This paper explores the development and implementation of pedagogical conditions for the use of GeoGebra as a tool for STEM education in the training of pre-service mathematics teachers. STEM education is discussed, and the potential and features of GeoGebra as a tool for implementing this concept are characterized. Three pedagogical conditions are proposed, including the creation of a cloud-oriented educational environment, the introduction of STEM-oriented investigations using GeoGebra, and the application of motivating measures to stimulate students. Criteria and indicators for the efectiveness of these conditions are developed, and a pedagogical experiment is conducted to test their efectiveness involving 343 students and 26 teachers across six Ukrainian institutions. The results confirm the efectiveness of the pedagogical conditions and demonstrate the potential for GeoGebra as a tool for providing STEM education in the training of pre-service mathematics teachers. The findings align with recent systematic reviews indicating that GeoGebra significantly enhances pre-service teachers' Technological Pedagogical Content Knowledge (TPACK), with targeted workshops showing measurable improvements in technological integration skills. The study contributes to addressing the critical need for scafolded professional development and institutional support in technology integration, while identifying key challenges including tool unfamiliarity and digital material design deficiencies. This paper provides insights and recommendations for educators seeking to incorporate GeoGebra and STEM education into their mathematics teacher training programs, emphasizing the importance of collaborative learning communities and incremental learning approaches.
Improving the quality of science, technology, engineering, and mathematics (STEM) education is a key
task for countries focused on strengthening economic competitiveness and developing human capital
to support science-based industries and technologies [
The strategic tasks for training pre-service teachers are determined in the laws of Ukraine “On Education” [5], “On Higher Education” [6] and other regulatory documents, which prioritize achieving a qualitatively new level of mathematical education through the introduction of progressive concepts, optimal combination of humanitarian and natural-mathematical components of education, the use of modern pedagogical and information technologies, and the preparation of a new generation of teaching staf. The adopted Concept of Development of Natural-Scientific and Mathematical Education (STEM Education) in Ukraine [7] is based on UNESCO documents, in particular, the Incheon Declaration “Education 2030” [8], where STEM education is recognized as a key strategy for achieving sustainable development goals. The concept provides for its wide-scale implementation at all levels of education, emphasizes the key role of mathematics in STEM education, and emphasizes the need for significant changes in the training system, including pre-service mathematics teachers.
Therefore, there is a social demand and legislatively justified necessity to improve the quality of professional training of pre-service mathematics teachers through the implementation of the STEM education concept.
Bilousova et al. [9] point out the significant didactic potential of computer mathematics systems for pedagogical purposes, such as the GRAN and GeoGebra packages, in implementing STEM education in higher and secondary schools. However, the problem of efectively using these systems as tools for implementing STEM education in the practice of professional training of pre-service mathematics teachers remains insuficiently developed in both theoretical and practical aspects.
Recent systematic reviews and meta-analyses have identified GeoGebra as one of the most efective dynamic mathematics software tools for enhancing pre-service teachers’ technological and pedagogical competencies [10, 11]. The global landscape of GeoGebra implementation in teacher education reveals significant growth, with over 340 journal articles published on this topic between 2007 and 2023 [ 11]. This widespread adoption underscores the critical role of technology integration in modern mathematics education and the pressing need for evidence-based pedagogical frameworks.
The analysis revealed contradictions between society’s demand for improving the quality of natural and mathematical education and its unsatisfactory state at the key level – the level of general secondary education; recognition of STEM education as the leading direction of modernizing natural and mathematical education and the insuficient level of implementing the STEM approach in the process of professional training of pre-service mathematics teachers; the potential of the GeoGebra package for implementing STEM mathematics education and the lack of scientifically substantiated approaches to efectively using the GeoGebra package as a tool for implementing the STEM education concept in the process of training pre-service mathematics teachers.
The relevance of the outlined problem, its insuficient development in pedagogical theory and practice, as well as the need to solve the identified contradictions, determined the object of research – the implementation of the concept of STEM education in the process of preparing future mathematics teachers.
The subject of research is the pedagogical conditions for using the GeoGebra package as a tool for implementing the concept of STEM education in the process of training pre-service mathematics teachers.
