Mathematical Olympiad Research Articles

Math universe: Designing a self-directed learning application for preparing students for mathematical Olympiads

Math universe: Designing a self-directed learning application for preparing students for mathematical Olympiads

KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL OLIMPIADE TINGKAT SMP

Mathematical representation abilities can be in the form of expressions, ideas or mathematical ideas, which originate from students' thoughts that emerge during learning in an effort to find mathematical solutions. There are three indicators of mathematical representation ability, namely verbal, pictorial and symbolic. The process of developing students' potential and thinking can be done by holding mathematics competitions or olympiads. The approach used in this research is qualitative with descriptive methods. Purposive sampling technique was used in this research to select samples with certain considerations. The aim of this research is to describe students' mathematical representation abilities in solving Olympiad questions. This research used a sample of 3 students each representing each high, medium and low representation ability group. Based on the results of research on visual representation abilities, some students already have high abilities, although there are some who are still medium or low. Meanwhile, in symbolic ability, there are many students whose abilities are high and only a few whose abilities are medium or low. For verbal representation, most students already have high abilities and only a few students have medium or low abilities

Stress in Chinese teachers who teach the mathematically gifted: a qualitative perspective.

Those who teach mathematically gifted high school students play a key role in both their identification and cultivation. Teachers who teach the Mathematical Olympiad in China work long hours and teach difficult content; they are under a significant amount of work-based pressure, and that is worthy of further study. This study analyzed the sources of stress for 33 Chinese teachers who teach the Mathematical Olympiad, collected data through semi-structured in-depth interviews, and adopted a subject analysis method based on Bronfenbrenner's ecological system that considers the influences that the complexity of socio-cultural and environment have on individual emotions. It is divided into five structural or environmental systems in which human beings develop, namely the macroscopic, external, meso, micro, and chrono systems. The research results show that the greatest influences on these teachers' stress come from the mesosystem and microsystem levels, and that the key players are students and school leaders. Educational policy and culture are found to be key factors from the macrosystem. Overall, long-term stress was seen to affect both teachers' moods and their physical health. Finally, the results offered implications for education policy and school management and suggestions for the cultivation and management of mathematics teachers who teach the gifted. Limitations of the study are discussed, and directions for future research are proposed.

The Book Review Column

Leslie Valiant, the father of computational learning theory, has written a new book, The Importance of Being Educable: A New Theory of Human Uniqueness (Princeton University Press, 2024), which proposes "educability" as a potentially more scientific theory of human cognition. Leslie Valiant, the father of computational learning theory, has written a new book, The Importance of Being Educable: A New Theory of Human Uniqueness (Princeton University Press, 2024), which proposes "educability" as a potentially more scientific theory of human cognition. Theorems of the 21st Century, Volume 1 by Bogdan Grechuk (Springer Nature Switzerland, 2019) deposits the first installment of important yet approachable results gleaned from the Annals of Mathematics in the first decade of the twenty-first century, from the point of view of an International Mathematical Olympiad gold and silver medalist.

Learning models and achievements of the most gifted students

The emergency of switching to an online learning model due to the COVID pandemic impacted the educational process in of schools world wide. We conducted an anonymous survey at the elite high schools in Serbia whose students won 45 medals at international Olympiads in mathematics, physics, and computer sciences in the last 4-year period (2019–2022). The impact of switching from in-person to online learning on the achievement of the gifted students was analyzed. The results of the research revealed a downward trend in the final grades and achievements in international Olympiads, which persists even after returning to the face-to-face educational model. This trend is confirmed by calculation of the Pearson correlation coefficient (−0.62) between school years and achievements in international mathematical Olympiads, international physics Olympiads, and international Olympiads in informatics. Gifted students’ satisfaction with online learning during the COVID pandemic was also analyzed using content analysis of open-ended questions. The surveyed gifted students showed a high level of self-criticism and maturity by expressing their opinion about online learning. In the group of gifted students, there is a higher level of agreement about harmful consequences of online learning on the level of their education and work habits than in other research conducted on similar topics. Moreover, the level of agreement is in a positive correlation with students’ achievements and final grades.

