Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1) Taylor’s polynomial linearization approximation, (2) the method of variable change, and (3) a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a) using the optimal value of the objective functions as the decision makers’ aspirations, and (b) the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem

A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems

This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method

FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

Fractions represent the manner of writing parts of whole numbers (integers). Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered, which are essentially related to visualizing operations with fractions

ROLE OF ADDITIONAL ACTIVITIES AND COMPETITION IN THE TEACHING OF MATHEMATICS

The development of science is essential when it comes to the development of society, while the mathematics necessary for the development of science. The fact that the children are all clearer, more capable and versatile, and their mathematical knowledge smaller and worse, motivated me to this research.How would our society be better you need to choose talented and creative young people who will represent the same company. One way of selecting children, and choosing the best are just competitions. In this work, attention will be focused on additional classes and competitions of teaching mathematics, as well as their importance in the education and development of children in schools.When it comes to gifted students, one of the main events where they can demonstrate their knowledge and skills are the competition.The overall objective of this research is to determine the extent to which the additional classes represented in schools and how many students go to additional classes and competitions in mathematics.The study included 103 primary school students in the municipality of Ilijaš. The results obtained in this study mostly on the representation of additional teaching of mathematics in schools or with, a small number of students. Because the necessary mathematical talent, the will and desire to learn mathematics. Viewed from the perspective that the disciples mathematics not so favorite subject, these are the expected results

INTERNET AMONG STUDENTS – FROM MATHEMATICAL RATIONALITY TO UNREALITY

Today’s modern lifestyle and contemporary ways of working and gaining knowledge in schools and universities could not be imagined without high technology – the Internet. Simply said, internet entered all the pores of contemporary life in big style. If used rationally, internet can truly facilitate work in all spheres of modern man’s life. However, internet also has a dark side which comes to light if its excessive use becomes internet addiction, or internet infatuation. We reached this hypothesis through everyday contact with students in class as well as our colleagues teachers. In order to determine if and to what extent internet addiction among students exists, we applied a generic method, that is, we used survey as one of techniques of research. The survey was conducted in October of academic year 2017/2018. Sample of 79 students was selectedfrom first and fourth grades in Secondary school “Muhsin Rizvić” in Kakanj

MATHEMATICAL CHARACTERISTICS OF THE CHILDREN THAT SHOWN ABOVE/BELOW AVERAGE SUCCESS AT THE MATHEMATICAL EDUCATION

In this study, we analyzed the emotional and conative characteristics of fourth grade students of elementary school as follows: motivation for learning math, situational interest in learning mathematics during teaching, mathematics anxiety, self-esteem in relation to academic achievement and attributions of success and failure in mathematics. In a sample of 200 students and 20 teachers were analyzed emotional and conative characteristics capable of above-average and below average in math-age students. The study used the descriptive method, a questionnaire and a test. The research results are presented graphically and in tabular form with an explanation and discussion. In the conclusion are set the directions which should further improve this insufficiently studied area

POSSIBLE CALCULATOR ADDICTION IN STUDENTS WHILE PERFORMING SIMPLE CALCULUS OPERATIONS IN SOLVING MATHEMATICS PROBLEMS

Contemporary learning processes in schools and universities could not be imagined without the use of computers and calculators. Naturally, all is good if they are used in order to acquire new knowledge or solve problems from expert subjects in technical schools, which demand large quantity of simple mathematical operations. However, what if frequent use of calculators, either pocket or those installed on every home and school computer, becomes an addiction in students who begin using them while calculating simple mathematical operations, such as multiplying or adding and detracting one-digit numbers or numbers smaller than 20, when they should know this by heart? We arrived at this hypothesis during knowledge tests for students after regular demonstrations and elaborations of Mathematics subject matter. In order to confirm or deny this hypothesis, generic/developmental method, that is, survey was used as one of research techniques (Selimović, 2013., p. 104). The survey was conducted in March during academic 2016/2017 and the sample consisted of 59 students in 2nd grade of Grammar School Tešanj