Implementing GeoGebra as a Tool for STEM Education in Pre-Service

Mathematics Teacher Training: Pedagogical Conditions and

Effectiveness

Valentyna V. Pikalova

National Technical University “Kharkiv Polytechnic Institute”, 2 Kyrpychova Str., Kharkiv, 61002, Ukraine

Keywords:

STEM Education, GeoGebra, Pre-Service Mathematics Teacher Training, Pedagogical Conditions, Cloud-

Oriented Educational Environment, Explorative Study, Motivational Measures, Pedagogical Experiment.

Abstract:

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 dis-

cussed, 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 environ-

ment, the introduction of STEM-oriented investigations using GeoGebra, and the application of motivating

measures to stimulate students. Criteria and indicators for the effectiveness of these conditions are developed,

and a pedagogical experiment is conducted to test their effectiveness. The results conﬁrm the effectiveness of

the pedagogical conditions and demonstrate the potential for GeoGebra as a tool for providing STEM educa-

tion in the training of pre-service mathematics teachers. This paper provides insights and recommendations

for educators seeking to incorporate GeoGebra and STEM education into their mathematics teacher training

programs.

1 INTRODUCTION

Improving the quality of science, technology, en-

gineering, and mathematics (STEM) education is a

key task for countries focused on strengthening eco-

nomic competitiveness and developing human capi-

tal to support science-based industries and technolo-

gies (Hrynevych et al., 2021). International com-

parative studies of the quality of STEM education

(PISA, TIMSS) are recognized indicators of the state

of a country’s STEM education. These studies allow

for comparing a nation’s educational progress with

global trends in its development. The latest PISA

studies have shown a signiﬁcant decline in the sci-

ence and particularly mathematics skills of Ukrainian

high school students (Mazorchuk et al., 2021). Re-

sults of recent admissions campaigns have conﬁrmed

a decline in interest among applicants in STEM ﬁelds,

which creates strategic risks for social, economic, and

technological development in Ukraine. In 2020, only

two of the ten most popular specialties chosen by ap-

plicants related to STEM education, and only one of

them involved information technology. The need to

https://orcid.org/0000-0002-0773-2947

increase the prestige of STEM education as a guaran-

tee of the country’s development necessitates improv-

ing the quality of professional training for pre-service

STEM teachers.

The strategic tasks for training pre-service teach-

ers are determined in the laws of Ukraine “On Ed-

ucation” (Verkhovna Rada of Ukraine, 2017), “On

Higher Education” (On Higher Education, 2017) and

other regulatory documents, which prioritize achiev-

ing a qualitatively new level of mathematical educa-

tion 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 teach-

ing staff. The adopted Concept of Development

of Natural-Scientiﬁc and Mathematical Education

(STEM Education) in Ukraine (Cabinet of Minis-

ters of Ukraine, 2020) is based on UNESCO docu-

ments, in particular, the Incheon Declaration “Edu-

cation 2030” (UNESCO, 2015), where STEM edu-

cation is recognized as a key strategy for achieving

sustainable development goals. The concept provides

for its wide-scale implementation at all levels of ed-

ucation, emphasizes the key role of mathematics in

860

Pikalova, V.

Implementing GeoGebra as a Tool for STEM Education in Pre-Service Mathematics Teacher Training: Pedagogical Conditions and Effectiveness.

DOI: 10.5220/0012073900003431

In Proceedings of the 2nd Myroslav I. Zhaldak Symposium on Advances in Educational Technology (AET 2021), pages 860-868

ISBN: 978-989-758-662-0

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

STEM education, and emphasizes the need for signif-

icant changes in the training system, including pre-

service mathematics teachers.

Therefore, there is a social demand and legisla-

tively justiﬁed necessity to improve the quality of pro-

fessional training of pre-service mathematics teachers

through the implementation of the STEM education

concept.

Bilousova et al. (Bilousova et al., 2022) point out

the signiﬁcant didactic potential of computer math-

ematics systems for pedagogical purposes, such as

the GRAN and GeoGebra packages, in implement-

ing STEM education in higher and secondary schools.

However, the problem of effectively using these sys-

tems as tools for implementing STEM education in

the practice of professional training of pre-service

mathematics teachers remains insufﬁciently devel-

oped in both theoretical and practical aspects.

