Simon Barlovits | MathCityMap

Our special for EURO 2024

It’s finally starting! On Friday, June 14, 2024, the opening match between tournament host Germany and Scotland will take place in Munich. A little later, the strong national teams from England, Spain and Portugal will also start the tournament. Group D will be particularly exciting, with the Netherlands, insider tip Austria and Poland competing alongside […]

It’s finally starting! On Friday, June 14, 2024, the opening match between tournament host Germany and Scotland will take place in Munich. A little later, the strong national teams from England, Spain and Portugal will also start the tournament. Group D will be particularly exciting, with the Netherlands, insider tip Austria and Poland competing alongside top favorites France.

Regardless of the outcome of the tournament, the European Championship will be the topic of discussion in the coming weeks! On our partner website fussballmathe.de, the team led by Prof. Dr. Matthias Ludwig (Goethe University Frankfurt) provides you with a wealth of information and materials for your mathematics lessons:

Do you know how you can (approximately) construct a soccer ball from 24 congruent kite squares?
How you can use the path rule to predict the probability of your national team reaching the round of 16?
Are you familiar with the birthday paradox and do you know what it has to do with EURO 2024?

You can find answers to these and many other questions at fussballmathe.de. You will also find our prediction of who will win the tournament.

We are looking forward to a great tournament in Germany under the motto “United by football. United in the heart of Europe”!

Share your experiences with mathematical modelling

Dear teachers, Are you interested in mathematical modelling? Or in the use of digital tools in math lessons? We are sure that you are interested in both, since you are using MathCityMap! With the linked survey we would like to find out more about your experience and use of modelling tasks in mathematics lessons. […]

Dear teachers,

Are you interested in mathematical modelling? Or in the use of digital tools in math lessons? We are sure that you are interested in both, since you are using MathCityMap!

With the linked survey we would like to find out more about your experience and use of modelling tasks in mathematics lessons. The aim of the survey is to record your needs and wishes in the area of modelling for a future project. Your feedback can contribute to the profitable further development of practical and research contributions on the topic of modelling in mathematics lessons. The time required for the survey is approx. 10-15 minutes.

Please find the survey (distributed via Google forms) in the following languages:

English (🇬🇧 🇺🇸 🇨🇦 🇦🇺 & many more): https://forms.gle/fTZjkth1H1FS43CY9
German (🇩🇪 🇦🇹 🇨🇭 🇱🇺): https://forms.gle/ShMEJCFjW6cTbmCT8
Greek (🇬🇷): https://forms.gle/1uFNzJzQHUMEv75F6
Portuguese (🇵🇹 🇧🇷): https://forms.gle/14rttZ4WndhQJse29
Swedish (🇸🇪): https://forms.gle/Eg2wLtNGQaJukxMYA
Spanish (🇪🇸 🇲🇽 🇨🇴 & many more): https://forms.gle/y8H2F3ebXUdeGvxZ7

We are looking forward to your participation up to and including February 23, 2024!

Trail of the Month: Un paseo pirata matemático

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 […]

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”.

***

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.

***

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.

MCM@home: Digital Learning Paths for Math Lessons

Dear users, we have already presented several MCM@home learning paths for distance learning within the MathCityMap app. In our new collection we have added some new learning paths. All your learners have to do is to enter the code in the free and GPDR-compliant MathCityMap app. Ready to start! We hope you enjoy working through […]

Dear users,

we have already presented several MCM@home learning paths for distance learning within the MathCityMap app. In our new collection we have added some new learning paths.

All your learners have to do is to enter the code in the free and GPDR-compliant MathCityMap app. Ready to start!

We hope you enjoy working through them!

