Search
Search Results
-
Bernd Zimmermann (1946-2018)
155-159Views:107Our great friend, the always helpful supporter of the Hungarian mathematics didactics, Bernd Zimmermann, the retired mathematics didactics professor of Friedrich Schiller University of Jena, passed away on 19th of July 2018. After a short chronology of his life, we remember some of the many areas of his work with strong Hungarian connections. -
Guided Discovery in Hungarian Education Using Problem Threads: The Pósa Method in Secondary Mathematics Classrooms
51-67Views:227In Hungary, ‘guided discovery’ refers to instruction in which students learn mathematical concepts through task sequences that foster mathematical thinking. A prominent figure of guided discovery is Lajos Pósa, who developed his method to teach gifted students. Rather than teaching mathematics through thematic blocks, the Pósa Method employs webs of interconnected problem threads in which problems are built on each other, and different threads are presented simultaneously, so that students work on problems from multiple threads at the same time. It was found that this method has been successful as extracurricular training for gifted students since the 1980s; however since 2017, as part of an ongoing research, the method has been applied to mainstream curriculum in two public secondary school classrooms. The present paper examines the design and implementation processes of problem threads in this public secondary school context.
Subject Classification: 97D40
-
Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:75In 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. -
Visualisation in geometry education as a tool for teaching with better understanding
337-346Views:305In primary and secondary geometry education, some problems exist with pupils’ space thinking and understanding of geometric notions. Visualisation plays an important role in geometry education, and the development of pupils’ visualisation skills can support their spatial imagination. The authors present their own thoughts on the potential of including visualisation in geometry education, based on the analysis of the Hungarian National Core Curriculum and Slovak National Curriculum. Tasks for visualisation are also found in international studies, for example the Programme for International Student Assessment (PISA). Augmented reality (AR) and other information and communication technology (ICT) tools bring new possibilities to develop geometric thinking and space imagination, and they also support mathematics education with better understanding.
Subject Classification: 97U10, 97G10
-
Strategies used in solving proportion problems among seventh-grade students
101-127Views:22In the 2023/2024 school year, 146 seventh-grade Hungarian students (aged 12-13) participated in our classroom experiment on solving proportion problems. At the beginning and the end of the teaching phase, both the experimental and the control groups solved a test. Regarding the answers of the students, in the pre- and post-test mostly consisting of word problems, we examined the success of solving the problems, as well as the solution strategies. For this, we used the strategies of proportional thinking that already exist in the literature of mathematical didactics. We intended to answer the following questions: To what extent and in which ways do the different types of problems and texts influence the solution strategies chosen by the students? How successfully do seventh-grade students solve proportion problems?
Subject Classification: 97D50, 97F80
-
Why do we complicate the solution of the problem? reflection of Finnish students and teachers on a mathematical summer camp
405-415Views:147This paper deals with reactions and reflections of Finnish secondary school students and teachers on Hungarian mathematics teaching culture. The experiences were collected at a mathematics summer camp in Hungary. -
Prime building blocks in the mathematics classroom
217-228Views:272This theoretical paper is devoted to the presentation of the manifold opportunities in using a little-known but powerful mathematical manipulative, the so-called prime building blocks, originally invented by two close followers of Tamás Varga, to support discovery of various concepts in arithmetic in middle school, including the Fundamental Theorem of Arithmetic or as it is widely taught, prime factorization. The study focuses on a teaching proposal to show how students can learn about greatest common divisor (GCD) and least common multiple (LCM) with understanding, and meanwhile addresses internal connections and levels of abstractness within elementary number theory. The mathematical and methodological background to understanding different aspects of the concept prime property are discussed and the benefits of using prime building blocks to scaffold students’ discovery are highlighted. Although the proposal was designed to be suitable for Hungarian sixth graders, mathematical context and indications for the use of the manipulative in both primary and high school are given.
Subject Classification: F60, C30, E40, U60
-
The mathematics textbook as an aid to differentiation: a first Hungarian example
35-53Views:81Differentiation is a way of teaching where each student is taught according to his/her personal needs. This technique is not widely used in Hungary yet, although this would be necessary due to the introduction of the two-level final examination and to a growing concern for equal opportunities and integrated teaching. One of the most significant aids to differentiation is an appropriate textbook, and that is why a group of professionals wrote a set of textbooks that supports this technique. The paper examines the requirements for a differentiated textbook, and the extent to which the textbook in question meets them. -
Teaching integral transforms in secondary schools
241-260Views:98Today, Hungarian students in the secondary schools do not know the idea of complex numbers, and they can not integrate except those ones who learn mathematics in advance level. Without this knowledge we can teach Fourier transform for students. Why should we teach Fourier transform (FT) or Wavelet transform (WT) for them? To teach image file formats like JPEG, (JPEG2000) we need to talk about integral transforms. For students who are good in computer programming, writing the program of 1D FT or 2D FT is a nice task. In this article we demonstrate how we can teach Fourier and Wavelet transform for students in secondary school. -
Mobile devices in Hungarian university statistical education
19-48Views:164The methodological renewal of university statistics education has been continuous for the last 30 years. During this time, the involvement of technology tools in learning statistics played an important role. In the Introduction, we emphasize the importance of using technological tools in learning statistics, also referring to international research. After that, we firstly examine the methodological development of university statistical education over the past three decades. To do this, we analyze the writings of statistics teachers teaching at various universities in the country. To assess the use of innovative tools, in the second half of the study, we briefly present an online questionnaire survey of students in tertiary economics and an interview survey conducted with statistics teachers.
Subject Classification: 97-01, 97U70, 87K80
-
"How to be well-connected?" An example for instructional process planning with Problem Graphs
145-155Views:183Teachers’ design capacity at work is in the focus of didactical research worldwide, and fostering this capacity is unarguably a possible turning point in the conveyance of mathematical knowledge. In Hungary, the tradition hallmarked by Tamás Varga is particularly demanding towards teachers as they are supposed to be able to plan their long-term processes very carefully. In this contribution, an extensive teaching material designed in the spirit of this tradition will be presented from the field of Geometry. For exposing its inner structure, a representational tool, the Problem Graph is introduced. The paper aims to demonstrate that this tool has potential for analyzing existing resources, helping teachers to reflect on their own preparatory and classroom work, and supporting the creation of new designs.
Subject Classification: 97D40, 97D50, 97D80, 97G10, 97U30
