INTERCONNECTION OF INFORMATICS AND MATHEMATICS IN SCHOOL AT AN EARLY STAGE OF STUDY

The relevance of the chosen research topic is to highlight the issue related to the formation of algorithmic thinking in primary school students in computer science lessons. The aim of the article is to identify the role of computer science and mathematics in the formation of algorithmic thinking style. To achieve this goal, the following methods were used: analysis, comparison, observation, synthesis. Statistical data processing was also used. The article states that the basis for algorithmic thinking is the formation of mathematical competence of junior high school students. In computer science lessons, students apply the acquired knowledge of mathematics by practical methods. Therefore, the appropriate level of students’ knowledge of mathematics is important. The article presents a table of success levels in mathematics and computer science for third and fourth graders of one of the primary schools in Uzhhorod. The level of success in studying mathematics was compared with the level of success in studying computer science by third-graders and similarly by fourth-graders. When comparing the two empirical distributions, we used the two-sample Kolmogorov-Smirnov agreement criterion. We have shown that the selected general populations are stochastically equivalent. Comparing the results of educational achievements in computer science and mathematics of students of 3rd and 4th grades, we came to the conclusion that the formation of mathematical competence helps in solving problems in computer science lessons that require logical thinking and algorithmic skills. We believe that more attention should be paid to the study of the basics of programming in school, the development of logical and algorithmic thinking in mathematics and computer science, as well as in elective classes.

Programar para aprender Matemáticas en 5º de Educación Primaria: implementación del proyecto ScratchMaths en España

Este artículo presenta los resultados de la investigación que ha medido el impacto causal de la intervención realizada en el marco del proyecto Escuela de Pensamiento Computacional, que el Ministerio de Educación y Formación Profesional de España puso en marcha en el curso académico 2018-2019. En concreto, el trabajo estudia si es posible mejorar el desarrollo de la competencia matemática del alumnado a través de actividades de programación usando el lenguaje Scratch en 5º de Educación Primaria. El diseño de la investigación consiste en un estudio empírico de intervención basado en las lecciones aprendidas del proyecto ScratchMaths, desarrollado por la University College London en Reino Unido. Se han usado dos grupos de estudiantes no equivalentes, grupo experimental y grupo de control, sin asignación aleatoria, con medición pre-test y post-test sobre la variable competencia matemática. Para ello, se ha contado con la participación de más de 3.700 estudiantes, que fueron asignados bien al grupo experimental -que trabajó la competencia matemática a través de actividades de programación informática- o al grupo de control -que lo hizo con otras actividades y recursos habituales en el área de Matemáticas. Los resultados muestran que el alumnado del grupo experimental desarrolló en mayor medida esta competencia que el alumnado del grupo de control, apreciándose un impacto significativo y positivo sobre la misma. Con un tamaño del efecto de la intervención d=0,449 puede afirmarse que el proyecto logró el efecto pretendido sobre la competencia matemática de los estudiantes. La generalización de experiencias de pensamiento computacional en el currículum podrá garantizar la mejora de la calidad de los procesos de enseñanza y aprendizaje. This article presents the results of an investigation that has measured the causal impact of the intervention carried out within the framework of the School of Computational Thinking project, launched by the Ministry of Education and Vocational Training of Spain in the 2018-2019 academic year. Specifically, the work studies whether it is possible to improve the development of students’ mathematical competence through programming activities using the Scratch language in 5th grade of Primary Education. The research design consists of an empirical intervention study based on the lessons learned from the ScratchMaths project, developed by University College London in the United Kingdom. Two groups of non-equivalent students have been used, the experimental group and the control group, without random assignment, with pre-test and post-test measurement on the mathematical competence variable. More than 3,700 students participated in the investigation, who were assigned either to the experimental group -which worked on the mathematical competence through computer programming activities- or to the control group -which did so with other common activities and resources in the area of ​​Mathematics. The results show that the students in the experimental group developed this competence to a greater extent than the students in the control group, with a significant and positive impact on it. Being the intervention effect size d=0.449, it can be stated that the project achieved the intended effect on the students’ mathematical competence. The generalization of computational thinking experiences in the curriculum can guarantee the improvement of the quality of the teaching and learning processes.

Conceptual replication and extension of the relation between the number line estimation task and mathematical competence across seven studies

A recent meta-analysis demonstrated the overall correlation between the number line estimation (NLE) task and children’s mathematical competence was r = .44 (positively recoded), and this relation increased with age. The goal of the current study was to conceptually replicate and extend these results by further synthesizing this correlation utilizing studies not present in the meta-analysis. Across seven studies, 954 participants, ranging from 3 to 11 years old (Age M = 6.02 years, SD = 1.57), the overall estimation-competence correlations were similar to those of the meta-analysis and ranged from r = −.40 to −.35. The current conceptual replication demonstrated that the meta-analysis captured a stable overall relation between performance on the NLE task and mathematical competence. However, the current study failed to replicate the same moderation of age group presented in the meta-analysis. Furthermore, the current study extended results by assessing the stability and predictive validity of the NLE task while controlling for covariates. Results suggested that the NLE task demonstrated poor stability and predictive validity in the seven samples present in this study. Thus, although concurrent relations replicated, the differential age moderation, lack of stability, and lack of predictive validity in these studies require a more nuanced approach to understanding the utility of the NLE task. Future research should focus on understanding the connection between children’s developmental progression and NLE measurement before further investigating the predictive and diagnostic importance of the task for broader mathematical competence.

