General – Page 4 – MathCityMap

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.

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.

MCM during the pandemic: teaching experiment on theme-based trails in an Italian upper secondary school

A master thesis on MathCityMap and its novelties At the Department of Mathematics and Computer Science of the University of Catania, the student of the Master degree course in Mathematics Emanuele Amico, under the supervision of Professor Eugenia Taranto, is working on his Master thesis. This is an experimental thesis whose aim is to analyse […]

A master thesis on MathCityMap and its novelties

At the Department of Mathematics and Computer Science of the University of Catania, the student of the Master degree course in Mathematics Emanuele Amico, under the supervision of Professor Eugenia Taranto, is working on his Master thesis. This is an experimental thesis whose aim is to analyse the impact of using MathCityMap on students’ learning in terms of problem solving and problem posing skills. The teaching experiment, which took place in May 2021, involved a grade 9 class at the Liceo Scientifico “A. Volta” in Caltanissetta (Sicily). Due to the emergency situation caused by the pandemic, the experimentation took place in indoor mode, using the MCM@home and Digital Classroom functionalities.

For more details, read the full report (in Italian) here.

MCM@home in Slovakia

Silvia Haringova of the Constantine the Philosopher university in Nitra presented the MathCityMap@home concept in online teacher trainings for around 700 teachers. Furthermore, she conducted lessons with more than 150 lower- and upper-secondary school students. In the interview, Silvia looks back on her student time and describes the teacher training concept. Looking back on […]

Silvia Haringova of the Constantine the Philosopher university in Nitra presented the MathCityMap@home concept in online teacher trainings for around 700 teachers. Furthermore, she conducted lessons with more than 150 lower- and upper-secondary school students. In the interview, Silvia looks back on her student time and describes the teacher training concept.

Looking back on student time: Participating in a course about MathCityMap

During the Intensive study programme (ISP) organized within the MoMaTrE project, which I participated in March 2018 at the Goethe-University in Frankfurt, I was taught everything necessary to create and implement my own trails in Slovakia.

Based on my participation in the ISP I chose a diploma thesis aiming at math trails. I describe the principles and specifics of the designing tasks for MathCityMap and my goal is also to create several math trails. I also deal with trails within the project Comenius Institute, an annual educational programme designed for pre-service, beginning and in-service teachers as well as heads of schools organized by the non-governmental non-profit organization Živica. Each year, 20 teachers have the opportunity to participate in this programme. The main goal of my project is to increase awareness of math trails in primary and secondary schools among various teaching communities throughout whole Slovakia.

Being a lecturer: Disseminating the MCM@home concept

With the project, I tried to motivate my classmates at the university and involve them in the design and implementation of math trails. I created a Facebook page (click here), where I regularly publish various articles trying to promote this new way of teaching mathematics outdoors using mobile technologies. In cooperation with the Comenius Institute, we organized a webinar about trails. The webinar was held online and was attended by more than 700 teachers of various subjects. During the students’ practice, I conducted 9 [MCM@home] trails with more than 150 lower- and upper-secondary school pupils.

A list with several MCM@home trails from all over the world can be found here:

Collection of MCM@home Trails

Our special on EURO 2021: Football in math lessons

It’s finally starting! On Friday, June 11, 2021, the opening match between Italy and Turkey will take place in Rome. A short time later, the strong national teams from Belgium, England and Spain will also start the tournament. Group F, in which top favorite France will be challenged by Germany and Portugal, will be particularly […]

It’s finally starting! On Friday, June 11, 2021, the opening match between Italy and Turkey will take place in Rome. A short time later, the strong national teams from Belgium, England and Spain will also start the tournament. Group F, in which top favorite France will be challenged by Germany and Portugal, will be particularly explosive.

