Научный журнал

European Journal of Natural History

ISSN 2073-4972

ИФ РИНЦ = 0,301

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Abdukadirov A.A. 1 Yusupov D.F. 2

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1 1The Ministry of Higher and Secondary Specialized Education of the Republic of Uzbekistan "Tashkent State Pedagogical University named after Nizami"

2 The Ministry of Higher and Secondary Special Education of the Republic of Uzbekistan "Urgench State University"

This article is: focused on the essence of the formalization of the predicate system on the topic “Algorithmization and Programming” of the Informatics course for building a neural network to assess students’ knowledge. The proposed method of formalizing the predicate system on the topic, based on the constructed neural network, allows you to assess the knowledge and competence of the student in this course, developed on the example of “Algorithmization and programming”, takes into account the following features of the problem being solved: incompleteness and uncertainty of the information about skills, skills and student knowledge; multi-criteria, due to the need to take into account a large number of private indicators associated with educational activities and the formation of knowledge and skills; the presence of both quantitative and qualitative indicators that must be considered when assessing the level of knowledge. The developed methodology for formalizing the system of predicates of a topic can be applied to any disciplines of a higher educational institution to assess the competence of students on the basis of a neural network by changing the nature and number of predicates.

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algorithm

mathematical logic

utterance

predicate

neuron

neural network

1. Igoshin V.I. Mathematical logic and theory of algorithms. 2nd ed., Sr. – M .: Academy, 2008. – 448 p.

2. Grinchenkov D.V., Pototsky S.V. Mathematical logic and theory of algorithms for programmers. Tutorial. – Moscow: KnoRus, 2017. – 206 p.

3. Callan, Robert. The basic concepts of neural networks.: Per.s Eng. – M .: Publishing house Williams, 2001. – 286 p.

4. Barsky A.B. Neural networks: recognition, management, decision-making. – Moscow: Finance and Statistics, 2004. – 176 p.

5. Sarayev P.V. Neural network methods of artificial intelligence: a tutorial / P.V. Sarayev .- Lipetsk: LSTU, 2007. – 64 p.

6. Krisilov VA, Kondratyuk A.V. Transformation of the input data of the neural network in order to improve their distinguishability. http://neuroshool.narod.ru/

7. Nazirov Sh.A., Kobulov RV, Bobojonov MR, Rakhmanov ?.S. With v ++ +++. “Voris-nashiruet” MCW, Toshkent 2013. – 488 p.

At the moments of making difficult decisions, a specialist tries to “look inside himself” and comprehend how he copes with difficult and sometimes not solvable formal logic tasks. The natural anxiety and thirst for knowledge overwhelms him along with the vague consciousness that the mathematical, algorithmic approach to the construction of complex cybernetic systems is artificially absolutized. Everything should be in order, everything should be weighed, and turning to himself, he repeatedly conducts a brainstorming on that mysterious, created by nature – on his own brain.

Mathematical logic, its important section “The Algebra of Sayings” and “Theory of algorithms”, really combined the principles of thinking and their automated embodiment [1, 2]. However, to realize thinking, nature has not created anything better than the human brain. It is a giant neural network, fixing cause-effect relationships, creating a knowledge base and owning procedures for logical inference. Thus, neural networks are really the basis for formalizing the means of thinking. Therefore, it is fair to assume that the study of neural networks is based on the achievements of mathematical logic.

Integration of pedagogical and intellectual information technologies, in particular neural network technologies [3, 4], defines a new kind of intellectual computer training facility – neural network computer training systems that individualize and adapt the learning process to the learner’s needs through the apparatus of neural networks. Neural networks are related to artificial intelligence technologies and represent mathematical models of biological neural networks. The main advantage of neural networks is that they allow you to create a mathematical apparatus of the predicate logic, which, under the conditions of diversity, large volume, inconsistency and insufficiency of various diagnostic information, is able to solve problems of image recognition and categorization. This mathematical apparatus allows: by measuring the characteristics of the student and applying methods of cluster analysis, group the contingent according to clusters of integrative individual characteristics; To differentiate the educational material according to various parameters; to build individual trajectories of training; take into account the dynamics and the possibility of changing the student’s trajectory.

Intensive use of information and communication technologies in the educational process requires the search for new methods and means of teaching, the development of a unified information environment for educational institutions, the mathematical formalization of the learning process as a poorly formalized object with the goal of developing models and algorithms for optimal management of it. The development of new methods of management and modeling of the educational process is a demanded task of today. With scientifically grounded research, study and analysis of educational process objects using modern, unique neural network technologies, there are fundamentally new possibilities for finding methods and means for improving the educational process.

