Trail of the month: Tracing circles and bodies in Hanover

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.