The purpose of the research is to theoretically justify, develop and experimentally verify the pedagogical conditions for using the GeoGebra package as a tool for implementing the concept of STEM education in the process of training pre-service mathematics teachers.
The research methods: • theoretical – analysis, comparison, systematization, and generalization of scientific literature to identify the state of the topic’s development and clarify the conceptual and terminological apparatus; analysis of the experience of implementing STEM education in the preparation of pre-service mathematics teachers; generalization and systematization of theoretical positions to justify pedagogical conditions for the use of the GeoGebra package as a tool for implementing STEM education in the process of training pre-service mathematics teachers; • empirical – observation, survey, testing, questioning, analysis of the results obtained.
The experimental research was conducted from 2015 to 2020 at the following institutions: H. S. Skovoroda Kharkiv National Pedagogical University, Kryvyi Rih State Pedagogical University, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, Lesya Ukrainka Volyn National University, K. D. Ushynskyi Chernihiv Regional Institute of Postgraduate Pedagogical Education, and the National Technical University “Kharkiv Polytechnic Institute”. A total of 343 students and 26 teachers were involved at various stages of the research.
The research design aligns with contemporary quasi-experimental approaches in educational technology research [12, 13]. Following established methodological frameworks for TPACK assessment, we employed validated instruments and mixed-method approaches to capture both quantitative improvements and qualitative insights into the transformation of pre-service teachers’ technological pedagogical competencies.
Based on the analysis of psychological and pedagogical literature [
The theoretical foundations of STEM education are being developed jointly by scientists and educators, taking into account practical experience. It has been established that despite diferences in the strategies of implementing STEM education in diferent countries, there is a shared understanding of the purpose of STEM education (improving human capital by developing STEM competencies and a natural science worldview in students), its key principles (integrative, interdisciplinary, transdisciplinary, activity-based, competency-based, person-centered, and research-oriented approaches), and the expected result in personal (acquisition of practical natural science, mathematical, IT, and engineering knowledge and skills to solve practical problems in educational and professional activities) and societal dimensions (increasing the country’s competitiveness in the international market of high technologies).
Based on the above, within the scope of the study, STEM education is understood as an innovative model of natural and mathematical education of the 21st century, and its implementation is considered a large-scale global experiment during which the content component of the model is determined (selection and structuring of educational content), the procedural component is tested (forms, methods, and means of teaching, specific aspects of organizing the educational process), and the conceptual basis is clarified (terminology, founding principles, etc.).
Recent research has identified specific pedagogical strategies that maximize the efectiveness of
GeoGebra integration in STEM education. Activity-based and task-based learning approaches have
emerged as the most efective pedagogical methods, promoting visualization, reasoning, and
higherorder thinking skills [
It is shown that mathematics has an integrative role in the complex of STEM disciplines, which is due to the universality of mathematical tools, the mathematization of various fields of knowledge, the significant influence of mathematical education on the cognitive, moral-volitional, and aesthetic development of an individual, and the exceptional importance of mathematical modeling and computational experimentation based on it as a leading method of scientific, engineering, technical, and practical human activities. The latter determines the leading role of computer mathematics systems in the implementation of interdisciplinary STEM projects.
The generalization of experience in implementing STEM education into the system of training preservice teachers of mathematics, natural sciences, and technologies has shown the need for further research in the context of modernizing higher pedagogical education based on the implementation of the concept of STEM education. This includes the theoretical justification of pedagogical conditions for using the GeoGebra package as a tool for its implementation.
Based on theoretical analysis, it has been proven that the special role of mathematics justifies the expediency of implementing STEM education primarily in the process of fundamental mathematical training for pre-service mathematics teachers. It is shown that the leading way to implement STEM education is through specially organized research and project activities, the main feature of which is the construction of the subject’s knowledge system in the process of acquiring and comprehending their own experience in such activities. The organization of research and project activities requires the construction of communities whose members possess ICT tools for conducting theoretical and empirical research. This necessitates the need for pre-service teachers to master social-constructivist technologies for organizing computer-based STEM-oriented research and methods for forming a complex of research competencies as components of the STEM competency system.
