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The application of the capabilities of information technology in the process of teaching mathematics by computer technology teachers has brought with it many advantages. The use of technology in schools is effective in terms of improving students' cognitive skills. When we look at the areas of use of new pedagogical technologies, they provide innovative learning with different educational materials in many teaching areas, especially mathematics education. Observations show that in most cases, the teacher works alone during the lesson, and the students remain observers. For teachers, it is desirable to improve the effectiveness of the use of technology in mathematics lessons, its structure and content and to determine the effectiveness of ‘Information Technologies in Mathematics Education’. This case study aims to investigate the impact of the integration of information and communication technology applications on mathematics education. Within the scope of this general purpose, semi-structured interview questions prepared by the researchers were asked. A qualitative method was used in the research. The opinions of 32 mathematics teachers who use technology in their high school courses were consulted. As a result of the research, it was concluded that technology-supported training is very effective in mathematics. It has been concluded that the use of a numerical field of mathematics and technology-supported applications is effective in developing skills in students. In the same way, it has emerged that mathematics teachers need in-service training about technology-supported trainings. Keywords: Mathematics, case study, technology, education, teaching, mathematics teaching, innovative

Mathematical learning in many developing nations is below average due to which students face difficulties in solving the equations and problems of mathematics as a result of limited understanding of the main concepts and reliance upon intuition as well as memorization. This study is focused on analyzing the effectiveness of senior graders’ education based on the development of mathematical intuition and logic in the context of Kazakhstan’s educational system. The quantitative research method and primary data sources were used for this research with a 147 sample size, which was selected by using a random strategy of sampling. With the use of IBM SPSS STATISTICS for data analysis, it was concluded that mathematical intuition and logic have a positive influence on the effectiveness of a student’s education. Effective strategies, such as rote learning instructions, problem-based learning, RME approach, mathematical reasoning, etc., are essential for enhancing the capabilities of studies in learning mathematics. It is found that there is a significant and positive association between student effectiveness and the logical reasoning abilities of students. Additionally, a positive and moderate relationship is noticed between the critical thinking of students, problem-solving abilities of students, and student effectiveness. Nevertheless, the main limitation of this study is that with small sample size, the findings of the study cannot be generalized; therefore, a large sample size would increase the reliability of the results in the future research. However, in the context of Kazakhstan, this study potentially contributes to the existing literature by presenting conclusive findings in the context of mathematical logic and intuition and student effectiveness.

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

Developing an effective and high-quality vaccine is an important issue in rabies prevention. This article presents the results of the studies aimed at selecting the optimum parameters for the cultivation of the VN-21 finite cell line and the CVS-11 strain of the rabies virus. Such parameters as inoculated cell concentration, the optimal dose of infection with the virus, the time and methods of cultivation, and the choice of the inactivant and the adjuvant were chosen.

The purpose of the study is to create and use a simple, but very effective mobile application available for use during the learning process, as well as for student’s independent work after university hours. We have used the X code integrated development environment, developed by Apple for iPhone and iPad, in order to create the application. Our mobile application was used as an element of the digital educational resource in physics and mathematics. Natural and technical students have also used it to prepare for the interim assessment, external evaluation and a unified national testing. Using a mobile application allows a student to make up for the worn out or missing laboratory equipment, to use a large database of reference data without long searching, to create, modify and use software packages. The listed capabilities of a mobile application, ultimately, improve the quality of student’s knowledge.