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mathematical achievements in these areas. All this leads to misunderstanding 
and careless attitude to the mathematics study by students. Thus, students 
underestimate the mathematics role in their future professional activities. 
Vast experience has been gained in various areas of pedagogical science 
in improving the vocational education problem: technical education, ways to 
improve vocational education in higher education [1, p.93891]. Nevertheless, 
the problem of vocational education and its psychological and pedagogical 
aspects are not sufficiently developed and it is not paid proper attention. 
Teaching a mathematics course in higher technical educational 
institutions in Kazakhstan has always faced big problems: poor pre-university 
preparation and a lack of desire to study mathematics, insufficient number of 
hours devoted to studying mathematics at university, but the main problem of 
all these problems is the fact that students have no desire to study 
mathematics, because they do not see and do not know its place in their future 
professional activities. Negative attitude of students to the mathematics study 
is compounded by the low initial level of the subject school knowledge. The 
performed analysis made it possible to identify the level of pre-university 
mathematical knowledge among the students enrolled in a technical 
university, it is 66.3%, of course it affects later during mathematics study at 
a university [2, p.29]. In order to perform this analysis, students were asked 
to solve independent work containing ten tasks from algebra and geometry 
course of a secondary school, the data are shown in table 1. 
Table 1 - Quantitative results of the initial level of mathematical 
knowledge for 2015-2018 academic year. 
Ac
ade
mi
cye
ar
S
pe
cialty
Numbe
r 
of
s
tudents
Assessment of the initial 
level 
of 
mathematical 
knowledge (%) 
Uns
ati
sf
ac
tor
y
S
ati
sf
ac
tor
y
Good
E
xc
ell
ent
2015 -
2016 
Biotechnology (1) 
42 
30.7 
30.2 
31.1 
8.0 
Chemical technology of 
organic substances (2) 
8 
15.8 
39.5 
34.2 
10.5 
Economics (3) 
25 
15.0 
40.0 
35.0 
10.0 

14 
Accounting and Auditing 
(4) 
18 
40.0 
30.0 
22.0 
8.0 
State and local government 
(5) 
11 
12.5 
43.8 
37.5 
6.2 
Marketing (6) 
10 
10 
40.0 
40.0 
10.0 
Mining (7) 
88 
11.1 
27.8 
38.9 
22.2 
2016 -
2017 
Biotechnology (1) 
44 
22.3 
38.3 
24.1 
15.3 
Chemical technology of 
organic substances (2) 
9 
22.6 
22.6 
37.1 
17.7 
Economics (3) 
18 
41.7 
33.3 
19.4 
5.6 
Accounting and Auditing 
(4) 
15 
27.3 
38.9 
32.5 
1.3 
State and local government 
(5) 
10 
7.1 
46.4 
32.1 
14.4 
Marketing (6) 
8 
57.1 
14.3 
21.4 
7.2 
Mining (7) 
59 
5.3 
42.1 
36.8 
15.8 
2017 -
2018 
Biotechnology (1) 
43 
40.8 
30.4 
18.3 
10.5 
Chemical technology of 
organic substances (2) 
6 
11.6 
29.9 
27.3 
31.2 
Economics (3) 
18 
8.8 
20.6 
52.9 
17.7 
Accounting and Auditing 
(4) 
15 
40.0 
27.1 
30 
2.9 
State 
and 
local
government (5) 
7 
20.0 
33.3 
33.3 
13.4 
Marketing (6) 
7 
- 
14.3 
71.4 
14.3 
Mining (7) 
62 
45.5 
18.2 
13.6 
22.7 
Analysis of the obtained results allows us to conclude that the level of 
pre-university mathematical knowledge of the given specialties’students is 
practically the same, and does not depend on the year of study (Pic. 1). 

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Pic. 1 - Average score of the initial level of mathematical knowledge of 
students in accordance with the specialties for 2015-2018 years 
The obtained results allow us to conclude that the average grade in 
mathematics does not depend on the specialty and the year of study. In the 
2015-2016 academic year the results were rated as «excellent» - 9.1% from 
the total number of students, «good» - 32.1%, «satisfactory» - 31.9%, 
«unsatisfactory» - 26.9%. In 2016-2017, «excellent» - 12.5% and «good» - 
27.5%, «satisfactory»- 36.1%, «unsatisfactory» - 23.9%. The results of the 
2017-2018 academic year are as follows: «excellent» - 13.6%, «good» - 
24.5%, «satisfactory» - 28.6%, «unsatisfactory» - 33.3%. 
In order to improve knowledge quality, we carried out an analysis of 
scientific and pedagogical literature with a view to identify methods and ways 
of improving knowledge, as a result, among the variety of ways and means 
developed by practice for the sustainable knowledge formation. We came to 
the conclusion that one way to improve the mathematical knowledge quality 
is the development of cognitive interest in mathematics [3, p. 8]. The 
cognitive interests are as follows: enthusiastic teaching, educational material 
novelty, historicism, demonstration of the practical application of knowledge 
in connection with life plans and orientations of students, the use of new and 
non-traditional forms of teaching, alternation of forms and methods of 
teaching, problem-based teaching, heuristic teaching, using of interactive 
computer tools, testing of knowledge, skills, and etc. [4, p. 122]. 
We introduced elements of career consulting in order to enhance 
cognitive interest in the mathematics study, thereby, affecting the level of 
mathematical knowledge. The educational process was built in such way that 

