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Abstract:
A system of work of a mathematics teacher in modern conditions should be
aimed at the development of students: their worldview, creative abilities, and cognitive
activity. Learning for everyone should be interesting and exciting. The competency-based
approach to teaching mathematics forces the teacher to review constantly the arsenal of
teaching and upbringing tools, choosing the most effective forms and developing them
together with students, based on knowledge and experience of students gained in math-
ematics lessons. Using a computer allows you to create an information environment that
stimulates the interest and inquisitiveness of students. The article reveals the features of
the use of information and communication technologies in the classroom as a means of
developing students’ creative thinking.
Keywords:
mathematics, information and communication technologies, computer,
mathematics lesson, interactive whiteboard, presentations, lesson plan, function, interest,
creative thinking.
INTRODUCTION
Mathematics, like no other science, can make a significant contribution to
implementation of tasks set for the school, since the activity of a mathematics
teacher is aimed at developing the skills of spatial imagination, logical thinking – in a
word, the development of intelligence. In mathematics lessons, various pedagogical
technologies can be used: modular training, project activities, and information and
communication technologies. In this case, learning becomes active, the emphasis is
on learning through practice, the productive work of students in small groups, the
use of inter-subject relationships, and development of independence. In a word, a
system of work of a mathematics teacher in modern conditions should be aimed at
the development of students: their worldview, creative abilities, cognitive activity.
Learning for everyone should be interesting and exciting.
TURAEV UTKIRBEK,
Department of Higher
Mathematics, Jizzakh Polytechnic
Institute, Jizzakh, Uzbekistan
OSTANOV KURBON,
Associate Professor, Candidate
of Pedagogical Sciences,
Department of Probability Theory
and Mathematical Statistics,
Samarkand State University
named after Sharaf Rashidov,
Samarkand, Uzbekistan
USE OF INFORMATION
AND COMMUNICATION
TECHNOLOGIES
IN MATHEMATICS
LESSONS AS A MEANS
OF STUDENTS’
CREATIVE THINKING
DEVELOPMENT
https://doi.org/10.47689/STARS.university-pp129-139
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STATEMENT OF A QUESTION
The competency-based approach to teaching mathematics forces the teacher
to review constantly the arsenal of teaching and upbringing tools, choosing the
most effective forms and developing them together with students, based on the
knowledge and experience of students gained at mathematics lessons. Using a
computer allows creating an information environment that stimulates the interest
and inquisitiveness of students.
The form and place of using computers in the lesson, of course, depends on the
content of this lesson, the goal set by the teacher. What are functions and features of
the application of educational programs? The following functions can be distinguished:
instrumental (making visual aids); demonstrating (showing ready-made demonstration
programs, slides, presentations, etc.); training (simulators); controlling.
Various types of lessons are possible with the use of information technologies:
lessons-conversations using a computer as a visual aid; lessons in setting up and
conducting research; practical work lessons; lessons-tests; integrated lessons, etc.
In recent years, along with computer technology, schools have received
interactive whiteboards, which are touch screen connected to a computer, the
image from which is transmitted to the board by a projector. Special software for
interactive whiteboards allows you to work with texts and objects, audio and video
materials, and Internet resources, make handwritten notes directly on top of open
documents, and save information.
A lesson in mathematics using ICT is visual, colorful, informative, interactive,
saves the time of the teacher, allows the teacher to work at his own pace, with
students in a differentiated and individual way, and makes it possible to monitor
and evaluate learning outcomes quickly.
The goals of ICT in the process of teaching mathematics are formation of skills
to work with information, the development of communication skills; preparation
of personality of “information society”; the opportunity to give the child as much
educational material as he can learn; formation of research skills, ability to make
optimal decisions.
The computer can be used at all stages of learning process: when explaining
new material, consolidating, repeating, and controlling ZUN. At the same time, for
the student, he performs various functions: a teacher, a working tool, an object of
study, a collaborating team, and a leisure (game) environment.
The main means of ICT in the study of mathematics are a computer as a universal
information processing device; a printer is a device that allows you to capture
information on paper.
