Trail of the Month | MathCityMap

The Trail of the Month for April was created at a picturesque location on Lake Constance, on the island of the city of Lindau in Bavaria. Together with his P-Seminar, a special type of course in the Bavarian gymnasiale Oberstufe, teacher Jan Neuendorf created the “Lindau Island Mathtrail” (Lindauer Insel Mathtrail), which is available in the MCM app under the code 376526 and in the MathCityMap web portal here.

Along the harbor and through lindau’s old town, the trail winds its way across the entire island and integrates various sights of the city, making it very interesting not only mathematically, but also architecturally and historically. The trail contains a total of ten tasks that focus in particular on the content of the eighth and ninth grades.

An interview about the background of the trail is given by Jan Neuendorf in the following interview:

How did you come across the MathCityMap project?

I first heard about the project from colleagues who had spoken about it in various training courses. Afterwards, I found out more about the MathCityMap project on the Internet. This gave me the idea to offer a P-seminar in mathematics, which had the goal to develop a Math-Trail on the island of Lindau and to make it accessible to interested people via the MathCityMap-App. The P-Seminar is a special feature of the gymnasiale Oberstufe in Bavaria. It supports students in their study and career orientation and focuses on the planning and implementation of a subject-related project.

Where is your trail located? What is special about your trail?

The trail is located on the island of Lindau in Lake Constance. With its historic old town, narrow streets, medieval buildings and picturesque harbor with lighthouse, lion and mountain view, the island provides a unique backdrop for the elaborate math trail. Therefore, it was also an exciting challenge to discover and develop suitable mathematical tasks on objects on the island. Thus, the trail combines sightseeing with math activities, which is an exciting combination.

How do you use MCM and why?

So far, MCM has served as a guiding idea for the P-Seminar in mathematics. The goal of the participating students was to plan and implement a math trail on the island of Lindau. In the future, the trail will be used in grades 9 and 10 as a subject outside the classroom or as part of our project week. It is certainly also desirable that other schools in the Lindau area will use the trail for classroom excursions and class action days.

Describe your favorite task on the trail. How can it be solved?

My favorite task of the trail is the task to the Mangturm (Mangtower) at the Lindau harbor. On the one hand, the task is to be solved directly at the harbor in the heart of Lindau, which gives the task an exposed place within the trail. On the other hand, it is a suitable task from the field of geometry, in which mathematics is applied in practice and in which geometry as the science of measurement can be understood in its most original form.
The task is solved with the ray theorem. The fascinating thing is that this theorem can be used to determine lengths that are difficult or impossible to measure.
If you form the 2m long meter stick into an isosceles, right-angled triangle and place it on the harbor railing in such a way that you can aim at the top of the tower via the tip of the leg of the meter stick that is far from your eye, you are not far from the solution. After you have measured the horizontal distance of your location to the Mangturm with the help of the railing elements, you add the height of the railing to this quantity and thus obtain the height of the tower.

The term mathematical walk could hardly be more apt than for the trail of the month March. This one comes from the largest city in Switzerland, Zurich. Here, Roland Wiss, a member of the school management and executive board of LIPSCHULE Zurich, has created the trail “Counting, measuring, calculating and estimating between Sechseläutenplatz and the city border” (Zählen, Messen, Berechnen und Schätzen zwischen Sechseläutenplatz und der Stadtgrenze), which can be accessed in the MCM app under the code 257781 and is available on the MathCityMap web portal here.

The trail stretches over a total length of 2.8 km and, as the title suggests, leads from the centrally located Sechsläuteplatz along a walking path alongside Lake Zurich to the city border. A total of twelve interesting mathematical tasks with a wide variety of content can be found along the route, which not only offers a chance to marvel at the beautiful nature surrounding the city of Zurich. What most of them have in common, however, is that there seems to be too little data to solve them.

Roland Wiss explains among other things the concept of the trail in more detail in the following interview:

How did you come across the MathCityMap project?

I am always interested in different ways to show my students the beauty and excitement of mathematics. This includes mathematical problems from everyday life and especially outside the classroom. For this reason, I regularly search the internet for exciting math projects. In doing so, I came across the MathCityMap project, which immediately appealed to me.

Where is your trail located? What is special about your trail?

