ОТ СОСТАВИТЕЛЕЙ
Настоящий номер журнала «Электронные библиотеки» является второй частью тематического выпуска, в котором представлены статьи авторов, подготовленных ими на основе докладов, сделанных на 9-й Международной научно-практической конференции «Математическое образование в школе и вузе: опыт, проблемы, перспективы (MATHEDU’ 2019)». Эта конференция состоялась 23–27 октября 2019 г. в Институте математики и механики (далее – ИММ) им. Н.И. Лобачевского Казанского федерального университета (далее – КФУ) и была посвящена 215-летию основания Казанского университета. Организаторами конференции были ИММ и Региональный научно-образовательный математический центр КФУ.
Лейтмотивом, связующим все прозвучавшие на конференции выступления, стало обсуждение проблем и дальнейших перспектив развития математического образования в условиях его цифровизации и перехода на новые образовательные стандарты. Данный номер журнала является продолжением вы-пуска, представленного в части 1 (номер 5 за 2019 год). Статьи, вошедшие во вторую часть выпуска, посвящены проблемам применения современных технологий обучения математике и компьютерных наук в вузе, создания цифровой образовательной среды для обучения математике.
Настоящий номер журнала «Электронные библиотеки» подготовлен за счет средств субсидии, выделенной КФУ для выполнения государственного задания в сфере научной деятельности, проект № 1.13556.2019/13.1.
А.М. Елизаров, Л. Р. Шакирова
Published: 15.12.2019
Full Issue
Articles
Organization of Independent Work On Mathematics At A Medical University
Abstract:
There were identified problems that arise in the teaching of mathematics a medical university. We considered the ways of organizing independent work at each stage of studying a subject by using an electronic training course implemented on the Moodle platform. We studied the students' attitude to the components of the course, which allows to assess which resources are the most demanded.
Keywords:
medical education, mathematics teaching, independent work of students electronic training course.
Geometric Constructions On a Plane with a Single Ruler
Abstract:
One section of a special course “Constructive Solid Geometry” is presented in this paper in short. The course is conducted to the students of Mari State University who are future Math's teachers. The material is arranged in such a way that it can be recommended to all Math's teachers as a part of their special course in their schools.
Keywords:
special course, building one line, system of axioms, the basic construction.
Multi-Level Mathematical Training of University Students
Abstract:
An important role for the purposeful development of the motivational component of the formed competences among students of engineering and natural-science (geological) specialties is played by the demonstration of the application of mathematical methods of calculations in engineering and geology. At the same time, the solution of practice-oriented tasks is of great importance.It is necessary to teach the student to master the material not only at the knowledge level, but also at the level of mastery of mathematical methods and models, interpolation and extrapolation not only in mathematics, but also in solving professional and life problems.
Keywords:
motivation, competence approach, practice-oriented tasks, mathematical methods, professional activity.
Competence Approach in Teaching Higher Mathematics Students of Bachelors of Direction of Preparation 13.03.02 – “Power and Electrical Engineering” in Oil and Gas University
Abstract:
The purpose of mathematical training of bachelors of technical specialties in the framework of the competence approach is the formation of mathematical competence of the specialist, which is expressed in the ability of graduates to apply mathematical methods in professional activities. Competences are acquired by students in the process of mastering the content of education fixed in educational standards and curricula of disciplines. Using new methods and forms of organization of the educational process, using new teaching tools, competencies are formed in lectures and practical classes in higher mathematics.
Keywords:
competence approach, mathematical training in oil and gas University.
Stem-Education in Modern School Within the Framework Of Design Activity in Natural Scientific Disciplines
Abstract:
The issue of STEM education in a modern school and methodological approaches to its implementation on the subjects of the natural science cycle as part of project activities are considered. An example of the stages of work on a project, a breakdown into subject areas, is given. Since STEM education involves not only gaining knowledge in individual subjects, but also putting them into practice, the key point in working on a project is practical application. Within the framework of the subject area of mathematics and computer science, this involves making calculations and presenting the final results using modern technical means. Thus, the subject of mathematics moves from the framework of academic knowledge to the framework of practical skills. In particular, the article provides an example of the formation of a student’s financial literacy as part of a project. STEM-training allows you to combine scientific methods, mathematical modeling, technological applications and engineering design. Thus, innovative critical thinking is formed, the opportunity and need for integrated training on topics within the framework of which active communication of students occurs and a new educational space is formed.
