Simon Barlovits | MathCityMap

MOOC: Register this week for our Online Teacher Training

* You can register until 28th March! The MOOC starts on 8th March!* Are you interested in doing outdoor mathematics with your students? Do you search for interesting and motivating ways of teaching? Do you want to get in contact with teachers all over Europe? Then our MOOC (Massive Open Online Course) on how to […]

*** You can register until 28th March! The MOOC starts on 8th March!***

Are you interested in doing outdoor mathematics with your students? Do you search for interesting and motivating ways of teaching? Do you want to get in contact with teachers all over Europe?

Then our MOOC (Massive Open Online Course) on how to create math trails with MathCityMap is the right choice for you! Register now!

With our MOOC, we intend to

introduce the system MathCityMap® for teaching mathematics outdoors with digital tools,
show you how you create your own tasks and trails in the system and honour the best tasks with badges,
share experiences on an international level.

We kindly invite all mathematics teachers to take part in this MOOC. It is part of the Erasmus+ project MaSCE³, co-funded by the European Union and therefore free of charge.

Basic information:

Start: 8th March 2021
Duration: 12 weeks
Language: English
Enrollment: http://dimamooc.unict.it/ (starts on 15th February 2021)
Certification: Certificate after completing the course (30 hours) + badges on DiMa Platform that you can put in your own wallet on http://badgr.com + an analog certification from MathCityMap

For more information please visit the project website www.masce.eu/mooc and watch our video https://youtu.be/Kc7CbZleq4A

We hope you are interested to join our MOOC and learn more about tasks, outdoor math and digital tools. It will be our pleasure to welcome you online on 8th March!

In case of questions, do not hesitate to contact your national organizing person:

Estonia: Andrus Rinde andrus.rinde@tlu.ee
France: Christian Mercat Christian.mercat@univ-lyon1.fr
Germany: Simone Jablonski jablonski@math.uni-frankfurt.de
Italy: Eugenia Taranto Eugenia.taranto@unict.it
Portugal: Elisabete Cunha elisabetecunha@ese.ipvc.pt
Spain: Claudia Lázaro lazaroclaudia@gmail.com

Information: The Massive Open Online Course (MOOC) “Task Design for Math Trails” is presented by the Erasmus+ funded MaSCE³ project.

Task of the Week: The snail’s journey

Dennis Kern, student at Goethe University Frankfurt, introduces our new assignment of the week: As part of an Intensive Study Programme for students from Europe, a group led by Dennis Kern created the task “The snail’s journey”. In the following, he gives us an insight into the European exchange program with MathCityMap. How did […]

Dennis Kern, student at Goethe University Frankfurt, introduces our new assignment of the week: As part of an Intensive Study Programme for students from Europe, a group led by Dennis Kern created the task “The snail’s journey”. In the following, he gives us an insight into the European exchange program with MathCityMap.

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

As a mathematics student at Goethe University in Frankfurt, I saw in the winter semester 2018/2019 that the course “MoMaTrE – Mobile Math Trails in Europe” was offered for the didactics part of my studies. There, students from different countries in Europe came to Frankfurt to discover and evaluate the MathCityMap project and the app together, as well as to create their own trails in groups and test them with school classes.

In addition, I used the app in another course at the university and have since even decided to write my academic term paper as part of my teaching degree on processing strategies when solving problems.

Describe your task. How can it be solved?

“The snail’s journey” we created together at the Historical Museum at Frankfurt’s Römerberg. We tried to investigate the experiences of an animal, which in a certain way can only move in two dimensions (because it must always be in contact with a surface), in our three-dimensional world. The animal in question is a snail. How does it cross a staircase? Of course, it cannot jump from step to step, but must crawl along the surface.

The task is to calculate how long this takes for this staircase. To do this, you have to measure the height and width of a step and multiply it by the number of steps (the steps are all about the same size). This gives you the distance the snail has to travel. If you then read from the task how fast a (garden) snail crawls, you can determine the required time by dividing. Finally, the result must be divided by 60, because it should be in the unit minutes.

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As part of the Intensive Study Programme, two math trails were created on the Römer in Frankfurt.

The task is part of the trail “ISP Frankfurt Lower Secondary” (Code: 131369) for grades 5/6. Also the trail “Upper Secondary ISP Frankfurt” (Code: 071368) for grades 7/8 was created.

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What are the didactic goals of the task?

As already mentioned, students are made aware of dimensional differences, because the snail is relatively small compared to the stairs and cannot fly or jump, and therefore as a snail you do not have the luxury of using the dimensional advantage here. In addition, we wanted to choose an object that is not immediately completely measured with one measurement.

There is also differentiation here, because lower-performing students are likely to make the same measurement ten times, while higher-performing ones realize that nine measurements can be saved. Then, with the conversion from centimeters to seconds, i.e. from distance to time, the handling of units from different categories is practiced, but also in one and the same unit, because you still have to convert the result from seconds to minutes.

