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• Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries

  73-110

  Tünde Kántor-Varga

  Views:

  75

  In the Great Library of the Debrecen Reformed College (Hungary) we find a lot of old mathematical textbooks. We present: Arithmetic of Debrecen (1577), Maróthi's Arithmetic (1743), Hatvani's introductio (1757), Karacs's Figurae Geometricae (1788), Segner's Anfangsgründe (1764) and Mayer's Mathematischer Atlas (1745). These old mathematical textbooks let us know facts about real life of the 16-18th centuries, the contemporary level of sciences, learning and teaching methods. They are rich sources of motivation in the teaching of mathematics.

• Artworks as illustrations in Hungarian high school Mathematics textbooks

  103-117

  Rita Kiss-György

  Miklós Hoffmann

  Views:

  141

  Three different series of Hungarian Mathematics textbooks used in grade 9-12 education for the past 30 years have been analysed in this research. Our aim is to show and evaluate how the visual arts have been connected to mathematical ideas in these textbooks. We have applied the six dimensions of evaluation, which have recently been introduced in (Diego-Mantec on, Blanco, Búa Ares, & González Sequeiros, 2019) to categorise the illustrations of the three different series. We show examples for each dimension from the textbooks, and we find that even if the number of artistic illustrations in these coursebooks have significantly increased, in most cases these sporadic examples are not closely related to the mathematical context, mainly used for ornamental purposes to decorate the core text. Based on this classification we conclude that the number of artistic illustrations with underlying math concepts making students' participation more active could and should be significantly increased.

  Subject Classification: 97U20

• Number theory vs. Hungarian highschool textbooks: √2 is irrational

  139-152

  Petra Csányi

  Kata Fábián

  Csaba Szabó

  Zsanett Szabó

  Éva Vásárhelyi

  Views:

  131

  According to the Hungarian National Curriculum the proof of the irrationality of √2 is considered in grade 10. We analyze the standard proofs from the textbooks and give some mathematical arguments that those reasonings are neither appropriate nor sufficient. We suggest that the proof should involve the fundamental theorem of arithmetic.

• Forming the concept of congruence I.

  181-192

  Éva Szeredi

  Views:

  102

  Teaching isometries of the plane plays a major role in the formation of the congruence-concept in the Hungarian curricula.
  In the present paper I investigate the way the isometries of the plane are traditionally introduced in most of the textbooks, especially the influence of the representations on the congruence concept, created in the teaching process.
  I am going to publish a second part on this topic about a non-traditional approach (Forming the concept of congruence II). The main idea is to introduce the isometries of the two dimensional plane with the help of concrete, enactive experiences in the three dimensional space, using transparent paper as a legitimate enactive tool for building the concept of geometric motion. I will show that this is both in strict analogy with the axioms of 3-dimensional motion and at the same time close to the children's intuitive concept of congruence.

• Dressed up problems - the danger of picking the inappropriate dress

  77-94

  Anna Muzsnay

  Csaba Szabó

  Views:

  154

  Modelling and dressed-up problems play an inevitably unavoidable role in mathematics education. In this study we would like to point out how dangerous is it to dress up mathematical problems. We go back to the principle of De Lange: The problem designer is not only dressing up the problem, but he is the solution designer, as well. We show three examples selected from Hungarian high school textbooks where the intended solution does not solve the problem, because the dressing changes the context and changes the problem itself.

• Outstanding mathematicians in the 20th century: András Rapcsák (1914-1993)

  99-110

  Tünde Kántor

  Views:

  133

  In this paper we commemorate the life and work of András Rapcsák on the occasion of the centenary of his birth. He was an outstanding professor and a scholar teacher. He was head of the Department of Geometry (1958-1973) and the director of the Institute of Mathematics at the University of Debrecen (Hungary). He played an important role in the life of the University of Debrecen. He was the rector of this university between 1966 and 1973.
  At the beginning of his career he taught at secondary schools in several towns. He wrote mathematical schoolbooks with coauthors. He also taught at Teacher's College in Debrecen and in Eger.
  He became to interested in differential geometry under the influence of Ottó Varga. The fields of his research were line-element spaces and related areas. He was elected an Ordinary Member of the Hungarian Academy of Science in 1965. He wrote 21 papers, 8 school and textbooks and 3 articles in didactics of mathematics.