This article presents a set of specialized software tools for educational data mining and describes the integration of the developed tools into the educational process of students of technical specialties. The developed set consists of three programs that implement the main tasks of educational data mining. Program No. 1 provides segmentation, analysis, and visualization of images of educational materials; Program No. 2 performs data clustering; Program No. 3 performs correlation and regression analysis to identify relationships and predict learning outcomes. The developed programs can be used to implement a systematic analysis of education quality, during which automated processing of educational data and the formation of recommendations for improving the educational process are performed. The programs are implemented in Python. A scheme for integrating specialized programs into the educational process has been developed. The scheme reflects the relationships between the programs that process educational materials, analyze the results of the educational process, influence students’ educational trajectories and the educational process.
Program No. 1, “SegmentFuzzy24,” is designed for segmentation, analysis, and visualization of images of educational materials. Such processing makes it possible to highlight the investigated elements of technical devices in order to focus students’ attention, as well as to determine the quantitative and geometric characteristics of multimedia presentation slides, including the number and size of symbols, the area of graphical objects, etc. Segmentation is performed using the region growing method. The determined characteristics are used for the classification of educational materials or are transferred to Programs No. 2 and No. 3 for further cluster, correlation, and regression analysis.
Program No. 2, “ClusterFuzzy23,” is designed for clustering educational data, including students’ learning outcomes and the characteristics of educational materials obtained from Program No. 1. Objects are divided into groups with similar characteristics using the K-means method. During the clustering process, the sum of the squared Euclidean distances between each object and the centroid of its cluster is minimized. Data clustering ensures their differentiated processing and contributes to the adjustment of educational trajectories. The clustering results can be transferred to Program No. 3 for further analysis. Fuzzy membership functions are used to determine the degree of membership of objects in overlapping clusters.
Program No. 3, “CorrelRegres25,” is designed for correlation and regression analysis of educational data obtained directly or as a result of clustering in Program No. 2. Correlation analysis is used to establish relationships between the characteristics of the educational process, while regression analysis is applied to model their dependencies using polynomial functions and to predict learning outcomes. The obtained models are used to adjust educational trajectories, while objects that have significant deviations from regression dependencies are classified as outliers.
The developed programs have been demonstrated on sample data to process real educational data, namely for image segmentation and visualization, clustering of educational data, and their correlation and regression analysis.
Data clustering and correlation–regression analysis were performed using the grades of N0 = 76 students in 12 subjects, assessed on a 100-point scale, for courses completed during the first and second years of study. The initial sample of N0 students was randomly divided into a training set (N = 60, 80% of the data) and a validation set (NV = 16, 20% of the data). The quality of the clustering results was evaluated using the Silhouette coefficient, Calinski–Harabasz index and Davies–Bouldin index. The analysis indicated that three or four clusters provide an appropriate representation of the data. The optimal polynomial degree pA = 3 for the regression model was determined based on the minimum root mean square error RmseV = 12.37458, obtained on the validation set. The relatively high RmseV value can be attributed to the influence of a considerable number of factors affecting students’ academic performance. The resulting regression model was used to predict students’ grades in a subject for the subsequent academic period based on their grades in the same subject during the previous period. A promising direction for further improvement of the developed prediction system is the integration of artificial neural networks.

