Category: General

The Trail of the Month July invites us to a mathematical walk through another European capital. This time we are in the beautiful city of Bern, Switzerland. The Trail of the Month was created by Damaris Burri as part of her master’s thesis at the PH Bern at the Institute for Secondary Level 1 and is available in the MCM app under the code 678321 and in the MathCityMap web portal here.

Running through the historic old town of Bern, the trail consists of a total of 12 tasks, some of which can be extended with sub-tasks. In terms of content, the tasks deal with topics from grades 7 to 9 (in Switzerland, the so-called third cycle), i.e. with areas and volume calculations, as well as gradients and units of measurement.

In the following interview Damaris Burri describes her experience with MathCityMap so far and gives additional background information about the trail:

How did you come across the MathCityMap project?

I came across the MathCityMap project during a mathematics didactics seminar at the PHBern. At the end of such a seminar, the lecturer introduced us in a few words to some links to websites that could be useful for teaching mathematics. One of these links led to the MathCityMap website. Looking for a topic for my master thesis, I remembered these links and explored MathCityMap and the world of mathtrails for the first time. I was thrilled and had found an exciting topic for my master thesis.

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

Bern’s Old Town is a UNESCO World Heritage Site and forms the historic core of the Swiss federal city of Bern. The Mathtrail “Berner Altstadt” invites you on a mathematical tour of the city. With its total of twelve tasks, the trail leads past many sights, such as the Kindlifresserbrunnen, the Bern City Hall, the Bear Park, the Bern Cathedral and the Zytgloggen Tower. At each task, students can expect a mathematical problem based on 7th and 8th grade basic geometry knowledge, as well as background information about the object. The goal of the trail is to show the young people that mathematics can not only be done in the classroom, but that objects from everyday life are also suitable for calculating. Furthermore, the Mathtrail should be fun and a positive experience for the whole class.

How do you use MCM and why?

I developed the trail as part of my master’s thesis specifically as an extracurricular learning space for mathematics lessons in cycle 3 (secondary level 1), which can be used freely over the three school years (7th to 9th grade). In Switzerland, students in the upper grades (7th – 9th grade) are increasingly taught in mixed-level groups. My Trail takes the resulting heterogeneity into account with tiered clues and subtasks. Each task has at least two tiered hints that help the youngsters understand the task and find a possible solution path. They also point out possible stumbling blocks. In the case of tasks that exceed the subject matter of the 7th grade, the tasks were divided into several sub-tasks. These guide the young people step by step to the solution.

In order to be able to solve the tasks of the Mathtrails “Berner Altstadt”, each participating group (consisting of 3 -4 students) must be equipped with a smartphone, a set square, a double meter and a calculator.

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

My favorite task is the task at the Zytglogge (time bell tower). The Zytglogge is one of the landmarks of Bern’s old town and was the first western gate before the city was expanded in the 13th and 14th centuries. The tower with its mechanical music box fascinated me already as a child. Every hour on the hour, the music box starts to play and the dancing bear train, the jester and the screaming rooster come to life.

The “Zytglogge” task refers to the doorway, where on one of the walls hang seven historical length measures that used to be used in the markets of Bern. In this task, the students have to indicate the length of the doorway to the length measure “Swiss foot”. To complete the task, learners must know and understand the principle of converting length measures. The students can determine the length of a Swiss foot both by measuring it or by observing it closely, because the length of 3/10 meter is engraved. To solve the task, they must also measure the length of the doorway and then convert the length obtained into “Swiss feet”.

The Trail of the Month of June comes from the small medieval town of Bruneck in the region of South Tyrol in northern Italy. Here, Melanie Forer and her third-grade students created the trail “Bruneck einmal anders” (Brunico a little different), which can be accessed with the MCM app under the code 353905 and is available on the MathCityMap web portal here.

The trail consists of a total of six tasks that mostly revolve around the topics of areas and volume calculation of basic and composite objects and areas. In addition, of course, you have the pleasure of getting to know Bruneck from a completely different perspective, while at the same time visiting sights such as the castle of Bruneck.

An interview about the creation of the trail and her experiences with MathCityMap is given by Melanie Forer below:

How did you come across the MathCityMap project?

I got to know MathCityMap in the context of the further training ” Mathematical Trails” of the Pedagogical Department in South Tyrol. Using the example of the project “matematica in città” in Bolzano, we interested teachers were invited to observe the environment with a mathematical eye and then familiarize ourselves with the app MathCityMap. The possibility to formulate and solve mathematical questions at extracurricular learning sites appealed to me very much, so I also brought this idea to my class, where it immediately received a lot of approval.

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

The small medieval town of Bruneck in South Tyrol, Italy impresses with its castle and the famous town alley. In 1741, the Ursuline Order settled in Brunico and in the following years the Ursuline Sisters built a church, convent, boarding school and school. Pupils of this equated secondary school have created the mathtrail “Bruneck einmal anders”, which is described as follows:

Starting from the school entrance at the Ursuline Church, the route goes through the eponymous Ursuline Gate via the historic Stadtgasse up to the Upper Town. From there it continues up to Bruneck Castle and across the suspension bridge to Hermann-Staudacher-Platz. Afterwards the trail goes back to the Schlossberg, down to the Rainkirche and over the trench to the Hintergasse. With the trail it is possible to get a new perspective on the sights of Bruneck by putting otherwise inconspicuous, everyday, geometric figures and bodies in the center of attention.

