Xorijiy lingvistika va lingvodidaktika
–
Зарубежная
лингвистика
и
лингводидактика
–
Foreign
Linguistics and Linguodidactics
Journal home page:
https://inscience.uz/index.php/foreign-linguistics
Enhancing critical thinking and problem-solving skills in
high school mathematics through GeoGebra
Arofatkhon KUCHKAROVA
Andijan State Pedagogical Institute
ARTICLE INFO
ABSTRACT
Article history:
Received June 2024
Received in revised form
10 June 2024
Accepted 25 July 2024
Available online
15 July 2024
This article examines the role of GeoGebra, a dynamic
mathematics program, in developing high school students'
critical thinking and problem-solving skills. The author
examines how GeoGebra's interactive and visual features help
educators create effective learning environments for mastering
geometry concepts. The program promotes the expansion of
traditional teaching approaches by integrating dynamic
mathematical systems. Hands-on explorations and challenges in
GeoGebra allow students to deepen their knowledge of
mathematics and develop the ability to manipulate and
visualize geometric objects while providing instant feedback.
2181-3701
/©
2024 in Science LLC.
DOI:
https://doi.org/10.47689/2181-3701-vol2-iss4-pp190-195
This is an open-access article under the Attribution 4.0 International
(CC BY 4.0) license (
https://creativecommons.org/licenses/by/4.0/deed.ru
Keywords:
critical thinking,
problem-solving,
GeoGebra,
geometry,
visualization,
mathematics.
GeoGebra
dasturi
orqali
umumta’lim
maktab
matematikasida tanqidiy fikrlash va muammoni hal qilish
qobiliyatlarini rivojlantirish
ANNOTATSIYA
Kalit so‘zlar
:
tanqidiy fikrlash,
muammoni hal qilish,
GeoGebra,
geometriya,
ko
‘
rish,
matematika.
Umumta’lim maktab matematika sohasida tanqidiy fikrlash
va muammoni yechish k
o‘
nikmalarini rivojlantirish juda muhim
hisoblanadi. Ushbu maqola dinamik matematika dasturi
GeoGebraning bu ta’lim maqsadlariga erishish uchun kuchli
vositasiga qanday e’tibor qaratilishini tahlil qiladi. GeoGebra
interaktiv va vizual imkoniyatlaridan foydalanib, pedagoglar
o‘
quvchilar uchun geometriya tushunchalarini
o‘
rganish uchun
qiziqarli muhit yaratishlari mumkin. Bu metodologiya
o‘
qitish
usullaridan tashqari, dinamik matematik tizimlarini
o‘
rganish
jarayoniga integratsiya qilish orqali s
o‘
nggi tahlil va
1
Doctoral student (PhD), teacher, Andijan State Pedagogical Institute. E-mail: ssshahriyor@gmail.com
Xorijiy lingvistika va lingvodidaktika
–
Зарубежная лингвистика
и лингводидактика
–
Foreign Linguistics and Linguodidactics
Issue
–
2
№
4 (2024) / ISSN 2181-3701
191
muammolar yechish mashqlari orqali
o‘
quvchilar matematik
asoslarini yanada chuqur
o‘rganadi va geomеtrik shakllarni
boshqarish va vizual ma’lumotlar orqali tasavvur qilishdan
ma’naviy ko‘
nikmalarini rivojlantiradi.
Развитие критического мышления и навыков решения
задач в математике средней школы с помощью
GeoGebra
АННОТАЦИЯ
Ключевые слова:
критическое мышление,
решение проблем
,
GeoGebra,
геометрия,
визуализация,
математика.
В
данной
статье
исследуется
роль
GeoGebra,
динамической математической программы, в развитии
критического мышления и навыков решения проблем у
старшеклассников. Автор анализирует, как интерактивные
и визуальные функции GeoGebra помогают педагогам
создавать эффективные учебные среды для освоения
геометрических концепций. Программа способствует
расширению традиционных подходов к обучению за счет
интеграции
динамических
математических
систем.
Практические исследования и задачи в GeoGebra
позволяют учащимся не только углубить свои знания в
математике, но и развить способность управлять и
визуализировать геометрические объекты, обеспечивая
мгновенную обратную связь.
INTRODUCTION
In contemporary education, the cultivation of critical thinking and problem-solving
skills stands as a cornerstone of effective learning, particularly in disciplines like
mathematics. High school mathematics programs strive not only to impart foundational
knowledge but also to equip students with analytical abilities essential for their academic
and professional futures. In this context, educational technologies have emerged as
powerful partners, transforming traditional teaching methods by integrating interactive
and dynamic tools into the learning process. Among these technologies, GeoGebra, a
versatile software suite designed for mathematics education, has garnered attention for
its ability to enhance student engagement and conceptual understanding through visual
and interactive explorations of mathematical concepts. Through its interactive platform,
GeoGebra offers educators innovative means to foster deeper learning and mastery of
geometric and algebraic concepts, thereby preparing students to meet the challenges of a
rapidly evolving technological landscape.