Given and created by students or a teacher for students; a multimedia projector
is a device that projects an image onto the screen by means of a signal received
from a computer, VCR, CD or DVD player, video camera, or television tuner, which
radically increases the level of visibility in the work of teacher, enables students to
present the results of their work to the whole class; screen as a device for projecting
an image from a computer; an interactive whiteboard is a touch screen connected
to a computer, the image from which is transmitted to the board by a projector,
special software for which allows you to work with texts and objects, audio and
video materials, Internet resources, make handwritten notes directly over open
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documents and save information, as well as devices for recording (inputting) visual
and sound information (scanner, camera, video camera), which make it possible to
include directly information images of the world around in educational process.
The use of ICT tools is a necessary condition for the modern educational
process, when the main thing is not transmission of fundamental knowledge, but
the development of creative abilities, the creation of opportunities for realizing the
potential of the individual. ICT is used not as a goal, but as another pedagogical
tool that contributes to the achievement of the goal of the lesson.
Computer in the lessons in the following forms: the use of media resources as
a source of information (disks); computer support for the teacher’s activities at
different stages of the lesson; using a computer to perform technological maps;
portfolio creation.
Multimedia accompaniment of lessons increases the efficiency of obtaining
knowledge by students. The term “multimedia” is a tracing paper from the English
word multimedia, which can be translated as “many environments” (from multi
– many and media – environment). Multimedia technology allows you to use
simultaneously different ways of presenting information in the form of numbers,
text, graphics, animation, video and sound.
Basically, when studying mathematics, various types of multimedia products
are used: this is a computer presentation that is created using the PowerPoint
program, it is a sequence of slides, and with the help of this program a presentation
is created to study new material.
The advantages of presenting information in the form of a presentation over
the information in the form of speech: a large amount of time is released, but
the presentation must match the pace of assimilation, and student recording; the
computer allows you to show a complex experience safely, to explain its essence,
but this should complement, not replace. The presentation facilitates greatly the
management of the lesson, and the organization of the work of students, but
requires the teacher to be confident in the technology, knowledge of programs,
and readiness to work as usual.
If necessary, in the learning process, the student can independently return to
that part of the information that he did not learn without distracting the teacher,
for example: the formula is erased from the board, and if the student did not have
time to write it down, then the teacher will have to interrupt the story and return
again to the formula. And vice versa, commenting on the material that is on the
slides, the teacher can dwell on certain points in more detail. For example, when
studying the topic “Prime and Composite Numbers”, you can introduce students
to the construction of the sieve of Eratosthenes using a presentation. This will
interest students, and they themselves will be able to try to build the sieve of
Eratosthenes in their notebooks.
Presentations-surveys: questions, tasks that activate students for further work
in the lesson, create a favorable climate. So, when repeating the topic “Ordinary
fraction” at the beginning of the lesson, you can repeat theoretical material using
the presentation and check the correctness of the implementation immediately.
Presentations for organizing both frontal and group work. With the help of
presentations, it is also possible to create routes for students, i.e. see the end result
of their work. For example, compiling a travel map, or playing by stations.
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Presentations for self-testing of knowledge, skills and abilities of students. At
any stage, using the presentation, you can carry out independent work, and then
students can check it. After completing the work, students can exchange notebooks
and check the work mutually. The use of presentations in the classroom is good
because less time is spent in the classroom, students see the result immediately;
demonstrate to students neat, clear patterns of design solutions; demonstrate
absolutely abstract concepts and objects; achieve the optimal pace of the
student’s work; increase the level of visibility during training; learn more material
show students the beauty of geometric drawings; increase cognitive interest; to
introduce elements of entertainment, to revive the educational process; introduce
level differentiation of training; encourage students to use their home PC to study
math; achieve the effect of fast reverse noah connection.
Advantages of using e-learning tools: digital educational resources: screen and
sound manuals; technical teaching aids are
– ability to repeatedly repeat, stop, which allows the teacher to focus the
attention of students;
– refer to theoretical material, make historical references, work with definitions
and laws;
– clarity of processes, clear images of installations and models, uncluttered;
– modeling of processes and phenomena;
– obtaining and analysis of graphic dependence.
