Olympiad Problems Research Articles

Using open online courses on programming in organizing independent work of students

The article highlights the need to use online courses on programming, including automatic code checking, in organizing independent work of high school students. An overview of open online courses designed to study the Python programming language, implemented on different platforms, is provided. The capabilities of each online course for solving educational problems, such as general training of students in programming, preparation for state exams, developing skills in solving Olympiad problems, organizing project activities, and career guidance for schoolchildren are discussed. The technical capabilities of the platforms on which the courses are presented are analyzed from the point of view of their didactic potential. Forms of organizing independent work of students using online courses on programming are proposed. The general algorithm for solving programming problems is specified taking into account the specifics of using the automatic system for checking and evaluating the solution implemented in online courses.

Systemic preparation of future mathematics teachers for training schoolchildren to solving Olympiad problems

The article actualizes the problem of developing the readiness of a future mathematics teacher to teach schoolchildren to solve Olympiad problems. Based on the analysis of scientific and methodological sources and the results of mathematics students’ self-assessment of their readiness for this type of activity, the need for a systematic approach to solving the identified problem is substantiated. The study outlines the author's view of the university training system aimed at developing future mathematics teachers with mathematical and methodological competencies that determine their readiness to teach schoolchildren to solve Olympiad problems, and outlines the problems that may arise during its implementation.

Objectives of the Regional Chemistry Olympiad

The main purpose of the article is to demonstrate the methods of solving and criteria for evaluating the Olympiad problems of the regional stage of the Republican Chemistry Olympiad 2024 in the Kyrgyz Republic. In the course of the study, the regulations of the Olympiad and the requirements for the Olympiad tasks of the regional stage were studied, the criteria for their evaluation were studied.

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

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

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.

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.

Formation of Research Skills of Future Teachers of Mathematics in Solving Olympiad Problems

This article addresses the critical need to enhance the professional training of teachers, specifically in the realm of teaching and research activities. The objective is to improve their cognitive and organizational skills to enhance the effectiveness of future educational endeavors. The article's primary focus is the development of a comprehensive model for instilling research skills in prospective mathematics educators. The study employs the "Diagnostics of Personal Creativity" test by E.E. Tunic as a principal assessment tool. This test aids in evaluating personal curiosity, analytical aptitude, the ability to think innovatively, and problem-solving capabilities, all of which are pivotal indicators of an individual's inclination towards research activities. The proposed model for cultivating research skills among future mathematics teachers hinges on a set of methodological parameters. These parameters are designed to elevate intellectual acumen by encouraging diverse cognitive comparisons within mental activities, forming the foundation for research-oriented thinking. The model underscores the gradual development of cognitive abilities across varying levels of depth, applied to solving complex Olympiad problems with intricate structures. In summary, this article presents a model that promises to significantly enhance the research skills of future mathematics teachers, thereby contributing to the advancement of the teaching profession and the holistic development of young learners.
 
 Received: 4 June 2023 / Accepted: 11 October 2023 / Published: 5 November 2023

Methodological Features of the Training Masters for Solving Mathematics Olympiad Problems

The article summarizes the experience of training masters of mathematics for organizing and conducting Mathematics Olympiads for schoolchildren. The purpose of the article is to characterize and summarize the methodological features of the training masters of mathematics for the organization of Mathematics Olympiads for schoolchildren. Among the research methods used, the following were decisive: analysis and generalization of scientific and methodical sources for the theoretical justification of the highlighted problem, modeling, and synthesis of the obtained data. Conclusions. Various possibilities of implementing such training have been analysed by the authors, taking into account the realities of the current state of the educational system of Ukraine. The methodical features of teaching master's students in mathematics to solving and creating mathematics olympiad problems and discrete subjects for schoolchildren are considered in the article. The benefit of the article is that the numerous examples of the implementation of the «to solve a problem – to replicate problems» approach proposed by the authors are presented, and the methodological expediency of its use in the educational process is substantiated. Conclusions. The authors have singled out the promising directions for further research in this field: the creation of appropriate educational and methodological support for the implementation of the approach «learning to solve a problem - learning to replicate problems» within the framework of other content lines of the course «Mathematics Olympiads problems: creation and solution» in the training of masters in mathematics (logical, stochastic, cryptographic, etc.) at pedagogical higher education institutions; the implementation of elements of this approach to the system of practicing teachers professional development the acquaintance high school students who study mathematics in depth with the relevant methods. The indisputable interest is in the creation of masters’ practice-oriented developments, as the part of their educational and research work, aimed at other aspects of the school mathematics education fundamentalization.