The educational and developmental potential of the GeoGebra package as a tool for implementing the
STEM education concept in the training of pre-service mathematics teachers is characterized, as well as
the defining features of the package in [
International research evidence supports the efectiveness of GeoGebra across diverse mathematical
domains. Studies have demonstrated significant improvements not only in geometry and calculus but
also in linear algebra, vectors, and analytic geometry [
The 20-year history of using the GeoGebra package in mathematics education has revealed its synergetic efect – the inheritance of STEM applications. The demand for the skills and knowledge of using GeoGebra acquired by pre-service mathematics teachers is not only relevant in their professional activities but also beyond its scope.
Using the GeoGebra package as a tool for implementing the STEM education concept required the development and justification of a complex of pedagogical conditions that ensure the efectiveness of such use. Considering that STEM education is a multi-purpose concept, the focus was on the goals that the use of the GeoGebra package contributed to achieving: developing students’ motivation to acquire mathematical education, forming beliefs about its significance and the efectiveness of mathematical knowledge, acquiring research competencies, and developing the ability for self-education and a desire to independently enhance their educational potential.
With these goals in mind, a complex of pedagogical conditions was developed and theoretically justified, which includes designing an educational process using GeoGebra that promotes the active involvement of students in the research and discovery process, using interactive methods of teaching and learning, and promoting self-education and research activities. The GeoGebra package also helps to develop students’ mathematical thinking, creative abilities, and research skills, as well as to integrate mathematics with other disciplines.
Thus, the GeoGebra package has significant potential as a tool for implementing the STEM education concept in the training of pre-service mathematics teachers. Its efective use requires the development of a complex of pedagogical conditions, which are aimed at promoting students’ motivation, developing their research competencies, and promoting self-education and research activities.
The first pedagogical condition is to create a cloud-oriented educational environment that contains software, informational, didactic, and methodological resources for organizing, supporting, and accompanying various types of student learning activities using the GeoGebra package: educational and cognitive, educational and research, scientific and research, and project-based.
The second pedagogical condition is to introduce a practical course in computer STEM-oriented research in the GeoGebra package into the educational process of training pre-service mathematics teachers, which is based on the principles of a technological approach, involving a step-by-step engagement of students in researching mathematical objects, objects from other disciplines, objects of the surrounding world, and gradually mastering the research tools of the GeoGebra package.
The third pedagogical condition is the use of a complex of tools to stimulate students’ STEM-oriented GeoGebra modeling, based on the organization of their extracurricular activities, involvement in the GeoGebra community, and the use of individual and group coaching.
Within the framework of extracurricular activities, students are expected to: • familiarize themselves with additional (non-program) materials that reveal the significance of mathematics, the value of mathematical modeling, the breadth of its applications in various areas of human activity, including creative ones; • prepare non-standard events to popularize such information; create illustrative support for such events using the GeoGebra package; • participate in the GeoGebra community, which promotes the transfer of pedagogical ideas and technologies, as well as the involvement of students in the development of GeoGebra models, GeoGebra projects, conducting and presenting their own GeoGebra research as a personal contribution to open world GeoGebra resources. The ability to see their own results on the site and participate in the scientific and methodological developments of teachers adds confidence to the student in the significance of the knowledge they receive in the educational process and in research and project work.
The use of individual and group coaching contributes to the development of the personal potential of pre-service math teachers, stimulates their independent cognitive activity, and increases the practical significance and demand for the results of computer STEM-oriented research using GeoGebra software. The pedagogical conditions are interconnected, interdependent, and complementary, which necessitates their comprehensive implementation.
Research has consistently identified several critical success factors for GeoGebra implementation. The
SQD (Synthesis of Qualitative Data) model strategies—including role modeling, reflection, design-based
learning, peer collaboration, authentic experiences, and continuous feedback—have shown positive
correlations with TPACK development [13]. However, studies reveal that many of these strategies remain
underutilized in practice, particularly at the higher levels of the SAMR (Substitution, Augmentation,
Modification, Redefinition) model [
During the preparatory stage of experimental work (2015–2017), educational and methodological support for using the GeoGebra package as a tool for implementing the concept of STEM education in the process of training pre-service mathematics teachers in higher education institutions was developed. This included a textbook for mastering the dynamic mathematics GeoGebra package as a tool for implementing the concept of STEM education; sets of research tasks and educational models for conducting STEM-oriented research in GeoGebra; a cloud-based complex of interdisciplinary models presented in GeoGebra Book; tasks for individual STEM-oriented research and educational activities of students using GeoGebra modeling; STEM project topics using the GeoGebra package; and working materials for organizing extracurricular STEM-oriented student work using GeoGebra modeling in the format of a discussion club (thematic developments, scenarios, presentations, compilations of audio and video materials, etc.).