I walk every morning in Zurich from Stadelhofen station to Lipschule and since I am a big fan of Fermi questions, I had the idea to design this trail along my way to work. I call a Fermi question an estimation about a problem, where the students seem to have no or insufficiently accurate data at a first superficial glance. However, when their explorer and detective eyes are awakened, students notice that they can decompose the question into several sub-problems for which they can find exact or approximate solutions. Combining and completing the partial results, they arrive at an overall result that is very close to the actual value. My students like to deal with Fermi questions and they learn a lot. So it was obvious for me to create a trail on the topic “Counting, Measuring, Calculating and Estimating”. Since the Lipschule is a comprehensive school with different age groups, I wanted to create a trail that contains tasks for many age groups. In addition, there is the wonderful location at the lake and the possibility to extend the trail to a day trip with (at least in summer) a swim in Lake Zurich.

How do you use MCM and why?

We regularly have a mathematics project week. One workshop of this week is called “Mathematics outside” and has the following content: “Mathematics is everywhere. We explore the surroundings from Sechseläutenplatz to Lipschule with a mathematical eye”. The MathCityMap app is perfect for this. I especially like the fact that the students are outside thanks to the app and solve many tasks in teamwork. They are also actively involved and have to solve the tasks and problems using appropriate tools. The students learn not only mathematics, but also teamwork and the use of clever solution and organization strategies.

Describe your favorite task on the trail. How can it be solved?

My favorite task is called “Area of a hexagon” because it can be solved in different ways and by different ages. On the one hand, the older students can use the area formula for the hexagon 3*√3*s*s/2 and count the paving stones along the sides to determine the number. On the other side, there are hexagons of equal area in the square, which are filled with paving stones. Younger students, who do not yet know the area formula, can determine the number in a clever way by counting and estimating. Since the hexagons filled with pavers all have similar patterns, the students can also think about the method the paving contractor used to lay out the pavers. It is therefore a place and a task that can stimulate a variety of thinking processes.

The Mathtrail of the month February comes from Indonesia, more precisely from the city of Makassar on the island of Sulawesi. Here, teacher Jamaluddin Tahuddin created the trail “Math Trail di Fort Rotterdam Makassar” a special math trail that leads through the historic fort of the city of Makassar with a total of six tasks. The trail can be accessed on the web portal and in the app under the code 157539.

You can find a short interview with the creator of the trail below. Have fun reading it!

How did you come across the MathCityMap project?

Every year, students go on a study tour in Fort Rotterdam. They work on a project assignment to make a report given by the Indonesian teacher. After attending training on how to strengthen numeracy skills through the MathCityMap application, I was interested in making a Math Trail in Fort Rotterdam. In addition to doing historical tours, students will also be able to do numeracy activities at Fort Rotterdam. Thus, this activity can involve many subjects, including Mathematics, Indonesian, English, History, and Science.

Please describe your Mathtrail.

Fort Rotterdam is one of the historical places in the city of Makassar. Everyone including students in Makassar know this place. So far, they have only seen Fort Rotterdam from a historical perspective. But now they will also be able to look at Fort Rotterdam from a numeracy point of view. Inside the fort, I’ve selected several objects that can serve as numeric contexts. So that people who visit Fort Rotterdam will not only do historical tours, but can also do numeracy tours.

How do you use MCM and why?

Students can use the MathCityMap application for activities to practice numeracy skills outside the classroom.
Students are organized into several groups and each group consists of 3-4 students. Each group only needs 1 smartphone so that all students can be involved even though not all have smartphones. The slow speed internet connection is also not a problem because every math trail that students will complete can be downloaded first so that it can be used offline. Teachers can also know how students solve each of the numeracy problems through a worksheet which can be downloaded through the MCM application.

Describe your favorite task of the trail. How can it be solved?

My favorite trail task is “Gerbang Gereja“ on the Math Trail in Fort Rotterdam City of Makassar. In addition to its unique shape, at the Church Gate students can also learn from the context of numeracy. In this task, students will calculate the maximum height of a box car that will carry cultural heritage objects into the building, the car has a width of 167 cm. To solve this problem, students must know the relationship between the radius of the circle, the slope, and the distance of the circle from the center of the circle.
Where the width of the box car is the minimum segment length and the distance from the center of the circle is the maximum height of the box car. So, to solve it, students must measure the width of the gate which is the diameter of the semicircular gate first.

