**EDUCATIONAL TECHNOLOGIES**

### Gamification in Cloud-Based Collaborative Learning

**Abstract.** Gamification is a widely accepted approach aimed at increasing the learner’s motivation. The paper presents a study on gamification approach in face-to-face collaborative learning, supported by cloud-based environment. The concept of gamification is discussed, paying detailed attention to the motivating power of game elements and techniques.The existing elements and techniques in electronic and video games, as well as their applicability in the learning process are shown. The relations between game elements, game techniquesand game actionsare introduced. A gamified learning methodology is proposed and experimented with 93 real university students. A survey is conducted with learners and the results are provided. The findings reveal that when implemented properly, gamification of collaborative learning can prove an effective and motivational tool in education.

*Keywords:* gamification of learning; game elements; game techniques

**Denitza Charkova, Elena Somova, Maria Gachkova**

*University of Plovdiv “Paisii Hilendarski” (Bulgaria)*

### Neural Networks in a Character Recognition Mobile Application

**Abstract.** The article deals with the problem of character recognition using an artificial neural network. Based on the selected data, a model of a convolutional neural network was built, parameters were selected, and the result of training the network was demonstrated. A mobile application with an embedded neural network model has been developed. The process of connecting an API for displaying information on recognized characters has been described. A mobile application with the functionality of recognizing Japanese characters is implemented.

*Keywords:* convolutional neural network; character recognition; mobile application; application programming interface (API)

**L.I. Zelenina, L.E. Khaimina, E.S. Khaimin, D.I. Antufiev, I.M. Zashikhina**

*Northern (Arctic) Federal University named after M.V. Lomonosov (Russia)*

### Applications of Anaglific Images in Mathematical Training

**Abstract.** The article presents the use of interactive approaches in mathematics education through anaglyph images. The basic functions and characteristics of the various applications through which such images can be created are presented. Examples of the adaptation of anaglyph images in mathematics training are described.

*Keywords:* anaglyph images; interactive training; mathematics training; e-learning; interactive education; education in mathematic; anaglyph

**1)Krasimir Harizanov, 2) Stanislava Ivanova**

*1)Konstantin Preslavsky University of Shumen (Bulgaria)*

*2)Peyo Kr. Yavorov Secondary School – Varna (Bulgaria)*

**EDUCATIONAL ISSUES**

### About the Vector Space of the Fourth Order Magic Squares (in Recreational Mathematics)

**Absract.** In the present study a more general (than the traditional) definition of the term magic squares of the fourth order is adopted and sufficient conditions for their existence are indicated. Essential vector-algebraic properties of the fourth-order magic squares have been studied by elementary means of linear algebra. A direct proof of the theorem for the dimensionality of their vector space is made, without using the more general theorem for the dimensionality of the vector space of the magic squares of order n (n ≥3). By solving a linear system of 10 linear equations with 17 unknowns, it is shown that when compiling a fourth-order magic square (in the general case), eight (of the sixteen) coordinates can be given arbitrarily. There are two formulated and solved problems which corroborate the propositional. The present paper is meant for some lessons in recreational mathematics.

*Keywords:* magic squares; vector space; Gauss – Jordan elimination; recreational mathematics

**Prof. Dr. Zdravko Lalchev, Dr. Irina Voutova, Assist. Prof.**

*University of Sofia*

### Method Of The Children In The Skyscraper

**Absract.** The article proposes a double counting method for proving combinatorial identities that is easily visualized and remembered by the students. It allows them to apply it creatively to many situations and to (re)discover related results by themselves.

The article is oriented towards preparation for mathematical contests mainly in junior high school, however the acquired techniques can be useful far beyond that age.

double counting; binomial coefficients; combinatorial identities

**Dr. Ivaylo Kortezov, Assoc. Prof.**

*Institute of Mathematics and Informatics
Bulgarian Academy of Sciences*

### Abraham Wald And Statistical Research On Aircraft Armor

**Absract.** This work investigates the actual and the legendary scientific research of Abraham Wald on the survival probabilities of planes with different number of hits from enemy fire. We give new explanation to the deduction of his basic equation. We explain his basic assumptions and their role in the process of derivation, which we display in more detail. We investigate the role of intuition in this statistical study and how ignoring it allows to formulate assumptions and derive equation about missing data, which is unknowable in the strict sense of the term. We discuss the roles of estimations for unknowable or unobservable variables and highlight the methodology of sequential relaxations of estimations for recursive approximation of real-world data by successive theoretical models.

*Keywords:* history; Wald; heuristics; statistics; probability; epistemology

**1) Prof. Dr. Latchezar P. Tomov
2) Mr. Georgi Doychinov**

*1) New Bulgarian University*

*2) National School for Ancient Languages and Cultures “Saint Constantine-Cyril the Philosopher”*

**COMPETITIONS AND OLYMPIADS**

### Analysis Of The National Online Contest In Informatics “Mladen Manev”

**Absract.** This paper presents the process of organizing and hosting the National Online Contest in Informatics dedicated to the memory of Mladen Manev. This description includes some technical and scientific aspects of the contest management system and the competition tasks. The presented analysis of the collected data during the competition such as participation statistics, problem difficulty, results and system workload is used to assess to what extent the aims of the competition have been successfully achieved.

*Keywords:* competition; informatic; online.

**1) Mr. Dobrin Bashev, student
2) Mr. Plamen Dinev, student**

*High School of Mathematics and Natural Sciences – Gabrovo, Bulgaria*

*2) Sofia University "St. Kliment Ohridski"*

### Contest Problems of this Issue