Published March 26, 2025 | Version v1
Journal article Open

The method of "small groups" in teaching mathematics to students of technical universities

Authors/Creators

  • 1. Тверской государственный технический университет

Description

The article considers an approach to resolving the contradiction between the need to activate the educational and cognitive activities of students aimed at developing the mathematical thinking of future engineers, taking into account individual abilities and the established system of organizing classroom classes in higher mathematics, focused on front-line activities. The purpose of the study is to adapt the "small group" methodology for the study of mathematics by undergraduates, to develop and test educational and methodological support for this activity. The research hypothesis is that improving the effectiveness of mathematical and creative thinking formation can be achieved by organizing "small group" learning at different stages of learning new knowledge and developing intellectual skills, which provides: consideration of the psychological and pedagogical features and didactic properties of this method, as well as the specific conditions of its implementation in teaching mathematics; compliance with the specifics of the sections of the subject, the stage of cognitive activity and the didactic tasks of this stage; creation of a task bank and their typology by type of activity; development of methods for monitoring and organizing students' classroom work. Students' work in small groups is considered as one of the methods of interactive learning. The didactic properties and functions of the mathematics teaching methodology in collaboration are described. A model of interaction is defined, and its correspondence to the elements of cognitive activity and educational tasks is theoretically substantiated. The typological features of tasks for the "small group" methodology are indicated. The controlled results, semantic correspondences and computational criteria of learning in the development of computational skills, critical thinking, and analysis of results are determined. The positive aspects, possible difficulties are noted and the results of the application of the considered methodology are presented. The practical recommendations are aimed at organizing classroom classes in higher mathematics at technical universities, as well as at using advanced training courses for higher school teachers.

Abstract (Russian)

В статье рассматривается подход к разрешению противоречия между необходимостью активизировать учебно-познавательную деятельность студентов, направленную на развитие математического мышления будущих инженеров, с учетом индивидуальных способностей и сложившейся системой организации аудиторных занятий по высшей математике, ориентированной на фронтальные виды деятельности. Цель исследования состоит в адаптации методики «малых групп» для изучения математики студентами младших курсов, разработке и апробации учебно-методического обеспечения этой деятельности. Гипотеза исследования – повышение эффективности формирования математического и креативного мышления может быть достигнуто организацией обучения студентов по методике «малых групп» на разных этапах усвоения нового знания и развития интеллектуальных умений, что предусматривает: учёт психолого-педагогических особенностей и дидактических свойств данного метода, а также специфических условий его реализации при обучении математике; соответствие специфике разделов предмета, этапу познавательной деятельности и дидактическим задачам этого этапа; создание банка заданий и их типологии по видам деятельности; разработку методики контроля и организации аудиторной работы студентов. Работа студентов в малых группах рассматривается как один из приёмов интерактивного обучения. Дано описание дидактических свойств и функций методики обучения математике в сотрудничестве. Определена модель взаимодействия, теоретически обосновано ее соответствие элементам познавательной деятельности и учебным задачам. Указаны типологические особенности заданий для методики «малых групп». Определены контролируемые результаты, семантические соответствия и расчетный критерий обучения при развитии вычислительных умений, критического мышления, анализа результатов. Отмечены положительные стороны, возможные затруднения и приведены результаты применения рассматриваемой методики. Практические рекомендации ориентированы на организацию аудиторных занятий по высшей математике технических университетов, а также на использование в курсах повышения квалификации преподавателей высшей школы.

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