LITERATURE ANALYSIS
Technology integration have been implemented in educational practices, such as
various observations, simulated experiments, and curriculum integrations as well. The
advantages of teaching with technologies in the science classroom include more
effectively delivering the dynamics of geometric shapes through multimedia animations,
enabling representative scientific thinking, and enhancing support for changing teachers’
roles [1]. According to scientists, these days teachers are urged to develop learners with
Xorijiy lingvistika va lingvodidaktika
–
Зарубежная лингвистика
и лингводидактика
–
Foreign Linguistics and Linguodidactics
Issue
–
2
№
4 (2024) / ISSN 2181-3701
192
relevant modern skills that match the needs of our changing world [2]. The majority of
teachers have acquired firsthand knowledge of IT through teacher training programs or
workshops. Despite the available resources, a significant number of school teachers still
show limited interest in integrating IT into their teaching practices.
RESEARCH METHODOLOGY
The main purpose of this study was to investigate the effect of GeoGebra in the
teaching and learning of mathematics in Andijan schools. The objective of this study was
to determine the effectiveness of using GeoGebra on students’ learning of graphs as
compared to the traditional approach. The experimental research in which pre-test-post-
test not equivalent control group design was used to examine the effectiveness of
GeoGebra software in teaching and learning mathematics.
ANALYSIS AND RESULTS
GeoGebra is a powerful educational tool that enables students to visualize
mathematical concepts, manipulate variables, and dynamically interact with geometric
constructions and algebraic representations (Figure 1). It provides a platform where
students can experiment with mathematical ideas, test hypotheses, and explore
relationships visually and intuitively. By bridging the gap between abstract concepts and
real-world applications, GeoGebra helps students develop a deeper understanding of
mathematical principles.
Figure 1. Animation of algebraic function.
Cultivating Critical Thinking
Critical thinking involves analyzing information, evaluating arguments, and making
informed decisions. In mathematics, it manifests as the ability to reason logically, identify
patterns, and apply problem-solving strategies. GeoGebra supports critical thinking by
encouraging students to:
Xorijiy lingvistika va lingvodidaktika
–
Зарубежная лингвистика
и лингводидактика
–
Foreign Linguistics and Linguodidactics
Issue
–
2
№
4 (2024) / ISSN 2181-3701
193
Figure 2. Calculate the surface in terms of an integral.
Explore Mathematical Relationships:
Through interactive graphs (Figure 2) and
geometric constructions, students can visualize how changes in variables affect
outcomes, fostering a deeper understanding of mathematical relationships.
1.
Formulate and Test Hypotheses:
Students can create conjectures about
mathematical properties or relationships and use GeoGebra to test these hypotheses
through dynamic simulations and experiments (Figure 3).
Figure 3. Dynamic graphs using GeoGebra.
2.
Analyze Data and Evidence:
GeoGebra allows students to input data, generate
graphs, and interpret results, promoting analytical thinking and data-driven decision-
making (Figure 4).
Xorijiy lingvistika va lingvodidaktika
–
Зарубежная лингвистика
и лингводидактика
–
Foreign Linguistics and Linguodidactics
Issue
–
2
№
4 (2024) / ISSN 2181-3701
194
Figure 4. Changes of functions’ graphs
.
Enhancing Problem-Solving Skills
Problem-solving is a fundamental skill in mathematics that extends beyond finding
solutions to specific questions. It involves identifying problems, devising strategies, and
persisting through challenges. GeoGebra enhances problem-solving skills by:
Visualizing Problem Scenarios:
Students can model complex problems using
geometric constructions and algebraic equations, gaining insight into problem structures
and potential solution paths.
Iterative Approach:
GeoGebra supports an iterative problem-solving process
where students can modify variables, adjust parameters, and refine their solutions based
on real-time feedback from the software.
Collaborative Learning:
GeoGebra's sharing and collaboration features enable
students to work together on problem-solving tasks, fostering teamwork and collective
problem-solving strategies.
Case Studies and Research Findings
Numerous studies have documented the positive impact of GeoGebra on students’
mathematical learning outcomes. Research indicates that students who use GeoGebra
show improvements in conceptual understanding, problem-solving skills, and overall
mathematical proficiency compared to those using traditional methods alone. Case
studies also highlight increased engagement and motivation among students, attributed
to the interactive and exploratory nature of GeoGebra.
CONCLUSIONS AND RECOMMENDATIONS
Incorporating GeoGebra into high school mathematics education holds immense
potential for nurturing critical thinking and problem-solving skills among students. By
providing a dynamic and interactive learning environment, GeoGebra empowers
students to explore mathematical concepts deeply, make connections across different
branches of mathematics, and develop the flexibility and creativity necessary for tackling
real-world challenges. As educators continue to innovate with technology-enhanced
learning tools like GeoGebra, they pave the way for a generation of mathematically
proficient and critically-minded individuals ready to contribute to an increasingly
complex world.
Xorijiy lingvistika va lingvodidaktika
–
Зарубежная лингвистика
и лингводидактика
–
Foreign Linguistics and Linguodidactics
Issue
–
2
№
4 (2024) / ISSN 2181-3701
195
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1.
L.R.Kipngetich, M.CH.Wekesa, T.J.Kiprop. The effectiveness of using GeoGebra
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2.
O.Umugiraneza, S.Bansilal, D.North. Exploring teachers’ use of technology in
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E.Nkansah, F.Ayiku, YA.Mensah, CF.Nkrumah, E.Atteh. COVID-19 pandemic:
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