This article presents a methodology for modeling and manufacturing three-dimensional (3D) geometric figures. The need for developing the methodology is substantiated, and its significance for the STEM training of future specialists in engineering specialties is demonstrated. An advantage of the methodology is the clear structuring of all its stages, levels, and steps, which simplifies the process of implementing STEM projects. Structurally, the methodology includes a preparatory stage and four main stages. Stage 1 involves designing the object model, which includes collecting information about its characteristics and developing a mathematical model. Based on the mathematical model, the main parameters of the investigated object (part) are determined and calculated. At Stage 2, the computer-aided construction of a three-dimensional model of the object is performed, taking into account the parameters determined at the first stage. The development of drawings and the 3D model is carried out in an appropriate software environment, in particular, in the AutoCAD computer-aided design (CAD) system. Based on the calculated parameters, different types of three-dimensional models of the object are created: wireframe, surface, and solid. Stage 3 involves the implementation of additive manufacturing, that is, the manufacture of a physical prototype of the investigated object using 3D printing. For models of significant overall dimensions or complex geometric shapes that complicate printing, preliminary decomposition of the model into separate parts is performed. After printing, the individual components are joined, and the resulting physical prototype undergoes appropriate post-processing. Stage 4 involves the validation of the  manufactured physical 3D model by assessing its conformity with the digital model of the object. Comparison of the physical and software models can be carried out based on the analysis of their photographic images using digital image processing methods. In addition, a visual assessment of the prototype and measurements of its main geometric parameters are performed. An example of the implementation of a STEM project aimed at the creation, investigation, and physical reproduction of a three-dimensional model of a small stellated dodecahedron by means of 3D printing is presented. According to the developed methodology, at the first stage, a mathematical model of the dodecahedron was developed. At the second stage, based on this model, wireframe, surface (polygonal), and solid (volumetric) models were sequentially developed. An important advantage of the proposed methodology is the step-by-step construction of the wireframe model, which begins with the construction of simple geometric primitives. At the subsequent stages, individual primitives and their groups are sequentially combined into more complex structural elements. This approach simplifies the construction process and enables the step-by-step creation of complex three-dimensional models. At the third stage, the model was decomposed, prepared for printing, and its individual components were manufactured using an FDM 3D printer. After that, the printed parts were assembled and the resulting product was post-processed. As a result, a physical model of the small stellated dodecahedron was manufactured, whose geometric dimensions and surface quality meet the requirements and objectives of the STEM project. A physical model of the small stellated dodecahedron was fabricated, with a pentagon edge length of b = 25.3 mm and a circumscribed sphere diameter of DS = 127.2 mm. The maximum dimensional deviation of the dodecahedron was 0.3 mm.

This paper presents an information system developed to automate the systems analysis of the quality of technical students’ training using correlation and regression methods. The article considers key problems of quality assessment and outlines the theoretical foundations of correlation and regression analysis in the context of educational data. The structure and algorithm of an information system designed for automated analysis of educational datasets are presented. The system allows to determine pairs of courses for which prediction of grades by means of regression analysis is performed with minimal error. In this study, grades from courses for the previous period were considered as known parameters x, and grades from courses for the next period were considered as predicted results y. The correlation analysis of educational data involved calculating the Pearson correlation coefficient Corr, which quantitatively describes the linear relationship between two parameters, x and y, in the educational dataset. The correlation coefficient Corr allows for a targeted investigation of relationships with high Corr values. The regression analysis of the data involved constructing a regression equation approximated by a polynomial of degree p to establish the relationship between the x and y parameters of the educational dataset. The accuracy of the approximation was evaluated using the root mean square error (Rmse) for the training set and RmseV for the validation set. The automatic selection of the polynomial degree pA, was performed according to the criterion of minimizing the approximation error RmseV on the validation dataset, while also ensuring the monotonicity of the regression equation. Developed in Python, the software performs correlation and regression analysis, prediction, outlier detection, and result visualization. This approach was applied to analyze the semester grades of students in the 'Computer Science' program, covering 12 courses over the first four semesters. Using the constructed regression equations, were forecasted students’ grades in six courses for the 3rd and 4th semesters based on their performance in the same courses during the 1st and 2nd semesters. The developed regression model also allows for evaluating students’ academic achievements through the outlier detection. The proposed correlation and regression analysis models are highly scalable, enabling the processing of educational data for large size. Integrating correlation and regression methods into the systems analysis of technical education quality allows for automated analysis of educational monitoring data, forecasting of student performance, outlier detection, and the recommendation of elective courses to optimize students’ educational trajectories.

Clustering of educational data was performed in the space of two parameters using the K-Means method. Students who are characterized by grades in certain types of activities were used as objects of clustering. Software for fuzzy data clustering is implemented in the Python language in the Google Colab cloud service. The obtained clusters are described by fuzzy Gaussian membership functions, which allowed to reliably determine the membership of each object to a certain cluster, even if the clusters do not have clear boundaries. Due to clustering, the most important characteristics of the educational process for a certain task are obtained, that is, this is how Data Manning tasks are solved. Fuzzy membership functions implemented using the scikit-fuzzy library. The developed program can also be used for educational purposes, as it allows a better understanding of the principles of cluster analysis and fuzzy logic. The correctness of the work of the developed program was confirmed during the processing of test educational data. The determination of the number of clusters was performed by software, taking into account the intra-cluster and inter-cluster distances, as well as the shape of the clusters. Automated selection of the number of clusters and cluster boundaries allows to reduce data processing time. The developed clustering tools are designed to increase the efficiency of system analysis of quality education.