The analysis revealed contradictions between so-

ciety’s demand for improving the quality of natu-

ral 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 mathe-

matical education and the insufﬁcient level of imple-

menting the STEM approach in the process of profes-

sional training of pre-service mathematics teachers;

the potential of the GeoGebra package for implement-

ing STEM mathematics education and the lack of sci-

entiﬁcally substantiated approaches to effectively us-

ing the GeoGebra package as a tool for implementing

the STEM education concept in the process of train-

ing pre-service mathematics teachers.

2 RESEARCH METHODOLOGY

The relevance of the outlined problem, its insufﬁcient

development in pedagogical theory and practice, as

well as the need to solve the identiﬁed contradictions,

determined the object of research – the implementa-

tion of the concept of STEM education in the process

of preparing future mathematics teachers.

The subject of research is the pedagogical condi-

tions 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 jus-

tify, develop and experimentally verify the pedagog-

ical conditions for using the GeoGebra package as a

tool for implementing the concept of STEM educa-

tion in the process of training pre-service mathemat-

ics teachers.

The research methods:

• theoretical – analysis, comparison, systematiza-

tion, and generalization of scientiﬁc literature to

identify the state of the topic’s development and

clarify the conceptual and terminological appara-

tus; analysis of the experience of implementing

STEM education in the preparation of pre-service

mathematics teachers; generalization and system-

atization of theoretical positions to justify peda-

gogical conditions for the use of the GeoGebra

package as a tool for implementing STEM edu-

cation in the process of training pre-service math-

ematics teachers;

• empirical – observation, survey, testing, question-

ing, 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 Univer-

sity, 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.

3 THEORETICAL

UNDERPINNINGS OF ICT USE

IN STEM EDUCATION

IMPLEMENTATION AT

PRE-SERVICE MATHEMATICS

TEACHER TRAINING

Based on the analysis of psychological and pedagog-

ical literature (Pylypenko, 2020; Shapovalov et al.,

2020, 2022; Valko et al., 2020; Hrynevych et al.,

2021; Martyniuk et al., 2021; Lukychova et al., 2022;

Slipukhina et al., 2022; Mintii, 2023), it has been

found that STEM education emerged as a response to

the challenge posed by the rapid development of tech-

nologies, which necessitates the orientation of educa-

tion towards the preemptive satisfaction of the needs

of the modern economy for specialists capable of en-

suring its development on a high-tech basis. The

experience of implementing STEM education in the

USA, France, Great Britain, Australia, Israel, China,

Singapore, Hong Kong, Canada, and other countries

was analised. In Ukraine, STEM education is consid-

ered a priority direction for the development of natu-

ral science and mathematics education, as declared in

Implementing GeoGebra as a Tool for STEM Education in Pre-Service Mathematics Teacher Training: Pedagogical Conditions and

Effectiveness

861

the corresponding Concept (Cabinet of Ministers of

Ukraine, 2020).

The theoretical foundations of STEM education

are being developed jointly by scientists and edu-

cators, taking into account practical experience. It

has been established that despite differences in the

strategies of implementing STEM education in dif-

ferent countries, there is a shared understanding of

the purpose of STEM education (improving human

capital by developing STEM competencies and a nat-

ural science worldview in students), its key princi-

ples (integrative, interdisciplinary, transdisciplinary,

activity-based, competency-based, person-centered,

and research-oriented approaches), and the expected

result in personal (acquisition of practical natural sci-

ence, 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 inter-

national market of high technologies).

Based on the above, within the scope of the

study, STEM education is understood as an innova-

tive model of natural and mathematical education of

the 21st century, and its implementation is considered

a large-scale global experiment during which the con-

tent component of the model is determined (selection

and structuring of educational content), the procedu-

ral component is tested (forms, methods, and means

of teaching, speciﬁc aspects of organizing the educa-

tional process), and the conceptual basis is clariﬁed

(terminology, founding principles, etc.).

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 develop-

ment of an individual, and the exceptional importance

of mathematical modeling and computational experi-

mentation based on it as a leading method of scien-

tiﬁc, engineering, technical, and practical human ac-

tivities. The latter determines the leading role of com-

puter mathematics systems in the implementation of

interdisciplinary STEM projects.

