Mathematical Olympiad Research Articles

Развитие беглости и оригинальности мышления старшеклассников при решении задач, связанных с числами Фибоначчи

On the basis of the requirements of modern reality with its economic, cultural and social problems, the basic concepts of modern education are changing significantly. School in modern society must focus on the personality of the student, on their holistic development. Various and complex processes that take place in modern society, require to teach, educate and develop people who will be able to solve problems in a non-standard way, i.e. will have inventive, or, as now more often said, creative thinking, the main parameters of which are fluency, originality and flexibility of thinking. To develop fluency and originality of thinking, it is necessary to broaden horizons, off erring the integration of academic subjects with the various aspects of reality around us. These days the tasks of the USE in Mathematics contain problems in probability calculus and combinatorics. Therefore, it is necessary to train high school students to solve such problems. The problems associated with Fibonacci numbers contain many popular publications in mathematics, they are analysed in the classroom of school mathematical circles, they are included in the set of tasks for mathematical Olympiads.

Всеукраїнська олімпіада з математики для вступників до КПІ ім. Ігоря Сікорського: аналіз результатів і майбутні перспективи

Analysis of All-Ukrainian Mathematical Olympiads for entrants of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" that was held in 2017 and 2018 is studied in the paper. Organizational aspects and application of computer technologies for conducting Mathematical Olympiads for University entrants, geography of the Olympiad participants has been analyzed. The subjects of the tasks, the form of their presentation at different rounds of the Olympiad, the methodology for conducting the first and second rounds, time framework foreach stage, specifics of the Olympiad work assessment using capabilities of the Moodle educational platform were studied. Peculiarities of online distance round of the Olympiad on the basis of Moodle platform are studied in detail. Quality of the taken extramural test was analyzed using classical test theory. On the grounds of this analysis a table and a histogram of interval frequency distribution of individual scores were built. Strong and weak sides of the use of computer technologies are revealedon example of the organized Olympiads. Outlook and possible directions of further development of Mathematical Olympiads for University entrants in nowadays conditions are outlined.

KETERAMPILAN BERPIKIR KREATIF SISWA DALAM MENYELESAIKAN SOAL OLIMPIADE MATEMATIKA BERDASARKAN LEVEL METAKOGNISI

The research aims to describe the level of creative thinking ability of students in solving mathematics olympiad problems based on students' metacognition levels by using the qualitative descriptive approach. The subjects of this study were the students at State of Junior High School (SMPN) 2 Jember involving the learning of Olympiad mathematics. The data collection was carried out based on the student's creative thinking ability test sheets, interviews, and observations. Test questions given to the students were mathematics olympiad questions. The analysis of the Miles and Huberman models were used for data analysis. The results exhibited that the level of creative thinking skills of the students in solving mathematics Olympiad questions were 29.41% (less creative), 41.18% (quite creative), 11.76% (creative) and 17.65% (very creative). On the other hand, the metacognitive level of SMPN 2 Jember students were 64.71% at level 2 (aware use), 23.53% at level 3 (strategic use) and 11.76% at level 4 (reflective use). In addition, the literatures indicate that there are several factors affectting the creative thinking skills and metacognition level, among them is an understanding of the information of the problem, compiling an appropriate strategies, skills of the chosen strategy, skills of answer elaboration, mastery of the Mathematics Olympiad material and a tendency to rely on the memorization or imitations based on previous or discussed solutions.

Run and Solve: Competitions in Mathematical Rogaining

Urban orienteering is a popular activity in Russia that combines physical and intellectual exercises. Many residents of megapolises are keen of it, including students and alumni of mathematical and technical study programs. We organized a similar competition focused on mathematics as a part of Caucasus Mathematical Olympiad. Over 300 people took part in the event, including schoolchildren and general public. This paper provides a guideline on preparing and carrying out such events.

