It is known that the huge computing resources of modern computers are used primarily to solve problems that arise in various applied areas in the process of mathematical modeling of real objects. The aim of this study is to present a theoretical justification of the need to train informatics future teacher in the field of computational informatics and to develop a methodology for teaching him/her in the context of the development of modern education. The competence-based and contextual approaches to teaching and the concept of pedagogical education funding are used in the research. The necessity of training future informatics teacher in the field of computational informatics has been justified and a methodology for teaching it based on web quests has been developed and experimentally tested. The implementation of the developed methodology for teaching computational informatics on the basis of modern educational technology web-quest will equip him/her with the necessary knowledge and ensure the development of his/her information and computational competence.