Ein wichtiges Thema in der Korrespondenz zwischen Tamás Varga und dem Ehepaar Reményi

Im Herbst 2019 wurde – parallel zur Tamás Varga 100 Konferenz – auch eine Ausstellung über Leben und Werk von Tamás Varga eröffnet. In dieser Ausstellung gab es ein Poster, auf dem Freunde und enge Kollegen von Tamás Varga aufgelistet waren. Zu lesen waren darauf die Namen von Gusztáv Reményi und seiner Frau. Der Teil ihrer Korrespondenz, der bei der Verfasserin dieses Artikels aufbewahrt ist, stellt – aufgrund der vielen beruflichen Aspekte – ein interessantes Dokument der frühen Stadien ihrer Freundschaft dar. Zuerst werden wir die Teilnehmer der Korrespondenz vorstellen und dann einige allgemeine Bemerkungen machen. Wir suchen dann nach Piagets Erscheinen in der Korrespondenz, indem wir Fragen stellen, die sich auf frühere Forschungen von Tamás Varga beziehen. Schließlich geben wir weitere mögliche Aspekte der Bearbeitung der Korrespondenz an.

Elementarisierung oder Vielfalt als Schlüssel für die Gestaltung eines Zugangs zur beurteilenden Statistik

Elementarisation is a legitimate didactical strategy, especially in a subject area such as inferential statistics, which is considered to be extremely difficult. Here one can also refer to Varga’s position on the didactics of mathematics and examine, which orientation results from it. For this purpose, Varga’s approach to mathematics didactics as a whole is summarised, which can best be characterised by the term complexity. Varga tries to make the complexity teachable by presenting suitable task systems and developing comprehensive handouts for guided-discovery learning. The core of the presentation is a system of tasks by Varga for inferential statistics for primary school, which Varga also supplements by comments on an experimental class for nine-year-olds (!). Varga introduces heuristically and playfully to the significance test and to p values. Finally, we discuss how to continue the learning paths from these heuristic considerations to the full field of inferential statistics. Classification: K10, K70, K50, D20. Keywords: Stochastic teaching, elementarisation, task systems, Statistical inference, Bayes inference, Varga’s approach.

Discovering mathematical knowledge by students as the way to successful learning of mathematics

Students in many countries have problems learning mathematics. Many students do not like mathematics. It is also a problem for teachers. The question has to be answered: Why does math education cause so many problems? We have set up the Centre for Creative Learning of Mathematics at the University of Bialystok (Poland). It is a place where we try to create appropriate athmosphere and circumstances for students of all ages to become active discoverers of mathematics, not just passive recipients of knowledge from books or teachers. As a theoretical background we took ideas from Tamás Varga, Zofia Krygowska, the theory of constructivism, the strategy of functional mathematics teaching and problem-solving method. Lessons and workshops for students in our Centre are based on the combination of the following ideas: The participants solve practical or theoretical problems (problem solving method) and carry out concrete, representative and abstract activities (strategy of functional mathematics teaching by Z. Krygowska) which help them discover and formulate knowledge (constructivism). The whole process corresponds very well to some of T. Varga's important ideas or his conviction of the main objectives of mathematics teaching: Students explore the knowledge themselves and think independently. The subject of mathematics is transformed into a thought formulation process in which students turn from the role of passive recipients to the active knowledge creation. Classification: A80. Keywords: T. Varga, Z. Krygowska, constructivism, strategy of functional teaching of mathematics, problem solving method, creative learning

Synthesizing the legacy of Varga and Dienes

Tamás Varga worked closely with Zoltán P. Dienes to provide learners with internally related experiences of creating and discovering abstract concepts, a procedure that Dienes described as “internalized action”. In instructing the way Dienes and Varga have promoted, “multiple embodiment” and the cognitive process of the learner in unaccustomed learning situations may be different for teachers and their pupils. Addressing this difference, we outline a lesson for pre-service teachers on comparing divisibility rules in various bases with the use of Dienes’s Multibase Arithmetic Blocks as an illustration of how to interface multi-level experiences. In order to answer the didactic problem of how embodied tools augment the learning process by structuring and organizing the learners’ experiences at different levels, we point to the principles that make the synthesis of the two innovators’ methods possible. Classification: A60, B59, C30, F60, Q69, U60 Keywords: Tamás Varga, multiple embodiment, Zoltán P. Dienes’s principles, multibase arithmetic blocks, divisibility rules, manipulatives, philosophy of mathematics

It is worth turning on GeoGebra 3D

I am a PhD student at the Doctoral School of Mathematics and Computer Science at University of Debrecen in the topic of Mathematical Competence Development with ICT. In this article, I present some examples, where the 3D version of GeoGebra can be applied successfully not only in research but also in everyday work. I have picked examples that require spatial representation but where it is much more complicated and less effective to achieve through concrete manipulatives than through any 3-dimensional dynamic geometric program. However, the two-dimensional version of any dynamic geometry program could be used to construct a figure, but besides easy constructing, formatting the figures is easier in the 3D version. Classification: D40, N80, U70. Keywords: development of spatial view, spatial experience, GeoGebra 3D worksheet.