Computer simulators in mathematics lessons can be used simulators, both
in the classroom and at home. They represent a system of tasks on topics and
go like electronic to the teaching materials. Features and disadvantages of
simulators: programs provided with reference materials and a large number of
tasks, exercises, questions; simulation of real processes, laboratory experiments;
release of the teacher from routine work; feedback, error detection, tips, examples
of problem-solving; students have the opportunity to work at home; students feel
less constrained and thanks to this they “try themselves”; the ability to evaluate
objectively student progress; the ability to record and analyze the answers of the
student and the group of students, but the skills of oral and written speech are not
formed.
ICT outside school hours can be used in the form of: virtual excursions, creative
homework: making a crossword puzzle, anagrams, rebuses, a question; work with
tests; student conferences.
The use of computer technology in teaching makes it possible to differentiate
educational activities in the classroom, activates the cognitive interest of students,
develops their creative abilities, and stimulates mental activity.
Based on the above, we can say that computer technology is one of the best
means that helps a person acquire knowledge in a quality manner and use it. And
also allows you to create conditions for enhancing the learning process. And if the
student himself participated in the process of creating presentations, and projects,
then this only doubles the effect of acquiring new knowledge. Therefore, a larger-
scale introduction of information technologies into the educational process is
necessary as a means of improving the quality of education.
The use of ICT contributes to the growth of the teacher’s professional skills,
increasing the efficiency of mastering the skills of independent search, processing,
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and presentation of knowledge, developing the personality of students, and
preparing for a comfortable life in the information society.
Therefore, the main directions for improving the quality of mathematical
education are: increasing the professional competence of the teacher; use in
educational process the integration of content and cognitive activity of students,
i.e. active approach: a) to form skills; b) use computer technologies, modern
pedagogical technologies, problem-based teaching methods, research and design
technologies; It is advisable to carry out control using ICT in a differentiated manner
at the basic level (reproductive), advanced and high
RESEARCH RESULTS
The practice of using an interactive whiteboard at school allows us to identify
the following areas of its use in educational process:
1. Presentations, demonstrations and model building. Using the right software and
resources in conjunction with an interactive whiteboard can improve understanding
of new ideas, as an interactive whiteboard helps teachers present new material in
a very lively and engaging way. It allows you to present information using various
multimedia resources, simplify the explanation of diagrams, help you understand a
complex problem, and study it in as much detail as possible.
2. Active involvement of students. Interactive whiteboards, using a variety of
dynamic resources and improving motivation, make classes fun for both teachers
and students. Working with an interactive whiteboard can help the teacher to
test students’ knowledge, and develop a discussion to clarify the material being
studied, which allows students to better understand the material. By guiding
the discussion, the teacher can encourage students to work in small groups. The
interactive whiteboard becomes the center of attention for the whole class.
3. Improving the pace and flow of the lesson. Using an interactive whiteboard
can improve lesson planning, pace, and flow. Files or pages can be prepared
in advance and linked to other resources that will be available in class. On the
interactive whiteboard, you can easily move objects and labels, add comments to
texts, pictures and diagrams, highlight key areas and add colors. In addition, texts,
pictures, or graphics can be hidden and then shown at key points in the lesson. Pre-
prepared texts, tables, diagrams, pictures, music, maps, and themed CD-ROMs, as
well as adding hyperlinks to multimedia files and Internet resources will set the
activity at a brisk pace. All resources can be commented on directly on the screen,
using the pen tool, and save notes for future lessons. Files of previous lessons can
always be opened to repeat the material covered. Such methods encourage active
participation in the classroom.
