Simon Barlovits | MathCityMap

Task of the Week: Climbing Frame

Patrick Rommelmann has created our new task of the week on the schoolyard of the Regenbogen-Gesamtschule Spenge – the task “Climbing Frame”. The task is located in the theme-based math trail “Route RGeS”, which focuses on the repetition of cylinders. Mr. Rommelmann has already tested the trail with a 10th grade class. How did […]

Patrick Rommelmann has created our new task of the week on the schoolyard of the Regenbogen-Gesamtschule Spenge – the task “Climbing Frame”. The task is located in the theme-based math trail “Route RGeS”, which focuses on the repetition of cylinders. Mr. Rommelmann has already tested the trail with a 10th grade class.

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

I became aware of the MathCtityMap project during my mathematics didactics training at Bielefeld University. At the university, a math trail has already been created, which I worked on in a seminar.
In the seminar for writing my master thesis the MathCityMap project came up again and I decided to create a math trail and test it with a school class. After positive feedback, I have now published the tasks so that other teachers can work on the math trail with their classes.

Describe your task. How can it be solved?

In this task, we are to determine the length of the lowest blue rope. The beauty of this task is that there are different possible solutions. The rope forms the shape of a circle. Therefore, the radius of the circle can be measured and then the circumference of the circle can be calculated.
A more intuitive solution option is to measure the entire circumference of the circle. However, this can take quite a long time if the many, individual sections have to be measured one after the other. A clever variant can be chosen here if only one section is measured and this is multiplied by the number of all sections.

What didactic goals are you pursuing with the task?

In particular, the variety of solutions should create an openness of the task. Open tasks are particularly well suited for heterogeneous learning groups, which are also increasingly found at this comprehensive school. In addition, the MathCityMap task had the typical didactic aspect of modeling on real objects.

What other tasks could be investigated on this exciting object be investigated?

Starting with questions about the circle, further questions about the shape of the climbing frame as a cone could arise at the climbing frame. In addition, the pole to which the climbing frame is attached could also be investigated. The pole has the shape of a cylinder, so for example with given density and weight, the length of the pole could be determined. The result could be used to check how secure the climbing scaffold is in the ground. Of course, the necessary information would have to be obtained beforehand.

Further comments on MCM?

As you can see from this nice example, mathematical questions can be found on many objects in our world. With MathCityMap, an app has been created that can successfully establish the application connection of mathematics to the objects.

The MCM Team wishes Merry Christmas

Dear users, Another year is drawing to a close (this time probably a very turbulent one for all of us). Christmas is just around the corner. Time for us to take a brief look back at the past year: This year, almost 5,500 new tasks were created in the system, so that we now count […]

Dear users,

Another year is drawing to a close (this time probably a very turbulent one for all of us). Christmas is just around the corner. Time for us to take a brief look back at the past year:

This year, almost 5,500 new tasks were created in the system, so that we now count a total of almost 17,600 tasks in the MathCityMap portal, of which about 7,000 tasks were published.
We also saw a sharp increase in registered users: Approximately 2000 new MathCityMap users registered in the system. In total, the MCM community now counts 6,200 members.
Our Erasmus+ project MoMaTrE (Mobile Math Trails in Europe) was successfully completed. We would like to thank our European partners from Lyon (France), Porto & Lisbon (Portugal), Santander (Spain) and Nitra (Slovakia) as well as our app developer team from autentek in Berlin for the great collaboration over the past three years. At the end of the project, the ROSETA proceedings all about extracurricular learning with digital media in science and technology subjects was published – of course, the focus here was also on our MCM system.
In May we were able to present our new MathCityMap web portal: In the new design, creating tasks & trails is even more fun – especially since there are now also awards for working with MathCityMap: For creating tasks & trails, running digital classrooms, downloads of your own trails or your contact to other MCM users, you can collect up to six badges each.
To make running MCM trails even more fun, we’ve also given our app a new design. In addition to the visual redesign, the app now offers the option to create tasks and trails directly on your phone.
To support virtual teaching and distance learning, we developed the MCM@home concept: due to the pandemic, the idea here was to solve tasks from home rather than on site. In total, more than 60 MCM@home trails were created worldwide, which were downloaded more than 1500 times. Fantastic!