Acceleration of software execution time for operations involving sequences or matrices

The article describes three methods for lowering program runtime that are solutions to computer science Olympiad problems involving sequences or matrices. The first method relies on the representation of some sequences as matrices, after which the program for calculating the sequence's members will have asymptotics equivalent to the exponentiation algorithm's time complexity and be O(log (n)). The second strategy is to improve the existing code in order to significantly shorten program runtime. For scientists who create code for scientific inquiries and deal with matrix multiplication operations, understanding this approach is crucial. The author's challenge is presented and solved using the third strategy, which is based on minimizing temporal complexity by looking for regularities.

Regarding Classification of n-sharing of Multivariate Mappings over Finite Fields and One NSUCrypto'2019 Olympiad Problem

A problem of great importance that arises in designing and implementation of a cryptosystem is countering side channel attacks. Often an appropriate mathematical algorithm, implemented on a specific physical device to work in the physical environment, becomes vulnerable to such attacks.The “function sharing” technique is a prospective and efficient way to avoid this problem. In the paper we investigate “non-complete sharing” of Boolean functions and mappings, and functions and mappings over finite fields and provide a complete description of the set of functions with n variables, which have sharing.The main findings are the following: introducing and investigating a new concept of “weak” non-complete n-sharing, establishing its connection with “weak” and “classical” n-sharing, and substantiating its advantages from the algebraic point-of-view as well as establishing and proving a criterion for the existence of weak non-complete n-sharing for an arbitrary function. The results also include an explicit description of a set of functions which have weak sharing in terms of algebraic normal form, obtaining the precise and simple descriptions for the boundary (“border”) cases: n = 2, n=m and binary fields. Applying these results to the AES S-box allows complete solving the problem, i.e. a complete answer to the question of a representability of the S-box of the AES cipher as a sharing is available. We believe that the same way can be successful for other cryptographic algorithms.

Preparation of high school students for solving tasks of the data mining olympiads

The article describes the preparation of high school students for the Olympiads on the basics of artifcial intelligence. An analysis of existing Russian and foreign competitions in artifcial intelligence for schoolchildren is presented. The main technologies of artificial intelligence are described. The place of data mining is determined as one of the basic sections of data science and an important fundamental skill for the implementation of tasks in the feld of artifcial intelligence. The features of the implementation of such Olympiads are highlighted, the difculties that participants may encounter when performing Olympiad tasks are identifed. As a solution to the problem, it is proposed to create educational modules for preparing for Olympiads in artifcial intelligence.The structure and content of the educational module for preparing high school students for the Olympiad "The Way to Success" (section "Fundamentals of Artifcial Intelligence"), held on the basis of Nosov Magnitogorsk State Technical University. An analysis of the creative task for preparing for the fnal round of the Olympiad is presented. The task is associated with the use of data mining methods, in the course of its implementation, the students examined a data set — comments of Internet users about a foreign series in order to determine their attitude towards the main characters of the series, to identify countries where the series turned out to be the most popular and discussed.The results of the qualifying round of the Olympiad showed the following: the schoolchildren who completed the training within the framework of the educational module were able to get into the fnal of the Olympiad, the rest of the schoolchildren could not overcome the threshold value of the qualifying testing. The article notes that preparation for modern Olympiads in any subject area is an important factor for passing to the fnal. However, teachers of informatics and mathematics are not yet ready to help schoolchildren solve Olympiad problems in artifcial intelligence, it is important that such educational tracks are provided for the participants by the organizers of the Olympiads.

Formation of Students' Research Skills in Solving Olympiad Tasks in Mathematics

The article is devoted to the problem of the formation of students' research skills when learning to solve Olympiad problems in mathematics. The peculiarity of the Olympiad task is that it is non-standard, outwardly similar to the academic task on the subject and requires logic and research. In this regard, the solution of the Olympiad problem in mathematics requires research skills in constructing a graphical and physical model, drawing up equations to describe the state of interacting objects, mastering the mathematical apparatus in atypical conditions. In addition, to determine the relevance of the research topic, a questionnaire was conducted through the Google platform, the participants of which were received from students of the educational program «training of a mathematics teacher» at a university and young professionals working in high school. As a result, situational tasks and critical situations were identified, which instantly contribute to the formation of research skills to meet modern requirements. Accordingly, it was analyzed that Olympiad tasks will help to break away from the usual system of thinking and look for new things. Based on historical data, it is known that students participating in the Olympiad have a high IQ. And, judging by the PISA results, the formation of research skills is important for the intellectual development of schoolchildren. For the formation of such skills and, as a consequence, cognitive independence of the individual when studying each topic of mathematics, it is recommended to include students in solving Olympiad problems. An example of a task system developed taking them into account in the preparation of mathematical Olympiad tasks is given.