Language	Grade	Titel	Code
English	7	[MCM@home] Pribina Square Nitra	052591
	9	Erasmus Days 2020 I	273177
	9	Erasmus Days 2020 II	583178
	9	MCM@Home: Semarang	232525
	10	[MCM@home] Berlin	052524
Spanish	8	Actividades en casa	062651
	8	El patio de mi casa es particular…	472991
	8	MathCity@Home 2º ESO	562551
	9	Campo de fútbol del Racing de Santander	782526
	9	Ruta PI de la FESPM	044282
	10	Matemáticas en el baloncesto	382998
	10	Noche Europea de los Investigadores-Noviembre 2020	893300
Italian	8	Matematica a tutto tondo per IDM 2021 – scuola secondaria di I grado	044258
	11	Matematica a tutto tondo per IDM 2021 – scuola secondaria di II grado	184244
Portuguese	8	MCM@Home: PT-Porto [7/8]	692543
	9	MCM@Home: PT-Porto [9]	062544
	9	MCM_PI_Guimaraes @ home	384252
	12	MCM@Home: PT-Guimarães	022552
Slovak	5	[MCM@home]Dubovce2	164107
	5	[MCM@home]Kombinatorika okolo prezidentského paláca v Bratislave	342691
	6	[MCM@home] Dvory nad Žitavou	292584
	7	[MCM@home] Pribinovo námestie Nitra	142598
	7	[MCM@home]Holíčsky zámok	392602
	7	[MCM@home]Senica	172870
	8	[MCM@home]Dubovce	342540
	8	[MCM@home]U včelárov	363332
	8	[MCM@home]Veľké Borové	393526
	8	Vratna@Home	562529
	9	[MCM@home] Detské ihrisko Nové Zámky	383533
	9	[MCM@home] Objemy a povrchy v lesoparku Žilina	152588
	9	[MCM@home]Skalica	692760
	9	[MCM@home]Stromy okolo rieky Nitra	174015
	10	[MCM@home]πNitra	084229
Indonesian	9	MCM@home: Matematika di Sekitar Kita	684255
German	3	Mathe-Adler Knobelaufgaben	072592
	3	Mathe-Adler Rätselspaß	282593
	3	Mathe-Adler: Folgen und Reihen	012519
	3	Mathe-Adler: Kombinatorik	262518
	3	Mathe-Adler: Zahlenrätsel	192515
	3	Rechentricks für die Mathe-Adler	073299
	4	Mathe-Adler: Neue Matherätsel	284659
	4	MathCityMap@home Fortbildung – Grundschule	353578
	6	Mathe-Adler: Knobeln für Fortgeschrittene	054098
	6	Mathe-Adler: 24 knifflige Rätsel	564802
	6	Rechnen mit Dezimalzahlen	392881
	8	MCM indoors: Mathematik-Wettbewerb 1	183150
	8	MCM indoors: Mathematik-Wettbewerb 2	073244
	8	MCM@Home: Lineare Funktionen	012514
	8	Umgang mit Termen	063152
	9	MCM@Home: Quadratische Funktionen	682517
	9	Jahresrückblick Klasse 9	792904
	9	MCM@Home LemaS Fortbildung Bremen	344106
	9	iM INTernet: Fortbildung zu MCM@home	154204
	9	MCM@home-Fortbildung	783277
	9	ZAA HS Pflichtteil 2019	354115
	9	ZAA HS Wahlteil 2018	014129
	10	ZAA HS Wahlteil 2019	144260
	10	Mathematik ist überall! Trail zum IDM 2021	134205
	10	MCM@Home: Ffm a. M.	692521
	10	Daten und Statistik	282769
	10	ZAA RS Pflichtteil 2012	464997
	10	ZAA RS Pflichtteil 2013	894693
	10	ZAA RS Pflichtteil 2019	164132
	10	ZAA RS Wahlteil 2018	124130
	10	ZAA RS Wahlteil 2019	174133

Did you also create a MCM@home learning path and would like to share it with other users? Great!

Then please write an email with…

the name of your MCM@home trail,
the related code,
the grade level,
and the language of the digital learning path

to barlovits[at]math.uni-frankfurt.de.

We would be very happy to add your contribution to the list as well!

Trail of the Month: Hünfeld City Trail

Johannes Balzer, a student teacher, has created a math trail in Hünfeld, Hesse. In the interview, he describes his “Hünfeld City Trail”. The Trail of the Month August can be accessed via the MCM app using the code 493631. How did you get to know about the MathCityMap project? I first became aware of the […]

Johannes Balzer, a student teacher, has created a math trail in Hünfeld, Hesse. In the interview, he describes his “Hünfeld City Trail”. The Trail of the Month August can be accessed via the MCM app using the code 493631.

How did you get to know about the MathCityMap project?

I first became aware of the MathCityMap project in my didactic seminar in mathematics during my practical semester. I was fascinated by the project because it offers the opportunity to do mathematics with students in their living environment.

Please describe your Mathtrail.

My math trail is special because it contains tasks with different levels of difficulty and can therefore be used, for example, in a school context to repeat important content from lower secondary school. I created the Mathtrail for my own project as part of my studies. At the same time, I would like to make a contribution so that students and people interested in mathematics perceive mathematical contexts in their personal environment. Especially in the classroom, this can counteract the often hasty judgment “I’ll never need that again later anyway”. In addition, it can be motivating for learners to leave the familiar learning setting of the classroom and deal with mathematical topics independently and playfully in their own environment.