Not only because of the Corona pandemic, but also caused by the presented further developments of our MCM system, the past year was exciting for us. However, the great development of the user numbers and tasks would not have been possible without your help and use of the platform. And so, despite all the changes, MathCityMap remains what it is: a digital system for school practice.

We wish you and your families a Merry Christmas and a Happy New Year 2021. We are already looking forward to welcoming many new members to the MCM community and discovering new, exciting tasks all over the world. Stay healthy!

Your MathCityMap Team Frankfurt

Task of the Week: The Stone Pillar

Jeniffer Sylaj Baptista is studying to be a teacher at the University of Luxembourg. In the interview, she tells us about her task “The Stone Pillar”, which she created in Sandweiler near the city of Luxembourg. How did you get in contct with the MathCityMap project? How do you use MCM and why? I use […]

Jeniffer Sylaj Baptista is studying to be a teacher at the University of Luxembourg. In the interview, she tells us about her task “The Stone Pillar”, which she created in Sandweiler near the city of Luxembourg.

How did you get in contct with the MathCityMap project? How do you use MCM and why?

I use the MCM project for university. I am studying “sciences de l’éducation” (teaching) at the University of Luxembourg. For the homework in the subject Didactics of Mathematics under the supervision of Yves Kreis, we have to create a Mathtrail with different tasks.

The MCM project is a great way to get students to see the mathematics in their environment and to solve mathematical problems in an exploratory way.

Describe your task. How can it be solved?

The task is: “How many stone faces does the stone column have in total?” Stone columns are built up into different stone tiers and these are then the same on each side. So all you really have to do is count the stone faces on one side and then multiply by the number of facets of the stone column, which in this example is 4.

What other tasks could be set on this interesting object?

For example, the volume of the entire stone column could be calculated in another task. Measuring the stone column could also be a small task.

MathCityMap congratulates Simone!

Simone from the MathCityMap team Frankfurt has made it – we congratulate Simone Jablonski on achieving her PhD! Simone has not only conceptually developed MathCityMap over the past three years, held great teacher trainings and busily published on MathCityMap, but also guided our two EU projects MoMaTrE and MaSCE³. Dear Simone,you are – both professionally […]

Simone from the MathCityMap team Frankfurt has made it – we congratulate Simone Jablonski on achieving her PhD!

Simone has not only conceptually developed MathCityMap over the past three years, held great teacher trainings and busily published on MathCityMap, but also guided our two EU projects MoMaTrE and MaSCE³.

Dear Simone,
you are – both professionally and personally – an irreplaceable part of our team. We are very happy to work with you.
Thank you for supporting us with words and deeds! We wish you all the best for your future!
Your MathCityMap Team Frankfurt

Here are some impressions from three years of MathCityMap with Simone:

Trail of the Month: A math trail for Markdorf!

The math teacher Fabienne Nykiel created the trail “A math trail for Markdorf!” together with her students. In the following, the teacher explains how the students of class 7c of the Markdorf educational center worked out the tasks. How did finding & creating the tasks work with your class? Describe the process from the first […]

The math teacher Fabienne Nykiel created the trail “A math trail for Markdorf!” together with her students. In the following, the teacher explains how the students of class 7c of the Markdorf educational center worked out the tasks.

How did finding & creating the tasks work with your class? Describe the process from the first idea to the finished trail.

A group of students designed a modeling task on triangular construction together with me in the centre of Markdorf. The teacher informed herself in advance which location might be suitable for a potential modeling task on a specific topic and led the group to this location.

