Author: Simon Barlovits

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.

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.

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 …