CoCalc as a Learning Tool for Neural Network Simulation in the Special Course "Foundations of Mathematic Informatics"

The role of neural network modeling in the learning content of the special course "Foundations of Mathematical Informatics" was discussed. The course was developed for the students of technical universities - future IT-specialists and directed to breaking the gap between theoretic computer science and it's applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic "Neural network and pattern recognition" of the special course "Foundations of Mathematic Informatics" are shown. The program code was presented in a CoffeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network's weights, etc. The features of the Kolmogorov-Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed.Comment: 16 pages, 3 figures, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer (ICTERI, 2018

USING COCALC AS A TRAINING TOOL FOR MATHEMATICS TEACHERS’ PRE-SERVICE TRAINING

This paper deals with the problem of theoretical justification and development of scientific and methodological support for using the cloud service CoCalc as a tool for the formation of mathematics teachers’ professional competencies. The following contradictions exist concerning the processes of forming these competencies: between the level of abstraction of mathematical objects and the possibilities of providing their visualization by computer interpretation; between the expediency of widespread use of ICT services for mathematical purposes in the training of pre-service teachers of mathematics and the lack of opportunities for their provision to ICT subdivisions and pedagogical universities; between the feasibility of using ICT outsourcing of cloud infrastructure for the pre-service training of mathematics teachers in Ukraine and the non-adaptability of foreign cloud-based mathematical services to the requirements of national educational standards; between the possibilities of application of cloud mathematical services in the process of formation of professional competencies of mathematics teachers and the absence of an adequate method for their implementation. The paper describes the professional training of mathematics teachers in universities of Ukraine, and considers the national and foreign experience of using the cloud-based services in mathematics teachers’ pre-service training and also the tendencies and prospects of using CoCalc in teaching mathematical disciplines. The process of system design of mathematics teachers’ professional competencies is characterized, and the model of using the cloud service CoCalc as a tool for forming mathematics teachers’ professional competencies is developed. The indicators and levels (high, sufficient, medium, low) were identified for each component of the pre-service mathematics teachers’ professional competence system within the proposed model. The method of using CoCalc as a tool for forming professional competencies of mathematics teachers is developed and its basic components such as purpose, content, tools, methods and results are elaborated. Information regarding the stages of research and also the experimental work objectives and content are presented; the quantitative and qualitative analysis of the main stages (ascertaining, formative) of the pedagogical experiment is performed, confirming the hypothesis of the study