Teaching Mathematics and Computer Science (DE-journals)
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Tétel Szabadon hozzáférhető Guided Discovery in Hungarian Education Using Problem Threads(2020-10-12) Matzal, Charlotte; Manahan, Kirsten; Galaty, Bridget; Wang, Haoyi; Barbarics, MartaIn 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: 97D40Tétel Szabadon hozzáférhető Interdisciplinary Secondary-School Workshop(2020-03-24) Fejes Tóth, Péter; Vankó, Péter; Borovcnik, ManfredThe paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing. Subject Classification: F90, K90, M50, R30Tétel Szabadon hozzáférhető Programming Theorems and Their Applications(2020-03-24) Fekete, István; Gregorics, Tibor; Kovácsné Pusztai, Kinga; Veszprémi, AnnaOne of the effective methodological approaches in programming that supports the design and development of reliable software is analogy-based programming. Within this framework, the method of problem reduction plays a key role. Reducing a given problem to another one whose solving algorithm is already known can be made more efficient by the application of programming theorems. These represent proven, abstract solutions – in a general form – to some of the most common problems in programming. In this article, we present six fundamental programming theorems as well as pose five sample problems. In solving these problems, all six programming theorems will be applied. In the process of reduction, we will employ a concise specification language. Programming theorems and solutions to the problems will be given using the structogram form. However, we will use pseudocodes as descriptions of algorithms resembling their actual implementation in Python. A functional style solution to one of the problems will also be presented, which is to illustrate that for the implementation in Python, it is sufficient to give the specification of the problem for the design of the solution. The content of the article essentially corresponds to that of the introductory lectures of a course we offered to students enrolled in the Applied Mathematics specialization. Subject Classification: D40Tétel Szabadon hozzáférhető Word problems in different textbooks at the early stage of teaching mathematics comparative analysis(2020-10-12) Szitányi, Judit; Biró, Fanni; Csíkos, CsabaIn a previous research, Csíkos and Szitányi (2019) studied teachers’ views and pedagogical content knowledge on the teaching of mathematical word problems. While doing so, they reviewed and compared Eastern European textbooks of Romania, Russia, Slovakia, Croatia, and Hungary to see how world problem-solving strategies are presented in commonly used textbooks. Their results suggested that teachers, in general, agreed with the approach of the textbooks regarding the explicit solution strategies and the types of word problems used for teaching problem-solving. They also revealed that the majority of the participants agreed that a word problem-solving algorithm should be introduced to the students as early as in the first school year. These results have been presented at the Varga 100 Conference in November 2019. As the findings suggested a remarkable similarity between the Eastern European textbook approaches, in the current study we decided to conduct further research involving more textbooks from China, Finland, and the United States. Subject Classification: 97U20, 08A50Tétel Szabadon hozzáférhető Introductory Computer Programming Courses in Mathematics Curriculum(2020-10-12) Jones, Leslie; Smith, TimWe present the results of surveys and curricular research on introductory computer programming courses that are required or recommended for mathematics degrees at U.S. colleges and universities. Our target schools were those with populations between 5,000 and 20,000 undergraduate students. A key result is a synopsis of programming languages in use in these introductory courses with Java, Python and C + + holding the top three spots. We found that 85% of the 340 schools in our pool require or recommend an introductory programming course as a component of a mathematics degree. Furthermore, most of these introductory programming courses are taught by faculty outside of the mathematics department. These results indicate that mathematics faculty value computer programming and should be actively involved in setting learning outcomes, incorporating skills and concepts learned in introductory programming courses into subsequent mathematics courses, and determining programming languages in use. Subject Classification: 97D30, 97P20, 97P40Tétel Szabadon hozzáférhető Capturing how students' abilities and teaching experiences affect teachers' beliefs about mathematics teaching and learning(2020-03-24) , Safrudiannur; Rott, BenjaminWe developed an instrument to investigate the effect of students' abilities and teaching experiences on teachers' beliefs about teaching and learning of mathematics. In this pilot study, we used the instrument to measure the beliefs of 43 Indonesian math teachers and five additional teachers. Then, for further investigation, we interviewed those five additional teachers. Results from the 43 teachers' responses to the instrument show that in contrast to teachers with less than five years of teaching, teachers with more than five years elicit significantly different beliefs about mathematics teaching and learning in different contexts related to students' abilities. Teachers' reports in the further investigation indicate that teaching experiences with high and low ability students in teaching mathematics could be a possible explanation of this contrast. Subject Classification: C20Tétel Szabadon hozzáférhető Simple Variations on The Tower of Hanoi(2020-03-24) Mneimneh, SaadThe Tower of Hanoi problem was formulated in 1883 by mathematician Edouard Lucas. For over a century, this problem has become familiar to many of us in disciplines such as computer programming, algorithms, and discrete mathematics. Several variations to Lucas' original problem exist today, and interestingly some remain unsolved and continue to ignite research questions. Nevertheless, simple variations can still lead to interesting recurrences, which in turn are associated with exemplary proofs by induction. We explore