Career paths of the International Mathematics Olympiad (IMO) medalists

Each year, six exceptionally talented high school students from each country participate in the International Mathematics Olympiad (IMO). We thoroughly searched the internet to find the career paths of 2785 IMO medalists who participated in the competition from 1986 to 2005. We have found that the career paths of IMO medalists depend on their home country, despite their similar levels of mathematical talent. For example, the extent to which medalists studied abroad varies significantly among countries in the same geographical region and with comparable income levels. We also found that there is a high concentration in medalists’ foreign education. For example, MIT educated more foreign medalists than any country except for the United States both at the undergraduate and Ph.D. levels. Roughly half of the medalists ended up working abroad. Education is found to be an important channel for the migrant medalists. Although majority of the medalists were educated in mathematics, more than three quarters of their non-academic jobs are either software or economics-finance related jobs. Most medalists who became academics are specialized in mathematics. While the rate of becoming a mathematician academic is not dependent on the income level of the medalists' home country, those from higher-income countries tend to have higher academic performance.

New trends in research skills development of future teachers: quantitative approach and empirical studies

The purpose of this study was to investigate the relationship between the use of technology and the development of research skills in future teachers, specifically current graduate students participating in Mathematical Olympiads. The study used a quantitative approach and analyzed data collected through a survey. The findings indicated that quantitative analysis skills, problem-solving skills, communication skills, and research methodology skills are the dimensions of research skills in future teachers. The results showed that the use of digital tools for literature searching and curation, online courses and workshops (OCWs), collaborative learning and discussion forums, and data analysis software significantly and positively affected research skills. However, the study failed to provide evidence that digital portfolios (DPs) affected research skills. The limitations of the study and recommendations for future research are discussed. In conclusion, the findings highlight the importance of technology in the development of research skills in future teachers and suggest that technology-based learning resources and tools should be integrated into teacher training programs.

New Math: How an AI proved dozens of geometry theorems from the International Mathematical Olympiad.

New Math: How an AI proved dozens of geometry theorems from the International Mathematical Olympiad.

Olympiad on Lightning-Fast Solution of Mathematical Problems as a Psychological and Pedagogical Phenomenon

The article presents the author’s approach of designing an Olympiad on lightning-fast solution of mathematical problems for students of pedagogical universities in order to develop their quick thinking. The aim of the article is to analyse different models of organising Olympiads in mathematics for pupils and students, and to justify the expediency of including Olympiads on lightning-fast problem solving in the educational system of schools and universities. The research methodology is based on the system-activity approach and the requirements of educational standards of basic secondary and higher education, taking into account the labour functions of the professional standard of a teacher. Research results. One of the possible options for organising a mathematics Olympiad for students – future teachers of mathematics is the Olympiad «Dragonfly» for lightning-fast solution of problems of the school course of mathematics of different levels of complexity. When designing the content of such an Olympiad it is necessary to observe a number of principles: balance, brevity, accessibility, dynamism. On the basis of the Institute of Mathematics, Physics and Informatics of the V. P. Astafiev conducted a study to identify the impact of the Olympiad «Dragonfly» on the development of quick thinking in students – its participants. The study confirmed the hypothesis that if students are systematically involved in the process of lightning-fast solution of school mathematical problems of the Olympiad «Dragonfly», it will contribute to the development of their quick thinking. Conclusion. The experimental work has confirmed the expediency of including the Olympiads on lightning-fast problem solving in the educational system of school and university.

Analisis Kesulitan Calon Guru Matematika dalam Menyelesaikan Soal Olimpiade Bidang Aljabar

Mathematics Education Undergraduate Study Program students as prospective teachers need to be prepared with good competencies so that they are ready to carry out the Olympic preparation program when they are already in the profession as teachers. Therefore, research will be carried out that aims to analyze the difficulties of prospective mathematics teacher students in solving Olympiad questions, which are the basis for designing Olympiad learning in higher education. This research was carried out with students from the VII-semester Mathematics Education Study Program at a university in Magelang using a qualitative approach. Data obtained through written assessments and interviews were then analyzed to identify difficulties in understanding concepts, difficulties in applying principles, and difficulties in solving verbal problems experienced by the subjects. The results of the data analysis show that these three types of difficulties were found in the steps for solving olympiad questions in algebra. Keywords: difficulty analysis, prospective mathematics teacher, mathematics olympiad

Effect of Enrichment Program on the Achievement of Vocational High School Gifted Students in Mathematics Competitions

The group of gifted students is a group of students who need special services in learning. SMK Negeri 1 Turen, is one of the schools in Malang Regency that has a platform for gifted students, in the form of a mathematics olympiad team. Every year there are beginner students who join the mathematics olympiad team. Therefore, matriculation is needed for them to catch up on the material they are missing. This research was conducted to find out how many enrichment program meetings are needed for beginner students to equalize their abilities with experienced students. The participants in this study were 10 students, consisting of 6 beginner students and 4 experienced students. Based on the Mann-Whitney test, the results of this study indicate that a long-term enrichment program (17 meetings) has a significant effect on students' achievement in mathematics competitions.