Any other comments about MCM?

I think it’s great to finally have a really good answer to the complaint “What do we need all this for?” from learners in math classes. Editing math trails with this app picks them up where they are all the time anyway – on their smartphones – and motivates them in a way that classic math lessons probably can’t do.

Task of the Week: An off-limits flowerbed

Emanuele Amico, teacher student of the University of Catania in Italy, created our new Task of the Week. In the interview, he describes the task “Una aiuola off-limits“ [“An off-limits flowerbed”] and gives us an insight how the University of Catania [partner in the MaSCE³ project] uses MathCityMap in teacher education courses. How did […]

Emanuele Amico, teacher student of the University of Catania in Italy, created our new Task of the Week. In the interview, he describes the task “Una aiuola off-limits“ [“An off-limits flowerbed”] and gives us an insight how the University of Catania [partner in the MaSCE³ project] uses MathCityMap in teacher education courses.

How did you get to know the MathCityMap system? How do you use MathCityMap?

I have started using MathCityMap only a few months ago. I am attending a Master’s Degree course in Mathematics at the University of Catania. During the lessons of the “Mathematics Education” course the teacher presented the MathCityMap project, highlighting the theoretical framework and the methodological aspects on which it is based, the needs to which it responds, the ways in which the objectives of the project are pursued. I had the opportunity to experience MathCityMap from both sides: as a student, through participation in a math trail prepared by the teacher and proposed to the class group, but also as a creator of my own task that met the requirements for publication [see “Criteria for a good task” on our tutorial page]. In this context, taking inspiration from a traffic island in the immediate vicinity of the Department of Mathematics and Computer Science, the idea of my first (and so far only) task “An off-limits flowerbed” was born.

Describe your task. Where is it located? What is the mathematical question? How can you solve it?

The task requests the calculation of the area of a surface identified by the marker strips delimiting a traffic island. It is clear that the area can be identified as a triangle, but it is also clear that it is not possible to measure directly any of the three heights of the triangle, because of the presence of plants and shrubs in the flowerbed inside the traffic island, which make it inaccessible. Therefore, to solve the task, it is possible to use trigonometry, and in particular to generalize of the formula for calculating the area of a right-angled triangle. By measuring the lengths of two sides of the triangle with a ruler or string, and measuring the angle between them with a goniometer, the student will be able to calculate the area required. An alternative way of solving the problem can be based on the use of the formula: A = ½*a*c*sin

What are the learning objectives of this task? What could students learn while working on this task?

From the didactic point of view, the task requires for a reflection about the best and most practicable way of solution (which sometimes does not coincide with the initial idea). The task is an invitation for the student to critically compare different solving strategies, to reflect on the necessity of knowing several methods and formulas that allow to reach the same objective, since often each of them is based on different assumptions and needs, in our case on the impossibility of making an internal measurement of the geometric figure.

Do you have any other comments on MathCityMap?

I believe that MathCityMap truly offers an authentic context for learning mathematics and I am sure I will continue to use it in the near future.

19.000 tasks on the MathCityMap Web Portal!

Ceren Kaya has created the 19,000 task on the MathCityMap Web Portal! As part of the seminar “New Media in Mathematics Education” at Frankfurt Goethe University, the use of MathCityMap in the classroom is of course also discussed. For this purpose, the student teachers get to know the MathCityMap system from the learner’s point of […]

Ceren Kaya has created the 19,000 task on the MathCityMap Web Portal! As part of the seminar “New Media in Mathematics Education” at Frankfurt Goethe University, the use of MathCityMap in the classroom is of course also discussed.

For this purpose, the student teachers get to know the MathCityMap system from the learner’s point of view and work on a math trail of their choice. In addition, the use of our tool Digital Classroom is reflected upon (teachers’ perspective).

From the author’s perspective, the students create their own assignments. For this purpose, a picture of the monument of the Hassia spring in Bad Vilbel as well as the corresponding dimensions of the base were given. The student teacher Ceren Kaya then created the task “Mathematics with a magic hand”, in which the volume of the base is to be calculated.

We look forward to many more tasks on MathCityMap!

Task of the Week: The Ring

Dominik Enders, a student of the German grammer school (Gymnasium) in Bad Neustadt, created our new Task of the Week (the task “Ring”). In the interview, he explains why the students at his school create their own MCM tasks. How do you use MCM and why? I participate in a project, led by teacher […]

Dominik Enders, a student of the German grammer school (Gymnasium) in Bad Neustadt, created our new Task of the Week (the task “Ring”). In the interview, he explains why the students at his school create their own MCM tasks.

How do you use MCM and why?

I participate in a project, led by teacher Ms Gleichmann, in which we create math trails for pupils from younger classes, which you can tackle in your free time or on hiking days.