At this location the modeling cycle was discussed again with the students in a didactically reduced form and it was then explained that this cycle is now run backwards (I have called this process of modeling “extended modeling”): In a single work phase the students explored the local situation and each of them thought about the potential possibilities of this location alone in order to design a possible modeling task for the specific topic. After this phase, each student presented his/her ideas. In the plenary session, the students used this as a basis for discussing and debating which idea was the most suitable, creative, individual and closest to reality, whereby several ideas could also be combined into one (‘Think-Pair-Share-Method’).

After the students had already had their goal and result in mind, they considered how they could achieve this goal in the world of mathematics, i.e. by mathematical work (estimating, measuring, calculating, constructing, …) and carried out their considerations simultaneously. In doing so, they filtered out the explicit hints that could later be given in the MathCityMap app. Each small group was fully motivated and enthusiastic. They all emphasized that it was a lot of fun to finally do something ‘useful’ with mathematics.

As a last step, the students formulated the task, the three hints and the final solution (with its range of solutions) in detail. I transferred this information to the web portal and created the individual tasks. At the end, all tasks were combined into a trail. As a project conclusion, the trail was run and worked through together on a school day. As far as the Corona regulation (again) allows it, the parallel classes also want to go through the trail.

What do you see as the advantages if the learners create the tasks themselves? What do you hope to achieve?

A big advantage that I have seen in this project was the improvement of the modeling competence of SuS, which has especially developed through “Advanced Modeling”. In addition, SuS also deals with the trained content competencies from a different perspective. Social skills are also trained, such as the ability to work in a team.

Therefore, I hope that I will not only be able to better train the modeling skills, but also a sustainability of the teaching content. I hope that SuS will not forget these mathematical contents and also the modeling skills.

A further advantage is the strengthening of the personality of SuS. They were all visibly proud of the fact that they designed the math trail themselves. The joy was even greater when they learned that the trail would be published and was nominated for the Math Trail of the Month.

Is there a task that you particularly like? If so, please describe it.

I think the task “A larger church clock for Markdorf” is very successful, because many skills are trained. On the one hand, it must be estimated that the gable is an equilateral triangle, whereupon the SuS must measure the width of the tower, which gives them the length of each side of the triangle. Only with this information can the SuS design the triangle on a sheet with a suitable scale and determine the center of the inscribed circle.

What I particularly like about this task is that it seems ‘unsolvable’ at first glance, because the gable is so far away and cannot be measured easily.

Task of the Week: The Dinosaur’s Suitcase

Melanie Schubert from Goethe University Frankfurt has created the task “The Dinosaur’s Suitcase” and reports in an interview about her experiences with MathCityMap. Dear Melanie, how did you get to know MathCityMap project? How do you use MCM? I got to know MCM while working at the Goethe University Frankfurt, where the system is […]

Melanie Schubert from Goethe University Frankfurt has created the task “The Dinosaur’s Suitcase” and reports in an interview about her experiences with MathCityMap.

Dear Melanie, how did you get to know MathCityMap project? How do you use MCM?

I got to know MCM while working at the Goethe University Frankfurt, where the system is developed. As part of our mathematical gifted students promotion program “Junge Mathe-Adler Frankfurt” I created the trail “Mathe-Adler Klasse 6” for SuS of the sixth grade as a kick-off event.

Describe your task. How can it be solved?

In my task the volume in liters of an oversized suitcase is to be determined. In front of the Senkenberg Museum in Frankfurt there is a large dinosaur figure with a suitcase standing in front of it. Within the task the SuS receive information about human suitcase sizes, if one would go on vacation for about 2 weeks. The SuS can calculate the volume of the suitcase by approximating the suitcase of the dinosaur as a cuboid and then convert the volume into dm³ to determine the number of liters. By specifying the liter sizes of our suitcases, the SuS have a possibility of self-control, in that the SuS can consider whether about 27 of our suitcases can fit into the suitcase of the dinosaur.

