Simon Barlovits | MathCityMap

At the YESS10 conference last week, Simon presented his upcoming study about students’ learning progress using the MathCityMap app. Of course, the YESS10 (YERME Summer School) took place online.

The MathCityMap idea was enthusiastically received by the participants of the conference. For example, the Israeli High-school Math teacher and researcher Eli Netzer, who analyzes Hebrew educational video (Link to Eli’s website), gave us this feedback:

I believe that MathCityMap is a valuable project for extracurricular mathematics learning. The project affords profound mathematical learning since it is based on three strong aspects: social, mobile and real mathematics learning.
I am looking forward to using the project site with my students, explore and add new mathematical interesting tasks and Math trails in the Tel-Aviv city.

In addition, Eli created this really cool illustration about the theoretical framwork of MathCityMap (left picture).

Illustration of the theoretical framework of the MathCityMap idea by Eli Netzer.

The usage of MathCityMap math trails is well-tested for the revision of various learned topics. However, math trails can also be used – as so-called Theme-based Trails – for the aimed work on one specific curricular topic.

Possible topics are proportion, fractions, linear functions, parabolas and quadratic functions as well as the intercept theorem. Click here to see an example for a Theme-based Trail about stereometry.

Theme-based Trails could be used for learning mathematics at home during the Corona breakdown: According to the motto MCM@Home, we prepared several trails in five languages which could be solved from home [click here to see all MCM@Home trails]. Two of them deal with only one topic. In other words, our MathCityMap team created two Theme-based Trails for MCM@Home. One is about linear functions and suitable for 8^th graders. The other one treats quadratic functions and could be solved by 9^th grade students. We also created Theme-based Trails for students from grade 3 up to grade 6 which deal with sequences & series as well as basical combinatorics.

Have fun by working on our Theme-based Trails!

During the Corona crisis, exponential curves, e.g. infection rates, are presented daily in the media. Therefore, we want to show you one – very pleasing – exponential development about our MathCityMap system:

In April 2017, MathCityMap had around 300 registered Users, 1.000 tasks were created in the web portal. One year later MathCityMap provided 3.200 tasks for the 1.200 Users. In spring 2019, the MCM community already consisted of 2.700 users, who created 7.200 MathCityMap tasks.

Today MathCityMap has ca. 4.600 registered users. In total, 12.800 tasks and 2.050 math trails were created in many different languages all over the world. Our MCM video is now available in nine (!) different languages (click here to see the YouTube playlist).

Dear user,

MathCityMap owes this fantastic development in recent years to your interest and creativity. In the current situation, we are happy to see the creation of numerous MCM@Home tasks and trails. After the crisis, we are looking forward to many mathematical outdoor tasks.

We wish you and your families all the best. Stay healthy!
Your MathCityMap team

How learning can be organized in Europe during the Corona crisis, is one urgent question in these days.

MathCityMap provides several MCM@Home-Trails in different languages. Students can work on them at home. As usual, the learners get hints and can compare their own solution with a sample solution. The possibility to get both support and an immediate feedback, can structure students’ learning progress at home.

In the last days, those potentials of MathCityMap for learning at home were highlighted by the German institution Pädagogischer Austauschdienst (PAD) and by the initiative Land of Ideas. The first-mentioned PAD lists here several Erasmus+ projects which supply Open Educational Resources. According to the motto #beyondcrisis, the Land of Ideas promotes diverse projects which can help to handle the Corona crises.

Stay healthy!

Background information:
MathCityMap is very proud to be an award winners of the competion Land of Ideas 2019.

How does the MathCityMap app work? How it can be used by students?

To answer those questions, we shot a short video. Prof. Dr. Matthias Ludwig, head of the MathCityMap team Frankfurt, explains in the video how the app can be used. Thanks a lot to our three actors from the Junge Mathe-Adler Frankfurt!
Click here to watch the video on YouTube.

Notwithstanding, learning mathematics outdoors is hard to imagine at the moment. We want to enable learners and teachers to use the MathCityMap system for tasks which can be solved at home. Therefore, we created some MCM@Home trails.

During Corona pandemic it became apparent that learning at home has some inherent issues. Especially the lack of feedback by the teacher is a real challenge for the students. Therefore, we decided to make out MathCityMap system available for learning at home.

Following we list several trails which can be solved at home. They can be called up by students by entering the given code in the MathCityMap app.

Wie wish you a lot of fun and success!
Stay healthy!

Title	Grade	Language	Code
MCM@Home: Semarang	9	English	232525
MCM@Home: Berlin	10	English	052524
MathCity@Home 2º ESO	8	Spanish	562551
Actividades en casa	8	Spanish	062651
Campo de fútbol del Racing de Santander	9	Spanish	782526
MCM@Home: PT-Porto [7/8]	8	Portuguese	692543
MCM@Home: PT-Porto [9]	9	Portuguese	062544
MCM@Home: PT-Guimarães	12	Portuguese	022552
MCM@Home: Risnovce	8	Slovak	452545
Vratna@Home	8	Slovak	562529
Mathe-Adler: Folgen und Reihen	3	German	012519
Mathe-Adler: Kombinatorik	3	German	262518
Mathe-Adler: Zahlenrätsel	3	German	192515
MCM@Home: Lineare Funktionen	8	German	012514
MCM@Home: Quadratische Funktionen	9	German	682517
MCM@Home: Ffm a. M.	10	German	692521

Our current task of the week is located in the German Hanseatic city Lübeck. Yvonne Kaiser created the GPS task „Ein Platz für die Statue – Umkreismittelpunkt des Dreiecks“ [„A location for the statue – circumcentre of a triangle”]. In the following she answers us several questions about her task and MathCityMap. Information about the task type GPS task, which can be easily created by using the Task Wizard, can be found here.