Criteria and indicators for the formation of the ability of pre-service mathematics teachers to use the GeoGebra package as a tool for implementing the concept of STEM education were also developed, including motivational-value (the awareness by pre-service teachers of the value of mathematical knowledge and the mathematical apparatus as the basis for computer research on any object; motivation to learn mathematics; readiness to overcome dificulties), praxiological (the ability of pre-service teachers to step-by-step plan computer research using the technology of its implementation; the ability to use the GeoGebra functional rationally for conducting research; the ability to analyze its results and make conclusions), and metacognitive (the ability of pre-service teachers to critically evaluate their own knowledge level for solving a problem; the ability to efectively use various ways of acquiring knowledge; the desire for constant educational growth; the ability to apply the GeoGebra package for conducting transdisciplinary research).
Each indicator is described at three levels of formation of pre-service mathematics teachers’ ability to use GeoGebra as a tool for implementing the concept of STEM education: reproductive (the ability to use GeoGebra to conduct subject mathematical research according to the teacher’s plan), partially exploratory (the ability to use GeoGebra to conduct independent and collaborative subject mathematical research and interdisciplinary research with the teacher’s support), and creative (the ability to use GeoGebra to conduct independent and collaborative transdisciplinary research). Tools for their diagnosis have been developed.
The exploratory and formative stages of the pedagogical experiment were conducted at the H. S. Skovoroda Kharkiv National Pedagogical University and Kryvyi Rih State Pedagogical University.
During the exploratory stage (2018), experimental and control groups were formed; the absence of a statistically significant diference at the 0.05 level in the levels of formation of mathematics teachers’ ability to use GeoGebra as a tool for implementing the concept of STEM education was proven.
During the formative stage (2018–2020), measures were implemented to introduce reasoned pedagogical conditions for using the GeoGebra package as a tool for implementing STEM education and testing a complex of educational and methodological materials. The stage’s tasks also included testing a complex of didactic materials that provide the implementation of these pedagogical conditions, tracking the dynamics of the process of using the GeoGebra package as a tool for implementing the concept of STEM education in the process of training pre-service mathematics teachers. The pedagogical experiment was conducted in natural conditions of the educational process with the involvement of students in the experimental group. Students in the control group were taught using traditional methods.
To implement the first pedagogical condition based on the use of specially selected and developed software, informational, didactic, and methodological resources during the preparatory stage of the experimental work, a cloud-oriented educational environment was created to organize, support, and accompany various types of independent student activity using the GeoGebra package (educationalcognitive, educational-research, scientific-research, project).
To implement the second pedagogical condition, a practical course on conducting computer STEMoriented research using the GeoGebra package was developed and implemented. The practical course provided for the sequential mastering by pre-service mathematics teachers of the technology of research
Levels and the research toolkit of the GeoGebra package in the process of step-by-step involvement in the study of mathematical objects, objects from other disciplines, real objects with the support of a specially created and constantly updated database of educational models. To support and direct the independent work of students during the practical course, a teaching and methodological guide was used. Each research project carried out by the student consisted of three stages. At the first stage, the student was involved in constructing a visual model of the mathematical object in the GeoGebra environment, guided by instructions for its construction (provided in the practical course in a table of dynamic drawing construction, which contains a step-by-step description of construction, comments, and illustrations) and mastering a certain toolkit of GeoGebra in this way. Next, the student carried out the study of the mathematical object according to the provided step-by-step plan, which reproduced the technology of research. Each step was accompanied by questions that drew the student’s attention to the essence of the obtained result. The second stage of the research was carried out by the student using the same model, but using it to study an interdisciplinary object, which required activation of knowledge from other disciplines. The questions posed were aimed at involving the student in the analysis and understanding of the results obtained, arousing his interest and initiative in satisfying it. The third stage led to a transdisciplinary level of research and concerned a real object, requiring the demonstration of a complex of acquired knowledge. The questions posed to the student aimed to arouse his natural curiosity, stimulate the development of a plan for further research, possibly with modification of the created model.
