Software Package to Support Students’ Research Activities in the Hybrid Intellectual Environment of Mathematics Teaching
Authors: Smirnov Eugeny , Dvoryatkina Svetlana , Martyushev Nikita , Shcherbatykh Sergey 
Published: February 2023

The urgent need of society for creative and critical thinkers dictates the need to manage and develop the project-based and research activities of schoolchildren. Neural networks, as effective tools for solving complex, multi-component, multifunctional problems, have created an opportunity to develop tools for the content and quality assessment of project-based, research activities and personal achievements of each student with a dynamic and stratified sampling of complex knowledge, to identify individual educational paths, tools and instructions for research and creative activity reflected on the layers of an artificial neural network. The purpose of this study is to define and develop the concept of supporting a hybrid intelligent system of project-based and research activities in a comprehensive information and educational environment to create an applied intellectual technology that supports project-based and research activities and classifies the growth of schoolchildren’s scientific potential. The paper considers the development of technologies for the pedagogical, algorithmic and information organization of ontological engineering and support models for project-based and research activities, as well as the growth of scientific student training based on the construction of an artificial neural network with a teacher and an array of training samples using expert systems and decision theory. It also defines the selection criteria, hierarchies and content of the generalized constructs of complex knowledge (modern achievements in science) by modeling creative activities while further predicting the growth of a student’s scientific potential based on the layers of the neural network. The original technology of training samples used for constructing hybrid neural networks was determined using expert systems, the psychological method of parallel slices and clustering of the personal characteristics of schoolchildren. An innovative intellectual environment is being introduced into the practice of mathematical education in high schools in Russia. The study made it possible to create applied intelligent technology to support and display the dynamic profiles of the project-based and research activities of schoolchildren and act as a growth classifier of their scientific potential. In terms of concept implementation, the phased growth technology to analyze students’ scientific potential was developed during the study of the generalized construct of complex knowledge. Individual educational workshops for school students to master project-based and research activities and display their dynamic profiles during the implementation of a hybrid intellectual environment for support and decision-making will allow school students to develop their personal potential, increase their educational motivation and allow researchers and educators to realize the potential of adapting modern achievements in science to school mathematics and create conditions for the modernization of educational programs in a developing digital environment.