The use of neural models and neural network technologies in the objects of the educational process creates the basis for new directions in universities to develop integrated intellectual systems of the educational institution. When administering an educational institution using neural network technologies, there will be no restrictions on the types and dimensions of the data being processed. The artificial neural network models at the logical level the activity of the nervous system of man and animals. Particularly interesting is the ability of neural networks to learn and remember information, which reminds people’s thinking processes. That is why in the early work on the study of neural networks, the term “artificial intelligence” was often mentioned. This interest is understandable: since an artificial neural network is in fact a model of the natural nervous system, the creation and study of such networks allows one to learn a lot about the functioning of natural systems, in particular, educational systems.

Now, let us consider the problems of formalizing predicates for building a neural network in the study of the section “Algorithmization and Programming” of the course Informatics with the aim of increasing the effectiveness of the learning process [5-7].

We introduce the notation: A is the set of students of the group. A = {A1, A2, .., AN} = {Abdullah, Sadullah, Boltaboy, ...}.

Students in the practical lesson independently learn the “Algorithmization and Programming” section of the Informatics course.

The set of basic algorithms of the section “Algorithmization and programming” of the course Informatics will be denoted in the form of a set:

Here: SS – is an algorithm of strictly sequential computational process;

SB – algorithm of a simple branching computing process;

CB – algorithm of a complex branching computing process;

SC – the algorithm of a simple recurring (cyclic) computing process;

CC – algorithm of complex cyclic computational process;

BC – algorithm of branching with a cycle;

CB – is a cyclic process with branching.

Teaching staff of the department who gives consultations on the section “Algorithmization and programming” of the course Informatics will be denoted as sets:

B = {B1, B2, B3, …} = {dots.Yusupov, senior lecturer, Setmetov, Ass. Ruzmetov, …}.

Suppose, the group’s headmaster, senor teacher Yusupov D. controls the process of studying the section “Algorithmization and programming” course Informatics by students and collects statistics of their ratings.

We formalize the goal of assessing the students’ knowledge on this subject:

1. Bring excellent students to minimum of 10 %;

2. Good students to increase the minimum of 25 %;

3. Grades students satisfactory to minimum of 65 %;

4. Grades students unsatisfactory to minimum of 0 %.

The stated goal in terms of mathematics is formalized as follows, for 5 types of algorithms

C = {C1,C2,C3,C4,C5,} = {SS,SB,CB,SC,CC},

The ratings of each student on mastering the main algorithms of this section will be evaluated as follows:

R = {R1,R2,R3,R4, R5} = {excellent, good, satisfactory, almost satisfactory, unsatisfactory}.

The activity of the student, on the study of basic algorithms, is formalized in an abstract form, for example:

• {A1, B2, SB} – the student A1 came to the teacher B2 to get consultation on the SB algorithm, i.e. the student Abdullah came to the senior teacher Setmetov to get consultation on the SB algorithm of a simple branched computing process;
• {A2, B1, SC} – A2 student came to the teacher B1 to get consultation on the SC algorithm, i.e. student Sadulla came to dots.Yusupovu to get consultation on the algorithm SC – the algorithm of a simple recurring (cyclic) computing process;
• {A5, B2, C1,}, {A7, B3, C5,}, etc ..

Presented abstract records from the point of view of mathematical logic will be written as follows:

{A1, B2, C3} => A1 ^ B2 ^ C3;

{A2, B1, C4} => A2 ^ B1 ^ C4;

{A5, B2, C1} => A5 ^ B2 ^ C1;

{A7, B3, C5} => A7 ^ B3 ^ C5.

The process of studying the basic algorithms of the “Algorithmization and Programming” section can be abstracted as follows:

{A1,B1,B2,SS,SB,CB,SC,CC,} => A1 ^ (B1vB2) ^ (SSvSBvCBvSCvCC). Thus, the student A1 came to the teacher B1 or B2 to get consultation on the algorithm of the SS or SB or CB or SC or CC.

{A1,B2,SS,SB,SC,B1,SC,CC} => (A1 ^ B2 ^ (SSvSBvSС) v (А1 ^ B1 ^ (SCvCC)) – this means that the student A1 has come to the teacher B2 for getting consultations on the algorithm SS or SB or CB, or student A1 came to the teacher B1 for consultation on the algorithm SC or CC.

From the point of view of system analysis, the process of studying the basic algorithms by students of the group having considered all possible variants and analyzing the results, one can make a conclusion on the assessment of knowledge by students in the form of logical statements – in the form of a system of predicates:

(1)

According to formalization, the first and second predicates mean that:

If the student A1 has come to the teacher B1 to get consultation on the algorithm C1 or C2 or C3 or C4 or C5, then after receiving it, the teacher evaluates the student’s knowledge of the R1 rating;

If the student A1 has come to the teacher B2 or B3 to get consultation on the algorithm C1 or C2 or C3, then after receiving it, the teacher evaluates the student’s knowledge of the R2 rating, etc.

Thus, the predicate system (1) for studying the basic algorithms of the “Algorithmization and programming” section and assessing students ‘knowledge will be the basis for building a neural network for assessing students’ knowledge.

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