Teaching with an interactive whiteboard is much more effective than teaching
with a computer and a projector alone, as it has a number of advantages: providing
a clearer, more efficient and dynamic presentation of material due to the ability to
draw and write on top of any application, save and print images on the whiteboard,
including any notes, made during the lesson without spending a lot of time;
developing student motivation through a variety of exciting and dynamic use of
resources; providing more opportunities for participation in teamwork, developing
personal and social skills; using different learning styles (the teacher can refer to
all kinds of resources, adapting to specific needs); ensuring a good pace of the
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lesson; providing the ability to save the used files at school network to organize the
repetition of the studied material; simplification of verification of learned material
on the basis of saved files; ensuring the multiple use of developed materials by
teachers, the exchange of materials with each other; stimulating the professional
growth of teachers, encouraging them to look for new approaches to learning.
In order for children in a modern school to be interested in mathematics, it is
necessary to use information technologies in lessons and additional classes, which
allow the formation and development of cognitive motivation of schoolchildren to
acquire new knowledge, helps create conditions for the success of each student in
the lesson, improves significantly clarity in the organization of the work of a class or
group of students, allows you to create an information environment that stimulates
the interest and inquisitiveness of the child, as well as to form communication skills
in schoolchildren.
The task of the teacher is to build educational work correctly, taking into account
the age-related psychological characteristics of children, where their thinking,
criticality, memory, attention, and speech will be improved. And this creates
favorable conditions for the development of communication skills in students. In
practice, the following techniques are used to develop the communicative skills
of students: demonstration of a sample answer; inventing questions on the topic;
a dialogue between teacher and students; interrogation of questions; verbal
counting; explanation of errors; work in pairs or groups; mathematical dictation;
commenting on the student’s answer at the blackboard.
As an example of the practical application of information technology in
mathematics lessons, consider the description of an algebra lesson and the
beginning of analysis in grade 11 “Repetition of material on the topic “Exponential
function”. Solving inequalities graphically.
The objectives of this lesson were: to review the properties of exponential
function and how they can be applied to solve equations and inequalities; to
teach students to apply information technology to solve mathematical problems;
improve the graphic culture of students.
Lesson plan: organizational moment, voicing the objectives of lesson and work
plan; student performances: exponential function and its properties; solution of
exponential equations; solution of exponential inequalities; explanation of graphical
method for solving equations and inequalities; consolidation of new knowledge –
oral solution of inequalities in a graphical way according to ready-made drawings;
written solution of exponential equation and exponential inequality; compiling and
recording an algorithm for solving an inequality in a graphical way; repetition of
graphing techniques in MS Excel (student’s message); safety briefing and practical
work in MS Excel using instructional materials – graphical solution of an exponential
equation; independent practical work to consolidate work skills; test; summarizing
the lesson. Homework assignment.
CONCLUSIONS
Thus, the use of information technology in teaching mathematics undoubtedly
gives the lesson great advantages over traditional forms of classes. But this in no
way means that every lesson and every stage of it must be conducted using a
computer, projector, or the Internet. The computer really has ample opportunities
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to create favorable conditions for the work of the teacher and students, brings to
a qualitatively new level of application of explanatory-illustrative and reproductive
teaching methods; the use of ICT in the classroom allows you to diversify the forms
of work, the activities of students, activate attention, and increase the creative
potential of the individual.
REFERENCES:
1. Afthanorhan W., Ahmad S., & Mamat I. (2014). Pooled Confirmatory Factor
Analysis (PCFA) using structural equation modeling on volunteerism program: A
step by step approach. International Journal of Asian Social Science, 4(5), 642–
653.
2. Al-Adwan A.S. (2020). Investigating the drivers and barriers to MOOCs
adoption: The perspective of TAM. Education and Information Technologies, 1–25.
3. Albelbisi N.A. (2020). Development and validation of the MOOC success scale
(MOOC-SS). Education and Information Technologies, 25(5), 4535–4555. https://
doi.org/10.1007/s10639-020-10186-4
4. Almasseri M., & AlHojailan M.I. (2019). How flipped learning based on the
cognitive theory of multimedia learning affects students’ academic achievements.