What didactic goals do you pursue through these tasks?

This task is intended to expand the spatial imagination, conversion skills, measuring skills and the competence of modeling.

A “Math Day” in Nierstein

Melis Yaren, mathematics teacher at the Carl-Zuckmayer Realschule in Nierstein, organized a “math day” for and with her 6th grade. At different stations, new perspectives on mathematics were opened up – MathCityMap was of course also used. Below Melis Yaren reports on the “Maths Day”. What is the math day about? What did the students […]

Melis Yaren, mathematics teacher at the Carl-Zuckmayer Realschule in Nierstein, organized a “math day” for and with her 6th grade. At different stations, new perspectives on mathematics were opened up – MathCityMap was of course also used. Below Melis Yaren reports on the “Maths Day”.

What is the math day about? What did the students do here?

I organized a math day with my class 6b (only in the class association because of Corona). There were a total of 5 different math stations and in each station different math problems. The goal is that I offer the students different perspectives on math based on these stations. At the 1st station “MathCityMap” the students presented the tasks/route of MCM, which we had solved in the math class before in the schoolyard. In the math day they also found new tasks for the app in the school grounds. At the 2nd station “Learning math digitally” the students presented the digital apps and web tools that we have learned and practiced so far with the tablets in math class. At the 3rd station “Learning math playfully” we had math games, tangram, geo boards, dice and wheel of fortune experiments. At station no. 4 they solved and presented Fermi tasks. At the 5th station “Guessing” they prepared guessing tasks (with smarties, beans, chocolate sweets, etc.) for their classmates and teachers.

How was MathCityMap used for this?

The students of 6b solved the tasks in the math class outside and later presented them in the math day (on 10.11). The route “Carl Zuckmayer Realschule Plus” was published last year – I created it for my project group (click here for the report). The tasks “barbecue hut” and “sports field” were best suited for the kids.

How was the feedback of your students on the math day and especially on MathCityMap?

The students definitely enjoyed experiencing math on the math day from a different perspective. Especially the app MCM!! The suggestion came from the students: they wanted to find new tasks for MCM on school grounds, discover them themselves and create them digitally. Now you ask in every math lesson if we can go out and do math outside 🙂

The new PDF Trailguide is here!

Today we would like to introduce our new PDF trail guide, which can be used as a paper version in addition to the smartphone app: As usual, you will find the trail guide in the menu bar under the title picture of your chosen math trail. By clicking on the PDF symbol you have three […]

Today we would like to introduce our new PDF trail guide, which can be used as a paper version in addition to the smartphone app: As usual, you will find the trail guide in the menu bar under the title picture of your chosen math trail. By clicking on the PDF symbol you have three options: Select the “Worksheet” option to download the new trail guide. There you will also find the standard version for the learners and the accompanying PDF for teachers.

In contrast to the standard version, the students receive a checkered paper for calculating. There is also space for entering the measurement results and a result field.

We wish you a lot of fun with the new PDF Trail Guide!

Here you can download the PDF version of your selected trail.

Task of the Week: Hercules Fountain

Our new Task of the Week is located in Montesarchio, an Italian town near Naples. Here, the math teacher Angela Fuggi created the task “Hercules Fountain”. In the interview, she presents her task and gives us an insight in the ERASMUS+ programme “Maths Everywhere”. How did you get to know MathCityMap? In this last […]

Our new Task of the Week is located in Montesarchio, an Italian town near Naples. Here, the math teacher Angela Fuggi created the task “Hercules Fountain”. In the interview, she presents her task and gives us an insight in the ERASMUS+ programme “Maths Everywhere”.

How did you get to know MathCityMap?

In this last school year I participated in the Erasmus project “ERASMUS + Maths Everywhere”. From 16th to 22nd February my school, the Istituto di Istruzione Superiore “E.Fermi” in Montesarchio (Benevento, Campania, Italy) hosted a group of 10 teachers and 29 students from Greece, Latvia, Spain and Turkey.