Which task do you find particularly interesting?

The task entitled “Fountain” asks for the weight of the granite stone from which the fountain is made. For the calculation, only the part of the fountain visible above the sidewalk is to be taken into account. The problem can be solved by dividing the granite stone into a cylinder and a cylinder stump and calculating their volumes. Adding the two volumes and multiplying them by the density of the granite stone gives the weight of the fountain we are looking for.

Further comments on MCM?

Shifting the place of learning from the school classroom or home study to the outdoors opens up numerous advantages from an infectious disease perspective, especially in these times of the Corona pandemic. Therefore, now is a good time to try out the MCM app and make math lessons (even) more varied and motivating.

MOOC: Teachers’ experiences with MathCityMap

On May 30, our great MathCityMap MOOC within the Erasmus+ project MaSCE³ ended. In this article we present experiences of teachers from all over the world. Experiences with MathCityMap: In the following statements, the teachers participating in the MOOC review on the course and their made experiences with doing mathematics outdoors with their classes. […]

On May 30, our great MathCityMap MOOC within the Erasmus+ project MaSCE³ ended. In this article we present experiences of teachers from all over the world.

Experiences with MathCityMap:

In the following statements, the teachers participating in the MOOC review on the course and their made experiences with doing mathematics outdoors with their classes.

Edinéia Zarpelon (Brazil, Upper secondary level):
I proposed the trail to my high school students and a couple of friends, math professors at the university. Unfortunately, due to the pandemic, only a few student volunteers walked the trail. Still, it was a very worthwhile experience and their feedback was very positive and encouraging. I am determined to continue using MCM in my classes.

Monika Haupenthal (Germany, Upper secondary level):
Repeating old things, gaining new knowledge and having fun – all this combines outdoor learning. This is what the students in my Q11 course experienced on the trail.
Slogan: Be ready, be careful, be correct, calculate, check, correct. The slogan is derived from the first letters of the stations.

Margherita Motteran (Italia, Secondary level):
We had fun trying to solve problems in reality mathematically. In order to determine the dimensions of real objects, students used different strategies that they developed themselves. This activity stimulated their imagination and increased their math skills. We plan to use MCM often in the future.

More statements of participating teachers from all over the world can be found here.

Mathe.Entdecker the Ore Mountains

The MathCityMap team visited the beautiful Zwönitz in the Ore Mountains last week. There, Simone, Philipp, Ken and Simon looked out for numerous exciting tasks. As part of the Mathe.Entdecker project of Stiftung Rechnen, a variety of interesting and challenging math trails for all grades are being created in Zwönitz. Here is already a small […]

The MathCityMap team visited the beautiful Zwönitz in the Ore Mountains last week. There, Simone, Philipp, Ken and Simon looked out for numerous exciting tasks.

As part of the Mathe.Entdecker project of Stiftung Rechnen, a variety of interesting and challenging math trails for all grades are being created in Zwönitz.

Here is already a small foretaste of the content of the tasks:

Do you know the legend of the headless horseman?
Do you know what ‘Klöppeln’ is?
Or when the coal mine in Zwönitz was closed down?

We are already looking forward to the opening of the Mathtrails in Zwönitz!

Math outdoors with MathCityMap: An experience report

Four classes at the Kleist School Eschborn (near Frankfurt) took part in our MathCityMap study over the past three weeks. In the process, the eighth graders were able to rediscover their own schoolyard: Equipped with folding rules, measuring tapes and, of course, the MathCityMap app, the learners each worked on two math trails on the […]

Four classes at the Kleist School Eschborn (near Frankfurt) took part in our MathCityMap study over the past three weeks. In the process, the eighth graders were able to rediscover their own schoolyard:

Equipped with folding rules, measuring tapes and, of course, the MathCityMap app, the learners each worked on two math trails on the topic of linear functions in groups of three. Among other things, they determined the slope of the skateboard ramp or the function term of the handrail.

Student Alea Henrich (G8b) summarizes her experience with MathCityMap as follows: “Personally, I really enjoyed the project! It was great to learn mathematics in a new way. Of course, the app can’t replace a classroom, but I think it’s great as a supplement to normal lessons. In addition, I see the app as helpful and more memorable, because you have your tasks as a real building, bench, square, etc. in front of you and can then check your solutions on your smartphone and get tips directly if necessary.”