IMPROVING MATHEMATICAL TEACHERS COMPETENCY 21TH THROUGH WORKSHOP DEVELOPMENT OF MATHEMATICAL OLYMPIC PROBLEMS BASED ON HIGH ORDER THINKING SKILLS IN SMP SOLOK SELATAN DISTRICT

The aim of study to improve competency junior high school mathematics teachers in Solok Selatan district in compiling Olympiad questions mathematics and solving problems based on high order thinking skills (HOTS). The target audience for community service is mathematics teachers incorporated in the Subject Mathematics Teacher's Consultation (MGMP) Mathematics in Solok Selatan. The method used in the service includes the presentation of material by the team community service then carried out the pre test and post test, the design of the question HOTS, discussion and question and answer sessions at the math Olympiad. Conclusions of this research is: There is a positive increase in teacher competency after being given training in compiling math Olympiad questions that the posttest results are better than the results pretest in the training to improve the competency of mathematics teachers in compiling the questions Mathematical Olympiad based on high order thinking skills of SMPN in Solok Selatan District

On approaches to assessing the solution of problems in mathematical olympiads for schoolchildren

On approaches to assessing the solution of problems in mathematical olympiads for schoolchildren

PENINGKATAN KOMPETENSI GURU PEMBINA OLIMPIADE MATEMATIKA SISWA SEKOLAH MENENGAH PERTAMA KABUPATEN MADIUN

The objective of this research is to describe the improvement of the competence of Olympic workshop participants in problem-solving of mathematics Olympiad for mathematics teachers of Junior High Schools in the Madiun Regency by using the qualitative descriptive approach. The subjects of this research were 66 participants of junior high school mathematics teachers workshop organized by Mathematics teachers in each junior high school or MGMP in collaboration with the Depatment of Education and Culture of Madiun Regency. The data collection were carried out with a written test in the description form consisting the results of pre-test, post-test, practice questions, presentations from each group and observation results during the workshop. The results indicated that the mathematics Olympiad workshop activities for Junior High School mathematics teachers in Madiun Regency could increase the understanding of workshop participants in solving mathematics Olympiad questions. This improvement could be seen from the answers of practice questions as well as from the presentations session whereas the teachers could clearly describe several topics such as an algebraic, number theory, geometry, combinatorics, and statistics. However, an advanced Olympics workshops are still needed to help the teachers of Junior High School mathematics Olympiad in Madiun Regency.

PELATIHAN PENDAMPING OLIMPIADE MATEMATIKA SMP KABUPATEN TULUNGAGUNG

This article discusses the activities of community service that raises the theme of mathematics olympiad training with the target is the teachers of math at junior level in Tulungagung regency. The reason for choosing this theme is to see competition in the increasingly rigorous world of education. School is aimed togive birth to outstanding students who can compete in the national, regional, and global arena. One of the problems faced in Tulungagung Regency related to junior high school mathematics is the lack of teachers or supervisors of the Olympics. Solutions offered to MGMP Matematika SMP Tulungagung is held training toteachers of mathematics junior high school for the future teachers can independently accompany students in the arena of mathematics olympiad. The response of the trainees' teachers showed a positive direction. The most important is the increasing insight or knowledge of the ins and outs of the mathematics olympiad.

The process of student’s thinking deduction level to solve the problem of geometry

Each thinking level van Hiele will describe the process of thinking a people use learning the geometric concepts and types of geometric ideas thinks. This research is a qualitative descriptive research what aims to describe the thinking process of students at the level of deduction in solving geometry problems. The collection data’s method in this research is test and interview method. The test is classification of students’ thinking geometry level according to van Hiele using instruments developed by Usiskin, so that the students get the level of deduction. The test of geometry to knowing the thinking process students use 1 problem from the International Mathematical Olympiad (IMO) field Geometry. Interviews were conducted to the students to confirm the student’s work. The results of this study indicated that students at the level of deduction to solving geometry problems as accordance with the characteristics of van Hiele geomeri thinking in its level.

Олимпиадные задания по геометрии, методические приемы их решения

The main content of the article is devoted to the geometric problems of mathematical school olympiads. The study revealed the types of operating with spatial images in the process of solving problems, the stages of forming spatial representations of students in the study of geometry and objectives of the course of visual geometry. It was concluded that the formation of spatial, topological, spatial, projective representations goes through successive stages, developing the geometric skills of schoolchildren. Olympiad tasks, designed on the basis of school programs and textbooks on geometry, make it possible to check the formation of the geometric skills of schoolchildren. The article may be of interest to mathematics teachers, students and schoolchildren who are interested in methods of solving olympiad problems in geometry.

