The Erasmus+ Project, entitled Mobile Mathematical Trials in Europe (abbreviation of the name of the project: MoMaTrE) offered ten students of Constantine the Philosopher University (UKF) in Nitra an interesting experience: An intensive study program at the Faculty of Education of the J.W. Goethe University in Frankfurt am Main, which took place March 18th to 30th, 2019. The study program was organized by the Department of Didactics of Mathematics and the Department of Didactics of Informatics of the University of J.W. Goethe under the auspices of Professor Matthias Ludwig, principal investigator of the MoMaTrE project. Other members of the home organization team were Simone Jablonski, Moritz Baumann-Wehner and Iwan Gurjanow.

The program was attended by a total of 30 mathematics students from universities from four project partner countries, namely Germany, Slovakia, France and Portugal. The Slovak team consisted of students of Faculty of Education at UKF in Nitra, primary education teacher: Lenka Felcanová, Kristína Galová, students of the Faculty of Natural Sciences at UKF in Nitra: teaching of academic subjects in combination with mathematics and in combination with physics: Kristína Hazuchová, Silvia Haringová, Katarína Laššová, Simona Szabová, Lenka Šubová and Lucia Gemmelová and two PhD students of the Theory of Teaching Mathematics: Veronika Bočková and Kristína Bulková. Part of the international team of intensive program teachers were doc. PaedDr. Soňa Čeretková PhD. and PaedDr. Janka Medova, PhD. from the Department of Mathematics of the Faculty of Natural Sciences.

The program consisted of lectures, practical workshops in the field, work with pupils of primary and secondary schools, visits to schools and a professional excursion. During the lectures, the students learned the theoretical basis of creating educational activities in a non-school environment, in the field, and they got acquainted with the theoretical basis of creating tasks about real objects and the principles of their inclusion in teaching of mathematics at school. The lecturers showed the students various ideas for creating new tasks and for using selected properties of historical monuments or other objects in the immediate vicinity of the school, suitable for creating tasks. Students also learned about the errors encountered by evaluators of mathematical tasks, about real objects and trails that are composed of the created tasks. The students then used all the acquired knowledge to create their own trails during the Intensive Study Program. Several lectures focused on working with the MathCityMap mobile phone app and working with the web portal. Students also expanded their knowledge of mathematical competencies and mathematical problem-solving strategies. The intensive program resulted in the creation of their own mathematical tasks about real objects, from which two mathematical trails were created in the historical part of Frankfurt am Main. The created mathematical trails were designed for pupils of primary and secondary schools from Frankfurt with which the university cooperates. Over the last two days of the Intensive Program, more than 130 pupils have successfully passed mathematical trails under the guidance of students of the Intensive Program.

The program also included classroom observations of mathematics lessons at primary and secondary schools in Frankfurt am Main. The students observed the work of the teacher with the pupils, his style of work and approach to the pupils, the use of teaching methods and forms, and at the end of the visit there was a space for discussion on the topics that the students of teacher studies found interesting.

Organizers of the Intensive Study Program organized a visit to the Mathematical Museum Mathematikum in nearby Gieβen for all of the Intensive Study participants. The museum houses objects with various mathematical knowledge, tasks and models. Visitors can try to solve mathematical tasks manually or by manipulation or by setting various parameters of the objects. From the director of the museum, a former mathematics teacher, the students learned that the museum is attended by school classes, families with children, and enthusiasts of solving mathematical tasks and mathematical mysteries. Numerous exhibitions have shown the connection of math to other sciences and real life. Great advantage of the museum is that visitors can solve the tasks individually or in small groups.

In addition to the intensive study program at the university, students spent their free time by visiting the Botanical Garden Palmergarden, historical landmarks, looking over Frankfurt am Main from the tallest building in the city, the Main Tower, and so they take away many non-mathematical experiences.

The climax of the Intensive Program was a competition of solving the tasks of a math trail in international teams, which took place in the beautiful surroundings of the main campus of the J.W. Goethe University. The competition was followed by presentations of students whose subsequent evaluation by an international group of university teachers was in a pleasant but challenging academic atmosphere. Finally, the students received certificates of completing the Intensive Study Programme and, among other things, awards for the most creative and the most mathematical tasks created.

The UKF students gathered a lot of experience and unforgettable moments from international cooperation and an irreplaceable experience of active teaching of mathematics, as well as professional, academic and social communication in English language.

Text: doc. PaedDr. Soňa Čeretková, PhD., Department of Mathematics, Faculty of Natural Sciences, MoMaTrE project coordinator at UKF in Nitra in cooperation with students – participants of the MoMaTrE Intensive Program