Journal of Computer Assisted Learning, 35(6), 769–781. https://doi.org/10.1111/
jcal.12386
5. Alonso-Mencía M.E., Alario-Hoyos C., Estévez-Ayres I., & Delgado Kloos C.
(2021). Analysing self-regulated learning strategies of MOOC learners through
self-reported data. Australasian Journal of Educational Technology, 56–70. https://
doi.org/10.14742/ajet.6150.
6. Alqahtani A.Y., & Rajkhan A.A. (2020). E-learning critical success factors
during the COVID-19 pandemic: A comprehensive analysis of e-learning managerial
perspectives. Education Sciences, 10(9), 216–232. https://doi.org/10.3390/
educsci10090216.
7. Alraimi K.M., Zo H., & Ciganek A.P. (2015). Understanding the MOOCs
continuance: The role of openness and reputation. Computers & Education,
80, 28–38. https://doi.org/10.1016/j.compedu. 2014.08.006.
8. Barnard L., Lan W.Y., To Y.M., Paton V.O., & Lai S.-L. (2009). Measuring self-
regulation in online and blended learning environments. The Internet and Higher
Education, 12(1), 1–6.
9. Bergdahl N., Nouri J., & Fors U. (2020). Disengagement, engagement
and digital skills in technology enhanced learning. Education and Information
Technologies, 25(2), 957–983. https://doi.org/10. 1007/s10639-019-09998-w13.
10. Education and Information Technologies Blayone T.J.B., Mykhailenko O.,
vanOostveen R., & Barber W. (2018). Ready for digital learning? A mixed-methods
exploration of surveyed technology competencies and authentic performance
activity. Education and Information Technologies, 23(3), 1377–1402. https://doi.
org/10. 1007/s10639-017-9662-6.
11. Buil I., Catalán S., & Martínez E. (2016). Do clickers enhance learning?
A control-value theory approach. Computers & Education, 103, 170–182. https://
doi.org/10.1016/j.compedu.2016.10. 009.
12. Burns E.C., Martin A.J., & Collie R.J. (2021). A future time perspective
of secondary school students’ academic engagement and disengagement:
Global dunyoda ilm-fan va ta‘limdagi innovatsion
rivojlanishning zamonaviy trendlari 15 dekabr, 2022 yil.
136
A longitudinal investigation. Journal of School Psychology, 84, 109–123. https://doi.
org/10.1016/j.jsp.2020.12.003.
13. Byrne B.M. (2010). Structural equation modeling with AMOS: Basic concepts,
applications, and programming (2nd ed.). Routledge. Cox M.J., & Marshall G. (2007).
Efects of ICT: Do we know what we should know? Education and Information
Technologies, 12(2), 59–70.
14. Craig S.D., & Schroeder N.L. (2017). Reconsidering the voice efect when
learning from a virtual human. Computers & Education, 114, 193–205. https://doi.
org/10.1016/j.compedu.2017.07.003 Creswell J.W. (2015).
15. A concise introduction to mixed methods research. SAGE. Darbyshire P., &
McDonald H. (2004). Choosing response scale labels and length: Guidance for
researchers and clients. Australasian Journal of Market Research, 12(2), 17–26.
16. Davis F.D. (1989). Perceived usefulness, perceived ease of use, and user
acceptance of information technology. MIS Quarterly, 13(3), 319–340.
17. Delcea C., Cotfas L.-A., Trică C., Crăciun L., & Molanescu A. (2019). Modeling
the consumers opinion influence in online social media in the case of eco-friendly
products. Sustainability, 11(6), 1796. https://doi.org/10.3390/su11061796.
18. Denovan A., Dagnall N., Dhingra K., & Grogan S. (2019). Evaluating the
Perceived Stress Scale among UK university students: Implications for stress
measurement and management. Studies in Higher Education, 44(1), 120–133.
https://doi.org/10.1080/03075079.2017.1340445.
19. DiStefano C., & Hess B. (2005). Using confirmatory factor analysis for construct
validation: An empirical review. Journal of Psychoeducational Assessment, 23(3),
225–241. https://doi.org/10. 1177/073428290502300303 El-Maghraby, A.S.A.
(2021).