The Trail of the Month January comes from the second largest city in the German state of Bavaria. Frederic Fell, a student of secondary school teaching, created the trail “Mathe-Rundweg an der Zeppelintribüne” in Nuremberg, which can be accessed in the MCM app under the code 273993. It is available in the web portal here.

The trail, which consists of a total of nine tasks, was created in the direct vicinity of the Nuremberg stadium, the home of 1. FC Nuremberg (Der Club), partly on the former Nazi Party Rally Grounds. In addition to the mathematics tasks, you can also explore historical topics.

Here you can find a short interview with Frederic Fell:

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

I am studying to become a secondary school teacher with the subject combination mathematics / physics at the Friedrich-Alexander-Universität Erlangen-Nürnberg. I am currently writing my admission thesis (similar to a bachelor thesis, but for student teachers) in the didactics of mathematics. My supervisor Stephanie Gleich offered the topic “MathCityMap” and I was immediately interested. This admission thesis is, among other things, about extracurricular learning places, but also about modeling. The practical part of the work is my trail.

Where is your trail located? What is special about your trail?

My trail is located in Nuremberg on the former Reichsparteitagsgelände, which was used as a place for propaganda during Nazi times. Today the area is used in many different ways, as a recreation area, as a DTM race track or as a venue for the “Rock im Park” festival.
The special thing about the trail is that the relics from the Nazi era are used for better purposes, like a math trail. Of course the Reichsparteitagsgelände is a place of history, but I think it’s great how you can also learn something about math in such a place. The trail is set for ninth grade students at the Realschule. My intention is that the trail can be used as a field trip at the end of ninth grade. So we hike, do a little math and afterwards we can have a picnic at the Dutzendteich.

Briefly describe one of your tasks. How can it be solved?

I would like to describe the task “Rainbow” in more detail. 8 pillars were painted on the grandstand. You have to determine the painted area. One pillar is too big to measure. With the help of the picture you can see that 4 rectangular plates were painted on each pillar. The area of a rectangular plate can be determined. This must be taken times 4 to determine the area of a pillar and this in turn times 8 to calculate the total area. This task is varied and requires a bit of “thinking around corners”. The photographer has provided me with the rights for the pictures used in this task.

Do you have any other comments about MCM?

MCM is a really great project and I’m glad I was able to work with it as part of my graduate thesis. When I’m a trained teacher, I’ll definitely incorporate math trails like this into my teaching.

The trail of the month December comes from the Czech Republic. Adéla Pantělejevová created the trail named “Olomouc centrum (jednodušší)” in the city center of Olomouc, the sixth largest city in the Czech Republic in the east of the country, while working on her thesis at Palacký University Olomouc. The trail can be accessed via the MCM app using the code 795612. It is available on the web portal here.

In total there are seven tasks, designed directly on the prominent buildings of the old town. So while walking the trail, you also get to know the most beautiful sides of Olomouc. You will find a short interview with Adéla on the trail and her experiences with MathCityMap below. Enjoy reading!

How did you come across the MathCityMap project?

Once our wonderful teacher Dr. Lenka Juklová arranged a lecture by Dr. Soňa Čeretková, which was about MCM (Soňa Čeretková is working on the MCM project in Slovakia) and I became very interested in this topic. During the lecture we had a chance to do a mathtrail around the faculty and I thought it would make a great topic for my thesis, since it had not been done in the Czech Republic yet. Dr. Juklová even suggested this topic to me so I am currently working on it under the supervision of Dr. Patrik Peška at the Palacký University Olomouc.

Please describe your Mathtrail.

This particular trail is designed mainly for primary school children. It was created as part of my thesis. Most of the existing trails are designed for high schoolers, however, I wanted to create a trail for younger learners too. It is very playful, fun, and intends to show how math can be connected to other school subjects and be found anywhere, in this case in the Upper Square in Olomouc. Although my studies are focused mainly on high school mathematics, I tutor also younger children and since several of them live around the center of Olmouc I wanted them to enjoy maths through MathCityMap aswell. I also implemented the pirate theme in my lessons, which should make the whole trail more interesting for children.