Using Lagrange’s Multiplier Method to Solve Mathematical Contest Problem

“Most people study mathematics to satisfy some requirements .Some Study Math to learn the tricks of nature so they may find out how to make things bigger or smaller or faster or more sensitive . But a few ,a very few ,study math because they wonder -not how things work ,but why they work .They wonder what is at the bottom of things -the very bottom ,if there is a bottom . This paper will be very useful to them .”-M.A.Rusho. Remember when you first participate any math contest or olympiad maybe national or International you see some terrible function and the question state that you have to find this function maximum or minimum value. You become frustrated thinking I have to take the derivative first then equalising it to 0 , then find the optimal value of X blah blah blah……. . now it’s time to reconstruct your mind for solving this type of Mathematical problem in a suitably way . First we have to think that is the difference between School textbook math problem And Olympiad Math Problem . The core difference is problem solving . But you may think that in school mathematics we all solve problem . But this problem solving is different like you can solve it by GUIDE or may a teacher can help or this problem may directly solved by any standard formula like( a+b)^2 . But in Olympiad problem You are totally in a new place , totally difference problem you didn’t see it . But you have too slove it now Many people find this difficulty .BUT IT IS not difficult if you solve it by making some useful strategies . This paper although written for High School Student’s but those who will read it thoroughly they will understand it is for useful for undergraduate or beg gainer of a graduate student from engineering background . Though Calculus , linear algebra , partial differential equation is not included in Math Olympiad Syllabus . But if you are really a Math Enthusiast I believe you already learn it !!! If you didn’t don’t be hesitate . Learn It from any book or course . Then came here to read this thesis paper . Best Wishes to all !!! Happy Problem Solving !!

Solving game problems using recursion

The article describes the methodology to game problems of Olympiads in informatics using recursive numbers generation. The study is based on the sequential solution of increasingly complex tasks. For each task, the following materials are given: the condition of the task, the idea of the solution with a proposal to come up with an independent implementation, the solution in the Pascal programming language. Distance learning system DL.GSU.BY is the effective technical base for teaching. It allows offer the student a condition of the task; send the solution for review; get a verdict from the system — a correct or incorrect solution; for incorrect solutions, the number of the test on which the solution did not pass is indicated. A student can take a test (input and output data), on which his solution did not pass, figure out what the error is in his program, correct and send the solution again. In addition, for each problem there is a link on it to the topic in the forum at site, where you can ask a question on solving this problem and / or read the answer if the questions have already been asked before.

Arranging Beetles

Summary This article, directed at undergraduate problem solvers and their mentors, discusses and solves an Olympiad problem and a generalization. We interweave subtle commentary about problem solving generally.

The mathematical competence of Olympiad participants as an indicator of the quality of mathematical training level

