresh air. The kids expect us to just hang out in the fresh air, but in reality we are learning math in a different environment. My classes are 45 minutes long, so I try to make the most of the time I have. That’s the reason I usually have 5 exercises on a trail. The kids are positively surprised that you can learn math outside the classroom. At the same time, other teachers are also very surprised that MCM has so much positive impact on the students.

In the spring, I introduced MCM to our teachers. After summer break, I want to create new trails for my students to get them back outside at the beginning of the school year. Here is a list of trails that I have used with my students in the past:

Code: 2611140

Code: 379549

Code: 139540

Code: 469539

Code: 089538

Code: 799537

Code: 359536

The package with the official partner school plaque and the MCM measuring instruments is already on its way to Estonia 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.

The partner school network of MathCityMap is growing by the week and we already welcome the sixth Portuguese partner school! The “Escola Secundária de Ponte da Barca” in the municipality of Ponte da Barca, located in the north of Portugal, has successfully applied, initiated by the local teacher Cláudia Barreto, and the package with the official partner school plaque and the MCM measuring instruments is already on its way to Portugal.

Cláudia Barreto described for us in the following report how the application as a partner school came about:

“Every year we celebrate “Science Day” at our school. This year the math group decided to challenge our students to participate in the math trails created on the school grounds. Two trails were created: one for students in the 7th, 8th and 9th grade (Trail code: 579742) and the other for the 12th grade students (Trail code: 236662).

All students were very enthusiastic and reacted extremely well to the activity. They especially enjoyed the opportunity to get outside and explore the mathematics that surrounds them.

In fact, they were able to see the applicability of the contents they learn on a daily basis in a real and practical context. Besides that, having the opportunity of working with technology gave them even more motivation and made the activity a lot more interactive for them.”

As always, we are very much looking forward to receiving more applications from all over the world.

Additional information on the partner school program and application requirements can be found both in the article on the first MCM partner school and on the homepage of our MaSCE³ project.

Our new Trail of the Month is located in Alcobendas, Spain. The trail in the town north of Madrid has been frequently used in teacher practice, as shown by the high number of more than 230 downloads. It was created by José Fernández de la Cigoña and Isabel Docampo for presenting MathCityMap during the Spanish mes de las matemáticas (month of mathematics; click here for the website and here for our report on the project).

In the following interview, José Fernández de la Cigoña highlights the use of the MathCityMap pirate narrative and introduces her trail “Un paseo pirata matemático por el Jardín de La Vega”.

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The following article was published in May 2021. Why we present it again?
José Fernández de la Cigoña and Isabel Docampo have since written a journal article about the trail and the MathCityMap pirate narrative, which can be accessed online here.

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How do you get in contact with MathCityMap?

We got in touch with MathCityMap by the Spanish website Marzo, mes de las matemáticas from whom we were asked to prepare a trail to contribute to the month of mathematics. So, we looked for some information, signed up for the MathCityMap MOOC and started creating on our trail. We aim at a broad revision of learned topics, mainly geometry but also divisibility, probability or proporcionality, among others.

Our students in school have already worked on the trail! In fact, we are a little surprised by the high number of downloads of our trail by other users.

Please describe your trail.

Our trail is placed in a park in Alcobendas, a city close to Madrid. The website Marzo, mes de las matemáticas guided us on the kind of tasks we could look for, and one great characteristic of this trail is that most of the tasks can be easily recreated in any city around the world [so-called Generic Tasks]. The special attribute of this trail lies in a story connecting all the tasks, a sort of pirate adventure based on the MathCityMap pirate narrative.

Please sketch one of your tasks. What is the mathematical question? How could you solve it?

The most inventive task in our trail is “La batalla final” (The final battle). It is located on a playground where you can find a pirate ship. The aim of the task is to find the probability of hitting the ship if you fire a cannon. So it’s about probability and geometry since you need to evaluate the ship area and the area of the playground to know the probability.

Why do you use the pirate narrative. What are its benefits?

Since we have been developed a pirate story, it seemed so natural to use the pirate narrative. In fact, this narrative inspired us to create the story.

In August, the Trail of the Month comes from Albstadt, a city in the south of the German state of Baden-Württemberg. In a joint project, the Zollernalbkreis District Media Center and the Baden-Württemberg State Media Center created the “Traufgängerle Hexenküche (witch kitchen) in Albstadt” mathtrail here, which can be accessed with the MCM app under the code 459518 and is available on the MathCityMap web portal here.

The trail consists of a total of twelve tasks that are designed to cover all content-related competencies that need to be acquired in elementary school. While working on the tasks, you can experience one of the many special hiking trails around Albstadt, which gives this trail a very special atmosphere.

Silke Schick, educational associate at the State Media Center Baden-Württemberg and co-creator of the trail, gives us a short interview below about the creation of the trail and her work with MathCityMap. Enjoy reading!

How did you come across the MathCityMap project?

During a brainstorming session for the Media Competence Days of the district media centers and the Baden-Württemberg State Media Center in June of this year, we stumbled across MathCityMap and then connected it with the premium hiking trails in the city of Albstadt.
Since math teachers are on the team, the idea came up for the students to design a trail during the time of the media literacy days that would invite them outside, while also creating an area for teachers to use for long-term math field trips. In the course of this, we developed a training for teachers to introduce the portal.

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

As a media center association, it is particularly important to us that the trail can be used by as many people of all ages as possible. Thus, we have chosen a trail that is located along a well-known hiking trail especially for children. This trail leads through a wooded area past a game preserve, there is a “witch’s kitchen” to discover and at the end it leads to an observation tower of a medieval castle. This trail can be used by families with children, grandparents with their grandchildren as well as school classes of elementary school or orientation school as an excursion destination and mathematical journey of discovery.

