General | MathCityMap

In the past weeks we presented on our website a variety of math trails, which were created during our award-winning MathCityMap seminar at the Goethe University Frankfurt. All of these trails have been tested by students on site and have also passed our expert review. Lastly, in this section we presented the trail “The Sinai Park” by Isabella Unkart.

At the end of this section we will choose the math trail by Jens-Peter Reusswig as the Trail of the Month October. The trail offers not only a variety of mathematical discovery possibilities, but also allows for interdisciplinary lessons: All tasks of the trail “The Thick Fir” have references to ecology: By working on this trail, the students not only learn mathematical content, but are also sensitized to biological facts and topics. Below, part 1 of our interview with Jens-Peter Reusswig is presented.

How did you find out about the MathCityMap project? Did you get to know and use MCM before the Mathtrail seminar?

I learned about the MathCityMap project for the first time in the mathematics-didactic advanced seminar “Teaching ideas in Sek I & II under the aspects of analysis” by Mrs. Schubert in the last semester. The app was introduced to us by a course participant and we could then walk a short path ourselves. At that time I only knew the app from the user’s point of view, but not from the perspective of a MathCityMap author.

Describe briefly the main content of the seminar.

The main content of the seminar was to understand the idea behind MCM, to get to know the web and app application and finally to develop a trail step by step by myself. The beginning therefore consisted of the development of theoretical basics to know where MCM has its origin and to be able to estimate the potential of extracurricular learning places. Afterwards the seminar gradually became more practice-oriented and we got to know MCM not only from the student’s perspective but also from the author’s perspective.

The team of experts had a lot to come up with, so that the digital exchange sometimes consisted of a podcast, a video message or a forum discussion.

In the seminar I learned …
1. Which criteria an MCM task must fulfill and which task variations can result from it on the different levels of understanding of terms according to Vollrath.
2. that it is not bad if a task sometimes goes through several revision circles.
3. it is worthwhile to use the task wizard from time to time.
4. you simply have to edit a trail yourself to know what is important.
5. MCM is leaded by an experienced team who put their heart and soul into the further development of the app and the portal.

Describe your trail in a few words.

The trail near Freigericht / Somborn leads along the forest nature trail to the clubhouse to the “Thick Fir” of the Schutzgemeinschaft Deutscher Wald on the Spessartbogen hiking trail. On the round way one is to guest in a miracle of nature. The forest is a place of recreation, carbon dioxide storage and economic area at the same time, but above all it is a boundless classroom.

The trail runs through this versatile learning location, combining mathematical challenges with ecological background knowledge to create a very special learning experience – inside and outside the app. This not only trains mathematical skills, but also promotes knowledge about the forest and its inhabitants.

Why did you decide to do a trail with a focus on ecology?

I chose to focus on ecology because I was looking for an extracurricular place of learning that is familiar to many learners and contains meaningful questions that can be answered with mathematical tools.

With the forest ecosystem I had found a suitable environment that also encourages discovery, amazes students and can be experienced with all senses. The trail also integrates the local learning offer, which has always informed walkers about the forest as a habitat and explains why it is so worth protecting.

How does this fit in with interdisciplinary learning?

Interdisciplinary learning aims at showing connections, in this case connections between maths and biology. It is important to make it clear to learners that ecological issues cannot be solved without mathematics, and at the same time, that without ecology, mathematics would lose an important field of application with pressing future questions. By linking the two disciplines, mathematical tasks are suddenly linked to the reality of life and anchored in an authentic application context.

For which grade levels is the trail intended?

Since the trail requires a good reading comprehension and often several solution steps are necessary, it is recommended that students in grades 9 and above work through the trail independently. However, if groups of learners explore the tasks in groups, it is possible to work through the trail earlier.

The Junge Mathe-Adler [engl.: Young Math Eagles] fly again! Our mathematical scholarship for gifted students from Frankfurt and the surrounding area under the lead of Simone Jablonski, Melanie Schubert and Steffen Burk started the new season with a highlight: Working on a math trail with MathCityMap!

Our new third graders as well as the students of the sixth grade worked on the tasks alongside their parents with great commitment and solved many a tricky mathematical problem. Here you can find the completed trails:

We are already looking forward to the upcoming sessions of the Mathe-Adler, which will be digitally completed in MCM@home format due to the current situations. Have fun & success!

MaSCE³ [Math Trails in School, Curriculum and Educational Environments of Europe] is a program funded by Ersamus+ which aims at the further development of MathCityMap. This year’s meeting with our project partners from France, Spain, Italy, Portugal and Estonia as well as from Germany had to take place online due to the current situation.

Nevertheless, we can look back on two very intensive and successful working days: During the project meeting new task formats, the embedding of augmented reality elements into our system and the development of theme-based trails were reflected and discussed.

