Teaching Mathematics and Computer Science (DE-journals)
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Tétel 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 Balanced areas in quadrilaterals - Anne's Theorem and its unknown origin(2019-07-04) Humenberger, Hans; Schuppar, BertholdThere are elegant and short ways to prove Anne's Theorem using analytical geometry. We found also geometrical proofs for one direction of the theorem. We do not know, how Anne came to his theorem and how he proved it (probably not analytically), it would be interesting to know. We give a geometric proof (both directions), mention some possibilities – in more details described in another paper – for using this topic in teaching situations, and mention some phenomena and theorems closely related to Anne's Theorem. Subject Classification: G10, G30Tétel Szabadon hozzáférhető Better understanding mathematics by algorithmic thinking and computer programming(2020-11-04) Fried, Katalin; Fekete, István; Princz, PéterTamás Varga’s mathematics education experiment covered not just mathematics, but also other related topics. In many of his works he clearly stated that computer science can support the understanding of mathematics as much as mathematics supports informatics. On the other hand, not much later than the introduction of the new curriculum in 1978, personal computers started to spread, making it possible to teach informatics in classes and in extracurricular activities. Varga’s guided discovery approach has a didactic value for other age groups as well, not only in primary school. Its long-lasting effect can be observed even in present times. Having reviewed several educational results in the spirit of Tamás Varga, we have decided to present an extracurricular course. It is an open study group for age 12-18. Students solve problems by developing Python programs and, according to our experiences, this results in a deeper understanding of mathematical concepts. Subject Classification: 97B10, 97B20, 97D50, 97N80, 97P20, 97P30, 97P40, 97P50, 97U70Tétel 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 A case study of the integration of Algorithm Visualizations in Hungarian programming education(2022-09-13) Bende, ImreIn this study, I will introduce how Algorithm Visualizations (AV) can help programming education or, in this case, the acquisition of basic programming theorems. I used two di erent methods to test this: in the first round, I examined in a larger group how much the students' ability to solve specific tasks changes after being introduced to a visualization tool, and then, what was their motivation and experience during this process. In the second round, I looked for the components that could be important when choosing a tool with the help of an in-depth interview with a smaller number of individuals. In both cases, I describe the research, experience, and results of the study, and then summarize them at the end. Subject Classification: 97P10Tétel Szabadon hozzáférhető Categorising question question relationships in the Pósa method(2020-11-04) Katona, DánielThe doctoral research of the author – with a reverse didactic engineering (RDE) methodology – aims at reconstructing the theoretical background of the ‘intuitively developed’ Pósa method for inquiry-based learning mathematics (IBME) in Hungarian talent education. Preliminary results of the second step of this theorization is presented, which applies tools of the Anthropological Theory of the Didactic (ATD). A model is proposed for categorizing question-question relationship with 3 categories: helping question, follow-up question and question of a kernel. The first two of them are claimed to represent two types (relevant or not) of generating-derived questions relationship. The model is also a prospective tool for connected task- and curriculum design and analysis within IBME development. Subject Classification: 97D20, 97D40, 97D50, 97E50, 97K30Tétel Szabadon hozzáférhető computational thinking problem-thread for grade 7 students and above from the Pósa method(2020-11-04) Bóra, EszterLajos Pósa has been developing his “learning through discovery” (Győri & Juhász, 2018) method since 1988. His weekend math camps are focused on fostering problem-solving skills and high-level mathematical-thinking skills in gifted students from grades 7 to 11. One of the core aspects of the method is the structure of the problems, all problems are part of a complex, intertwined, and rich network. In this article we analyze a computational thinking problem-thread and its role in the camps’s network of problems (Gosztonyi, 2019), and show some aspects of the method. The insights gained using this method can be useful in other contexts. The possible adaptation of the method to secondary and high schools is briefly discussed as well. Subject Classification: 97D40Tétel Szabadon hozzáférhető Computer cooking vs. problem solving(2024-07-12) Csernoch, Mária; Nagy, Tímea; Csernoch, JúliaComputer cooking is a task-related phenomenon where students (end-users) must blindly follow a long list of orders without any connection to the content of the problem, if there is any. Despite its low efficacy, this method is widely used and accepted in informatics both in the learning-teaching process and testing. The National Base Curriculum 2020 in Hungary is in complete accordance with the ‘Informatics Reference Framework for Schools’, but the course books hardly use the latest results of computer education research. The present paper provides examples of how the results of computer education research can be integrated into teaching-learning materials and classroom practices and discusses the effectiveness and consequences of the different solutions, where tool-centred approaches are compared to problem-focused solutions. Subject Classification: 94-01Tétel Szabadon hozzáférhető Connections between discovery learning through the Pósa Method and the secondary school leaving examination in three Hungarian mathematics classrooms(2022-09-13) Urbanski, Michael; Daunt, Zoe; Saluja, Tarang; Barbarics, Márta; Juhász, PéterThe Pósa Method is a guided discovery learning method that has been used in Hungarian education in the form of extracurricular