How do you use MCM and why?

My goal is to show teachers how to make mathematics interesting and fun, how to use the modern technology which is available for us, and moreover to show students that mobile phones and the internet don’t have to be used only for playing games or buying clothes online, but that they can be also helpful for looking up information, educating themselves, etc.. Furthermore, I recommended these trails to my friends and classmates, who are mostly secondary school teachers and high school teachers. Some of them had already started using it in their classes or it served them as a template for creating their own trails. One of my friends is now using MCM even in his physics classes.

My friend and I are currently trying to collect some task ideas for creating a template, which could be used in a lot of different places. What we have prepared so far can be soon used in other cities. I’m very much looking forward to it.

Describe your favorite task of the trail. How can it be solved and what can students learn from it?

My favourite task of this trail is definitely “Orloj”. It is a task with several sub-tasks, in which you have to understand the meaning of each dial and determine the number and type of different ornaments.. Students get to practice hours, days, weeks, months of the year, zodiac signs, as well as orientation and location, basic arithmetic along with characters and occupations. This task is not just about mathematics, rather it also tests general knowledge of third grade students. In the task students have to choose their answers from a list of options, add numbers and names to blank spaces, etc.. So it is not like other tasks where their answers have to fall within a certain interval.

November’s Trail of the Month comes from the capital of the German state of Lower Saxony. The trainee teacher Franziska Hormann created the trail “Circles and bodies on the trail in Hanover”, which can be accessed in the MCM app under the code 386349. It is available in the web portal here.

On this mathtrail you will find a total of nine tasks implemented on the buildings and artistic sculptures of Hanover’s city center.

How did you come across the MathCityMap project?

As a former student at Goethe University, I was already able to get to know MCM during my studies in the module Upper School Didactics, where I also designed my first tasks. In Frankfurt, the app is widely used, so I was surprised that in Hanover, where I am currently completing my traineeship, there are only a few MCM trails and the project was hardly known among teachers or at our study seminar. However, my interest in sharing and spreading it in my home region was correspondingly great, especially since the beautiful old town of Hanover offers ample opportunities to apply mathematics…

Please describe your Mathtrail.

The Mathtrail is specially designed for the topic of circle and solid calculation, which is taught in the 10th grade in Lower Saxony. On a circular route through the old town past well-known places such as the New Town Hall, the Market Hall and Church or the Ballhof, students can apply their knowledge of the circumference and area of circles, surface area and volume of cylinders and spheres and test it on authentic problems.
The trail is particularly suitable at the end of the unit, when all the formulas are already known and the constructed tasks from the textbook have had their day. I myself tried it out as part of a project day with a 10th grade class, and since the topic is usually taught at the end of the school year in Lower Saxony, such a project day before the vacations is particularly worthwhile, on the one hand to do mathematics in the world around us at an extracurricular learning site, and on the other hand to offer an alternative to the annual movie watching in the last few weeks.

How do you use MCM and why?

Since I am still at the beginning of my professional life, I have so far only used MCM for this specific trail in the said 10th grade. In my opinion, MCM is especially (but not only) suitable for geometry topics, in which I will gladly use it again in other grades. On the one hand, as a teacher myself, it is a pleasure to design the tasks and to rediscover old familiar things with a different view. In addition, the possibility of publishing the paths means that other teachers can also benefit from the efforts. On the other hand, I feel it is important to experience mathematics in real-life contexts that are as authentic as possible, to become active myself and to have to puzzle. MCM can make all this possible with well-set tasks, where the groups have to coordinate and find heuristic strategies for calculating solutions together, which also promotes their ability to work in a team.
Last but not least, out-of-school learning venues are rare in the subject of mathematics. MCM makes it possible, regardless of the proximity to facilities such as the Mathematikum in Giessen, etc., to design an extracurricular learning venue that can be adapted to one’s own lessons with manageable effort and thus make mathematics experienceable in a different way.

Describe your favorite task of the trail. How can it be solved?