How do you get in contact with MathCityMap?

At the moment, I participate in a further training as a mathematics teacher on secondary level. During the training, we should create a MathCityMap math trail about geometric objects.

Please describe your task. Where is it placed? What´s the topic of the task?

The task formulation is: The statue in front of the building in the Kalkbrenner street should be placed on the school yard, so that the statue has the equal distance to our three school buildings. Find the point, which has the same distance to the three marked points.

To solve this task, the students firstly have to walk to the three marked points. They recognize that those three points are the corner points of a triangle. By using tape measures and protractors the students can determine at least two perpendicular bisectors. The intersection of those two lines is the circumcentre of a triangle, which is the quested point.

Which didactic aims do you want to stimulate through this task?

The aim of the task is to practice the geometric construction of perpendicular bisectors not only on a sheet of paper in the classroom but outdoors on the school yard. As the building behind the statue will be teared down prospectively, the question raises, where the statue will be placed afterwards. Thus, the story in the task formulation awakes further motivation.

Do you have any other commentary on MathCityMap?

Until now, I’ve never used MathCityMap in class. Therefore, I’m really looking forward to try it out and to observe, how students will work on this problem.

Today is Pi Day! Therefore, we want to celebrate the mathematical constant Pi on todays 3/14. For all fans of Pi, we created a fantastic math Trail consisting of multfarious tasks about this amazing number: “Pi – An irrational good Trail”. In that trail you will find tasks about the area of an circle (segment), the volume of a cylinder and of a truncated cone as well as the number of posters on an advertisment pillar!

For all fans of Pi, we list the first 100 digits of Pi in the following:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

58209 74944 59230 78164 06286 20899 8628 034825 34211 70679

Our new Trail of the Month, the math trail “Rund um Casio” [“Around Casio”], was created by Philipp Anders during his school internship at the Casio central in Norderstedt, Germany. The journalist Claudia Blume published an article about his trail in the newspaper Hamburger Abendblatt. In the following, Philipp Anders reports about his experiences with MathCityMap.

How do you want to use MathCityMap?

We created the trail in Norderstedt to enable students to work on math tasks outside while visiting the Casio central. Thereby, the students can discover that mathematics are deeply connected to their daily life. We are very proud to publish the first math trail in Norderstedt.

How do you perceive MathCityMap as a student?

I’m an eleventh grad student at the German Gymnasium. In my opinion, MathCityMap is a welcome change to ‘classic math class’. In addition, I really enjoyed creating my own MathCityMap tasks. It was really fun. By creating my own trail, I was really impressed that one can find mathematics nearly everywhere in everyday life.

Please describe your trail. What´s the topic of the task?

Our trail consists out of four tasks. The first one asks after the volume of a stone bench. Here it is possible to measure square stone slabs. Unfortunately, those slabs aren’t congruent. Therefore, we identified their average in order to calculate the volume of the bench. The second task deals with the street which leads to the Casio central. The street has the shape of a semicircle. We want to find out their length. To calculate the length, we measure the radius of the semicircle.

The third task is about the distance between a viewpoint and the runway of Hamburg airport. To calculate this distance, the students have to count the number of periodically attached lights between the viewpoint and the runway und multiply them with the estimated distance between two of the lights. Our final task is about area calculation: The students should calculate the area of the Casio parking garage minus the area of the driveway.

Our new Task of the Week was created by Angelica Benito Sualdea and Alvaro Benito Nolla de Celis in Madrid. In the following they will answer us some questions about their task “El volumen KIO” [engl. volume of one KIO tower].

How do you get in contact with MathCityMap?

We’ve been interested in Math Trails as an educational tool for the last recent years, and we discover MathCityMap during a talk in a conference. We really liked the idea and we immediately started to think in uploading some of our trails we had already created into the platform. It took us some time, but we finally did!

Please describe your task. Where is it placed? What´s the topic of the task?

The task is placed in a characteristic square in the north of Madrid. The square is dominated by two twin towers (the Puerta de Europa Towers, commonly known as the KIO Towers) which are oblique prisms bending one to each other with an angle of 14 degrees of inclination. Since 1996, they symbolise a picturesque “entrance” to the city. From a close look it realised that the towers are surrounded by a rectangular lattice, which divides each tower in a web of black aluminium windows.

Our task asks after the total volume of one of the KIO towers. It provides information about the dimensions of one of the windows: 1.20m x 1.34m. Since its volume is the same as the volume of a straight tower with the same base, to solve the task it is only needed to calculate the number of windows covering the base and the number of windows covering the height of the tower. By counting carefully, it can be checked that there are 30 windows along the base of the tower and 86 from the ground to the top, which implies that

Vol(KIO Tower) = A*h = (30*1.20)^2*(86*1.34) = 149.351 m^3

Which didactic aims do you want to stimulate through this task?

We would like to stimulate student’s ability of solving a complex problem (in this case, calculating the volume of a skyscraper) by just knowing the information of a small element of it (the dimensions of a window of the tower). We find very useful to teach that reducing problems to simpler ones is a powerful mathematical tool. Also, since the tower is an oblique prism, it’s volume is the same as the corresponding right prism, and this task is a stimulating real life example.

Do you have any other commentary on MathCityMap?

We love the app! we will continue creating trails and encourage our students to experience and design new trails.

Author: Simon Barlovits

MathCityMap was presented at the YESS10 conference

MCM@Home: Theme-based Math Trails

MathCityMap’s exponential growth

MCM@Home: Learning at Home in Europe

Video: Learning mathematics by using the MathCityMap app?

MCM@Home: All MCM@Home trails at a glance

Task of the Week: A location for the statue

MCM celebrates the Pi Day!

Trail of the Month: Around Casio

Task of the Week: El volumen KIO