20. Garrison D.R., Anderson T., & Archer W. (2000). Critical inquiry in a text-
based environment: Computer conferencing in higher education. The Internet and
Higher Education, 2(2–3), 87–105. Gatignon H. (2010).
21. The influence of instructional design on learner control, sense of achievement,
and perceived effectiveness in a supersize MOOC course. Computers and Education,
128, 377–388. https://doi.org/10.1016/j.compedu.2018.10.001 Kirkwood A., & Price L.
(2015).
22. Achieving improved quality and validity: Reframing research and evaluation
of learning technologies. European Journal of Open, Distance and E-learning, 18(1).
https:// www.eurodl.org/index.php?p=special&sp=articles&inum=6&article=672&a
rticle=678.
23. Koh J.H.L. (2020). Three approaches for supporting faculty technological
pedagogical content knowledge (TPACK) creation through instructional
consultation: Three approaches of TPACK creation. British Journal of Educational
Technology. https://doi.org/10.1111/bjet.12930
24. Komalawardhana N., Panjaburee P., & Srisawasdi N. (2021). A mobile game-
based learning system with personalized conceptual level and mastery learning
approach to promoting students’ learning perceptions and achievements.
International Journal of Mobile Learning and Organization, 15(1), 29–49.
25. Kühl, T., & Zander, S. (2017). An inverted personalization efect when learning
with multimedia: The case of aversive content. Computers & Education, 108, 71–84.
https://doi.org/10.1016/j.compedu. 2017.01.013
STARS International University
137
26. Lai J.W.M., & Bower M. (2019). How is the use of technology in education
evaluated? A systematic review. Computers & Education, 133, 27–42. https://doi.
org/10.1016/j.compedu.2019.01.010.
27. Lai, J. W. M, Bower, M., De Nobile, J., & Breyer, Y. (2022). What should we
evaluate when we use technology in education? Journal of Computer Assisted
Learning. https://doi.org/10.1111/jcal.12645.
28. Larmuseau C., Cornelis J., Lancieri L., Desmet P., & Depaepe F. (2020).
Multimodal learning analytics to investigate cognitive load during online problem
solving. British Journal of Educational Technology, 51(5), 1548–1562. https://doi.
org/10.1111/bjet.12958 Leavy, P. (2017).
29. Research design: Quantitative, qualitative, mixed methods, arts-based, and
community based participatory research approaches. Guildord Press. Lin H.-H.,
Lin S., Yeh C.-H., & Wang Y.-S. (2016).
30. Measuring mobile learning readiness: Scale development and validation.
Internet Research, 26(1), 265–287. https://doi.org/10.1108/ IntR-10-2014-0241.
31. Loizzo J., Ertmer P.A., Watson W.R., & Watson, S.L. (2017). Adult MOOC
learners as self-directed: Perceptions of motivation, success, and completion.
Online Learning, 21(2), n2. https://eric.ed. gov/?id=EJ1149353.
32. Marsh H.W., Hau K.-T., Balla J.R., & Grayson D. (1998). Is more ever too much? The
number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral
Research, 33(2), 181– 220. https://doi.org/10.1207/ s15327906mbr3302_1 1 3.
33. Education and Information Technologies Martinez-Lopez, R., Yot, C., Tuovila,
I., & Perera-Rodríguez, V.-H. (2017). Online self-regulated learning questionnaire
in a Russian MOOC. Computers in Human Behavior, 75, 966–974. https://doi.org/
10.1016/j.chb.2017.06.015
34. Maxwell J.A. (2016). Expanding the history and range of mixed methods
research. Journal of Mixed Methods Research, 10(1), 12–27. https://doi.org/
10.1177/1558689815571132.
35. Mishra P., & Koehler M.J. (2006). Technological pedagogical content
knowledge: A framework for teacher knowledge. Teachers College Record, 108(6),
1017–1054.