THE BISECTOR TRIANGLE WITH A 90° ANGLE

For the examination of the triangle discussed in the article, profound knowledge of plane geometry is required, and grasping the specific approach to solving it can be quite challenging without prior knowledge of what to rely on. The focus is on a triangle with a 120° angle, commonly known as the Shebarshin problem. The article presents both computational and purely geometric methods for solving a problem of elevated complexity. This particular problem appears in entrance exams for universities and in mathematical Olympiads at the highest levels. The theme of singular triangles remains constantly relevant in geometry. For instance, many properties and theorems are known about an orthocentric triangle, which have been discussed in detail and already proven. I propose to consider in detail the properties and theorems of an equally interesting triangle, the sides of which connect the bases of the bisectors of the interior angles of the triangle. The goal of my article is to alleviate the drawback of complexity while retaining accessibility and originality in the geometric problem involving a triangle with a 120° angle and an inscribed bisectral triangle with a corresponding 90° angle.

Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned

Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned

Solving olympiad geometry without human demonstrations

Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1–4, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges1,5, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004.

ВСЕУКРАЇНСЬКА ОЛІМПІАДА КИЇВСЬКОГО НАЦІОНАЛЬНОГО УНІВЕРСИТЕТУ ІМЕНІ ТАРАСА ШЕВЧЕНКА З МАТЕМАТИКИ

Mathematical Olympiad is an intellectual competition that gives talented students the opportunity to demonstrate their knowledge, logical thinking and ability to solve complex mathematical problems. Olympiads stimulate in-depth study of mathematics, expand knowledge and improve students' skills. The work presents solutions to the problems of the 2024 All-Ukrainian Mathematics Olympiad of Taras Shevchenko National University of Kyiv were considered.

Quality of education and performance of public schools in Minas Gerais at the Mathematical Olympiad

Resumo No presente estudo analisou-se a relação entre a qualidade da educação – estrutura escolar física, estrutura escolar pedagógica, docentes, discentes e políticas educacionais - de escolas públicas de municípios mineiros e os seus desempenhos, de premiados, na OBMEP. Tal investigação tem como diferencial a utilização de uma abordagem quantitativa, demonstrando que a OBMEP é relacional, baseada na qualidade social da educação e na ótica não equânime do sucesso das escolas públicas em políticas relacionadas à educação. Na literatura existente, a OBMEP foi discutida preponderantemente pelas abordagens pedagógicas ou de conteúdos das provas, e não como ação a ser influenciada nas escolas. Com uma amostra de 420 escolas públicas pertencentes à regional MG06 da OBMEP, aplicou-se um modelo de regressão de Poisson, associando-se variáveis representativas da qualidade social da educação - fatores intra e extra escolares - com o desempenho na OBMEP, quantidade de medalhas obtidas pelas escolas. Percebeu-se que para apresentar um desempenho satisfatório, ou seja, obter sucesso na OBMEP, alcançando-se premiações, é necessário que as escolas públicas tenham infraestrutura adequada, em condições para o exercício do trabalho docente, estudantes em situações favoráveis de acesso e permanência no ensino regular, além da atuação permanente do Estado mediante o desenvolvimento de políticas públicas educacionais. Tais resultados sinalizam a necessidade de maior comprometimento das esferas políticas e sociais para a melhoria da qualidade da educação pública básica no Brasil, para que ocorra maior divulgação do potencial da OBMEP como política pública de inclusão social e não só para a busca de resultados e premiações.

Mathematical Olympiad issues to identify students' reasoning ability using Polya's model

This research aims to describe the level of mathematical reasoning ability of students in solving mathematical Olympiad problems based on problem-solving of the Polya model. This study employed descriptive analysis with a qualitative approach. Data were collected by using observation, documentation, and interviews. The study subjects were 27 junior high school students participating in the National Science Competition in Indonesia. Meanwhile, the Miles and Huberman analysis model was used as the data analysis. The results of this study indicated that: (1) the level of students’ mathematical reasoning-ability based on the problem-solving of Polya models in the category of "sufficiently competent" (high-group students), in the category of "less competent" (medium-group students), and in the category of "incompetent" (low-group students); (2) the most complex and rarely performed stages by students in Polya’s model were at the "devising a plan" and "looking back" stages; and (3) the Polya's model used in solving mathematical Olympiad test items was more suitable for those considered as routine-questions, and it was not suitable for non-routine questions. This study also showed that, on average, the students had difficulty finding initial ideas to start working on the test items.