Assessment of mathematical competence using the Estonian national e-tests

Eesti matemaatika e-tasemetööde eesmärk on hinnata matemaatika aineteemade õpitulemusi, aga ka matemaatikapädevust kui üldpädevust. Samas on töid koostades lähtutud ülesannete kategoriseerimisel aineteemadest ning puudub ülevaade, kuivõrd hästi võimaldavad e-tasemetööd hinnata matemaatikapädevuse kui üldpädevuse dimensioone. Siinses artiklis antakse ülevaade matemaatikapädevuse käsitustest ja analüüsitakse Eestis põhikooli II kooliastme matemaatika e-tasemetöid, lähtudes matemaatikapädevuse uurimisraamistikust. Tulemused näitasid, et 2020. aasta töös keskenduti kõigile kuuele alampädevusele, kõige enam protseduurilisele pädevusele ja kõige vähem arutluspädevusele. Varasemates töödes on aga osa alampädevusi jäänud hindamata. Samuti ilmnes, et vähe on tähelepanu hinnangu andmisel ning rohkem tõlgendamisel ja pädevuste kasutamisel. Uuringu tulemused aitavad avada matemaatikapädevust kui üldpädevust ning toetada pädevuse hindamist nii tasemetöödes kui ka õpetajate igapäevatöös. Summary

Developing students' mathematical competence through equipping them with necessary knowledge about metacognition- and activities in teaching mathematics in secondary school

Metacognition theory has been interested in research since the 70s of the twentieth century in the world. It can be seen that the thinking process, perception and metacognition of students and mathematical competence is one of the focus of research on mathematics education. However, the problem that is always interested by researchers in mathematics education is how to develop mathematical competence? What factors influence this capacity development process? How to support students to become better math problem solvers, especially in math? To find solutions to the problems posed above, a number of studies in the world and in Vietnam have focused on the relationship between metacognition and problem solving; At the same time, find ways to apply metacognition in the process of teaching mathematics. This study focuses on the goal of developing learners' competencies; Especially for the goal of developing mathematical competence for high school students through Mathematics, there is a need to research and exploit the thinking and cognitive factors in learning Mathematics to find solutions to overcome these problems.

METHODOLOGICAL PROBLEMS OF TEACHING HIGHER AND APPLIED MATHEMATICS OF STUDENTS OF ELECTROMECHANICAL DIRECTION

The article considers the main problems characteristic of mathematical education in higher technical institutions. The purposes and tasks of training of higher and applied mathematics of students of technical specialties, and also separate features of training of students of an electromechanical direction to mathematical disciplines are covered. Achieving the current goal of modernization of mathematics education in technical universities is associated with the solution of a number of pedagogical issues. The problem is the systematic and comprehensive reform of mathematics education in accordance with current trends in both production and education. The content of mathematical education needs to be changed, in particular: curricula and study programs, the level of educational material, methods, teaching technologies, procedures for diagnosing the quality of teaching. Curricula of specialties should contain mathematical disciplines, which include special mathematical sections that allow to provide quality training of professionally oriented disciplines and allow to form mathematical competence as part of the professional competence of the future professional. The solution of the problem of formation of mathematical competence as a part of professional competence of graduates of technical universities becomes actual. This necessitates the strengthening of the professional orientation of the content of teaching mathematics, the intensification of the activity approach in learning technologies, the importance of the formation of appropriate value orientations of students. Actualization of students' activities strengthens the role of such educational technologies as multilevel learning, independent work of students, computer technology, project activities. Thus, additional mechanisms are created for the systematic acquisition of knowledge and skills by students, for the systematic control of the formation of mathematical competencies, for a differentiated approach to learning. To improve the quality of mathematical education of students of technical universities it is necessary to pay attention to the construction of mathematical models of real production problems and methods of their solution. The use of mathematical modeling methods leads to the need for a deeper study of the relevant sections of mathematics. This approach changes the structure of training, gives the opportunity to use more independently the independent work of students. At the same time, students' knowledge will be deeper and stronger.