36. Moreno-Marcos P.M., Alario-Hoyos C., Muñoz-Merino P.J., Estévez-Ayres I., &
Kloos C.D. (2018). Sentiment analysis in MOOCs: A case study. 2018 IEEE Global
Engineering Education Conference (EDUCON), Santa Cruz de Tenerife, Canary
Islands, Spain. https://doi.org/10.1109/EDUCON. 2018.8363409.
37. Muller F.A., & Wulf T. (2020). Technology-supported management education:
A systematic review of antecedents of learning effectiveness. International Journal
of Educational Technology in Higher Education, 17(1). https://doi.org/10.1186/
s41239-020-00226-x.
38. Nicol A.A., Owens S.M., Le Coze S.S., MacIntyre A., & Eastwood C. (2018).
Comparison of high technology active learning and low-technology active learning
classrooms. Active Learning in Higher Education, 19(3), 253–265. https://doi.
org/10.1177/1469787417731176.
39. Nikolopoulou K., Gialamas V., & Lavidas K. (2020). Acceptance of mobile
phone by university students for their studies: An investigation applying UTAUT2
model. Education and Information Technologies, 25(5), 4139–4155. https://doi.
org/10.1007/s10639-020-10157-9.
Global dunyoda ilm-fan va ta‘limdagi innovatsion
rivojlanishning zamonaviy trendlari 15 dekabr, 2022 yil.
138
40. Onwuegbuzie A.J., & Daniel L.G. (2002). A framework for reporting
and interpreting internal consistency reliability estimates. Measurement and
Evaluation in Counseling and Development, 35(2), 89–103. https://doi.org/
10.1080/07481756.2002.12069052.
41. Ozudogru M., & Ozudogru F. (2019). Technological pedagogical content
knowledge of mathematics teachers and the effect of demographic variables.
Contemporary Educational Technology, 10(1), 1. https://doi.org/10.30935/cet.
512515 Paas, F. G. (1992).
42. Training strategies for attaining transfer of problem-solving skill in statistics:
A cognitive-load approach. Journal of Educational Psychology, 84(4), 429–434.
43. Park, S.Y., & Song K.S. (2020). Examining social presence and collective
efficacy on international online collaborative learning. Journal of Interactive
Learning Research, 31(2), 101–114.
44. Phillips R., Kennedy G., & McNaught C. (2012). The role of theory in learning
technology evaluation research. Australasian Journal of Educational Technology,
28(7), 1103–1118. https://doi.org/ 10.14742/ajet.791.
45. Pickering J.D., Lazarus M.D., & Hallam J.L. (2019). A practitioner’s guide
to performing a holistic evaluation of technology-enhanced learning in medical
education. Medical Science Educator, 29(4), 1095–1102. https://doi.org/ 10.1007/
s40670-019-00781-7.
46. Mixed-methods research in education: Exploring students’ response to a
focused feedback initiative. SAGE Publications. Shamim, M. (2018). Application
of cognitive theory of multimedia learning in undergraduate surgery course.
International Journal of Surgery Research and Practice, 5(2), 1–6.
47. Sternberg R.J., Castejón J.L., Prieto M.D., Hautamäki J., & Grigorenko E.L.
(2001). Confrmatory Factor Analysis of the Sternberg Triarchic Abilities Test in Three
International Samples: An Empirical Test of the Triarchic Theory of Intelligence.
European Journal of Psychological Assessment: Official Organ of the European
Association of Psychological Assessment, 17(1), 1–16. https://doi. org/10.1027//1015-
5759.17.1.1.
48. Sun L., Ruokamo H., Siklander P., Li B., & Devlin K. (2021). Primary school
students’ perceptions of scafolding in digital game-based learning in mathematics.
Learning, Culture and Social Interaction, 28, 100457. https://doi.org/10.1016/j.
lcsi.2020.100457.
49. Wu B., & Chen X. (2017). Continuance intention to use MOOCs: Integrating
the technology acceptance model (TAM) and task technology ft (TTF)
model. Computers in Human Behavior, 67, 221–232. https://doi.org/10.1016/
j.chb.2016.10.028 1 3.