Keywords:
STEM-education, project activities, teaching methods.
“Technology of Guiding Questions” As a Method of Training To Solve Geometric Problems for Proof
Abstract:
“Technology of leading questions” as a teaching method is considered in the article. Substantial features of learning technology are disclosed. Pedagogical approaches to learning technology are considered. The components of learning technology as elements of the content structure are considered. The concepts: “leading question” and “technology leading questions” are defined. An example of the application of “technology leading questions” is proposed. The relevance of learning technology for the formation of skills to solve geometric problems on the proof is explained.
Keywords:
geometry, methods of teaching geometry, proof, learning technology, leading question, technology leading questions.
To Teaching the Course “Linear Algebra” in Higher Education
Abstract:
In the article discusses the questions of building the course “Linear Algebra” in higher education, the goals and objectives of training are considered. Also touched upon are the problems of teaching theoretical material in mathematics.
Keywords:
linear algebra, theoretical material, evidence-based approach.
Forms of Interaction Between Participants of the Educational Process at the Master's Degree
Abstract:
In the article describes the principles of creating an educational space at the master's level that meets new meanings in education, and offers effective forms of interaction of participants in the educational process, corresponding to the selected principles.
Keywords:
educational space, principles, forms of interaction.
Implementation of Case-Technology in the Process of Teaching Mathematics of Students-Bachelors of the Oil and Gas Case
Abstract:
The problem of the formation of personality activity in teaching mathematics is very complex. The question remains for the teacher of mathematics: what methods to apply so that teaching mathematics is effective and practice-oriented, develops personality activity in collective mathematical activity? The paper describes the specifics of the use of case technology in teaching mathematics.
Keywords:
oil and gas industry, oil and gas education, the problem of sustainability of innovative development, case technologies.
The Poster Report As a Means of Considerd Representation Of Results Of Teaching And Methodical Activity By Future Teachers Of Informatics During Teaching Practice Title
Abstract:
The learning activities of students during pedagogical practice are aimed at preparing and conducting computer science lessons, and methodological – at analyzing the success of choosing and implementing various approaches, methods, forms and means when working with pupils. The poster report gives students the opportunity to present the results of these activities in a meaningful, considered and interrelated way.
Keywords:
informatics didactics, teaching practice, poster report.
Active Methods in Teaching Students of Pedagogical Universities to Mathematical Disciplines
Abstract:
In the article discusses the use of active methods in teaching students pedagogical areas of mathematics.
Keywords:
active methods, teaching mathematics, training teachers of mathematics.
The Use of Authentic Scientific Texts in the Process of Teaching Students to Solve Tasks of Differential Geometry
Abstract:
In the article presents the classification of problems by differential geometry, which is based on the nature of the relationship between the elements of the problem and the relationship between the reproducing and creative activity of students in their decision. It is shown that an important source for the choice of texts of problems and methods of their solution are the works of scientists – creators of classical differential geometry. Work with the corresponding scientific text allows the student to master such an educational strategy as methodological reduction.
Keywords:
differential geometry, problem solving, historical material.
Teaching Students Mathods of Self-Regulation in Solving Mathematical Tasks
Abstract:
Actual problem of modern theory and methods of teaching mathematics – teaching methods of self-regulation in the process of solving mathematical tasks.
Keywords:
teaching methods, mathematical tasks, methods of self-regulation.
From the Experience of Using the Method of Step Representations in Preparing Students for Scientific and Practical Festivals
Abstract:
Digitalization of the Russian economy requires appropriate changes in the system of education and training. Transformations in the system of secondary education should begin in the subject area «Mathematics and informatics». The paper shows the experience of training and participation of school students in the sections of mathematics, informatics, bioinformatics of scientific conferences.
Keywords:
step representations, scientific and practical conferences, representation of common fractions, reproduction of binary sequences, modeling of biological objects, modeling of chaotic structures.
On the Invariance of Indefinite Integral On the Method of It’S Calculation
Abstract:
Invariance of the indefinite integral on the method of its calculation is noted. Model problem that can be used for the demonstration of this invariance is treated and solved via three different methods. Significance of formation and development of student’s mathematical culture is noted.