Describe your task. How can it be solved?

My problem is about a ring-shaped piece of sports equipment on a playground, of which you are supposed to find the area of the upper side. Assume that the edges of the ring are smooth, i.e. without indentations.

First you have to calculate the area of the circle up to the outer edge of the ring (tape measure/inch stick and pocket calculator are required) by determining the radius and then
calculate the area of the circle. Using the same procedure, calculate the smaller area of the circle enclosed by the inner edge of the ring. Then you only have to subtract the smaller area from the larger one to get the area of the top of the ring.

What didactic goals do you pursue with the task?

The task refers to the teaching content of the 8th grade and represents an application of the pupils’ knowledge on the topic of the area of a circle. The circle-ring is more demanding, but this can be mastered by using the area formula for two circles. The reference of mathematics in the 8th grade to a piece of sports equipment on a playground, which the pupils know from their everyday experience, should be motivating. By measuring lengths (radii), the topic of sizes from Year 5 is also addressed, as well as the importance of measuring accuracy.

Note: The task “Shoe size of the statue” was also created by a pupil of the Rhön-Gymnasium. It was the 15,000th task at MCM – great!

Online Course: Task Design for Math Trails

The Erasmus+ funded MaSCE³ project proudly presents its Massive Open Online Course (MOOC): Task Design for Math Trails. Are you interested in doing outdoor mathematics with your students? Do you search for interesting and motivating ways of teaching? Do you want to get in contact with teachers all over Europe? With our MOOC, we […]

The Erasmus+ funded MaSCE³ project proudly presents its Massive Open Online Course (MOOC): Task Design for Math Trails.

Are you interested in doing outdoor mathematics with your students? Do you search for interesting and motivating ways of teaching? Do you want to get in contact with teachers all over Europe?

With our MOOC, we intend to

introduce the system MathCityMap® for teaching mathematics outdoors with digital tools,
show you how you create your own tasks and trails in the system and honour the best tasks with badges,
share experiences on an international level.

We kindly invite all mathematics teachers to take part in this MOOC. It is part of the Erasmus+ project MaSCE³, co-funded by the European Union and therefore free of charge.

Basic information:

Start: 8th March 2021
Duration: 12 weeks
Language: English
Enrollment: http://dimamooc.unict.it/ (starts on 15th February 2021)
Certification: Certificate after completing the course (30 hours) + badges on DiMa Platform that you can put in your own wallet on http://badgr.com + an analog certification from MathCityMap

For more information please visit the project website www.masce.eu/mooc and watch our video https://youtu.be/Kc7CbZleq4A

We hope you are interested to join our MOOC and learn more about tasks, outdoor math and digital tools. It will be our pleasure to welcome you online on 8th March!

In case of questions, do not hesitate to contact your national organizing person:

Trail of the Month: Monuments of Lille

Severin Philippe, a math teacher of Lille, is the author of our current Trail of the Month. Last year, he created the math trail “Balade autour des monuments de Lille“ (Code: 361576) in order to organize a mathematical city walk through Lille for European exchance students. How do you use MathCityMap? In January 2020, I […]

Severin Philippe, a math teacher of Lille, is the author of our current Trail of the Month. Last year, he created the math trail “Balade autour des monuments de Lille“ (Code: 361576) in order to organize a mathematical city walk through Lille for European exchance students.

How do you use MathCityMap?

In January 2020, I organized the trail for my students and their German, Romanian and Italian penfriends during the Erasmus+ exchange week in France. I use MathCityMap every year with my students and one of my colleagues who teaches French – students have to look for information about Lille monuments before the trail.

Please describe your trail. Where is it placed?

I used to do this trail before and I discovered the MathCityMap application only afterwards. This city centre trail of Lille is the first one I have created so far.

Why did you create this route? Which didactic aims do you want to stimulate through this trail?

I created this trail because it’s important to me to show my students that mathematics is everywhere around us. The students tend to be more active and motivated outside the classroom.

Task of the Week: Chinese Multiplication

Our new assignment of the week shows how MathCityMap can support Distance Learning. In this interview, our student assistant Franzi Weymar explains how she uses MathCityMap in the context of the gifted education program “Junge Mathe-Adler Frankfurt”. How do you use MCM with the math eagles? The Junge Mathe-Adler Frankfurt are a project for mathematically […]

Our new assignment of the week shows how MathCityMap can support Distance Learning. In this interview, our student assistant Franzi Weymar explains how she uses MathCityMap in the context of the gifted education program “Junge Mathe-Adler Frankfurt”.

How do you use MCM with the math eagles?