I believe that all tasks have their charm and sometimes require less and sometimes more modeling competence. I like the starting task of the trail with the Hase fountain, for example, because in the beautiful brick backdrop between the Old Town Hall and the Market Church, you first have to perceive this historic structure simplified as a cylinder and then come to the determination of the water volume via various paths, the circumference of the basin or the partly estimated radius, whereby the correct unit must not be neglected at the end. In this task you also have to have the courage to hold the folding rule properly in the water for once.
I like tasks where the solution is not immediately obvious and where you have to fiddle a bit without increasing frustration. That’s why the solution interval should not be too small, which I learned myself during the test.

The trail of the month September comes from Switzerland. Here, primary school teacher Roger Pellaton created the “Skulpturenweg Leywald Reinach” which can be accessed via MCM app using the code 384906. It is available on the web portal here.

There are a total of twelve tasks on this math trail, most of which were designed directly on the trail’s magnificent wooden sculptures.

How did you come across the MathCityMap project?

I’ve worked with Actionbound before, and even earlier with GeoCaching. This year, students from the FHNW (University of Applied Sciences Northwestern Switzerland) are on a year-long internship at our school. The students were given the task of digitally implementing map work in a 6th grade class. From the FH they brought the hint MathCityMap, which was unknown to me until then, and they wanted to know from me what other alternatives there were. After a bit of exchange and joint evaluation, we decided to implement the project with MathCityMap. MCM was new to all of us, so we experimented a bit together and immediately documented our experiences for the rest of the college, so that other teachers could benefit from the preliminary work already done.

Please describe your Mathtrail.

The sculpture trail in Reinach is well-known all around. Most of the children already knew it when I tried this trail with them. They were already there in kindergarten, most likely in junior high school, and with their parents often as well. Nevertheless, they see it with completely different eyes when they have to solve a very specific math problem at a certain sculpture. In the middle of the forest! The device in their hand gives them additional feedback as to whether they have solved the task correctly. You can’t get any further away from the classroom than being in the forest, surrounded by artistically carved wooden figures that exude a peculiar calm and fascination. What’s more, with a trail like this, you’re not only carrying the math out of the classroom, you’re also carrying it right into the parents’ home when the next walk-through involves the parents.

How do you use MCM and why?

At our school, all middle school students (4th/5th/6th grades) are equipped with iPads in ascending order. We started with the 4th graders this year, and the new 4th graders will join them after the summer vacations. As a class teacher of such a class, I also accompany the entire IT project at our school on the pedagogical side. This is called PICTS (Pedagogical IT Support). As PICTS, one of my tasks is to show the teachers ways in which they can use the iPads of their class profitably in the classroom. So I visualize such tools and projects on an ongoing basis, trying out much of these in my own class first, then bringing them back to my colleagues.

Since I consider self-directed interpretation of assignments and tasks to be one of the most central key competencies of modern life, I am grateful for tools such as MCM that allow my students to have experiences that are highly effective for learning in a protected setting. The fact that Corona, Lockdown, and distance learning have given IT a noticeable boost on the one hand is great, but on the other hand this crises shrinks the world of children to an unpleasantly small 13 inches, which does not make me happy. MCM starts exactly there and puts math tasks outside the classroom into a new context. I liked that, and unsurprisingly, so did my students.

Describe your favorite task of the trail. How can this be solved?

I don’t really have a “favorite” task. I generally like tasks that hold something surprising, or open a previously closed door. The Snow White task, for example, where the children have to put themselves in the dwarves’ shoes and figure out which dwarf can see which other dwarf or not, that’s one such task. Or when, during the task with the “Gluggerbahn” (Glugger = Swiss German for marble), they suddenly find out what the piece of string is for that they were supposed to stuff into their pockets at the beginning of the trail. Sometimes, as a teacher, you are lucky enough to be present at such moments.

In this interview with Sona Ceretkova, we focus on the learning path “[MCM@home]Veľké Borové” which is awarded as MathCityMap Trail of the Month in April 2021! The first part of the interview can be seen here. The second part is available here.

Collection of MCM@home Trails:

Click here to get an overview about all digital learning paths which were created by MathCityMap partners

Dear Sona, do you use MCM or MCM@home regularly in university courses?

Future mathematics teachers have a trail included as a project within the subject Methods of Solving Mathematical Problems. The students get a complex understanding of the methodology of outdoor mathematics teaching as well as the MCM application and MCM portal. Their task is to create their own trail in their place of residence, with at least five tasks.