We thank all partners for this great meeting!

At MEDA 2020 (Mathematics Education in the Digital Age) the MathCityMap system was presented today in two presentations:

Ana Barbosa and Isabel Vale, partners in our Erasmus+ project MaSCE³, presented a study on the attitudes of primary school teachers towards digital media, more specifically towards teaching with MathCityMap. The corresponding contribution was published in the MEDA Proceedings (pp. 135-142).

In his presentation, Simon Barlovits, an employee of the Frankfurt MathCityMap system, explained the use of topic-based MathCitMap math trails. In the article (together with Moritz Baumann-Wehner and Matthias Ludwig) a guideline for the creation of theme-based trails is also presented. The article can be found in the MEDA-Proceedings on pages 143-150.

It’s hard to believe, but the three MoMaTrE project years will end on Monday. In order to complete the outputs and results on time, we met with the partners for the final meeting in Lisbon last week. All seven outputs were successfully completed and uploaded to the MoMaTrE project website www.momatre.eu in the section “The Project”.

In addition to intensive work phases, we set up tasks on site and valued the Portuguese culture with Fado music. Our special thanks go to all partners involved, their ideas and their commitment in the recent years. It was a great time and we achieved a lot for the European math trail community!

The seminar “Mathtrails – Digitalization of Outdoor Mathematics Education” of the Goethe University Frankfurt was awarded as one of 13 projects by the MINTchallenge of the Stifterverband for excellent digital teaching during the Corona pandemic. In the seminar, our MCM educators Iwan Gurjanow and Simon Barlovits presented the MathCityMap system to student teachers. Currently, we present the math trails which were created during the seminar in the section “Tested Trails in the Rhine-Main Region”.

With the MINTchallenge under the motto “Studying from a distance”, the Stifterverband’s MINT Club “presents digital teaching and learning formats that enable students to continue their MINT studies during the corona pandemic, and in the long term will be an enriching addition to the MINT studies. With more than 150 candidatures, the Club-MINT-Challenge has met with a great response and shows that the MINT study programmes have mastered the digital semester with creative and innovative ideas”. Click here for the presentation of the thirteen award winners by the Stifterverband.

We are very pleased that our Mathtrail seminar was awarded by the Stifterverband!

On July 20, Sanne Kleinhenz, a German student at the Rhön-Gymnasium in Bad Neustadt, created the 15,000 task on the MathCityMap web portal. After the summer holidays, Sanne and her class mates will publish three new trails in Bad Neustadt. We are looking forward to it! In the following interview, Sanne Kleinhenz explains how MCM is used in her school.

Dear Sanne, how did you get to know MathCityMap? How do you use MCM at school?

I am a student at Rhön-Gymnasium and we work with MathCityMap in the P-Seminar. The project seminar in Bavaria is designed to prepare upper school students for their choice of studies and profession. The P-Seminar is generally about learning to work independently and in groups. We (14 students) have chosen the P-Seminar with the name MathCityMap (leading subject mathematics). First we got familiar with the app and website by creating a small trail through our school building together.

Divided into three groups we created tasks at different locations in Bad Neustadt. The idea was not that everyone should do their tasks alone, but that we work together and finally have three varied trails. Before the summer holidays we created all tasks (three for each student). In the new school year we will discuss together which tasks will be included in the trails and if they need to be improved.

Working with MathCityMap is very suitable for our P-Seminar, because at the beginning a lot of planning has to be done together, then the tasks are created independently and it is necessary to exchange with your classmates during this time.

The task formulation of the 15,000th task “Shoe size of the statue” is: Shoe sizes can be determined with the help of the Parisian stitch. The number of Parisian stitches needed for the length of the foot is the shoe size. Calculate the shoe size of the statue and round your result to whole numbers. (1 Paris stitch = 2/3 cm). What is the idea behind your MCM task “Shoe size of the statue”?

Since this task is probably the first one of the trail, it should be an easy start. To avoid that the students are confused and immediately overchallenged by the task, the first hint should make clear what the first step is. First of all you need the length of the foot, i.e. you have to measure it. So the first hint should show that it is easier to solve a task in steps.

In order to solve a task correctly, one must always understand what exactly is required. The second hint is to help the students to find the right steps when they do not know what is required. After that only the actual solving of the task is missing. The task can be solved in different ways. As indicated in the last hint, the rule of three can be used. But another way of thinking is also possible (indicated in the 2nd hint): You ask yourself how many Parisian stitches fit into the foot length, i.e. the length divided by the Parisian stitch.

The statue to be examined has a foot length of 39 cm. Using the rule of three (or by dividing the foot length by the Parisian stitch), it can now be calculated that this equals shoe size 59.