In the work, an analysis of modern methods of Educational Data Mining (EDM) was carried out, on the basis of which a set of methods of EDM was developed for the training of vocational education teachers. The basic methods of EDM are considered, namely Prediction, Clustering, Relationship Mining, Distillation of Data for Human Judgment, Discovery with Models. The possibilities of using artificial neural networks, in particular, networks of Long-Short-Term Memory (LSTM), to predict the results of the educational process are described. The main methods of clustering and segmentation of educational data are considered. The basic methods of EDM are complemented by specialized methods of digital image pre-processing and methods of artificial intelligence, taking into account the peculiarities of the training of future specialists in engineering and pedagogical specialties. As specialized methods of digital image pre-processing, methods of filtering, contrast enhancement and contour selection are used. As specialized methods of artificial intelligence, methods of image segmentation, object detection on images, object detection using fuzzy logic were used. Methods of object detection on images using convolutional neural networks and using the Viola-Jones method are described. To process data with a certain degree of uncertainty, it is proposed to apply the methods of EDM and Fuzzy Logic in a integral manner. Ways of integrating Fuzzy Logic with methods of data clustering, image segmentation and object detection on images are considered. The possibilities of applying the developed complex of specialized methods of EDM in the educational process, in particular, when performing STEM (Science, Technology, Engineering and Mathematics) projects, are described.

In the work, the software implementation of the face mask recognition system using the Viola-Jones method and fuzzy logic is performed. The initial images are read from digital video cameras or from graphic files. 
Detection of face, eye and mouth positions in images is performed using appropriate Haar cascades. The confidence of detecting a face and its features is determined based on the set parameters of Haar cascades.
Face recognition in the image is performed based on the results of face and eye detection by means of fuzzy logic using the Mamdani knowledge base. Fuzzy sets are described by triangular membership functions. Face mask recognition is performed based on the results of face recognition and mouth detection by means of fuzzy logic using the Mamdani knowledge base. Comprehensive consideration of the results of different Haar cascades in the detection of face, eyes and mouth allowed to increase the accuracy of recognition face and face mask.
The software implementation of the system was made in Python using the OpenCV, Scikit-Fuzzy libraries and Google Colab cloud platform. The developed recognition system will allow monitoring the presence of people without masks in vehicles, in the premises of educational institutions, shopping centers, etc. In educational institutions, a face mask recognition system can be useful for determining the number of people in the premises and for analyzing their behavior.

A STEM project was implemented, which is intended for students of technical specialties to study the principles of building and using a computer system for segmentation of images of railway transport using fuzzy logic. The project consists of 4 stages, namely stage #1 "Reading images from video cameras using a personal computer or Raspberry Pi microcomputer", stage #2 "Digital image pre-processing (noise removal, contrast enhancement, contour selection)", stage #3 "Segmentation of images", stage #4 "Detection and analysis of objects on segmented images by means of fuzzy logic". Hardware and software tools have been developed for the implementation of the STEM project. A personal computer and a Raspberry Pi 3B+ microcomputer with attached video cameras were used as hardware. Software tools are implemented in the Python language using the Google Colab cloud platform. At each stage of the project, students deepen their knowledge and gain practical skills: they perform hardware and software settings, change program code, and process experimental images of vehicles. It is shown that the processing of experimental images ensures the correct selection of meaningful parts in images of vehicles, for example, windows and number plates in images of locomotives. Assessment of students' educational achievements was carried out by testing them before the start of the STEM project, as well as after the completion of the project. The topics of the test tasks corresponded to the topics of the stages of the STEM project. Improvements in educational achievements were obtained for all stages of the project.

The software for clustering students according to their educational achievements using fuzzy logic was developed in Python using the Google Colab cloud service. In the process of analyzing educational data, the problems of Data Mining are solved, since only some characteristics of the educational process are obtained from a large sample of data. Data clustering was performed using the classic K-Means method, which is characterized by simplicity and high speed. Cluster analysis was performed in the space of two features using the machine learning library scikit-learn (Python). The obtained clusters are described by fuzzy triangular membership functions, which allowed to correctly determine the membership of each student to a certain cluster. Creation of fuzzy membership functions is done using the scikit-fuzzy library. The development of fuzzy functions of objects belonging to clusters is also useful for educational purposes, as it allows a better understanding of the principles of using fuzzy logic. As a result of processing test educational data using the developed software, correct results were obtained. It is shown that the use of fuzzy membership functions makes it possible to correctly determine the belonging of students to certain clusters, even if such clusters are not clearly separated. Due to this, it is possible to more accurately determine the recommended level of difficulty of tasks for each student, depending on his previous evaluations.