Задачи республиканской олимпиады школьников по математике

The main direction of the article is to consider methods for solving the problems of the fi nal stage of the 2018 republican mathematical olympiad of schoolchildren in the Kyrgyz Republic. In the course of the study, the position of the olympiad, the principles of confi guration and requirements for the olympiad tasks were studied. The content of the selection round of the city olympiad of schoolchildren conducted offl ine and the methods for solving problems of the 4th stage of the republican olympiad of schoolchildren considered in this paper may be of interest to heads of methodological sections, mathematics teachers who prepare their students for participation in mathematical competitions for students and schoolchildren studying methods for solving olympiad problems.

Problem posing in the context of teaching for advanced problem solving

Three teams of pre-service mathematics teachers were engaged in an assignment of designing teaching sequences aimed at empowering high-school students to understand solutions to International Mathematics Olympiad problems. The assignment was rich with problem-posing opportunities. The data – the sequences, posed problems and reflections – were analyzed in order to reveal the underlying structure of the participants' problem-posing experiences. The findings support two conclusions. First, problem posing in mathematics teacher education can be promoted a-didactically, as an implicit objective of an activity having teaching for problem solving as an explicit goal. Second, problem posing that requires pre-service teachers to cope with mathematics that is challenging for them, provides rich learning opportunities and can result in worthwhile posed problems.

Open olympiad as a means of mathematical enlightenment of school students

Mathematical Olympiad movement plays an important role in the development of mathematics, enhancing the prestige of education in the international arena, as well as in shaping the student’s personality, fostering a desire to achieve high results, determination, readiness for long-term work. The question of classical mathematical olympiads is well described in literature, but non-standard forms of intellectual competitions in mathematics, which include open olympiads, are practically not considered.The article provides a historical overview of the open olympiads appearance and development, describes the characteristics that make it possible to classify the olympiad to an open type, justifies the use of open olympiads as a means of mathematical enlightenment for students, discusses the competition period of the olympiad and the approaches to the choice of themes for the open organized olympiad.The paper provides a comparative analysis of open and traditional mathematical competitions according to different criteria. The goals and objectives of both types of olympiads as well as the requirements that are put forward to the formulation of tasks for open olympiads are described. Special attention is paid to the issue of preserving the health of schoolchildren participating in the olympiad, the interdisciplinary nature of the tasks, and possible informative blocks of open mathematical olympiads are described.The article describes the organizing experience of an open competition dedicated to N. I. Lobachevsky, gives examples of original authors’ assignments, describes a mechanism for checking students’ works, describes the possible difficulties that are missing when testing regular olympiads, but occurring in open type olympiad works. The analysis of the pedagogical and psychological results is given, the development of general educational skills of students participating in the open olympiad is described, conclusions on the prospects of using the open type olympiads for mathematical education of schoolchildren are made.

Milestones in the life course of distinguished mathematicians and mathematically gifted adolescents .

The paper presents the results of research on milestones (significant events, critical points, crystallizing experiments) in the course of life of outstanding mathematicians and mathematically talented adolescents. The work covers the period of approximately last 80 years. Four distinct group of mathematicians had received their education and pursed their scientific careers at that time: late, distinguished professors of mathematics, distinguished professors of mathematics who are still alive, PhD students and doctors of mathematical faculties, laureates of mathematical olympiads. The author’s intention was to indicate milestones – key events and moments in their history determined by the author (or those indicated by the interested) to reach the highest position and recognition in the field of mathematics. Those are, for example, important experiences in a person’s life that played a huge role in choosing mathematics as a direction for further development or reasserted that mathematics is the right choice. The considerations were based on a holistic, humanistic approach and a biographical approach from the perspective of Charlotte Bühler The course of human life. The techniques that have been used include document analysis and narrative interviews. According to the recommendations of Buhler’s results were presented graphically on the timelines.

What Happened to the Participants of the Math Olympiad 1971? A Multiple-Case Study Concerning the Occupational Success of the Winning Team from Hungary, Math Olympiad-Occupational Success.