Tamás Vargas Reformbewegung und der ungarische Guided Discovery-Ansatz

This paper presents Tamás Varga’s work focusing especially on the Hungarian Complex Mathematics Education reform project led by him between 1963 and 1978 and the underlying conception on mathematics education named “guided discovery approach”. In the first part, I describe Varga’s career. In the second part, I situate his reform project in its international and national historical context, including the international New Math movement and the Guided Discovery teaching tradition, something which is embedded in Hungarian mathematical culture. In the third part, I propose a didactic analysis of Varga’s conception on mathematics education, underlining especially certain of its characteristics which can be related to Inquiry Based Mathematics Education. Finally I briefly discuss Varga’s legacy today. Classification: A30, D30, D40, D50. Keywords: Tamás Varga, Guided Discovery approach, Inquiry Based Mathematics Education, history of mathematics education, curricular reform.

Das Erbe von Tamás Varga – Film, Didaktik und narrative Identität

On the occasion of Tamás Varga's 100th birthday, I conducted video interviews with Hungarian and foreign colleagues and with family members from Tamás Varga. At the Varga 100 conference, a 45-minute film composed of these interviews was shown during the opening ceremony. The following narrative emerged from my work as a reporter and scriptwriter: The memory of Tamás Varga is permanently alive, the ideas that go back to him are also always present throughout the processes of change in mathematics teaching. From this point of view, there is a mathematics didactic tradition in Hungary, which is consist of many components connected to Tamás Varga and form a narrative that expresses all the characteristics. Classification: A30, D30 Keywords: Tamás Varga, Hungarian mathematics didactic tradition, narrative memory

Tamás Varga und sein inspirierender Einfluss auf den Mathematikunterricht – ein Blick zurück

This article takes up some details of Tamás Varga's legacy from the perspective of a former student. The focus is on his ideas, opinions, reviews and articles on mathematics education in secondary schools. Two school books had a special impact at that time in Hungary, the mathematics textbook (1949/50) by Rózsa Péter and Tibor Gallai for the 1st class of middle schools (14-15 years) and its continuation „Mathematics for the 1st class of middle schools“ (1956) by Tamás Varga and László Faragó. Some of the problems Tamás Varga posed in the Mathematical Journal (e.g. Farkas Bolyai's theorem about the decomposing equality of plane figures and problems with the object area of the definitions of plane figures) are also important. The following explanations refer to his articles on mathematics education and his dissertation on complex mathematics education (1975). Classification: A30, C10, D30, U20. Keywords: History of mathematics education, Hungarian math books for secondary schools, beginning of math lessons by guided discovery

Guided discovery for preservice teachers

In this paper, we present an approach to teacher education at a study abroad program in Hungary for American and international pre-service and in-service teachers. The aim of the program is for participants to learn about the guided discovery pedagogy used in Hungarian mathematics classrooms, stemming from the work of Tamás Varga, which is closely related to inquiry based learning. The program applies the principles of guided discovery to teacher education itself: participants are immersed in the guided discovery approach, hence their view of mathematics is challenged, and they look for their own tools to likewise challenge their future students. In the paper, we illustrate this approach to teacher education by describing an example of a guided discovery task to which participants are exposed, and discuss how they engage in their own task design and reflection. Classification: B50 Keywords: mathematics education, guided discovery, teacher education, pre-service teachers, in-service teachers, problem series, task design, inquiry based learning

Arguing and Proving in Vargas´s German-Language Work

Vargas’s work focused on children´s autonomous activities as well as on their intrinsic motivation in mathematics classrooms and was designed in the sense of the so-called genetic method (Ambrus & Vancsó, 2017, p. 7). His goal was to enable learners to discover mathematics in various every-day situations and to find appropriate mathematical models (Ambrus & Vancsó, 2017, p. 10). In a playful way, he wanted to convey methods, models and basic concepts of mathematics and especially the rules of logic. However, a main and basic area of mathematics, which also should be communicated to children from the very beginning, and which is not independent of logics, is the area of arguing and proving in mathematics. The question, how Varga placed and communicated arguments and proofs suitable for 1st-to-4th-grade learners, will be answered by analysing his German-language book Engel, Varga & Walser (1974). In this issue, two of his favourite mathematical areas, namely combinatorics and probability theory are brought to bear. ZDM Subject Classification: E50, K20, K50 Key words and phrases: Reasoning and proving in the mathematics class-room, Combinatorics, Probability concept and probability theory