this richness of the Tower of Hanoi beyond its classical setting to compliment the study of recurrences and proofs by induction, and clarify their pitfalls. Both topics are essential components of any typical introduction to algorithms or discrete mathematics. Subject Classification: A20, C30, D40, D50, E50, M10, N70, P20, Q30, R20Tétel Szabadon hozzáférhető Entwicklung eines Messinstruments zu den Grunderfahrungen des Informatikunterrichts(2020-03-24) Kiener, AndreasThe three basic experiences of computer science education (GI) take into account the personal perceptions and attitudes of students to computer science education. The aim of this study is to develop an inventory to capture these learners' perceptions and perspectives in order to select content or to track learners' development in relation to computer science. Exploratory factor analysis (EFA), partial least square analysis (PLS) and con rmatory factoranalysis (CFA) was used in this study to generate and select items and establish reliability and validity. Subject Classification: Q20, Q50Tétel Szabadon hozzáférhető Teaching model-based testing(2020-10-12) Németh, Gábor ÁrpádDifferent testing methodologies should play an important role in the education of informatics. In the model-based testing (MBT) approach, the specification of the system is described with a formal model. This model can be used to revise the correctness of the specification and as a starting point for automatic test generation. The main problem with MBT is however, that there is a huge gap between theory and practice and that this approach has a high learning curve. To cope with these problems, current paper shows, how the MBT approach can be introduced to students through a small scale example. Subject Classification: P50Tétel Szabadon hozzáférhető Report of Meeting Researches in Didactics of Mathematics and Computer Sciences(2020-03-24) Kónya, E.; Szanyi, Gy.The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sárospatak, Hungary, on the Comenius Campus of the Eszterházy Károly University, from the 24th to the 26th of February, 2020. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Eszterházy Károly University. The 76 participants – including 15 PhD students – came from 9 countries, 23 cities and represented 33 institutions of higher and secondary education. There were 4 plenary, 48 session talks and 4 poster presentations in the program.Tétel Szabadon hozzáférhető How do secondary school students from the Kurdistan Region of Iraq understand the concept of function?(2022-02-04) Hussein, Yusuf Fakhraddin; Csíkos, CsabaThe study investigates secondary school students' understanding of the concept of function. The paper focuses on three main aspects: students' ability to define the concept of function; students' ability to recognize different representations of function; and students' ability to convert between different representations. A test was developed to assess the three main constructs of the study and administered to 342 students in secondary schools in the Kurdistan Region of Iraq. According to the results, students have diffculties in recognizing different representations of function and conversion between them. Connections between different parts of the test may provide hints on educational challenges of how to appropriately teach functions. Subject Classification: 26Bxx, 97D60Tétel Szabadon hozzáférhető Differentiated instruction not only for Mathematics teachers(2022-02-04) Gyöngyösi-Wiersum, ErikaThe aim of differentiated development in a heterogeneous group of learners (DDHG) is to reduce school leaving without education, using an adaptive and innovative teaching-learning environment and using the most effective strategies, methods and techniques. Furthermore, this strategy helps in developing skills for learners and building cooperation between learners in heterogeneous classes through the use of the special, status-management educational procedure, and finally its strength is to sort the status ranking among learners, and to change the social structure of the class. Our goal is to figure out how to share best practices with teachers. One of the effective ways to renew teaching practice is through further training for teachers. As a trainer of the Logic-based subprogram of the Complex Basic Program (CBP) the author of the paper has experienced how well logic-based and decision-making strategies work in other subjects as well as in mathematics. Subject Classification: 97D40Tétel Szabadon hozzáférhető constructive and metacognitive teaching path at university level on the Principle of Mathematical Induction(2021-10-14) Telloni, Agnese Ilaria; Malara, Nicolina AntoniaWe present the main results about a teaching/learning path for engineering university students devoted to the Principle of Mathematical Induction (PMI). The path, of constructive and metacognitive type, is aimed at fostering an aware and meaningful learning of PMI and it is based on providing students with a range of explorations and conjecturing activities, after which the formulation of the statement of the PMI is devolved to the students themselves, organized in working groups. A specific focus is put on the quantification in the statement of PMI to bring students to a deep understanding and a mature view of PMI as a convincing method of proof. The results show the effectiveness of the metacognitive reflections on each phase of the path for what concerns a) students' handling of structural complexity of the PMI, b) students' conceptualization of quantification as a key element for the reification of the proving process by PMI; c) students' perception of the PMI as a convincing method of proof. Subject Classification: 97B40, 97C70Tétel Szabadon hozzáférhető Young women's barriers to choose IT and methods to overcome them - A case study from Hungary(2021-10-14) Szlávi, Anna; Bernát, PéterWomen's scarcity in the STEM, especially in the IT sector is pronouncedly evident. Young women are obstructed from entering and remaining in IT by a broad range of social, educational, and labor market factors. In our paper, we would like to analyze the main barriers girls face in choosing IT, while also proposing potential methods to help them overcome these obstacles. In the