The Junge Mathe-Adler Frankfurt are a project for mathematically particularly interested as well as gifted students. Normally, the students are offered the opportunity to deal with mathematical problems and topics outside of the school setting every two weeks at the Institute for Didactics of Mathematics and Computer Science at Goethe University Frankfurt. However, the pandemic situation this year required special circumstances, as the usual face-to-face sessions could not take place. Using the MCM platform, it was possible to design trails with thematically coordinated tasks for both home and outdoor use. This made it possible to offer the students a versatile and varied range of activities and to successfully implement extracurricular, mathematical support during this special time.

Describe your task. How can it be solved?

In general, the trail “Rechentricks für die Mathe-Adler” [engl.: “Calculation Tricks for the Mathe-Adler”], from which the task “Chinesische Rechenmethode_Aufgabe 1” [engl.: “Chinese Multiplication_Task 1”] is taken, deals with calculation tricks for fast multiplication.

The Chinese multiplication method is about multiplying two two-digit numbers together in a simple and quick way by visualizing them through a figure. The tens and ones digits are first mapped into corresponding numbers of slanted lines. By counting the intersections of the lines from left to right, the place values of the result can be read from the hundreds place to the ones place. In the task selected here, the students should now try to read off the result of the multiplication task shown (22-22) by counting the intersections and assigning them to the corresponding place values. The hints and the sample solution serve as help and explanation for the students to be able to solve the task or to understand it well. Previously, the Chinese multiplication was explained by means of an example task.

What can students learn here?

By working through the trail on the various calculation tricks, students can learn simple and quick procedures for solving multiplication tasks, which can also be useful to them in their everyday school life. In addition, the thematization of the cultural reference of the different arithmetic tricks promotes the examination of mathematical topics from other countries, because mathematics can be found everywhere.

To what extent can the MCM@home concept help organize homeschooling in mathematics?

Within the MCM@home concept, the Mathe-Adler team is offered the possibility of setting up a digital classroom in addition to the interactive learning setting for students. This means that at the same time as the Young Mathe-Adler session would normally take place in presence, a learning space, the so-called Digital Classroom, is activated for a selected time slot with the respective tasks. This ensures that we as the Mathe-Adler team can see the learning progress of the participating students in real time, can respond to questions and comments from the students during the session via the chat portal, and thus, despite the distance learning, there is a direct exchange with them. In addition, students always receive direct feedback on their learning success through hints and the sample solution provided. Homeschooling in mathematics can thus be organized in an appealing, versatile and simple way using the MCM@home concept.

A look back at the MCM@home Teacher Training!

Yesterday, 12 German mathematics teachers participated in our MCM@home training, which was delivered online by Matthias, Gregor and Simon. In three practical phases, the participants learned about the MCM@home idea from the perspective of the learners, the teachers and the MCM authors: Learners’ Perspective: Teachers worked on our “MCM@home professional development” trail, which can be […]

Yesterday, 12 German mathematics teachers participated in our MCM@home training, which was delivered online by Matthias, Gregor and Simon. In three practical phases, the participants learned about the MCM@home idea from the perspective of the learners, the teachers and the MCM authors:

Learners’ Perspective: Teachers worked on our “MCM@home professional development” trail, which can be accessed and worked on via the MCM app using the code 783277.
Teachers’ perspective: we introduced teachers to the Digital Classroom as an analysis and diagnostic tool for evaluating digital learning trails.
Authors’ perspective: In addition to creating three tasks, teachers also each created their own trail and shared it with a workgroup.

Conclusion: In an “instructive, straight and well organized and structured program” (comment of a participant) we presented MCM@home as one promising opportunity for Distance Learning and are looking forward to many new MCM@home tasks!

A brief look at the MCM statistics

Dear users, MathCityMap as a participatory project thrives on you using the existing tasks & mathtrails and creating your own tasks & trails. Today we would like to present you some numbers from the MathCityMap statistics: A total of 18,600 tasks have been published on the MathCityMap web portal since mid-2016 – of which nearly […]

Dear users,

MathCityMap as a participatory project thrives on you using the existing tasks & mathtrails and creating your own tasks & trails. Today we would like to present you some numbers from the MathCityMap statistics:

A total of 18,600 tasks have been published on the MathCityMap web portal since mid-2016 – of which nearly 6,000 were published in 2020. Of these, approximately 7,000 tasks were published.
2100 new users have registered with MathCityMap in 2020. In total, the MCM community now counts 6,400 members.
The most downloaded mathtrails war 2020 the trail “Forum 2020” by Christian Mercat in Marseille and the trail “[EN] Berlin Gendarmenmarkt” by Simone Jablonski. The MCM@home trail “Campo de fútbol del Racing de Santander” by Claudia Lazaro won the third place.
In total, our more than 60 MCM@home trails for distance learning in the Corona pandemic have been downloaded more than 1500 times. Fantastic!

We are already looking forward to welcoming many new members to the MCM community in 2021 and discovering new, exciting tasks all over the world.

Your MathCityMap Team Frankfurt