How do you use MCM and why?

The trail was a pilot project that will lead to us making similar project trails available throughout Baden-Württemberg. Starting in the upcoming 2022/2023 school year, advisors at district media centers will train local teachers on how to use MCM for their own schoolyard or city. A great option for doing math together outdoors.

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

There are two favorites in the team:
In the “Albstadt Town Musicians” task, you have to find all the wooden animals in the forest, measure them and add up their height. As a team, you have to agree on where and how to measure.
The second favorite is the “Tower” station. The task is to count steps. We had three generations with us when we created it and ended up with three different solutions. The challenge was for everyone to find an optimal counting strategy on the way up and to keep it up. Fitness training was included.

The current update extends MathCityMap with the possibility to include AR scenes as well as in the communication via the digital classroom. In addition, some bugs are fixed and the performance is significantly improved in some places.

Augmented Reality (AR) in MCM tasks

It is now possible to link MCM tasks with AR elements. Within the MASCE project, a portal specialized in the creation of AR scenes (marker or GPS-based) has been created under the name EducatAR (https://educatar.eu). After a short registration, AR scenes can be created there.

To link an MCM task with an AR scene, only the link to the AR scene has to be entered in the task form. In the MCM app, a new button now appears for tasks with AR, which takes the user directly to AR mode to view the scene.

Didactic ideas for using augmented reality will be discussed in a separate post in the near future.

Multimedia chat in the digital classroom

The chat functionality of the digital classroom has been extended in the portal to include the ability to send images and audio recordings. As part of this, the audio chat has also been extensively tested in the app and bugs have been fixed so that the functionality should now be available to all.

In addition, teachers in the digital classroom now have the option to “ping” individual groups to find out their approximate location. This feature is hidden behind a magnifying glass icon on the group tile.

Other changes:

The layout of tasks has been reworked with visual grouping to make it clearer.
The performance when loading profile data has been significantly increased.

All features will be fully available once the updated version of the MCM app has been fully rolled out.

We are very pleased to welcome the first Spanish MathCityMap partner school to our ever-growing network of partner schools! The “IES María Moliner” in the city of Segovia, north of Madrid, successfully went through the application process initiated by math teacher Sonia González Pascual.

In the following short report Sonia González Pascual describes the created trails at her school and she presents her experience with MathCityMap so far.

“At the moment we have two trails for different grade levels near our school, with
a total of 15 tasks created by myself.

These trails are designed for students ages 13 to 17. One of them “Volúmenes entorno al Acueducto”, can be used to practice calculating the Volumes of some simple three-dimensional figures to practice. In a fantastic historical setting students can calculate the volumes of stone figures they find while discovering the Roman aqueduct of Segovia: piramids, prisms, spheres, truncated cones… It is necessary to use a tape measure or something similar. Since it can often be difficult to find an exact solution, I often use the “interval” answer format.

The other trail “Frisos en pocos metros”, takes advantage of another important feature of our city: the “esgrafiado” or sgrafito. This is an architectural ornamental technique used to decorate plaster and wall coverings.
Stencils with serial geometric motifs are often used. In the trail, students have to look for plane movements in some sgraffito or window and balcony railings for example reflections or rotations. They learn about subgroups of isometry, often using the multiple choice format to enter the answers.

It is important to cross-link the knowledge that was acquired in a previous session in the classroom. Students are actually very motivated with the MCM app. The use of the cell phone, the search of the tasks via GPS and the possibility to leave the school make MathCityMap a very interesting learning environment.

I have already used our trails with MathCityMap with different students of different ages and they have rated it very positively. I have also shown the app and especially my trails to a group of math teachers. My goal is to bring this app and its possibilities to as many people as possible.”

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 more applications from all over the world.

The last article on Generic Tasks deals with the most unusual category in the Task Wizard, GPS tasks. These tasks can be created by the wizard in a very short time and can be easily implemented on any larger area and can therefore be integrated into any trail as needed. The first article on Generic Tasks, which also tells you how to get to the Task Wizard and what Generic Tasks are, can be found here.

In the category of GPS tasks we are not bound to specific objects, which has to do with the approach of the tasks. For example, one possible task is:

“Walk a line AB which is 50 meters long.”

To create the task, you only need to define a place where the task is to be performed. The person performing the task then uses a GPS function in the app to set two points while walking that are 50 meters apart. The route can be either directional, i.e. running in a certain cardinal direction, or non-directional.

Other possible tasks are, for example, tracing a square or an isosceles triangle. In addition, as seen in the first image of this article, you can ask for points that are equidistant from two or three points previously determined in the app, such as the sculptures.

We hope that with this series of articles on Generic Tasks we were able to introduce you to our Task Wizard and its possibilities to simplify the process of creating tasks. Have fun trying it out!

Dear MathCityMap Users,

during the last years not only the MathCityMap system with its various functions has constantly developed. Our community has also continued to grow, for which we would like to thank you all very much!

In order to be able to develop interesting and customized innovations for you in the coming years, we would like to learn even more about our community. For this purpose, we have created a survey that you can access via the following link:

Click here for the survey!

We would be very pleased if you would participate in the survey and we thank you very much for your engagement with and for MathCityMap and for your feedback.

Your MathCityMap Team from Frankfurt

Category: General

The MathCityMap Team at the GDM Annual Conference

Trail of the month: Mathematics outdoors

The first Estonian partner school!

Portugals next partner school

Trail of the Month: Un paseo pirata matemático

Trail of the month: Traufgängerle witch kitchen in Albstadt

AR and more in MCM update from 26.07.22

Augmented Reality (AR) in MCM tasks

Multimedia chat in the digital classroom

Spain joins the partner school program

Generic Tasks: GPS Tasks

MathCityMap Survey 2022