Pengembangan Mathematics Olympiad Digital Book (MODiB) Berdasarkan Strategi Pemecahan Masalah Polya untuk Meningkatkan Kreativitas dan Hasil Belajar Matematika Siswa Sekolah Dasar

Mathematics Olympiad is a prestigious competition that is growing and has many enthusiasts in Indonesia. Thus the need for math olympiad teaching media is getting higher. The purpose of this research is to develop a digital book that is 1) valid, 2) practical and 3) effective for improving learning outcomes and mathematical creativity of elementary school students, which is named MODiB (Mathematics Olympiad Digital Book). MODiB contains Elementary Mathematics Olympiad material according to the OSN syllabus and in solving problems using the Polya Problem Solving Strategy. MODiB development applies the 5 steps of ADDIE (Analysis, Design, Development, Implementation, Evaluation). The subjects of this study were SD DCS Semarang students who had passed the selection for OSN guidance. Starting with analyzing the condition of coaching mathematics Olympiads at SD DCS Semarang and recording the needs needed to foster the OSN team, designing and developing MODiB accompanied by validators who are material experts and media experts, and then implementing MODiB at SD DCS Semarang. Evaluation is carried out at each stage and after implementation is complete. From the research results, data were obtained: 1) the feasibility results of the material on MODiB were 89.09% which were included in the feasible category to be tested on students, and the feasibility results of learning media were 88.57% in the feasible category to be tested on students, 2) practical results MODiB according to students is 80.48% which is included in the practical category, 3) the results of the analysis of increasing learning outcomes with the gain test obtained a score 0,244 that is included in the low category based on the Gain score category according to Hake, and 4) the value of mathematical creativity of 16 respondents (53.3 %) increased, 4 respondents (13.3%) remained and 10 respondents (33.3%) decreased. Overall, the average increase in the value of mathematical.

METHOD OF "CHOOSING AN ARBITRARY POINT"

The vector method is one of the most general approaches for solving geometric problems. The universality of this method is so broad that it is applied in algebra, mathematical analysis, geometry, and physics. It is used to solve problems of increased complexity, entrance exams for universities, and high-level mathematical Olympiad problems. The vector method is relatively new in mathematics. Primarily, I propose using it to solve problems that involve vectors in their statements. Such problems will be discussed below in this article. The solutions obtained through this method often have a more concise form, unlike traditional solutions, which can sometimes appear too cumbersome. However, I want to emphasize that comparing classical and vector methods is inappropriate. These are different "languages of mathematics," and we are learning to "speak" in one of them.

Impact of the African Institute for Mathematical Science Teacher Training Program on Students’ Interest to Learn Mathematics and Science, Rwanda

<p style="text-align:justify">This study examined the impact of the Rwanda African Institute for Mathematical Science, Teacher Training Program (AIMS-TTP) on 228 secondary school students’ interest to learn Mathematics and science taught by 7058-trained teachers over 5-years across 14 districts. Students were exposed to various AIMS-TTP interventions, including industrial visits, science hours, and international day for women and girls in science, mathematics competition, robotics and mathematics challenge, and the Pan African Mathematics Olympiad (PAMO). A survey research design was employed to collect data about students’ interest to learn Mathematics and science, and data on students’ choices of combinations were obtained from the National Examination and School Inspection Authority (NESA) for the academic years 2017 to 2022. Data analysis using bivariate correlation and regression analyses revealed a positive and significant relationship (p<.05) between AIMS-TTP interventions and students’ interest to learn Mathematics and science. Besides, linear regression model indicated that hands-on activities, exposure to mathematics and science role models, science hour and smart classroom were the best predictors of students’ interest to learn mathematics and science (β=.197, p< .05; β=.217, p<.05; β=.234, p< .05; and β=.218, p<.05 respectively). They contributed 66.7 % (Adjusted, R2 = .667, p < .05) of the variance in students’ interest in learning mathematics and science. The AIMS-TTP interventions significantly improved students’ interest to learning mathematics and science. Recommendations include comprehensive training programs with direct student engagement, diverse competitions, and ongoing teacher support through professional development. Future research should focus on students’ STEM interest in Technical, Vocational Education, and Training schools.</p>