16 
in each of the presented specialties, we divided a group of students into the 
control and experimental groups. In the process of studying mathematics by 
experimental groups, elements of career consulting were introduced at each 
stage of teaching, that is during lectures, conducting practical lessons; we 
demonstrated to students the place of each individual topic in their future 
professional activity, although this is quite problematic, because the 
mathematics study was conducted with a very limited number of credits. The 
educational process of the control group was carried out without taking into 
account career consulting. 
This introduction allowed us to increase interest in the mathematics 
study, and so we mean the following mathematics education basis: 
mathematics is a necessary tool to the students of technical specialties for 
deeper and more complete mastering of special disciplines, which in turn will 
allow to become a highly qualified specialist in a professional field in the 
future. Therefore, by career consulting the mathematics course to the 
student’s future professional activity, we can achieve the following: 
- improve student progress; 
- teach to use mathematical methods in professional activities; 
- teach students to work with modern technologies, as they are created 
on the mathematical methods application; 
- carry out scientific work at the intersection of sciences engineering-
mathematics-technology. 
Introduction into the educational process began in the 2015-2016 
academic year. We had developed many problematic exercises and these 
exercises have a career consulting. While solving such problems students are 
faced with a professionally oriented problem, which can be solved by 
applying mathematical knowledge. Thus, students can clearly see how deeply 
mathematical methods have penetrated into modern science, and how 
problems of various sciences are solved by means of mathematics. In our 
point of view the solution of such problem tasks should be the main activity 
in practical classes. However, it should be emphasized that the solved tasks 
will cause cognitive interest if they are diverse in their content, form and 
methods of solution. While doing the tasks of technology, engineering, 
economics, mining, etc., we also gain our goal to strengthen interdisciplinary 
connections of mathematics with theoretical and special courses at the 
university. 
Problem solving develops such qualities as willpower, flexibility of 
mind, quick wit, perseverance in achieving a goal, logical thinking, which are 
necessary in professional activity. Having difficulty during the problem 
solving tasks, a student feels the need in searching and obtaining new 

17 
knowledge that he needs to solve the problem he is experiencing, while the 
student’s cognitive interest rises to a higher level. Problem-based learning 
offers a system of training sessions with the main goal of creating conditions 
under which students discover new knowledge, master new ways of finding 
information, develop creative thinking. Elements of problem-based learning 
allow maintaining and developing interest in mathematics, making lessons 
more interesting, intriguing [5, p.351]. In the process of conducting a final 
form of control, written test work, we also use professionally oriented tasks. 
According to the results of the experimental work, it was revealed that 
conducting the same initial training in the discipline, the students in the 
control group have lower results than the students studying in the 
experimental group. In the 2013-2014 academic year, the average grade was 
3.8; in the 2014-2015 academic year it amounted to 3.7 points. Starting from 
2015-2016, when students began to study in control and experimental groups, 
a sharp difference began to be observed, since the results of the control group 
became equal - 3.6 points, but at the same time, the results of the experimental 
group increased to 4.0 points, the difference between groups amounted to 0.4 
points. The situation is similar in the 2015-2016 academic year, but only the 
control group has the same average grade - 3.6, and the experimental one - 
4.1, in the 2017-2018 academic year, the result of the control group decreased 
to 3.5, and the experimental group was 4.1 points. 
So, the average grade of the initial level of mathematical knowledge in 
the control group was 2.99, in the experimental group it was 3.04 (difference 
was 0.05 points, which is 1%), and the final level of mathematical knowledge 
in the control group was 3.57, in the experimental one, 4.07 (difference is 
0.50 or 11.4%). 
Formative experiment results indicate that the students of experimental 
groups have a higher quality of mathematical knowledge. Therefore, we can 
conclude that the proposed pedagogical technology presence in the 
educational 
process, 
namely 
the 
problem-professionally 
oriented 
tasks’solution, allowed us to develop cognitive interest in the mathematics 
study among university students, thereby to contribute increasing in the level 
of mathematical knowledge. 
Literature 
1. Abayeva N.F., Yegorov V.V., Golovachyova V.N., Mustafina L.M., Yerakhtina 
I.I., Mustafina B.M., About Professional Orientation of the Mathematics as a Discipline for 
Students Majoring in Biotechnology. Indian journal of science and technology: Volume 9, 
Issue 19, May. - 2016 – P. 93891.
2. Abayeva N.F., Yerakhtina I.I., Udartceva S.M. O prikladnoj napravlennosti 
discipliny «Matematika» dlja special'nosti «Mashinostroenie» // Reports of the Kazakh 
Academy of education. – Astana, 2019 - №1. - P. 28-35. 

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3. Abayeva N.F., Yerakhtina I.I. Nekotorye pedagogicheskie aspekty obuchenija 
matematike na primere tehnologicheskih special'nostej vuza // Reports of the Kazakh 
Academy of education. – Nur-Sultan, 2019 - №4. - P. 6-15. 
4. Zhukenova G.B., Tolegenova T.G. Diagnosticheskie metody razvitija 
poznavatel'nyh interesov u uchashhihsja v obrazovatel'nom processe // Reports of the Kazakh 
Academy of education. – Nur-Sultan, 2017 - №1. - P. 120-126. 
5. 
Abayeva 
N.F., 
MustafinaL.M., 
YerakhtinaI.I., 
ZhurovV.V., 
AlimovaB.Sh.Development of cognitive interest in the study of mathematics among students 
majoring in mining. OPCIONJOURNAL, UNIVERSITYOFZULIA, VE. Venezuela, Año 
33, No. 85. (2019) - P. 344-361. 
Түйін 
Мақалада техникалық университеттің студенттері үшін математиканы 
оқытудың ұсынылған және әзірленген педагогикалық технологиясын енгізу бойынша 
тәжірибелік жұмыстың нәтижелері келтірілген.
 
Резюме 
В статье приводятся результаты опытной работы по внедрению предложенной 
и разработанной авторами педагогической технологии обучения математике для 
студентов технического вуза. 

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