50. Education and Information Technologies Yang S.-H. (2016). Conceptualizing
efective feedback practice through an online community of inquiry. Computers &
Education, 94, 162–177. https://doi.org/10.1016/ j.compedu.2015.10.023.
51. Yu J., Choi H., & Kim J. (2019). Multigroup Analysis and Measurement
Equivalence: Korean And Chinese Consumers of Korean Cosmetics. Social
Behavior and Personality, 47(3), 1–19. https://doi. org/10.2224/sbp.7499 Zhou, M.
(2016). Chinese university students’ acceptance of MOOCs: A self-determination
perspective. Computers & Education, 92–93, 194–203. https://doi.org/10.1016/j.
compedu.2015.10.01.
STARS International University
139
52. Абдуллаев А., Инатов А., & Останов К. (2016). Некоторые методические
особенности применения информационных технологий в процессе обучения
математике. In Информатика: проблемы, методология, технологии (PP. 7–10).
53. Абдуллаев А.Н., Инатов А.И., & Останов К. (2016). Роль и место использо-
вания современных педагогических технологий на уроках математики. Сим-
вол науки, (2-1), 49–51.
54. Останов К., & Хайитмурадов Ш. (2020). Использование инновационных
технологий в процессе обучении школьного курса математики. Научные ис-
следования, 15.
55. Останов К., Инатов А., Химматов И., Рахимов Б., & Воробьев Н.Н. (2018).
О некоторых способах развития творческой активности учащихся при реше-
нии уравнений. ББК 72 – С. 108.
56. Останов К., Султанов Ж., Хайитмурадов Ш.С., & Остонов М.К. (2019). Об
использовании нестандартных задач в процессе активизации мышления уча-
щихся. Проблемы науки, (12 (48)), 98–99.
57. Останов К., Хайитмурадов Ш., & Муртазаев М. (2019). О формировании
творческого мышления учащихся в процессе обучения математике. ББК, 72, 19.
58. Нурмаматов М., Инатов А.И., & Останов К. (2017). О различных подходах
формирования творческих способностей учащихся на уроках математики.
Молодой ученый, (24), 374–376.
59. Абдуллаев А., Останов К., & Усанов Р.Ш. (2022). Об использовании ком-
пьютерных технологий при изучении математики. Наука, образование и куль-
тура, (1 (61)), 5–7.
60. Абдуллаев А.Н., Останов К., & Пошоходжаева Г.Д. (2022). Методические
аспекты использования информационно-коммуникативных технологий в
процессе обучения математике. Проблемы науки, (1 (69)), 5–7.
61. Абдуллаев А.Н., Останов К., & Пошоходжаева Г.Д. (2022). Использование
средств икт для формирования творческих умений учащихся по математике.
Наука и образование сегодня, (1 (70)), 5–7.
62. Останов К., Махмудов Х.Ш.О., & Усмонов Х.З. (2021). Об использовании
различных нестандартных упражнений в развитии творческой активности
учащихся на уроках математики. Наука и образование сегодня, (9 (68)), 5–6.
63. Тилавова Ш.Е., Тилавов Р.А., & Останов К. (2022). Использование обще-
мыслительных приемов в формировании творческого мышления учащихся в
процессе обучения математике. In Научные исследования xxi века: Теория и
практика (PP. 152–155).
64. Останов К., Бобоев Б.Э., Уралова О.Б., & Толлиев И. (2019). Применение
педагогических технологий при изучении максимума и минимума функций.
ББК 72 Д103.
65. Останов К., Хайитмурадов Ш., & Муртазаев М. (2019). О формировании
исследовательских умений у учащихся при изучении расположения корней
квадратного уравнения. ББК 72 И115.
66. Останов К., Инатов А., Абдурахмонова М., & Шамсиева Г.А. (2018). О не-
которых способах развития мышления учащихся в процессе решения геоме-
трических задач. ББК 72 А105.
Останов К., Пулатов О.У., & Азимов А.А. (2018). Использование нестандарт-
ных исследовательских задач в процессе обучения геометрии. Вопросы нау-
ки и образования, (1 (13)), 120–121.