The focus of the project meeting in Montesarchio was “Math in the street”. Mathematics was viewed in close connection with the geographical area and its artistic and cultural heritage. One of the main activities was a treasure hunt and it was at this moment that MathCityMap came into play. The path created with the related activities had to be loaded onto MathCityMap and for this reason I started to use the app.

Please describe your task. How could you solve it?

My task related to the fountain located in the main square of Montesarchio. The artistic work, dating back to the second half of the 19th century, consists of a circular base with a basin, surmounted by a sculptural group of four lions and on a podium the figure of the warrior Hercules, the same mythical character who also appears on the emblem of the municipality. The task formulation is as follows:

In Umberto I square (the most famous square in Montesarchio) there is a fountain with 4 lions that surround Hercules, the Olympian god. The 4 lions are arranged at the vertices of a square on the side L. The statue of Hercules is supported by a circular base placed above the lions. Seen from above, this base is inscribed in the square with the 4 lions at the top. After measuring the distance between two consecutive lions, and therefore the side of the square, calculate the area of the circular base that supports the statue of Hercules (m²).

How could you solve it? Which is the didactic aim of this task?

The distance between two consecutive lions is the side of square L=2m. The side of the square coincides with the diameter D of the inscribed circumference, L = D, D=2m. The area of the circumference is A=π⋅(D:2)²=π⋅(2:2)²≈3,14 m²

The didactic aims were to represent, compare and analyze geometric figures and to work with them, identifying variations, invariants and relationships, above all starting from real contexts.

MCM@home in School & University Education

How can online and distance learning be organized in times of digital (university) teaching? In a GDM article, the MathCityMap team presented MCM@home as an idea for teaching mathematics during the corona pandemic. What is MCM@home about? As usual, MCM@home uses the two components of MathCityMap – the web portal and the app. While teachers […]

How can online and distance learning be organized in times of digital (university) teaching? In a GDM article, the MathCityMap team presented MCM@home as an idea for teaching mathematics during the corona pandemic.

What is MCM@home about?

As usual, MCM@home uses the two components of MathCityMap – the web portal and the app. While teachers create tasks in the web portal, students can edit them with the help of the MCM app. In doing so, they receive hints, feedback on the task and insight into a prepared sample solution. So far as usual.

But the task formats differ, of course: Now the tasks are no longer worked on on site at an interesting object outdoors, but solved from home. Consequently, all necessary information is provided in the task – or can be counted, estimated or measured on the basis of the task picture.

Why should I use MCM@home?

Many students complained about a (perceived) lack of personal feedback from the teachers during the corona lockdown. At the same time the teachers noticed that the technical equipment and the handling of technology are high barriers for the Distance Leanring. Both problems are addressed by MCM@home:

When using the Digital Classroom, teachers can view the progress of their students in real time (e-portfolio) and provide targeted feedback via chat. Of course, students can also use the chat to ask for specific help (see picture). Thus, MCM@home offers the possibility of synchronous online teaching.
Since only a smartphone is needed for MCM@home and almost all learners know how to use modern cell phones safely, technical barriers and problems are not to be expected.

Do MCM@home trails already exist?

We already presented a whole series of MCM@home trails in spring. You can find them here. Two examples of MCM@home-trails we would like to briefly outline here:

Mathe-Adler Riddles (code: 282593) for students of the 3rd & 4th grade: The trail was created for the youngest learning group of the Mathematical Gifted Young Math Eagles Frankfurt under the direction of our MCM-educator Simone Jablonski.
OSK meets MCM: Algorithms & Modeling (code: 343258) for teacher students on upper secondary level: In the course “Didactics of Upper Secondary Courses”, which is supervised by Gregor Milicic and Simon Barlovits from the MCM team, students will develop their own MCM@home trails. The trails should contain both mathematical and didactical questions. We have already prepared an example trail on Algorithms & Modeling.