Introduction. The relevance of the research on the formation and assessment of the level of development of competencies in the mathematical educational field is due to the fact that the subject competence of the participant of the Olympiad predetermines his victory in the competition. And the Mathematical Olympiad, as a form of education, has potential not only for the formation, development, but also for determining the level of mathematical competence of its participants. The research problem is to justify the didactic potential of the mathematical Olympiad as a tool for determining the level of mathematical competence of school students. Aim of the study: to theoretically substantiate, develop and specify the content, indicators of mathematical competence of mathematical Olympiad participants Methodology and research methods. The methodological basis of the study is determined by: the activity and competence-based approaches to teaching; a retrospective analysis of psychological and pedagogical studies affecting the formation and development of key and subject competencies of schoolchildren; an analysis of the content of mathematical Olympiads; an analysis of the results of Kyrgyz Republic schoolchildren in international mathematical Olympiads; the study and generalization of the experience of juries of Olympiads. Results. The subject Olympiad forms a competence-based educational environment in which the levels of formation of key and subject competencies of its participants are most fully displayed. The competence-based approach to training in the Olympiad environment is characterized by the formulation of objectives from the point of view of the activity approach to the formed competence. Subject competence is leading in determining the quality of the student’s Olympiad activity. The mathematical Olympiad is one of the effective forms of both the formation and development, and the determination of the level of mathematical competence of its participants. The introduction of presented system for preparing schoolchildren for mathematical Olympiads, using model’s formation of mathematical, informational competencies in the experimental group, led to an increase in students' knowledge of the theory and practice of solving Olympiad problems in mathematics by 12,95%; the qualitative indicator of knowledge of the school curriculum in mathematics increased by 15,25%. The index of absolute indicators in the experimental groups in the theory of Olympiad mathematics was 53,12%, in the methods of solving Olympiad problems – 55,38%. In control groups, these indicators were 41,23% and 42,36%, respectively. The qualitative indicator of exam results of schoolchildren of the Olympic reserve turned out to be 19% higher. The results of the questionnaire survey participants of the Olympiads confirm the expediency of using technology for the development of critical thinking, the project method of teaching, ICT in the process of preparing for the Olympiads, contributing to the emergence of motivation to study an extracurricular course in mathematics in 68% of students, 42% of students showed a desire to participate in the Olympiads. The results obtained confirm our conclusions that the development of the mathematical competence of the participants of the Olympiads is successfully realized only in a situation of continuous Olympiad activity.

Mathematical Analysis: How Would AI Tackle Math Olympiad Problems?

Mathematical Analysis: How Would AI Tackle Math Olympiad Problems?

Mathematical Analysis: How Would AI Tackle Math Olympiad Problems?

Mathematical Analysis: How Would AI Tackle Math Olympiad Problems?

Solving school Olympiad problems as a means of quality profession-oriented training of future Physics teachers

The relevance of the study is explained by the need to increase the level of teaching Physics, to identify and develop creative abilities of both schoolchildren and students, future teachers of Physics. The preparation for Olympiads and their holding helps to raise interest in Physics. The analysis of scientific sources shows that, despite the interest of scientists in the problem of organising and improving the preparation of students for the Physics Olympiads, this problem needs further study. In particular, the pedagogical conditions for preparing students for the Physics Olympiads have not been identified; effective methods, forms and means of teaching, possibilities of information and communication technologies aimed at training students for the Physics Olympiads have not been sufficiently studied, which is especially relevant in distance training. The purpose of the study is to identify and implement pedagogical conditions for training students majoring in Secondary Education (Physics) at Ushynsky University, to develop skills in solving school Olympiad problems. In accordance with the set goal, pedagogical conditions for preparing future Physics teachers to solve school Olympiad problems have been identified and introduced into the educational process, namely: creation of interactive interaction between teachers and students in the process of solving Olympiad problems; use of modern Internet technologies, distance learning methods in the educational environment as an important factor in intensifying independent work in the process of profession-oriented training in solving school Olympiad problems. According to students, the introduction of certain pedagogical conditions contributed to increasing the level of profession-oriented training aimed at future teachers of Physics, the development of these skills: the ability to interest students in Physics; create an atmosphere of emotional enthusiasm in teaching Physics; teach basic algorithms and approaches to solving non-standard problems; to teach non-standard thinking and initiative not only in solving physical problems, but also in solving life situations; to increase the level of knowledge of English in a professional direction.

Development of Online Student Olympiad Training Materials for Elementary School Teachers in Magersari Mojokerto Subdistrict in the COVID-19 Pandemic Era

In March 2020, the World Health Organization (WHO) declared COVID-19 as an international pandemic. This condition definitely affects the learning process, especially Mathematics learning in elementary school, and one of the goals expressed by Badan Standar Nasional Pendidikan (BSNP), namely that students have the ability to understand concepts, reason, solve problems, communicate ideas, and have an attitude of appreciating the usefulness of mathematics in life. Most elementary school teachers in Magersari District have not been able to do problem solving training for students and they need help to improve their abilities in assisting their students in solving Math Olympiad problems. Therefore, an activity was held to development of online student olympiad training materials for elementary school teachers in Magersari Mojokerto Subdistrict. Base on the evaluation, it can be concluded that this activity can improve the ability of teachers to develop Math Olympiad questions at the elementary school level and be able to solve them with problem solving steps; In solving problems related to integers, teachers can apply the properties of integer operations, and do not use formulas that are not familiar to elementary school children; And also, this activity is felt to be fun and in accordance with its objectives.