second part of the paper, we will present a case study to illustrate in detail how the combination of the above methods can be put into practice to address and tackle the complex set of barriers girls face. We will first introduce a Hungarian annual program, Girls' Day ("Lányok napja"), specifically aimed to promote STEM to girls, then we will present two specific events organized for the 2020 edition of the program and designed with the above principles in mind. The interactive presentation, exposing girls to female role models of the field in a gamified way, and a game development exercise, building Scratch programming skills, have attempted to provide young women both with positive perspectives and experiences in IT, which are instrumental in helping them to surmount entrenched obstacles and raise their interest in the field. Subject Classification: 97P10, 97U30Tétel Szabadon hozzáférhető Wichtige Momente aus der ungarischen Geschichte des Analysisunterrichts(2021-10-14) Vancsó, Ödön; Burian, HanaTörner et al. (2014) paper gives an outstanding review about teaching analysis at high school level in (Western) Europe. We tried to extend this paper with some results from the Hungarian Math History (Beke and Rátz 1897-1924, after second World War 1949-1960, the current situation-first of all based on schoolbooks, and we also included an experiment from 1984-1989 by E. Deák, which was interrupted and partially forgotten). In summary, this paper deals with the turning points of the brief history of teaching secondary school analysis in the XXth century in Hungary, including some conclusions at the end. Subject Classification: 97A30, 97C30, 97D30, 97E50, 97I20, 97I40, 97U20Tétel Szabadon hozzáférhető Artworks as illustrations in Hungarian high school Mathematics textbooks(2021-10-14) Kiss-György, Rita; Hoffmann, MiklósThree 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: 97U20Tétel Szabadon hozzáférhető time spent on board games pays off(2021-10-14) Dukán, András Ferenc; Fried, Katalin; Szabó, CsabaThe impact playing has on the development of thinking is an important topic of psychology of learning, brain research and mathematics didactics. Our research is also connected to the aforementioned topic. We investigated the effects of playing board games on competence motivation and the development of mathematical competencies. In this paper, we present the results of an experiment carried out in a secondary school class. The experimental group spent one of three weekly mathematics lessons playing board games. Apart from the several advantages of playing games in general, we can conclude that, based on the results of the national competence measurement, the mathematical competence of the students developed properly. The readiness and the progress of the pupils were compared on the basis of input and output tests and an initial knowledge measurement and, at the same time, we compared their level of mathematical competence with the results of the national competence measurement. Subject Classification: 97C70, 97D40Tétel Szabadon hozzáférhető retrospective look at discovery learning using the Pósa Method in three Hungarian secondary mathematics classrooms(2022-02-04) Daunt, Zoe; Saluja, Tarang; Urbanski, Michael; Barbarics, MartaWhile the Pósa Method was originally created for mathematical talent management through extracurricular activities, three "average" public secondary school classrooms in Hungary have taken part in a four-year experiment to implement the Pósa Method, which is based on guided discovery learning of mathematics. In this paper, we examine the students' and teachers' reflections on the Pósa Method, and how student perspectives have changed between their first and last year of high school. Overall, teachers and students had a positive experience with the Pósa Method. Furthermore, our research indicated that this implementation has met several objectives of the Pósa Method, including enjoyment of mathematics and autonomous thinking. Subject Classification: 97D40Tétel Szabadon hozzáférhető shift of contents in prototypical tasks used in education reforms(2022-02-04) Fuchs, Karl JosephThe paper discusses the shift of contents in prototypical tasks provoked by the current educational reform in Austria. The paper starts with the educational backboard of the process of changes in particular with the out tting of the students' abilities in different taxonomies and its implementation in the competence models of Mathematics. A methodological didactical point of view on the process is given additionally. Examples out of a specific collection of math problems which arise from the educational reform are integrated and analysed in the context of educational principles and methods. The discussion ends with a short evaluation of the role of traditional approaches to tasks in the ongoing reform. A bundle of tasks as proof that they are still alive is presented finally. Subject Classification: 97B50, 97D40, 97D50Tétel Szabadon hozzáférhető tools for developing a spatial geometric approach(2020-11-04) Stettner, Eleonóra; Emese, GyörgyTamás Varga writes about the use of tools: "The rational use of tools - the colored bars, the Dienes set, the logical set, the geoboard, and some other tools - is an element of our experiment that is important for all students, but especially for disadvantaged learners." (Varga T. 1977) The range of tools that can be used well in teaching has grown significantly over the years. This paper compares spatial geometric modeling kits. Tamás Varga uses the possibilities of the Babylon building set available in Hungary in the 1970s, collects space and flat geometry problems for this (Varga T. 1973). Similarly, structured kits with significantly more options have been developed later, e.g. ZomeTool and 4D Frame. These tools are regularly used in the programs of the International Experience Workshop (http://www.elmenymuhely.-hu/?lang=en). Teachers, schools that have become familiar with the versatile possibilities of these sets, use them often in the optional and regular classes. We recorded a lesson on video where secondary students worked with the 4D Frame kit. We make some comments and offer some thoughts on this lesson. Subject Classification: 97G40, 97D40