Task of the Week: The snail’s journey
Dennis Kern, student at Goethe University Frankfurt, introduces our new assignment of the week: As part of an Intensive Study Programme for students from Europe, a group led by Dennis Kern created the task “The snail’s journey”. In the following, he gives us an insight into the European exchange program with MathCityMap.
How did you come across the MathCityMap project? How do you use MCM and why?
As a mathematics student at Goethe University in Frankfurt, I saw in the winter semester 2018/2019 that the course “MoMaTrE – Mobile Math Trails in Europe” was offered for the didactics part of my studies. There, students from different countries in Europe came to Frankfurt to discover and evaluate the MathCityMap project and the app together, as well as to create their own trails in groups and test them with school classes.
In addition, I used the app in another course at the university and have since even decided to write my academic term paper as part of my teaching degree on processing strategies when solving problems.
Describe your task. How can it be solved?
“The snail’s journey” we created together at the Historical Museum at Frankfurt’s Römerberg. We tried to investigate the experiences of an animal, which in a certain way can only move in two dimensions (because it must always be in contact with a surface), in our three-dimensional world. The animal in question is a snail. How does it cross a staircase? Of course, it cannot jump from step to step, but must crawl along the surface.
The task is to calculate how long this takes for this staircase. To do this, you have to measure the height and width of a step and multiply it by the number of steps (the steps are all about the same size). This gives you the distance the snail has to travel. If you then read from the task how fast a (garden) snail crawls, you can determine the required time by dividing. Finally, the result must be divided by 60, because it should be in the unit minutes.
As part of the Intensive Study Programme, two math trails were created on the Römer in Frankfurt.
What are the didactic goals of the task?
As already mentioned, students are made aware of dimensional differences, because the snail is relatively small compared to the stairs and cannot fly or jump, and therefore as a snail you do not have the luxury of using the dimensional advantage here. In addition, we wanted to choose an object that is not immediately completely measured with one measurement.
There is also differentiation here, because lower-performing students are likely to make the same measurement ten times, while higher-performing ones realize that nine measurements can be saved. Then, with the conversion from centimeters to seconds, i.e. from distance to time, the handling of units from different categories is practiced, but also in one and the same unit, because you still have to convert the result from seconds to minutes.
Any other comments about MCM?
I think it’s great to finally have a really good answer to the complaint “What do we need all this for?” from learners in math classes. Editing math trails with this app picks them up where they are all the time anyway – on their smartphones – and motivates them in a way that classic math lessons probably can’t do.