Technology of multilevel interuniversity indicators as a factor for increasing academic mobility. Experience based on Russian federal educational standards

Academic mobility has become a characteristic feature of modern higher education. The mobility of students from one university to another, both nationally and internationally, is becoming commonplace. This trend, of course, carries many positive aspects, increasing the competitiveness of the students themselves, and providing the dynamically changing needs of the modern labor mar-ket1 [1]. However, this sets new goals and objectives for higher education institutions, which were not relevant before Russia joined the Bologna process [2; 3].

Specialists of higher education know that the same educational programs in different universities are provided at times with a completely different set of studied modules [4; 5]. When moving from one university to another, even at the level of one region and within one study program, a student must, as it is commonly called, “cover the difference in plans” – what means that the student retakes at the host university those disciplines that he/she “has not studied” earlier. At the same time, the content of the module does not make a difference. If the name of the module is not included in the home university curriculum, this automatically requires that the mobile students have to retake this subject at the host university. Also, a student may find himself/herself in a similar situation if he/she substantially changes his/ her study area moving to the next cycle of higher education, e.g. the postgraduate program , but some specific competencies have already been mastered by him/her during the undergraduate program [6; 7].

Even within the one university, the process of transition between related subject areas is associated with the need to retake a number of modules, often essentially identical. Let us give a typical example. KNRTU-KAI is a technical university that educates engineers for high-tech industries and the IT industry. In particular, education is underway in such undergraduate programs as Aircraft Engineering (subject area code 24.03.04), and Applied Mathematics and Informatics (subject area code 01.03.02), whose curricula are available on the university website2. According to the ideology of intra-university mobility implemented over the past 5 years, the curricula are built in such a way that during the first two years of study (Semesters 1-4), students have the opportunity to change the study program to another one, if budget places are available. Both of these subject areas require a strong mathematical background at the initial stage of training.

On the first program (24.03.04), within the framework of professional activity, specialists will build aircraft (Aviation Engineering), on the second (01.03.02), specialists will develop software (Software Engineering).

So, for the subject area 24.03.04, this is a three-semester course of Higher Mathematics, which includes such branches as Linear Algebra and Analytical Geometry, Mathematical Analysis, Differential Equations, Probability Theory and Mathematical Statistics, Equations of Mathematical Physics (Semester No. 1-3, Total Workload is 18 Credit Points)3. Within the framework of the subject area 01.03.02, students receive the same competencies from a wider set of disciplines. Some courses are studied separately, e.g. Linear Algebra and Analytical Geometry (Semester No. 1, 4 Cr. Points), Mathematical Analysis I-II-III (Semester No. 1-3, 16 Cr. Points), Differential Equations added with elements of equations of mathematical physics (Semester No. 4, 5 Cr. Points), Probability Theory and Mathematical Statistics (Semester No. 3-4, 7 Cr. Points)4.

Even with a superficial comparison of the mathematical blocks of these two directions, a number of logical conclusions that are understandable to any teacher can be drawn:

– Despite the different names, the modules cover the same branches of Mathematics, and form essentially the same general professional competences called OPK-1 in the corresponding Federal State Educational Standard of Higher Education, which is also confirmed by the similarity of indicators for achieving these competencies. For example, for the disciplines of the theoretical mathematical block5, and for the block of computational mathematical disciplines6;

– Depth of mastering the branches in this two programs, however, is different, which is easy to see from the almost two-fold difference in the number of credits allocated for mastering the module7;

– Students wishing to change the area of future professional activity from Software Engineering to Aviation Engineering, almost completely cover the mathematical block of the receiving subject area, and they do not need to retake the module “Higher Mathematics”. This is explained by the complete alignment of the studied list of modules of the mathematical block for 01.03.02 subject area with the list of mathematical block for 24.03.04 subject area, while the workload of the mathematical block in the first program significantly exceeds the workload of the similar block in the second program;

– At first glance, students who change their activity from Aviation Engineering to Software Engineering also do not need to retake a number of modules of the receiving subject area, as they studied them as part of the generalized course of Higher Mathematics. However, due to the smaller number of hours allocated for each branch of Mathematics, the full mastery by the student of the competencies in accordance with the academic program of 01.03.02 subject area is not obvious and requires an in-depth study of this issue.

According to current practice, students of both directions, when changing their programs of study, are required to retake a full list of modules with clearly distinct names. This approach requires a lot of additional time from both the students and the teachers of the receiving subject area, which complicates the already difficult period of adaptation of the student to the new requirements and learning conditions on the one hand, and takes a lot of the teacherʼs time on the other.

The solution to the problem can be the creation of a system of multilevel indicators reflecting the mastering of certain clearly defined professional competencies. The indicators of the upper level will reflect the mastery of some sections of knowledge in general, with a decrease in the levels, the more precise details will be made. Thus, a tree of indicators, or competencies, will be built for each subject area. Each course studied within the framework of the academic program should be equipped with a similar tree, which will allow, when moving a student, to compare the levels of mastering competencies at a given level, and to reevaluate as a whole according to the mastered part of the curriculum without reference to the name of a specific module. This will significantly simplify the process of students’ mobility between subject areas within one university, as well as from one university to another.