Alea also offers a tip for the summer vacations: “If you want to, try the free app MathCityMap during your vacations – not only for the repetition of what you learned this year or last year, but also get to know places in your environment with a math trail.”

You can read Alea Henrich’s complete report here on the website of the Heinrich-von-Kleist-Schule Eschborn.

The MathCityMap Task Formats

The MathCityMap team has recently developed several new task formats! By now, MathCityMap offers nine task formats plus the possibility to create subtasks. All task formats are shortly presented in the following. Furthermore, we make available an Example Trail including all task formats. This trail can be viewed in the web browser here respectively by […]

The MathCityMap team has recently developed several new task formats! By now, MathCityMap offers nine task formats plus the possibility to create subtasks. All task formats are shortly presented in the following.

Furthermore, we make available an Example Trail including all task formats. This trail can be viewed in the web browser here respectively by the code 065522 in the MathCityMap app.

The interval is the ‘classic’ MathCityMap task format. It is to be used whenever measurements are necessary, e.g., to determine a length, an area or a volume.

Interval

The format Exact Value can be used for counting tasks or for combinatorial problems: How many windows do you spot on the house wall? How many possibilities do I have to lock my bike at this bicycle stand?

Exact Value

To raise more than one questions on a measuring activity, the task format Vector (Interval) can be used. Example: Determine the length, width and height of the pictured cuboid. Also, the task format can be applied for questions concerning spatial geometry.

Vector (Interval)

NEW TASK FORMAT!

Analogously, we offer the Vector (Exact Value) format which can be used to set several counting tasks or combinatorial problems at once.

Vector (Exact Value)

NEW TASK FORMAT!

If several numbers are the expected solution in a task, but the order in which the numbers are to be entered is not important, the Set task format can be used. In the app, only the numbers are entered into input fields. An example of a Set task can be found in the math trail above mentioned.

Set

NEW TASK FORMAT!

The Information Station is a task format without an input field in the app. It is implemented to offer important facts, e.g., to historical buildings, persons or realities during the math trail.

Information Station

NEW TASK FORMAT!

Another new task format is Fill In The Blanks: Within this format, gap texts can be easily worked on outside the classroom, e.g., to analyse objects outdoors in technical language, to deal with data from information boards or to raise questions on data of historical realities.
Note: Please use the “strict” mode if a number should be filled into the gap.

Fill In The Blanks

NEW TASK FORMAT!

Also, available data can be queried within the Multiple Choice format like in a quiz. Thereby, at least two answer options must be given, of which at least one is correct.

Multiple Choice

The GPS Task format allows users to create tasks in which the students have to find a pre-defined position (e.g., the middle of the given points) or position themselves in a pre-defined figure (e.g., building a equilateral triangle)
Note: This type of task works best in more rural areas since the GPS signal is often too weak in cities.

GPS Task

Lastly, we offer the possibility to pre-structure more complex tasks by dividing them up into optionally or mandatory Subtasks. One example for using Subtasks is given in the upper mentioned trail.

Subtask

NEW TASK FORMAT!

MathCityMap in Portuguese Teacher Education

Two students of the Master degree course in Mathematics and Sciences Education of Instituto Politécnico de Viana do Castelo, Antony Lopes and Liliana Francisco, respectively under the supervision of Ana Barbosa and Isabel Vale, have focused their thesis in the use of MathCityMap. The work developed by Antony Lopes aimed to understand the way 6th […]

Two students of the Master degree course in Mathematics and Sciences Education of Instituto Politécnico de Viana do Castelo, Antony Lopes and Liliana Francisco, respectively under the supervision of Ana Barbosa and Isabel Vale, have focused their thesis in the use of MathCityMap.

The work developed by Antony Lopes aimed to understand the way 6^th grade students apply Geometry concepts in a math trail using MathCityMap. Although it was not possible to collect data with students due to COVID-19, the published report grounds and explains all the methodological options and also presents all the data collection techniques, including the procedures that led to the trail submission in MCM. The author also presents a theoretical discussion of the expectations concerning the results. The report can be found here.

The work of Liliana Francisco is still under development and aims to understand how 6^th grade students solve tasks, within the scope of isometries, designed to be applied outside the classroom through a math trail with MathCityMap. This study is being conducted with 23 students and data is being collected, resorting to observation, documents (task solutions), questionnaires, interviews and photographs. The report will be published soon.