The trail is a part of five mathematical projects within one semester and it`s evaluation is included in the overall course grade. We are planning to prepare methodological guidance for students on the trail “peer assessment” with summative assessment principles.

Describe one of your tasks. How can it be solved? What can students learn by solving this task?

Bus stop: The bus stop at the end of the village of Veľké Borové is called Škrlák. Here the bus turns and goes back. For how many hours will there be no bus departure from the village of Veľké Borové?

Solving the problem is not difficult, it does not require special mathematical knowledge. It is important to study the timetable carefully. In some literature, the ability to read, interpret and orient oneself correctly in documents, in various schemes and plans or maps is called: document literacy. When reading a timetable, document literacy is linked to mathematical competencies that every person needs in everyday life.

Many people do not realize that when looking for answers to questions about time, about time orientation, when counting time periods, etc., they use a number system based on the number 60. In addition, in the timetable, which is located at the bus stop, there is not only time data, but other data, that provides the possibility to create tasks in a real context. In the diagram, we can read the codes of the days of the week on which the bus operates, the dates during the year when the bus does not operate, the name of the terminal but also the names of other places in which the bus stops. It is also important to note whether such timetable is still valid. Paper timetables published at bus or train stops may be unnecessary for many, as most of the information can be found on the Internet. But many, especially senior citizens, need this kind of “security” on paper. And how do you find the necessary information if your mobile phone has just run out of battery or you are in a place in the mountains where there is no internet coverage? A paper itinerary is a certainty.

Any further comments on MCM?

MathCityMap is an inspiring application with great potential in teaching mathematics at all school levels as well as in teacher training and in further education of teachers. We are currently preparing a trail on the topic: “Trees”. In the tasks we will deal with various numerical parameters of individual trees or groups of trees or alleys. Each task will be supplemented with interesting information about the tree type. The aim of the trail will be not only to strengthen mathematical literacy, but most of all to draw attention to the ecological and environmental significance of trees in the area where we live – a realization that trees are exceptional living organisms and that they significantly and often inconspicuously affect our lives.

The trail will be incorporated into the material for students, future teachers of STEM subjects, and it is a part of the intellectual output of the international project ENSITE. The project is being prepared by a consortium of eleven European universities led by the University of Education in Freiburg. Thus, many future teachers at universities across Europe, from Norway to Cyprus, will learn about MathCityMap trails. We are convinced that we will inspire them.

Collection of MCM@home Trails:

Click here to get an overview about all digital learning paths which were created by MathCityMap partners

Dear Sona, what are your experiences with MCM@home? How did the students work on the digital learning path?

We offered [MCM@home] Veľké Borové to two different groups of pupils and students as a relaxation, a reward for their work in online math classes during the autumn of 2020.

The first group was a group of teenagers (ages 14 – 19). They are students of a secondary art school, a total of 145 students. They chose their study also because they feel like artists who do not need mathematics. This is reflected in the study program, with only one hour of mathematics per week and the students, logically, consider mathematics to be a “necessary evil and suffering”. The most appropriate strategy for teaching mathematics in such an environment is to prepare and teach each mathematics lesson as a separate event. The MCM trail fascinated all the artists-students, there were only a few exceptions. After completing the trail, the teacher received appreciative feedback such as: “This kind of math is also for those who do not need or like mathematics.” The main reason is the use of the application on a mobile phone and immediate feedback after sending the result. This is, as it has already been stated several times, the strongest emotional impact of the MathCityMap principle of solving mathematical problems.

Compared to solving tasks with the original outdoor MCM trail, strong emotions will not disappear, when solving MCM@home tasks. On the contrary, emotions gain strength, because, as the students admitted, parents or siblings helped them solve problems from home. In addition, the place where the trail was located on the map, was known to some of the students. They had visited the village of Veľké Borové, Chočské vrchy Mountains or the neighboring valleys, Kvačianska and Prosiecka, registered in the UNESCO list of protected areas, as part of family trips in the past. The trail tasks brought back positive, pleasant memories and the students were happy to share their personal experience with the teacher and classmates during the online lesson.

Did you also make experiences using MCM@home on uiniversity level?