Keywords:
primitive, indefinite integral, methods of integration.
Working Notebook On Differential Equations As a Means of the Organization of Independent Work of High School Classes
Abstract:
In the article uses additional opportunities to study the elements of the theory of differential equations (hard and soft models). The use of a workbook on a differential equation as a means of organizing the independent work of high school students is considered.
Keywords:
independent work, differential equations, high school students, appropriate education.
Formative Assessment of Future Teachers’ Cognitive Activity In The Process of Solving Problems Within Math Courses
Abstract:
A system of criteria for evaluating the solution of problems from the subject area while training future teachers of mathematics is described. The criteria are formulated in terms of activities and are aimed at strengthening the professional component of the process of mastering mathematical disciplines. Using this system of forming criteria in the study of basic structures of calculus is proposed.
Keywords:
professional pedagogical education, mathematical education, criteria-based assessment, activity approach to learning, facilitation.
Application of the Methodology Mathematical Fights When Learning Geometry
Abstract:
Individual geometry projects for the seventh, eighth, and ninth grades of middle school were created. Each project contains twelve tasks. Each task is described using a drawing. By defending school geometry projects, students engage in the geometric battle.
Keywords:
geometry, psychology, intelligence, planimetry, school projects, drawings of tasks, protection, defend projects, geometric battle.
Mathematical Speech as a Development of the Mathematical Knoweledge of Students
Abstract:
The following questions are mentioned: teaching mathematics at the present stage and its purpose; mathematical language students – as a major component of mathematical training; scientific – psychological and scientific – methodical speech of pupils of secondary schools; the development of mathematical speech of pupils.
Keywords:
mathematics, learning, mathematical purpose speech learning, memory, thinking.
Formation of Economic Culture of Students at the Lessons of Mathematics in Primary School
Abstract:
In the article discusses the problems of formation of economic culture of younger students in the process of teaching mathematics, provides examples of the economic module of school mathematical problems.
Keywords:
mathematics, economic culture, methodology.
Run and Solve: Competitions in Mathematical Rogaining
Abstract:
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.
Keywords:
mathematical games, parametrized problems, travelling salesperson problem, urban regaining, outdoor activity.
Implementation of the Impact of Ict on Methods of Teaching Mathematics in Higher Education
Abstract:
In the article presents a variant of the methodology of preparation and implementation of the content of the mathematical discipline of one humanitarian direction of training students for the use of ICT. As an example, the use of e-mail and mobile ICT tools of trainees is chosen.
Keywords:
author's methodical system of training, didactic possibilities of ICT means, principle of discretization.
About Formation of Professional Competences of Future Technicians-Programmers in the Course of Training in Programming
Abstract:
In the article describes the experience of formation of professional competences of future technicians-programmers in teaching programming.
Keywords:
professional competences, structural and object-oriented programming, Lazarus programming system.
Students’ Competencies Development: Formation of Organizational Skills
Abstract:
In the new era, when the public employment structure is changing towards the proportion of routine labor reduction, the task of formation the project thinking and organizational skills among students is of high priority. In this article the analysis of educational and developmental opportunities of one of the organizational individual ways of studying advanced math was executed on the basis of pragmatist, competency-based, and technologic approaches. It was found out that all elements of the considered concept were formed during the application of this method. Also, the described way is promoting the quality improvement of students’ mathematical background without essential pressure increase on the professor.
Keywords:
competency, project thinking, individual work, point rating system, training quality, mini-max, advanced math.
Generalization of Innovative Approaches to the Modernization of Methods of Teaching Algebra in School
Abstract:
In the article proposes a set of methods for teaching algebra at school, which contributes to the adaptation and development of the personality of the student, to increase the efficiency and scientific nature of teaching mathematics.
Keywords:
personalized training, intersubjective training, referenceservice training, mobilizacija, a method of presenting entity, the method of finding the essence, the method of cognitive semantic models.
From the Experience of Teaching the History of Informatics Using Case Technology
Abstract:
In the article describes the basics of case technology. Examples of cases on the history of Informatics are given. Methodical approaches to the development of cases and the organization of the educational process with their use are explained.
