I.I. YERAKHTINA
Candidate of Pedagogic Sciences,
Dean of Mechanical Engineering Faculty
Karaganda State Technical university
L.M. MUSTAFINA
Candidate of Physics-Mathematical Sciences,
associate professor of Higher Mathematics Department,
Karaganda State Technical university
A.R. YARULLINA
Assistant of Higher Mathematics Department
Karaganda State Technical university
Annation
According to world trends, mathematical methods are more widely used
in modern technologies, equipment and scientific research every year.We
have developed a pedagogical technology that allows us to develop a
cognitive interest to study mathematics, and so to encourage students to self-
perfection of their mathematics knowledge and to improve astudents’
progress in mathematics. The article presents experimental work results on
the proposed pedagogical teaching technology implementation.
Key words: teaching mathematics at university; career counseling
INTRODUCTION. As practice shows, a role of mathematics is
inconspicuous in the process of preparing a future specialist in technical
university, because in all cases, of course, professional disciplines come to
the forefront, while theoretical ones, including mathematics, are drawn back.
This is due to the fact that rapid mathematization of all are as of technology
is not taken into account in university’s educational process, and this process
is based on the fact that new technologies and methods are introduced with
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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
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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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