International Basic Sciences Knowledge Contest

Mamalyga Raisa Fedorovna


XI International Contest in mathematics is held in honor of the scientific and pedagogical staff of the Studio “Geometry-Computer-Geometry” under the leadership of Raisa Fedorovna Mamalyga


Raisa Fedorovna Mamalyga was born on May 9, 1945. In 1966 she graduated from the mathematical faculty of Sverdlovsk State Pedagogical Institute, in 1970 she finished postgraduate studies at the Department of Algebra and number theory under the guidance of P.A. Freidman. Since 1970 she has been working at the Department of Geometry of the Institute. In 1989 she was elected to the position of senior teacher. In 2005 she defended her thesis for the degree of Candidate in Pedagogical Sciences on the theme “Development of spatial thinking of students at pedagogical university in the formation of concepts in the geometry”. In the same year she became an associate professor of the Department of Geometry.

In 2002 Raisa Fedorovna established the Studio “Geometry-Computer-Geometry” at the Mathematical Faculty of Ural State Pedagogical University (Yekaterinburg), in which enthusiastic students, fans of geometry and computer, got together.

The main focus of the Studio is to study the possibilities of information technologies during learning of school subjects, in particular geometry.

The studs were concerned about slump of students in the study of geometry. They think that “Geometry is the alpha and omega of school education”. The Studio motto was chosen with maximalist enthusiasm: “While the geometry is studied at the Russian schools, Russia is live”. Here was the goal: to bring the teaching of geometry to the life interests of the students at most, to make the process of learning the complex science alive and exciting. After analyzing the content of school geometry, the studs noticed that the bulk of the material relates to the III century BC (the Euclid’s geometry) followed by a small inclusions (elements of vector algebra of XVII-XVIII centuries). Isn't this one of the reasons for the loss of interest to the geometry of the learners? May they be needed “new breath”: new tools, new forms, and new content? One of the modern branches of mathematics, a real “treasure”, fractal geometry, has attracted attention of students for a long time.

Thus a new interesting pedagogical idea was born: the introduction of fractal geometry elements in the educational process of students. Initially it was necessary to answer the following question: is it possible to study the fractal geometry at school? Many believed that the mathematical base of fractals cannot be successfully learned by students (even at high school); some asserted that the theory of fractals is difficult to understand to graduates. It was decided to experiment at the Mathematical Faculty. In 2007 it was organized the seminar “Fractal geometry” for students of 1-2 year at the Department of Geometry. After the seminars the students developed a study program of fractals for high school students. Subsequent testing of program at schools in Yekaterinburg and Rezh showed that fractal geometry is amenable to study by students and raises their interest. First successes were come: tenth-grader was first with the essay “Using “Fractal Explorer” in computer graphics” in the city competition of essays, and the studs, making the results of the work done in the project “Fractals for schools”, took second place in the interuniversity contest of socially significant student projects “My initiative in education”, St. Petersburg (2009).

Experience with the students of the 10th grade of secondary schools (2008-2009) showed that they can be formed with the necessary knowledge for the assimilation of the theory of fractals elements. Members of the Studio have wondered whether such experiment will be successful in mass implementation in educational institutions. What books and how much can the students are taught the integrated course? Is it possible the earlier acquaintance with the elements of fractal geometry?

The next stage of activity (2009-2011) was aimed at finding answers to the questions. For this purpose they organized systematic study group “Fraktalenok”. Students were divided into two groups: Junior (grades 5-6) and Senior (grades 7-8).

The studs prepared a training manual to practice with the first group (didactic tale “FractaL-OGO!”). In addition to the manual, presentations and guidelines were prepared to these lessons; the author's didactic games were used.

The cover of the book “FractaL-OGO!”

During the course the students have mastered the knowledge necessary for the study of the elements of fractal geometry, including the interface of Logo and its basic commands. The activities of the trainees were to analyze the finished images with fractal elements. Also their own illustrations were created manually, with a pencil on paper, and automatically, in the Logo environment. The final goal of the annual study was the formed complex concept “fractal” of the students, the development of visual culture and artistic and creative abilities of children, the establishment of the foundations of aesthetic taste. The basis of the content of the second year of teaching was the classification of self-similar fractals developed by students. The basis of classification was the way of building. One of the main goals of the course was the formation of students’ concept of fractal dimension and skill of dimension counting known as fractal sets and fractal structures created by them in the learning process.

Over the period (2009-2011) the work of the Studio was evaluated not only in Yekaterinburg, but also at national level. So in 2010 the first-ever in Yekaterinburg (and maybe in the whole country?) exhibition “Fractal spring” was held, which presented the works of Yekaterinburg schoolchildren and students of Ural State Pedagogical University, made with a brush and with the help of specialized software (Logo, Photoshop, Paint). Large-scale exhibition brought victory in the contest of socially significant student projects “My initiative in education”, St. Petersburg (2010). At the international conference “Mathematics. Computer. Education” (Pushkino, 2011) the performance of the Studio members with the report “Formation of the visual culture on the elective “Fractals. Visual culture. Aesthetics” among students of secondary level” was appreciated as the best poster presentation.

With the increasing number of those wishing to study the elements of fractal geometry, the study group “Fraktalenok” grew out in the center of additional education “SaMoKaT”. There was also a change in the organization of educational process: two step division was replaced by a three-step one:

• Stage I - Origami (grades 5-6);

• Stage II - LogoWorlds (6-7 classes);

• Stage III - Pascal. Fractals. Parquets (8-9 grades).

The appearance of a separate course of study “Origami” was associated with the response to the questions: is it possible an earlier acquaintance with the elements of fractal geometry? The Studio came to the conclusion that study of the elements of fractal geometry must be preceded by the formation of the concept of "similarity" for the youngest students of fractals: the ability to see similar figures, identify and replicate them. The paper plastics art, such as “origami”, has a great potential for this purpose.

The idea of popularizing the theory of fractals gradually (from 2012) began to acquire various “fancy” shapes: there have been developed such projects as “Virtual Museum”, “Make a present of Japan to the children”. One of the most striking results of the Studio’s work is an annual competition and festival “IMAGIRO theatres”, that is a unique project, in which children make theatrical and puppet shows, where all the heroes and the characters are made in the technique of origami. Moreover, students are actively working with remedial orphanages and boarding schools, where origami classes are held, helping children to adapt in society and to develop fine motor skills.

Today the Studio continues its work looking for new creative and scientific achievements. The decade of fruitful work is just behind. Only in the last academic year the students participated in four international conferences; organized the workshops “Origami” and “The Creator of fractals”, which were held in the framework of the Eurasian economic forum and the National student conference; became once again the winners of the contest “My initiative in education”; presented the case stands in regional exhibitions “Education. Work. Career” and “Education from A to Z. Career”. Members of the Studio are annually invited to the International exhibition of industry and innovations INNOPROM.

Now members of the Studio include not only students of the native mathematics faculty, but also students of other faculties: faculty of foreign languages, linguistics, and computer science. Join “the fractal flow” and the current teachers, inspired by the ideas of fractal geometry, seriously carry away their students. The Studio’s graduates prove that “former students” don’t exist. Having achieved their first success in the Studio, they all rushed to new heights as inquisitive researchers, talented teachers, bright organizers, successful developers of contests and other intellectual competitions.

More details at what projects scientific and pedagogical staff of the Studio is currently working, you can find at the website  and in the group Vkontakte:


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