To implement the third pedagogical condition, a set of tools to stimulate students to engage in STEM-oriented GeoGebra modeling was developed and applied. In particular, extracurricular activities were organized in the form of a discussion club, where the leading method of cognitive activity was GeoGebra modeling. Students were also involved in GeoGebra community activities by developing GeoGebra models and presenting their own GeoGebra research as a personal contribution to open world GeoGebra resources, including GeoGebra Book, for the exchange of ideas and technologies, as well as the implementation and adaptation of productive international experience in the educational process of training pre-service math teachers to use the GeoGebra package in STEM education, which played a powerful motivational factor for students. The club format contributed to the growth of various interactions between teachers and students on the principles of mutual respect and trust, the establishment of partnership relations between them, the implementation of individual and group coaching, which found expression in personalized student counseling, directing them towards achieving significant educational results, engaging in the development of practical STEM projects, and jointly conducting full-fledged scientific STEM research throughout the entire cycle of training pre-service math teachers. After completing the experimental work, the level of formation of pre-service math teachers’ ability to use the GeoGebra package as a tool for implementing the concept of STEM education was determined (table 1).
The results of our experiment align with international findings on GeoGebra efectiveness.
Metaanalyses have shown that pre-service teachers who undergo structured GeoGebra training demonstrate
significant improvements in multiple domains: mathematical connection skills (efect size d = 0.68),
proof and reasoning abilities (d = 0.72), and technology integration confidence ( d = 0.81) [
During the control stage, the results of the conducted experiment were analyzed. The obtained results allowed us to conclude about the positive efect of implementing the developed pedagogical conditions on the level of formation of pre-service mathematics teachers’ ability to use GeoGebra software as a tool for implementing the STEM education concept. The verification was carried out using the Pearson correlation coeficient, which confirmed that the diference factor in the distributions of the students of control and experimental groups is statistically significant at the 0.05 level. Therefore, the research hypothesis was confirmed that the use of GeoGebra software as a tool for implementing the STEM education concept in the process of training pre-service mathematics teachers will be efective under the implementation of justified pedagogical conditions. 6. Conclusions 1. The research proposes a solution to the scientific problem of substantiating the pedagogical conditions for using GeoGebra as a tool for implementing STEM education in the training of pre-service mathematics teachers. The generalization of the results of theoretical research and the conducted pedagogical experiment allow the following conclusions to be made. 2. The analysis of psychological and pedagogical literature showed that STEM education is an innovative approach that is being implemented and developed jointly by scientists and educators from many countries of the world who are interested in the development of science-intensive production and high technologies. STEM education is being spread at all educational levels, which determines its special importance in the system of training pre-service teachers, since the teacher is the main driving force for change in education. 3. STEM education is defined as an innovative model of natural-mathematical education of the 21st century, and its implementation is a large-scale world experiment, during which the content component of the model is determined (the selection and structuring of the content of education is carried out), the procedural component is tested (the forms, methods, means of teaching, the specificity of organizing the educational process in its specific aspects are used), and the conceptual component is refined (terminology, basic principles, etc.).
Integrated, activity-based, and technological approaches are highlighted as key components of STEM education. Increasing the volume and significance of independent research requires its rational organization on technological principles.
The potential of mathematics as a STEM discipline in both school and university education is analyzed. The integrative role of mathematics in the complex of STEM disciplines is determined by the universality of the mathematical apparatus, its widespread use, the mathematization of various ifelds of knowledge; the significant impact of mathematical education on the intellectual, moral, and aesthetic development of the individual; and the exceptional importance of mathematical modeling and computational experimentation based on it as the leading method of scientific, engineering, and practical human activity.
The problems in training mathematics teachers for the implementation of STEM learning are
outlined, which necessitate the need for theoretical justification and research regarding the
modernization of higher education in the context of efective implementation of the STEM
concept.
