Peculiarities of teaching students of nonmathematical specialties higher mathematics in crisis conditions

Abstract

Formulation of the problem. Modern society needs highly trained specialists. Ukraine, like all other industrialized countries, has a technical infrastructure that must be constantly maintained, developed and updated. Insufficient personnel training can lead to the decline of production, the destruction of infrastructure and the halting of civilizational development, which can have numerous negative consequences. Mathematical training occupies a special place in the training of future specialists who ensure the viability of the state. Recently the decline in the quality of mathematical training of specialists was noted in various areas. The problem is important and relevant. Understanding the relevance of this problem at the state level led to declaring the academic year 2020-2021 to be the year of mathematics education in Ukraine [1]. The problem of mathematical training of pupils and students is relevant for many countries of the world. Scientists note the general trend of decreasing the level of mathematical knowledge of pupils and students, presence of significant difficulties in studying mathematics courses [24, 29, 44], which affects the decrease in the level of their educational motivation or complete refusal from studying. At the current stage of society's development, schools and universities use various methodical systems of teaching mathematics, which are theoretically grounded and experimentally verified. A school teacher and a university teacher can choose different forms and methods of teaching. Unfortunately, unexpected situations can suddenly occur and radically change everyday life. It happened in 2019, when many countries found themselves in the conditions of the Covid-19 pandemic. Military operations are underway in our country from February 24, 2022. Other countries suffer from natural and environmental disasters (earthquakes, hurricanes, floods, etc.). We call such conditions to be crisis ones. Any country in the world can find itself in such conditions. It is obvious that in such conditions both students and teachers experience psychological stress, a very high level of anxiety. Negative emotions often lead to rejection from the “normal life”, the level of educational motivation decreases to an absolute unwillingness to learn. From the ethics point of view in the article we do not describe personal opinions of students and teachers in our university, their psychological state of mind, what they feel after the start of military operations on the territory of our state. We want to only mention that psychological support services work intensively at the university. Our experience of teaching university students a higher mathematics course allowed us to conclude that in crisis conditions it is necessary to find all opportunities to continue the educational process, because it contributes to the stabilization of the psychological state of mind of university students and teachers. Additional efforts of teachers aimed at supporting educational motivation and positive emotional state of students are needed. The educational process in such conditions is possible only in the form of distance or blended learning. As a result of the search for educational technologies that are effective in the conditions of distance or blended learning, we came to the assumption that in the process of teaching a higher mathematics course to students of non-mathematical specialties it is effective to use elements of the “programmed learning” technology (in terms of content) and elements of technology called “flipped classroom” (in terms of the form); the effectiveness of students’ learning can be significantly increased in case of mandatory generalization and systematization of educational material in mathematics with the use of visualization tools. In order to verify the effectiveness of the use of the mentioned technologies in the process of teaching higher mathematics to students of non-mathematical specialties, we conducted an experimental study, which involved the following tasks: analysis of theoretical provisions and experience of introducing programmed learning technology into the educational process, technology of the “flipped classroom”, and technology of visualizing educational material; development of methodological recommendations for the implementation of the mentioned technologies in the process of teaching a higher mathematics course to students of non-mathematical specialties in accordance with the curriculum; experimental verification of the influence of the developed methodical recommendations on the quality of students' assimilation of mathematical knowledge. Analysis of latest research and publications. The idea of programmed learning arose quite a long time ago. Modern researchers associate it with the works of the famous American psychologist S. Pressey, who patented special machines for testing students' knowledge in the 20s of the 20th century. The author of the developments believed that the assimilation of knowledge is going step by step, the transition to learning new material is possible only if correct answers are given to previous questions or the teacher corrects incorrect answers [31, 32]. The idea of programmed learning received further development in the works of the American psychologist B. Skinner. The scientist claimed that it is important to constantly «reinforce» the student with positive evaluations, stimulation in the learning process, that means encouraging the student with the help of achieving certain success every day in the so-called «short term» [38, 39]. Therefore, B. Skinner suggested dividing the educational material into small portions, which must be learned gradually. The idea of programmed learning was developed into a coherent theory in the works of the scientist. This theory was further developed in the works of various scientists, in the studies of psychologists and teachers of the Soviet educational system [7, 17, 20, 21, 26, 33]. The analysis of scientific studies on the substantiation of the theoretical foundations of programmed learning and its implementation in the schools’ practice of this period allow us to draw a conclusion about the effectiveness of this form of education [15]. Today scientists continue the discussion about the advantages and disadvantages of distance and blended learning, the search for effective methods of distance learning of mathematics continues [14, 18, 28, 41, 43]. The technology of the «flipped classroom» is the most popular one. It can be interpreted as a «pedagogical model in which the typical elements of a lecture and homework are swapped. The flipped classroom approach relies on concepts such as active learning, … . The value of the flipped classroom is in changing time of a lecture into time for a workshop where students can question lecture content, test their application skills, and interact during hands-on sessions» [6]. A large number of articles are devoted to the comparative analysis of the effectiveness of traditional and flipped learning in distance and blended learning in universities [2, 9, 11, 12, 23, 24, 37]. Most authors confirm the conclusion that the technology of the «flipped classroom» is more effective compared to the traditional one in terms of students' success, their social interaction and educational motivation. A specific feature of mathematical concepts is a high level of abstraction. This fact is the cause of difficulties in learning the educational material in mathematics for many students of various specialties. One of the effective means of teaching mathematics, which allows you to improve the understanding of mathematical facts, is the visualization of educational material. There are different approaches to the interpretation of the concept of «visualization». Researchers are looking at different aspects of this process. For example, visualization as a way of exploring the world [8]; visualization as a learning tool [25]. The importance of visualizing educational material in the process of learning mathematics has been substantiated rather long time ago. The analysis of the use of visualization tools in learning and teaching mathematics [3, 30] showed that the relevance of this problem is increasing in recent years. Research into the role of visualization in mathematics learning and teaching continues. Scientists investigate the influence of visual representations of pupils and students on the ability to solve problems [13, 42]; the use of visualization techniques to increase the level of creativity of students [5]; the role of visual images in the process of solving problems from the theory of probabilities [45]; the use of various visualization tools in the earning process [4, 22]. The new stage of visualization research in education is associated with the development of information, communication, and digital technologies [16, 19, 35, 36, 40]. The purpose of this article. To substantiate the effectiveness the use of elements of "programmed learning" technology (in terms of content), elements of "flipped classroom" technology (in terms of form) and technology of visualizing educational material in the process of teaching a higher mathematics course to students of non-mathematical specialties in crisis conditions.