The Context And Content Approaches To Teaching Mathematics At The Economic University

Literature review

The combined use of several technologies usually has an integrative nature. It takes more than a decade to study integrative aspects in professional higher education. Integration as the convergence and unification of particular elements on the basis of their relationship implies qualitative transformation of both the entire system and its particular elements. Makarova (2008) identifies two areas of the integration study:

• education reflects the integrative tendencies of the science and culture developing and united in a single global picture, they create the basis for the learner’s worldview;

• education represents an integrated field of activity where the learner’s personal and professional becoming takes place.

The experince of the integrative approach to the basic mathematical preparation of the bachelors of Economics is represented in the works of the lecturers of the Financial University (Denezhkina, Popov, & Samylovskiy, 2012; Goncharenko, Denezhkina, Popov, & Shapoval, 2014). The early profiling in teaching of mathematical disciplines to the students in Economics, according to the authors (Konnova, Rylov, & Stepanyan, 2016a), contributes to the increased interest in the subject, a deeper understanding of economic patterns and the conscious use of mathematical models in the solving of the practical-oriented challenges.

It’s a comprehensive vision of education that represents a context-based learning that is an activity-based educational technology formulated by Verbitskiy in the 1990s successfully tested in Russian education, remaining relevant today. Verbitskiy (2004, 2017) provides three origins, on its basis the theory and technologies of context learning have been developed:

• the activity learning theory developed in Russian psychology;

• theoretical generalization of the diverse experience of uses, forms and methods of the active learning including problem-based ones;

• the influence of the subject and social context of the student’s future professional activity on the process and the results of their academic activity.

European university professors share their unique experience in the use of integrative and context learning technologies in the teaching of foreign languages. For example, Gil-Salom and Benlloch-Dualde (2016) present a methodology that was used for the integration in the evaluation of oral presentation in German (as a foreign language) done by the Polytechnic University of Valencia students. Tareva (Tareva & Tarev, 2018) views methods implying rethinking (redefinition) the role and status of a foreign language:

• in the continuous humanitarian person education (Life-Long Learning - LLL);

in the organic combination of productive work with learning a foreign language and student’s activities, such as research, rationalization, invention and innovation (Practice-Based Professional Learning - PBPL);

• in the enhancing of the interconnection between learning a language and the subject content of professional disciplines (Content and Language Integrated Learning - CLIL).

The last one (CLIL) presents a particular interest to our research since it creates the best opportunities for the character development that is able to independently set and overcome professional challenges, to effectively communicate in the professional sphere in native and foreign languages. Ting (2010, 2011) who led the development of the methodology, writes that CLIL has the potential for a significant revision of both the content of education and the language training through kinds of induction. She believes that the teacher should guide students to the deep understanding of the conceptions of the studied discipline through interactive sessions and suggests using the 50:50 ratio for Content: Language in the educational training and the foreign language teaching.

Salisbury’s (2018) work presented a study on the effect that the lecturer who has previous experience of Course Management System (CMS) has on the quality of education and students’ end results. Pavón & Gaustad’s (2013) study analyzes key issues faced by universities in the developing of bilingual programs and proposes effective measures for dealing with them.

The work of Goldfarb et al (2018), as the origin of the classification of the complex problematic cognitive-communicative tasks in the field of technical education, should be highlighted among the studies of the CLIL methodology. Also the Bahls & Wray’s (2015) work is noteworthy that describes the effect of using the technical software on the undergraduates’ mindset and computational processes in the fields of science, technology, engineering and mathematics.

Comparative analysis of context and content approaches

As a promising method for the embodiment of the ideas of early profiling it was decided to use context and content approaches in an integrated manner. Let us compare them. (Table 01 )

Integration of context and content approaches in ‘Computer Practicum’

For several years the authors have been working on the creating of an integrated comprehensive approach to early profiling of the educational process (Konnova, Rylov, & Stepanyan, 2016a). Its ideas include the gradual transformation of the presentation of the mathematical courses and teaching methods. The authors attempted to develop a system of accessible practice-oriented challenges in the textbook ‘Economic applications of higher Mathematics in case studies’ (Konnova, Rylov, & Stepanyan, 2016b).

‘Computer Practicum’ has been introduced in the Financial University’s first year ‘Economics’ and ‘Management’ baccalaureate curriculum since 2017. The main goals of the new discipline are (Zadadayev, 2017):

• to provide students with the knowledge of computational methods in the implementation of mathematical models;

• to form practical skills for applying the computer technologies used in economics and finance.

The programming language R and Microsoft Excel are used as tools. As for the content course it is based on the higher mathematics’ material. It should be noted that together with the ‘Computer Practicum’ discipline the students study ‘Mathematics’ which provides important opportunities for a deeper understanding of mathematical patterns and a practical use of mathematical methods in future professional activity.

The ‘Computer Practicum’ classes take place in computer rooms and, naturally, aim to introduce students to the modern information technologies’ abilities, to form specific technical skills. However, it’s irrational for Economics’ students to study ‘Computer Science’ only as a discipline itself: time requires the intensification of teaching, to study several subjects simultaneously. This approach allows not only to expand the students’ knowledge on specific subject areas but also to draw a connection between them and their interpenetration (diffusion). All this positively influences the effectiveness of the process of subject mastery and corresponds with the students’ educational needs.

Challenges met by students with the practical use of mathematical methods and the objective difficulty of the mathematical disciplines’ content have become a major cause for expanding the mathematical component in educational process. The content of ‘Mathematics’ discipline was the foundation of ‘Computer Practicum’, that is a content for the new discipline. Furthermore, the new opportunities for filling the educational activity with the professional economic context have emerged (Figure 01 ).

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Table 02 , presented below, contains information on the approximate distribution of the course’s theoretical input, indicating the formed computer skills and the affected economic context.

It should be noted that the material of the mathematical content does not duplicate the content of ‘Mathematics’ discipline but effectively complements it with visualization and approximate numerical computations. It is these calculations that are most commonly used in applications. Yet, in the traditional mathematics they are not being paid enough attention, so naturally they cause problems for students.

It is noted that the integration of the context and content approaches is not a mechanical combination of the three columns of Table 02 . In the process of the parallel learning of ‘Mathematics’ and ‘Computer Practicum’ all three components are being strengthened since they occur through mutual necessity and are in constant interconnection.

The professional context is not limited by adding economic issues to the material. According to Verbitskiy (2004, 2017) we can also identify the substantive and technological and the social context, both of them relating to the students' future professional activity. The substantive and technological context includes:

• work with data;

• the study of functional dependencies;

• linear programming;

• introduction to the simplest financial instruments.

The social context is presented by:

• the individual learning curves;

• group work;

• development of the information culture;

• basic skills of dealing with crisis situations;

• project activity.

Feed back

Let us cite the results of the survey of the Financial University students of two faculties who have studied the ‘Computer Practicum’ discipline for two semesters. 58 students of the Faculty of Public Administration and Financial Control (Audit and Control) and 182 students of the Faculty of Financial Markets took part in the survey.

The questions of the anonymous electronic survey were given to the students after they have received their final grades and were referred to the satisfaction with the received knowledge, teaching materials and the accessibility of the discipline presentation. The distribution of responses to the questionnaire providing an important information about the usefulness of our experiment is shown below (Figures 02 - 04 ).

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According to the responses, 58% of the students understand the usefulness of the studied practicum for their future professional activity, 88% consider the course useful. 98% of respondents see the direct ties of the basic of computer technology knowledge to resolving mathematical challenges, and 71% of respondents are aware of their potential application in meeting economic challenges.