Design Methodology for Electronic Training Problems Aimed at Development of Mathematical Problems Solving Competence

The aim of the study. The fourth industrial revolution demands highly qualified personnel as important factor of economic growth, which imposes serious requirements on the formation of key and subject competencies among graduates of higher educational institutions. A particularly important role is assigned to the mathematical competence which is required to solve complex and science-intensive problems. Given the growing share of e-learning and distance learning at the university, it is necessary to intensively develop the methodology for mathematical competence formation in the electronic environment, and create effective teaching tools on its basis. The current level of digitalization of education already allows organizing independent work of students in the electronic environment at a sufficiently high level. In the literature we can find various methods and tools, aimed at the formation of the cognitive component of competencies. However, the issue of skills’ development in the electronic environment is still underrepresented. The purpose of this study is to develop a methodology for creating electronic training problems, which aims at forming a practical component of mathematical competence – the competency of solving mathematical problems.Materials and methods. In the study we performed a comparative analysis of scientific and methodological literature, regulatory and methodological documents, as well as professional and federal educational standards of higher education. The development of a model of electronic training problems was carried out using methods of structural modeling. The developed methodology was implemented in the educational process, and the confirmation of its effectiveness was obtained by statistical analysis of the results of the pedagogical experiment.Results. We proposed a methodology for electronic training problems development aimed at formation of mathematical problems solving competency. The methodology is based on existing approaches to problem solving formalization. In the presented structural model of an electronic training problem, the aspects of problem solving discovered earlier by other authors, are supplemented by the contextual aspect. This aspect is intended for linking the regarded problem with the material, studied at the moment and, if possible, with future professional activity of a student. The proposed methodology for organizing feedback in an electronic training problem contributes to the formation of metacognitive skills among students through the elements of tutoring.Conclusion. On the basis of the proposed methodology, 8 electronic training problems were developed for the course “Probability and Mathematical Statistics” and tested in the educational process of the Siberian Federal University. The effectiveness of the electronic training problems for the development of mathematical problems solving competency was assessed in the course of a pedagogical experiment. The purpose of the experiment was to study the impact of the electronic training problems in the competency formation for particular topics of the course. Using student’s test for independent samples and the Mann-Whitney test we confirmed that the designed electronic training problems positively affect the formation of mathematical problems solving competency. In the future, the proposed methodology can be included in the teaching toolkit for the formation of mathematical competence in an electronic environment.

THESAURUS APPROACH: ON THE FORMATION OF MATHEMATICAL COMPETENCE AND COMPETENCE OF FUTURE ENGINEERS

In the article, the question of improving the formation of mathematical competencies and competencies of future engineers on the basis of a fast-paced approach is developed, in particular, the main concepts, the main issues of the topic, the importance of building a thesaurus, which includes the methods of activity for solving these issues.

PEDAGOGICAL CONDITIONS FOR FORMING BILINGUAL MATHEMATICAL COMPETENCE IN BASIC SCHOOL STUDENTS

Introduction. In the process of bilingual education, schoolchildren must not only qualitatively master the content of the subject but also overcome language difficulties. There is a connection between speech and mathematical activities. The essence and structure of bilingual mathematical competence are based on this relationship, allowing bilingual students to effectively acquire knowledge in the conditions of national-Russian bilingualism. We have also proposed ways of forming bilingual mathematical competence focused on developing mathematical speech culture and teaching schoolchildren to use multicultural knowledge. Aim. The article aims to characterize the pedagogical conditions directed at the emergence of bilingual mathematical competence among basic school students (grades 5 to 9) within national-Russian bilingualism. Material and methods. The study relies on theoretical methods of comparative analysis, synthesis, and generalization provided by the scientific and methodological literature on the researched topic. Results and discussion. Works indicating a clear relationship between the language of instruction and the subject of Mathematics were analyzed. The need to take into account the mother tongue of schoolchildren in bilingual education was established. In addition, it was found that the degree of native and Russian language proficiency affects the mathematics achievement of bilingual students. According to the analysis, bilingual education should lead to the emergence of competencies distinguished by a high level of language proficiency and high-quality mastering of the subject. Conclusion. The concept of “bilingual mathematical competence” got a detailed description in the course of the research. This concept combines components of a school subject, languages ( native and Russian), and a component of intercultural communication. The following pedagogical components were described: 1) tasks aimed at mastering terminology, symbols, and graphic images; verbal and logical constructions of the mathematical language; written educational texts; 2) illustrated Yakut-Russian, Russian-Yakut terminological dictionary in mathematics for the 5th and 6th grades, which includes 349 terms and set phrases; 3) bilingual strategies aimed at reducing the linguistic complexity of mathematical problems (by replacing unfamiliar or rare words; changing the passive voice to active verb forms; reducing long names and indications; highlighting individual conditional sentences, or changing the order of the conditional and main sentences; replacing complex questions to simple ones; clarification of abstractions using more specific information); 4) methods and techniques of bilingual teaching of mathematics (consecutive translation, visual aids, immersion teaching, semantization); 5) tasks that contain historical, ethnocultural, and local history materials.