activities for "gifted" mathematics students. A four-year experiment implemented the method in three more "average" classrooms. This article reports on the relationship between the Pósa Method and the standardized secondary school leaving mathematics exam (Matura Exam in short) in Hungary. Data consists of students' survey responses, teacher interviews, and exam results from the three Hungarian classrooms who took part in the four-year experiment. We identify aspects of the Pósa Method that can benefit and hinder exam performance. In addition, we find that learning through the Pósa Method for the four years of high school has adequately prepared students for the exam. Subject Classification: 97D44, 97D54, 97D64Tétel Szabadon hozzáférhető Consequences of a virtual encounter with George Pólya(2022-12-07) Mason, JohnThe consequences of a virtual encounter with George Pólya as a teacher are recorded. An instance of his influence on my mathematical thinking is recounted through work on one of the problems in one of his books. Subject Classification: 01A99, 11A05, 97-03, 97D50Tétel 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 Correction to Gofen (2013)(2022-02-04) Gofen, AlexanderIn the article "Powers which commute or associate as solutions of ODEs?" by Alexander Gofen (Teaching Mathematics and Computer Science, 2013, 11(2), 241–254. https://doi.org/10.5485/TMCS.2013.0347 ), there was an error in Conjecture 1 (p. 250), and consequently, in the References (p. 254).Tétel Szabadon hozzáférhető Correction to Mneimneh (2019)(2023-09-28) Mneimneh, SaadIn the article “Simple variations on the Tower of Hanoi: A study of recurrences and proofs by induction” by Saad Mneimneh (Teaching Mathematics and Computer Science, 2019, 17(2), 131–158. https://doi.org/10.5485/TMCS.2019.0459 ), there was an error in Table 1 (p. 155), and consequently, the first paragraph of Section 8 (p. 154) also needed correction.Tétel 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 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 An examination of descriptive statistical knowledge of 12th-grade secondary school students - comparing and analysing their answers to closed and open questions(2023-08-28) Jánvári, ZsuzsannaIn this article, we examine the conceptual knowledge of 12th-grade students in the field of descriptive statistics (hereafter statistics), how their knowledge is aligned with the output requirements, and how they can apply their conceptual knowledge in terms of means, graphs, and dispersion indicators. What is the proportion and the result of their answers to (semi-)open questions for which they have the necessary conceptual knowledge, but which they encounter less frequently (or not at all) in the classroom and during questioning? In spring 2020, before the outbreak of the pandemic in Hungary, a traditional-classroom, “paper-based” survey was conducted with 159 graduating students and their teachers from 3 secondary schools. According to the results of the survey, the majority of students have no difficulties in solving the type of tasks included in the final exam. Solving more complex, open-ended tasks with longer texts is more challenging, despite having all the tools to solve them, based on their conceptual knowledge and comprehension skills. A valuable supplement to the analysis and interpretation of the results is the student attitudes test, also included in the questionnaire. Subject Classification: 97K40, 97-11, 97D60Tétel Szabadon hozzáférhető Experiences in the education of mathematics during the digital curriculum from the perspective of high school students(2024-02-20) Kosztolányi, József; Torma, GáborDue to the COVID-19 epidemic, Hungarian schools had to switch to a digital curriculum for an extended period between 2019 and 2021. In this article, we report on the experiences regarding the education of mathematics during the digital curriculum in the light of the reinstated on-site education, all through the eyes of high school students. Distance education brought pedagogical renewal to the lives of many groups. Students were asked about the positives and negatives of this situation. Subject Classification: 97C90Tétel Szabadon hozzáférhető Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks(2024-07-12) Albano, Giovannina; Telloni, Agnese IlariaWe designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics. Subject Classification: 97U70, 97H60Tétel Szabadon hozzáférhető Freudenthal fantasy on the bus, an American adaptation(2020-11-04) Kerekes, Judit; Jakab, TündeIn the 1960’s two mathematicians, Hans Freudenthal in the Netherlands and Tamás Varga in Hungary, had argued that people learn mathematics by being actively involved and investigating realistic mathematical problems. Their method lives on in today’s teaching and learning through the various components of cooperative and active learning, by taking ownership in learning, and learning through student dialogue. The goal is to create a welcoming classroom atmosphere in which play takes the front seat. One such scenario is visiting various (animal) stations at the zoo by bus (illustrated by pictures). Passengers are getting on and off the bus at each station (illustrated by arrows), which is modeled on the open number line. This adapted and modified action research was carried out with 5-yearl-old children in public schools of Staten Island, NY in 2019. Subject Classification: 97D40, 97F20, 97F30Tétel Szabadon hozzáférhető Gamification in Higher Education(2021-03-18) Kovácsné Pusztai, KingaThe way of thinking and the way of life of the today's children and teenagers have changed radically. Some of the well-established pedagogical methods that were used for decades have become obsolete. Therefore, we need to look for a new method to approach Generations Z and Alpha. Gamification, which has been known since 2010 and means the use of game elements in other areas of life, offers an opportunity to do so. In addition to a brief description of gamification, my article shows some possibilities for using it at the university. Furthermore, I investigate the impact of gamification on the student in "Algorithms and Data Structures" university course. Subject Classification: 97P30