4. The educational and developmental potential as well as defining features of the GeoGebra package
as a tool for implementing the STEM education concept in the process of training pre-service
mathematics teachers have been revealed. The GeoGebra package is positioned as a computer
mathematics system oriented towards supporting educational and research activities. The package
is powerful and continuously improved by an international team of developers. It has a wide
range of applications in STEM education and its branches (such as STEAM, STREAM, etc.),
scientific and practical activities of diferent directions. The full-featured version of the package
is freely available in Ukrainian. It is independent of hardware and operating systems and has a
cloud-oriented version. There is a large base of freely distributed educational STEM resources
created by the open GeoGebra community. The package allows for visualizing computer models
in virtual and augmented reality and their materialization through 3D printing.
5. Pedagogical conditions for using the GeoGebra package as a tool for implementing the STEM
education concept in the process of training pre-service mathematics teachers have been developed
and theoretically substantiated. These include creating a cloud-oriented educational environment
that contains software, informational, didactic, and methodological resources for organizing,
supporting, and accompanying various types of student learning activities using the GeoGebra
package. Introducing a practicum in conducting computer-based STEM-oriented research in the
GeoGebra package into the educational process of training pre-service mathematics teachers.
Using a set of tools to stimulate students to engage in STEM-oriented GeoGebra modeling based
on organizing their extracurricular work, involving them in the GeoGebra community, and using
individual and group coaching.
6. A pedagogical experiment was conducted to verify the efectiveness of the reasoned pedagogical
conditions for the use of the GeoGebra package as a tool for implementing STEM education in
the preparation of pre-service mathematics teachers. Criteria and indicators were developed for
the formation of the ability of pre-service mathematics teachers to use the GeoGebra package
as a tool for implementing the concept of STEM education: motivational-value (pre-service
teachers’ awareness of the value of mathematical knowledge and the mathematical apparatus as
the basis for computer research of any objects; motivation to learn mathematics; readiness to
overcome dificulties); praxiological (ability of pre-service teachers to step-by-step plan computer
research using the technology of its conduct; ability to use GeoGebra functionality rationally
for research; ability to analyze its results and draw conclusions); metacognitive (the ability
of pre-service teachers to critically evaluate their level of knowledge for solving the problem;
ability to efectively use various ways of acquiring knowledge; desire for continuous educational
growth; ability to use the GeoGebra package for conducting transdisciplinary research). The
reproductive, partially exploratory, and creative levels of formation were characterized for each
criterion, scales were developed for their measurement, and diagnostic tools were determined
and selected. The experimental data were processed using mathematical statistics methods. The
results obtained confirmed the efectiveness of the reasoned pedagogical conditions for the use
of the GeoGebra package as a tool for implementing the concept of STEM education in the
preparation of pre-service mathematics teachers.
7. The findings of this research contribute to the growing body of evidence supporting technology
integration in mathematics teacher education. Our results align with international trends showing
that successful GeoGebra implementation requires a multifaceted approach combining
technological, pedagogical, and content knowledge development [
The research conducted does not exhaust all aspects of the analyzed problem. We consider the development of a model of professional training of pre-service mathematics teachers on the basis of an integrative approach and methodological principles for implementing STEM education in the training of pre-service physics, computer science, and technology teachers as promising directions for further scientific research.
Based on comprehensive analysis of current research trends and identified gaps, several critical areas
warrant future investigation:
1. Tracking pre-service teachers’ technology integration practices from initial training through their
ifrst five years of teaching to assess sustained pedagogical change and identify factors supporting
long-term GeoGebra adoption [
These future directions reflect the evolving landscape of educational technology and the ongoing need for evidence-based approaches to teacher preparation in the digital age.
The research was carried out in accordance with the plan of scientific research of the Kryvyi Rih State Pedagogical University within the framework of the comprehensive theme “Theoretical and Methodological Foundations of Using Mobile Information and Communication Technologies in Education” (No. 0116U001867) and according to the work plan of the joint scientific research laboratory on the use of cloud technologies in education of the Kryvyi Rih State Pedagogical University and the Institute for Digitalisation of Education of the National Academy of Educational Sciences of Ukraine (Kyiv).
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