A second group of students (60 female students) was a group of future elementary school teachers. Mathematics in this university program is divided into several theoretical and practical subjects. The students received the [MCM@home] Veľké Borové trail as a reward for their performance during the whole semester in the subject: Methods of solving mathematical problems, taught in a Digital Classroom. Similarly like with the secondary school students, in the case of this group of future teachers, more than half of whom have no positive attitude towards mathematics, the MCM trail lesson had a strong emotional impact.

In the feedback, the students talked about the thrill they felt when sending the result of the task, about the disappointment if the result was not correct and about the joy if the application immediately praised them for the correct answer. Some students also mentioned that they know the location and like to think back to their experiences of hiking in this area of Slovakia. Several students showed interest in creating their own tasks and requested methodological instructions for creating MCM tasks and trails.

… to be continued …

Sona Ceretkova was one of our international partners in the Erasmus+ project MoMaTrE which aimed at the development of MathCityMap from 2017-2020. In the last year, Sona and her team from the Constantine the Philosopher University in Nitra, Slovakia, created several MCM@home digital learning paths. In this interview, we focus on the learning path “[MCM@home]Veľké Borové” which is awarded as MathCityMap Trail of the Month in April 2021!

Collection of MCM@home Trails:

Click here to get an overview about all digital learning paths which were created by MathCityMap partners

Dear Sona, please describe the idea of MathCityMap and MCM@home.

MathCityMap trails are originally designed to solve problems about real objects in the outdoors. The MCM@home version was introduced in the spring of 2020, during the first lockdown of schools across Europe. It has become a welcomed activity in online math classes or as a homework, since schools are still closed in most European countries. The MathCityMap application opens up many opportunities for every teacher to make online classes of mathematics more interesting.

One of the possibilities is to create a new MCM@home trail for a selected thematic unit, which students should be able to master in the given school year. For example, geometry of solids, tasks to calculate the volume, surface or the weight of a given object. A very appropriate topic is also combinatorics or tasks for verifying mathematical skills in calculations of distance, speed and time. The interdisciplinary topic of mathematics and physics is in elementary school mathematics usually taught as part of a whole: Word problems solved by linear equations.

Of course, when creating a new trail, the author – the teacher, has to go outside, take pictures of the objects and find out data about the objects, which he/she then incorporates into the tasks. Another possibility is to create a new MCM@home trail from an existing classic outdoor MCM@home trail. Here arises the magical opportunity to take a virtual walk wherever the original MCM trail was created.

How can students work on MCM@home trails?

Students can solve the trail directly in the Digital Classroom, usually individually, and send the teacher a screenshot of the solution of the tasks or trails. Because each task and each trail in the MathCityMap app is scored, the teacher can grade students based on their performance, the total number of points earned, or the number of points earned for solving each task.

Another possibility is to send students the assignment as a pdf and ask them to send the solution of individual or selected tasks back within the set time limit, including a documentation of the solution steps (scan or picture). In this procedure, the teacher can verify which methods of problem solving students have used, whether they have mastered the methods and procedures presented to them in the class or studied from the textbook or other materials, whether they make numerical errors or whether there is a problem with insufficient math knowledge in mathematization of the real situation, etc.

Of course, it is also possible to use the Digital Classroom application to directly monitor the progress of individual students during online math lessons. However, it is necessary to take into account the technical capabilities of students, the quality of internet connection at their home address and it is not appropriate to evaluate students based on how fast they have solved the tasks in the trail. Task in pdf format are suitable when there are students in the class, who do not have a digital device, mobile phone or tablet.

… to be continued …

Category: Trail of the Month

Trail of the month: Lindau Island MathTrail

Trail of the Month: Counting, measuring, calculating and estimating between Sechseläutenplatz and the city border

Trail of the month: Math Trail di Fort Rotterdam Macassar

Trail of the month: Mathtrail at the Zeppelin grandstand

Trail of the month: Olomouc centrum (jednodušší)

Trail of the month: Tracing circles and bodies in Hanover

Trail of the Month: Skulpturenweg Leywald Reinach

Trail of the Month: Veľké Borové – 3rd Part

Trail of the Month: Veľké Borové – 2nd Part

Trail of the Month: Veľké Borové – 1st Part