This article is an attempt to rethink the concepts of “methodic” and “methodologic / methodical system” as basic to educational technology. What should be the structure of a methodical system? What is primary – the methodical system or the methodology? How are methodical systems created and developed? How do educational technology and a methodical system relate? How does changing the components of a system make it emergent? These and other issues are explored through the development of a new class of teaching methods – computer-based training systems.

The authors of the given article continue the series presented by the 2018 paper “Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot”. This time, they consider mathematical informatics as the basis of higher engineering education fundamentalization. Mathematical informatics deals with smart simulation, information security, long-term data storage and big data management, artificial intelligence systems, etc. The authors suggest studying basic principles of mathematical informatics by applying cloud-oriented means of various levels including those traditionally considered supplementary – spreadsheets. The article considers ways of building neural network models in cloud-oriented spreadsheets, Google Sheets. The model is based on the problem of classifying multi-dimensional data provided in “The Use of Multiple Measurements in Taxonomic Problems” by R. A. Fisher. Edgar Anderson’s role in collecting and preparing the data in the 1920s-1930s is discussed as well as some peculiarities of data selection. There are presented data on the method of multi-dimensional data presentation in the form of an ideograph developed by Anderson and considered one of the first efficient ways of data visualization.

The article substantiates the necessity to develop training methods of computer simulation of neural networks in the spreadsheet environment. The systematic review of their application to simulating artificial neural networks is performed. The authors distinguish basic approaches to solving the problem of network computer simulation training in the spreadsheet environment, joint application of spreadsheets and tools of neural network simulation, application of third-party add-ins to spreadsheets, development of macros using the embedded languages of spreadsheets; use of standard spreadsheet add-ins for non-linear optimization, creation of neural networks in the spreadsheet environment without add-ins and macros. After analyzing a collection of writings of 1890-1950, the research determines the role of the scientific journal “Bulletin of Mathematical Biophysics”, its founder Nicolas Rashevsky and the scientific community around the journal in creating and developing models and methods of computational neuroscience. There are identified psychophysical basics of creating neural networks, mathematical foundations of neural computing and methods of neuroengineering (image recognition, in particular). The role of Walter Pitts in combining the descriptive and quantitative theories of training is discussed. It is shown that to acquire neural simulation competences in the spreadsheet environment, one should master the models based on the historical and genetic approach. It is indicated that there are three groups of models, which are promising in terms of developing corresponding methods – the continuous two-factor model of Rashevsky, the discrete model of McCulloch and Pitts, and the discrete-continuous models of Householder and Landahl.

The article substantiates the necessity to develop training methods of computer simulation of neural networks in the spreadsheet environment. The systematic review of their application to simulating artificial neural networks is performed. The authors distinguish basic approaches to solving the problem of network computer simulation training in the spreadsheet environment, joint application of spreadsheets and tools of neural network simulation, application of third-party add-ins to spreadsheets, development of macros using the embedded languages of spreadsheets; use of standard spreadsheet add-ins for non-linear optimization, creation of neural networks in the spreadsheet environment with-out add-ins and macros. The article considers ways of building neural network models in cloud-based spreadsheets, Google Sheets. The model is based on the problem of classifying multi-dimensional data provided in “The Use of Multiple Measurements in Taxonomic Problems” by R. A. Fisher. Edgar Anderson’s role in collecting and preparing the data in the 1920s-1930s is discussed as well as some peculiarities of data selection. There are presented data on the method of multi-dimensional data presentation in the form of an ideograph developed by Anderson and considered one of the first efficient ways of data visualization.

A review of the methodological literature on computer modeling shows the existence of different approaches to its teaching in secondary and higher education. It is a common approach in which the construction of models is carried out using the apparatus of higher mathematics, which is possessed mainly by senior students. This leads to the transfer of the course “Methods of mathematical modeling” for 7-8, and sometimes 9-10 semesters, which reduces its role in shaping the worldview of the future specialist, which takes place in high school and junior high school. This state of affairs forced us to create a propaedeutic course “The basics of computer simulation”, which was developed by the joint efforts of the Department of Informatics and Applied Mathematics of Kryvyi Rih State Pedagogical University and the Department of Informatics of the Kryvyi Rih Tsentralno-Miska gymnasium. The methodological support of the course is a textbook designed for high school students and junior high school students.