How do you use MCM and why?

I use MathCityMap to offer very practical, modern mathematics lessons that are close to the students’ lives. Through new digital media, such as MathCityMap, the student world can become a place of learning and a new approach to mathematics can be created. The mathematical perspective no longer remains only in the classroom, but is increasingly applied in the playground, on the way to school or in leisure time.

This school year, I will again be working with a small group of students to collect new tasks and take on the mathematical challenge.

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

My favorite task is the “bridge at the castle”. With a bit of a thrill, but of course with maximum safety, you can enjoy a wonderful view of Bruneck Castle. The task is to measure the area of the fence and calculate the cost of redesigning it. The special thing here is the varied approach to determining the length, with measuring and counting with meter tape folding rule or other aids such as thread, step length, etc.. To be able to solve the task, basic knowledge of calculating the area of rectangles and an understanding of direct proportionality is needed.

Also from Slovakia the first schools are joining the partner school program of MathCityMap. We are very happy to welcome “ZŠ s MŠ Lipovce” and “Základná škola Revúca” as the new and fifth / sixth partner school, which successfully passed the application process.

The process at ZŠ s MŠ Lipovce was initiated by Sylvia Smolková, a dedicated mathematics teacher at the school, which has a kindergarten, primary and secondary school.
Four trails were created for grades 5 (075303), 7 (025383), 8 (675400) and 9 (565437), which lead the school’s students across Lipovce and let them discover the community in a new way. Trying out the trails with the classes was a lot of fun for all involved and especially the experience of doing mathematics outside was a great motivational factor, as Sylvia Smolková told us.

At Základná škola in Revúca, the application was submitted by Michaela Štefko, who described her experience with MCM as follows:

“I work at the primary school in Hviezdoslavova street in Revúca. Our students are always open-minded to new and interesting forms of learning. As soon as we came across the application and the portal Mathcitymap, we immediately decided to use it in our lessons. So far, we have created two trails in the area of our school for the 5th and 6th grade. We are currently working on another one for the 7th grade. My colleague and I have recently started to design a mathematical walk in our town. We would like to present the monuments and significant places in our district town. Our students have already passed both routes, they were all excited, they formed groups very quickly and worked nicely on every single task. They even suggested that they take part in creating other tasks. We want to improve students´ reading comprehension, teamwork and also communication skills. Additionally, we see a great benefit in the fact that students, whose favourite school subject is not mathematics, took part in solving mathematical problems.”

The packages with the measuring tools and the official partner school plaque are already on their way to the schools and, as always, we are very much looking forward to receiving further applications from all over the world.

All further information about the partner school program and the prerequisites for the application can be found in the article about the first MCM partner school as well as on the homepage of our project MaSCE³.

Through the Trail of the Month of May, we get to know a European capital from a slightly different angle. We’re talking about Finland’s largest city, Helsinki, where Nina Salminen, a local mathematics, chemistry and physics teacher, created the Helsinki Tour trail, which is available in the MCM app by using the code 129638 and on the MathCityMap web portal here.

On this extensive mathematical walking trail we get to know the city and its sights in connection with six mathematical tasks based on intermediate level topics. Starting at the Sibelius Monument, the trail covers a total distance of 2.9 km, passing the Olympic Stadium, the Parliament Building and the famous Temppeliaukio Church, which was carved directly into a rock.

In a short interview Nina Salminen tells us how she got to know MathCityMap and gives us some background information about her trail:

How did you come across the MathCityMap project?

My Italian colleague Giovanna Zito from Brindisi asked me to join an Erasmus+ project, where a MathCityMap trail is being planned with students in each of the five countries participating in the project. I found out about the MathCityMap project and made one trail with my students near our school, Munkkiniemi School. This spring we went further and planned two trails in the center of Helsinki.

Please describe your Mathtrail.

Along the trail you will see points of interest in Helsinki and at the same time solve short math problems. For each task, you will get to know one of Helsinki’s attractions. Thus, the route also serves as a tourist tour in our capital. Math problems are suitable not only for students but also for anyone who wants to recall the basics of mathematics or enjoy problem solving.

How do you use MCM and why?

MCM trail brings good variation for math lessons. A trip outside breaks up the monotony of the school day. Showing math in different contexts is also a good way to reach students who, for one reason or another, don’t like math and don’t think they’re good at it.

We can also get around the trails on theme days or when there are foreign guests at our school. The trail makes it easy to introduce our hometown. The Finnish mobility of the Erasmus+ project will take place in May and all 50 students from five different countries will take the MCM trail.

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

My students have come up with ideas for the tasks and were so excited about planning them that I consider everyone a favorite. The tasks differ from each other and many of them require knowledge of geometry. In addition to connect math with real life, students get to know their hometown. They also learn to work together as a group when solving tasks and navigating from one task to another.