Scientific Program > Workshops

Hungarian teachers will offer several workshops illustrating Varga's method and Hungarian traditions of teaching by problem solving and mathematical discovery. The workshops cover different levels of education (primary, lower and upper secondary school).

Session 1

6 November 16h30 – 18h

Varga’s method at the primaryschool level:
measurement and unit conversion

Ágnes Konrád
ELTE Gyertyánffy István Primary School

Young learners don’t understand the abstract concept of mathematics such as measurement. In other words, understanding the relationship between the units of measurement and index number very difficult for them. Thus converting between metric units is also very difficult. Children can only understand these trough concrete, practical experience.
The practical experience such as estimation, measurement by comparison, using standard and non-standard units can support children in understanding.
During this workshop we will discuss how we teach mesuring and unit conversion using Tamás Varga’s method and complete some suggested activities. We will estimate and compare using non-standard measuring devices to experience how children discover the relationship between the unit and index number.


Varga’s method at the lower secondary school level: Tamás Varga, the Wizard, the Explorer, the Game Master

Erika Jakucs
Fazekas Mihály High School

In the workshop we collect small morsels from the mathematical roamings of a grade 5 class (students aged 10-11). We get the taste of how deciphering a series of small wizardries leads to a surprise by a mathematical concept that may even turn out to be an old friend. We string some very different problems on a strand (are they that different?), and we may find that the two ends of the strand are connected.
Meanwhile we also savor how grade 5 students explained their ideas, made mistakes, experimented, and got to the goal.
And if someone deciphers the secret of the wizard, they get a chance to enchant the audience themselves.


Varga’s method at the high school level: problem solving in elementary geometry

Eszter Varga
Bornemisza Péter High School, Eötvös Loránd University of Budapest

The methods and teaching materials of Tamás Varga’s Complex Experiment in Mathematics Education have never been elaborated in such depths for upper secondary education as they were for primary school. Nevertheless, the principles and attitudes of the guided discovery approach are very much present in the practice of some Hungarian expert teachers. As the curriculum gets more formal, the instruction gradually draws away from concrete experiences and manipulatives, but great effort is made to maintain vivid classroom dialog and high responsiveness to students’ ideas and contributions. Despite the fact it is time consuming, this teachers sometimes restrain themselves from providing the students with ready-made definitions and methods to give them the opportunity to experience Mathematics as their own creation.
This workshop attempts to simulate this classroom environment. Participants will work on elementary geometry problems in small groups, followed by a whole-group discussion. The problems to be discussed are known in the Hungarian secondary education, but they will be presented in a new arrangement. The workshop will finish with an informal conversation about the experiences and the further potential of the discussed problems.


Session 2

7 November 14h – 15h30

A Finnish adaptation of Varga’s work: Road to the understanding of the decimal system (primary level)

Anni Lampinen
Varga-Neményi Association (Finland)

Usually we use the decimal system (base ten) to represent numbers. This system is one of the most important concepts in learning mathematics. Understanding the base ten is not an easy task for a young pupil. Varga offers us a versatile approach where pupils can first experience other base numbers. When we bear in mind the age of a pupil the key words are play, joy and doing together! This workshop will give you the experience of learning the decimal system as it is taught in Finland in the footsteps of Varga.
Anni Lampinen is the founder and chairman of the Varga–Neményi Association established in 2005 in Finland. She is also the editor and author of learning and instructional material of the Varga-Neményi method in Finland. She has had a pivotal role in developing the method for the Finnish school context. She was a member of the board which established the new national core curriculum for basic mathematical education 2014 in the Finnish National Agency for Education. She also develops  practices and concepts for in-service teacher education.


Teaching mathematically talented students by the Pósa-method

Péter Juhász
Alfred Rényi Institute of Mathematics, Hungarian Academy of Sciences; Szent István High School

Lajos Pósa is a Hungarian mathematician and educator. Pósa developed a method of teaching mathematics centered on the idea that students should learn to think like mathematicians. Pósa’s pedagogy uses the task thread, or a series of tasks that build on each other and gradually guide students toward understanding. By engaging with these threads, students discover mathematical concepts through their own work. Initially Pósa’s method was intended for talented students and was implemented in more than 350 weekend math camps. Recently a small group has started doing a research implementing it in more general school settings.
The workshop will begin with a brief introduction on Pósa and his work. It follows a short description of basic principles of the method. Then participants will experience Pósa’s method by working on several tasks intended for high school students, followed by discussions of the tasks. We will share our experiences of using Pósa’s method in Hungarian high school classrooms.


Teacher training for American students in the spirit of Tamás Varga

Réka Szász
Budapest Semesters in Mathematics Education

The workshop demonstrates how Budapest Semesters in Mathematics Education—a study abroad program for American and international preservice and inservice teachers—develops its participants’ teacher knowledge. The goal of the program is to introduce participants to the Hungarian mathematics pedagogy through guided discovery, which stems from the work of Tamás Varga. BSME participants often play a dual role: first they are exposed to mathematics tasks in the role of a student; then they reflect on the experience and engage in task design from a teachers’ point of view. Workshop participants will experience and discuss this method through tasks involving the Logifaces game. The Logifaces game is a recent Hungarian invention, and a great tool to strengthen students’ mathematical thinking and teachers’ task design skills.


Alternating Path Algorithm with Party Hats

Dávid Szeszlér1, Júlia Kornai2
1Budapest University of Technology and Economics, 2ELTE Radnóti Miklós Primary and Secondary School

A high school graduating class is preparing for their prom. All students in the class give a list of all their classmates of opposite sex they are willing to waltz with. How could we assemble the maximum number of dancing couples? This type of problem comes up in practical, real-life applications too, for example when assigning workers to jobs to be carried out.
Originating from the Hungarian mathematician Dénes Kőnig from the 1930s, the Augmenting Path Algorithm is an efficient method for solving this problem. It has become one of the classics of graph theory, it is often part of introductory discrete mathematics courses at universities around the world.
In this workshop, we present a way to teach this algorithm in an interactive, participatory way: students discover the method and then they perform it together. Finally, the statement and the proof of Hall's Theorem, one of the fundamental theoretical results in this field, is born from the common experience. Obviously, our method follows the long-standing tradition of teaching mathematics in a playful way that focuses on the joyful experience of individual discovery - a tradition that was so successfully promoted and developed by Tamás Varga.
We tested the method twice in summer camps of the ELTE Radnóti Miklós High School, one of the most prominent secondary schools in Budapest. We will also try and share our experiences and observations obtained in these camps.

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