Development of the number of registered users and task on the web portal.

In June, we celebrated the 5,000th user joining the MCM community, now there are already 5260 users. In the past two weeks, 381 new tasks were created, so that we now have a total of 15,381 tasks (as of 04.08.2020).

The MathCityMap team thanks all users for their multifaceted ideas. We are looking forward to many more tasks and trails!

On Monday, Iwan and Simon from the MathCityMap team Frankfurt (About Us: The MCM Team) measured, calculated and counted in the beautiful town of Bingen on the Rhine and in Groß-Gerau, Germany.

As part of the Mathtrail Seminar at the Goethe University Frankfurt, which is guided by Iwan and Simon, students created their own trail near their living place.A mutual review of the tasks is also part of the seminar: Both for experienced MCM users and “MCM rookies” a second look at the task is worthwhile, e.g. to modify the solution interval, improve the hints or clarify the task formulation.

We had a lot of fun while working on the two trails and are looking forward to their publication!

Solving math trail tasks in Groß-Gerau …

It’s the advertising pillar’s birthday! The first advertising pillar was installed in Berlin 165 years ago today. The advertising pillar has prevailed – and still shapes the cityscape today. Of course, the advertising pillar is also interesting from a mathematical perspective: In addition to calculating the volume or the surface area of the circular cylinder, the question of the maximum number of advertising posters can also be asked.

Advertising pillar at the Commerzbank:
How many DIN A0 posters can be attached to the advertising pillar on edge and without overlap? DIN A0: width = 84cm; height = 119cm.

To answer this question, learners have to measure the height and the circumference of the advertising pillar in order to calculate the number of posters. Learners are often surprised by the actual size of the circumference. The height of the advertising pillar is then divided by the height of the poster [number of rows of posters] and the circumference of the pillar by the width of the poster [number of posters per row]. The product of both calculations is the number of posters that can be attached. If the posters may also be hung crosswise, the calculation described must be repeated in order to determine the maximum number beyond doubt.

And now the best: For the advertising pillar task, MathCityMap provides a prepared template, a so-called Wizard Task.

Last October, the MathCityMap team from Frankfurt visited the city of Constance [dt. Konstanz]. At Lake Constance our team is laying out a total of 14 new trails, which will be released today!

With the support of the Stiftung Rechnen and the city of Constance we have created many interesting math trails for classes and families in the beautiful city of Konstanz. The Mathe.Entdecker trails [engl. Discovering.Maths trails] lead around the harbour, along the Rhine promenade, through the city centre or through the Paradise Quarter. In addition, a “border trail” was created on the German-Swiss border. However, the grand opening with school classes trying out the mathtrails had to be cancelled due to the Corona pandemic. With the following links you can access the articles of Stiftung Rechnen and Marketing und Tourismus Konstanz GmbH about our new math trails.

In the following we list all our created trails in Konstanz. We wish you a lot of fun and success!

Titel incl. Link	Code	Duration\| Distance
Konstanz Innenstadttrail [Around the City of Constance]	672257	2h 10 min \| 1.400 m
Konstanz Hafentrail [Around the Harbour of Constance]	022256	2h 20 min \| 1.100 m
Konstanz Grenztrail [Along the Swiss-German Border]	492255	2h 10 min \| 1.700 m
Ein Nachmittag in Konstanz [An Afternoon in Constance]	352258	4h 20 min \| 3.400 m
Mathe für Entdecker – Klasse 3/4 [Discovering Maths – Grade 3/4]	472261	1h 30 min \| 1.000 m
Konstanz Familie – Klasse 3/4 [Families in Constance – Grade 3/4]	452260	2h 50 min \| 3.400 m
Mathe am Rhein – Klasse 5/6 [Maths along the Rhine – Grade 3/4]	472262	2h 20 min \| 2.200 m
Quer durch Konstanz – Klasse 5/6 [Across Constance – Grade 5/6]	092264	2h 10 min \| 1.500 m
Konstanz Familie – Klasse 5/6 [Families in Constance – Grade 5/6]	562263	3h 00 min \| 3.300 m
Mathe im Paradies – Klasse 7/8 [Maths in Paradise – Grade 7/8]	292265	1h 40 min \| 1.300 m
Quer durch Konstanz – Klasse 7/8 [Across Constance – Grade 7/8]	072277	2h 10 min \| 1.500 m
Mathe am Rhein – Klasse 7/8 [Maths along the Rhine – Grade 7/8]	192276	1h 50 min \| 700 m
Mathe am Rhein – Klasse 9/10 [Maths along the Rhine – Grade 9/10]	132259	2h 10 min \| 1.400 m
Mathe im Paradies – Klasse 9/10 [Maths in Paradise – Grade 9/10]	132267	2h 40 min \| 1.900 m