Keywords:
methods of teaching Informatics, case-method, history of Informatics.
About Features of Design of Individual Educational Routes in Mathematics
Abstract:
In the article discusses some approaches to the problem of pedagogical design of educational activities of students taking into account their individual characteristics. Features of the design of individual educational routes in mathematics are revealed.
Keywords:
individualization of instruction, individual educational route, design of individual educational routes in mathematics.
An Approach to Presentation of the Lobachevskii Geometry to Secondary School and First Year University Students
Abstract:
The group of motions of the Lobachevskii plane, as well as that of the Euclidean plane, is generated by reflections in straight lines.This allows ones to develop an approach to constructing the Poincaré model of Lobachevskii plane based on the properties of inversions and pencils of circles in the Euclidean plane.
Keywords:
absolute geometry, inversion, Lobachevskii geometry, horocycle, Poincaré model, pencil of circles, equidistant curve.
Qualitative Analysis of the Relationship Between Teachers and Students`not-Knowing in the Process of Solving Reasoning Tasks
Abstract:
Mason and Spence’s (1999) work demonstrate a detailed view into the concept of knowing. Although they highlight the importance of not-knowing as a first step, it is a topic that is not well researched. This study aims at expanding that research, by analyzing not-knowing expressions from teacher to student and possible connections to be found. During a course of geometric reasoning student teachers were asked to reason with a tangram while simultaneously recording their expressions of not-knowing and reflecting on it periodically. Student teachers were then tasked to teach this lesson to their students, who would also reflect and express their forms of not-knowing. Findings presented no real link between teacher-student expressions of not-knowing, but two major conclusions were made. Individuals altogether struggle conveying their not-knowing clearly and when they did express it, these expressions leaned heavily on not-knowing-that and not-knowing-how forms. A discussion follows to interpret said findings. A conclusion is made detailing key points in the study and what comes next for the concept of not-knowing.
Keywords:
knowing, not knowing, secondary school mathematics teachers.
How to Assign Points for Chores
Abstract:
Many parents reward their children for doing different chores. The problem is that: while in the beginning, kids are very enthusiastic about performing chores and collecting points, by the time when they have accumulated a sufficient number of points, they become less and less interested. In this paper, we provide a decision theory solution on how many points to assign for consecutive chores.
Keywords:
chores, utility theory.
Egyptian Fractions Re-Revisited
Abstract:
Ancient Egyptians represented each fraction as a sum of unit fractions, i.e., fractions of the type 1/n. In our previous papers, we explained that this representation makes perfect sense: e.g., it leads to an efficient way of dividing loaves of bread between people. However, one thing remained unclear: why, when representing fractions of the type 2/(2k+1), Egyptians did not use a natural representation 1/(2k+1)+1/(2k+1), but used a much more complicated representation instead. In this paper, we show that the need for such a complicated representation can be explained if we take into account that instead of cutting a rectangular-shaped loaf in one direction – as we considered earlier – we can simultaneously cut it in two orthogonal directions. For example, to cut a loaf into 6 pieces, we can cut in 2 pieces in one direction and in 3 pieces in another direction. Together, these cuts will divide the original loaf into 2 * 3 = 6 pieces. It is known that Egyptian fractions are an exciting topics for kids, helping them better understand fractions. In view of this fact, we plan to use our new explanation to further enhance this understanding.
Keywords:
Egyptian fractions, teaching fractions, history of mathematics.
Anatole France`s Statement on Education Transformed into a Theorem
Abstract:
Education researchers often cite a statement from Anatole France: "An education isn't how much you have committed to memory, or even how much you know. It's being able to differentiate between what you know and what you don't." In this paper, we show how this statement can be transformed into an exact theorem.
Keywords:
Anatole France's statement, logic.
How to Assign Grades to Tasks so as to Maximize Student Efforts
Abstract:
In some classes, students want to get a passing grade (e.g., C or B) by spending the smallest amount of effort. In such situations, it is reasonable for the instructor to assign the grades for different tasks in such a way that the resulting overall student's effort is the largest possible. In this paper, we show that to achieve this goal, we need to assign, to each task, the number of points proportional to the efforts needed for this task.
Keywords:
Grade assignment, maximizing student efforts.