The aim of this multiple-case study was to find out how the most successful team of the 1971 Mathematical Olympiad in Hungary developed professionally. It is impressive that in 1971, no fewer than four participants on the Hungarian team received gold medals and four participants received silver medals. Seven of the eight analyzed participants on the team came from a grammar school in Budapest. Three of the four gold medal winners achieved remarkable academic positions. On average, professional positions were achieved (as scored by the magnitude prestige scale) well above the average for a normal grammar school sample. Interestingly, the calculated average of the Hungarian team (156.5 ± 15.5) was slightly higher than that of the comparison team from Sweden (142.8 ± 30.5), but this difference was not significant (p = 0.351). In principle, excellence seems to result in excellence. For several former participants on the Hungarian team, it was shown that they continued to be extremely successful in the field of mathematics, with a thematic focus in the field of statistics and probability calculations.

FACILITATING THE DEVELOPMENT OF THINKING AND CLEVERNESS DURING THE INTRODUCTION OF DRAFTS IN EDUCATIONAL INSTITUTIONS

The authors of the work analyzed the first steps of the Dniprodzerzhynsk City Federation of Checkers NGO in the direction of the introduction of backpacking in the educational institutions of Kamyanetska for the purpose of developing students' memory and attention, analytical and mathematical abilities, ingenuity and intelligence. With an attempt to find an effective approach to the search and education of intellectually gifted youth in our conditions, on the part of the city council, in the regions of the country there is a search for ways of expanding the circle of communication, the possibility of self-expression, promoting the development of the logic of thinking, concentration of attention, education of the will of students in general education schools , by introducing into towns learning games of checkers from an early age. During the study, it was possible to notice an increased interest in mathematics in almost all children who were fond of drafts. With the growth of sports figures among pupils of checkout outlets, there is an improvement in the quality of general subjects, especially in mathematics. Schoolchildren during the study were always among those who actively participated in school mathematical olympiads and easily took part in the second round of the All-Ukrainian Olympiad. The obtained conclusions are confirmed by the analysis of mathematical abilities of pupils of 6 classes in Kamianske according to the data of the city Olympiad in 2017 year.

Keterampilan Siswa Memecahkan Masalah Olimpiade Matematika Ditinjau dari Kepribadian Tipe Senising dan Intuiting

This study aims to determine the problem-solving skills of olympiad mathematics based on sensing and intuitive personality types. The study was conducted at a private junior high school in the city of Surabaya. The subjects of this study were 2 students with sensing intuitive personality taken from students who were given the Mathematics Olympiad training, namely 1 student with sensing personality and 1 student with intuitive personality. Olympiad questions are given to explore the skills of both subjects in solving problems. The results of research students who have sensing personality (S1) are less able to define a particular topic on the question, S1 is able to work with a structure based on what is recognized, S1 has difficulty with the related topics that are being solved with other topics. S1 has difficulty in determining other solutions related to the problem being solved. Students who have the intuitive personality (S2) are able to define the meaning of a particular topic on the problem, S2 is able to link the topic to the problem with other topics, S2 is able to explain other solutions to the problems solved, S2 is able to present a more structured solution.

Invisible Geniuses: Could the Knowledge Frontier Advance Faster?

A better understanding of the determinants of idea/knowledge production remains critical for long-run growth. Toward this end, this paper establishes two results using data from the International Mathematical Olympiad (IMO). First, individuals who excelled in teenage years are especially capable of advancing the knowledge frontier. Second, such talented individuals born in poorer countries are systematically less likely to engage in knowledge production. IMO participants from low-income countries produce 34 percent fewer publications and 56 percent fewer citations than equally talented rich-country counterparts. Policies to encourage talented youth to pursue scientific careers—especially those from poorer countries—could advance the knowledge frontier faster. (JEL D83, O30, O47)

Student from Ireland wins Silver Medal at 60th International Mathematical Olympiad

Student from Ireland wins Silver Medal at 60th International Mathematical Olympiad

Конструктивные задачи в олимпиадах по математике и информатике

Constructive problems arise in all areas of mathematics. They are very important in working with schoolchildren and students, as they are one of the easiest ways to stimulate students' productive activities. This work is devoted to the role of constructive tasks in remote olympiads in mathematics and computer science. Also tasks of this kind can be used to monitor the intellectual activity of students in the educational process.