Regardless of the outcome of the tournament, the European Championship will be the hot topic in the upcoming weeks! On our partner site fussballmathe.de, the team around Prof. Dr. Matthias Ludwig (Goethe University Frankfurt) provides you with a variety of information and materials for your mathematics lessons:

Do you know how to (approximately) make a football out of 24 congruent kite quadrilaterals?
Or how you can use the path rule to predict the probability of Germany making it to the round of 16?
Do you know the birthday paradox and what it has to do with the EURO 2021?

You can find material for these and many other questions at fussballmathe.de. In addition, you will find there our prediction who will be the winner of the tournament…

MOOC: MathCityMap all over the world

Yesterday the great MathCityMap MOOC within the Erasmus+ project MaSCE³ ended. In this article we present experiences of teachers. And of course, we also want to thank all participants and in particular all organizers of the MOOC. Experiences with MathCityMap: In the following statements, the teachers participating in the MOOC review on the course […]

Yesterday the great MathCityMap MOOC within the Erasmus+ project MaSCE³ ended. In this article we present experiences of teachers. And of course, we also want to thank all participants and in particular all organizers of the MOOC.

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.

Veronica Sambataro (United Kingdom, Secondary level):
I attended this course as a postgraduate student and a future teacher. For testing the math trail, I decided to involve my households – and it was very fun. Some of them told me that it was really fun discovered new formulas and enjoying with math! I will use MathCityMap for sure when I will be a teacher a day!!

Gina Patricia Paz Huamán (Peru, University level):
Today I applied with a group of students of Higher Education the “Mathematical Route in Pueblo Libre” that I prepared with the MathCityMap application. This experience has been positively valued by them who consider that it will be very motivating to use it with the students of Basic Education for whom the activity was prepared. It has been very exciting to use the digital classroom in this activity, to see how the groups are formed, the progress of each one of them and how they solve the challenges posed.

Margherita Motteran (Italia, Secondary level):
Today 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.

Thanks a lot!

The entire MathCityMap team Frankfurt would like to thank the main organisers of the MOOC. Within the MaSCE³ project, the MOOC was prepared, guided and accompanied by:

Eugenia Taranto (Italy), Christian Mercat (France), Elisabete Cunha (Portugal), Claudia Lázaro (Spain), Andrus Rinde (Estonia) and Simone Jablonski (Germany).

Thank you very much for your commitment!

Exam preparation with MCM@home

Norbert Goeth participated in our MathCityMap training series in cooperation with the Hessian Ministry of Education. In the interview, the teacher tells us about the use of MathCityMap for exam preparation. Where do you personally see the added value of MCM@home?I see the added value in the successive streamlining of the collection of the […]

Norbert Goeth participated in our MathCityMap training series in cooperation with the Hessian Ministry of Education. In the interview, the teacher tells us about the use of MathCityMap for exam preparation.

Where do you personally see the added value of MCM@home?
I see the added value in the successive streamlining of the collection of the previous year’s ZAA tasks, if these are provided with a schedule with the possibility of control. At the beginning of the year, the STARK booklets (containing the final exams of the last years) are purchased – and initially disappear unread. Beginning in late summer, teachers point out the need for these preparations (in addition to normal instruction), but the response is hesitant and restrained. I think the MCM@home paths for these assignments are a great way to give teachers a tool to easily see which students are working on the assignments, where they are struggling, and where you need to increase the pressure on solution commitment.

What did your learners report back to you?
I told my class 10 about my training and the tool. Yes, the idea is well received and depending on their learning attitude, they have emphasized more the supporting or controlling options in their assessment.

What MCM@home digital learning paths have you created yourself?
ZAA tasks from the years that will not be printed by STARK publisher in the current books in the future (ZAA-2012-RS and ZAA-2013-RS, each mandatory tasks), currently I am dealing with the elective tasks.

Searching for more information?
An overview of all MCM@home learning paths can be found here.

How did the creation of your trails work out?
Pretty well. The program is largely self-explanatory, though the pitfalls are always in the details. Overall, creating tasks, if you want to do it well, is time-consuming. But that’s where MCM is no different than anything else, because the effort isn’t on MCM.

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”.

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.