The generalization of experience in implement-

ing STEM education into the system of training pre-

service teachers of mathematics, natural sciences, and

technologies has shown the need for further research

in the context of modernizing higher pedagogical ed-

ucation based on the implementation of the concept

of STEM education. This includes the theoretical jus-

tiﬁcation of pedagogical conditions for using the Ge-

oGebra package as a tool for its implementation.

4 JUSTIFICATION OF

PEDAGOGICAL CONDITIONS

FOR USING THE GEOGEBRA

PACKAGE AS A TOOL FOR

IMPLEMENTING THE

CONCEPT OF STEM

EDUCATION IN THE

PREPARATION OF

PRE-SERVICE MATHEMATICS

TEACHERS

Based on theoretical analysis, it has been proven that

the special role of mathematics justiﬁes the expedi-

ency 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 ac-

tivities, 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 com-

munities whose members possess ICT tools for con-

ducting theoretical and empirical research. This ne-

cessitates the need for pre-service teachers to mas-

ter social-constructivist technologies for organizing

computer-based STEM-oriented research and meth-

ods 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 (Kra-

marenko et al., 2020; Drushlyak et al., 2021). Ge-

oGebra is positioned as a computer mathematics sys-

tem aimed at supporting the educational and research

activities of students and teachers. The package has

a developed functionality and continuous improve-

ment by an international team of developers, and a

wide range of applications in STEM education and

its branches (STEAM, STREAM, and others), scien-

tiﬁc and practical activities of various directions. The

full-featured version of the package is freely avail-

able in Ukrainian, independent of hardware and op-

erating system, and has a cloud-based version. The

large database of freely distributed educational STEM

resources created by the open GeoGebra community,

the possibility of visualizing computer models in vir-

tual and augmented reality, and their materialization

by 3D printing are also noted.

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

862

The 20-year history of using the GeoGebra pack-

age in mathematics education has revealed its syner-

getic effect – the inheritance of STEM applications.

The demand for the skills and knowledge of using Ge-

oGebra 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 imple-

menting the STEM education concept required the de-

velopment and justiﬁcation of a complex of pedagog-

ical conditions that ensure the effectiveness 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 achiev-

ing: developing students’ motivation to acquire math-

ematical education, forming beliefs about its signif-

icance and the effectiveness of mathematical knowl-

edge, acquiring research competencies, and develop-

ing the ability for self-education and a desire to inde-

pendently enhance their educational potential.

With these goals in mind, a complex of pedagog-

ical conditions was developed and theoretically justi-

ﬁed, which includes designing an educational process

using GeoGebra that promotes the active involvement

of students in the research and discovery process, us-

ing 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 po-

tential as a tool for implementing the STEM educa-

tion concept in the training of pre-service mathemat-

ics teachers. Its effective use requires the develop-

ment of a complex of pedagogical conditions, which

are aimed at promoting students’ motivation, develop-

ing 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 accompa-

nying various types of student learning activities us-

ing the GeoGebra package: educational and cogni-

tive, educational and research, scientiﬁc and research,

and project-based.

The second pedagogical condition is to introduce

a practical course in computer STEM-oriented re-

search in the GeoGebra package into the educational

process of training pre-service mathematics teach-

ers, which is based on the principles of a technolog-

ical approach, involving a step-by-step engagement

of students in researching mathematical objects, ob-

jects from other disciplines, objects of the surround-

ing 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 organiza-

tion 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 model-

ing, 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 stu-

dents in the development of GeoGebra models,

GeoGebra projects, conducting and presenting

their own GeoGebra research as a personal con-

tribution to open world GeoGebra resources. The

ability to see their own results on the site and par-

ticipate in the scientiﬁc and methodological de-

velopments of teachers adds conﬁdence to the stu-

dent in the signiﬁcance of the knowledge they re-

ceive in the educational process and in research

and project work.

The use of individual and group coaching con-

tributes to the development of the personal potential

of pre-service math teachers, stimulates their inde-

pendent cognitive activity, and increases the practi-

cal signiﬁcance and demand for the results of com-

puter STEM-oriented research using GeoGebra soft-

ware. The pedagogical conditions are interconnected,

interdependent, and complementary, which necessi-

tates their comprehensive implementation.

5 ORGANIZATION, CONDUCT

AND RESULTS OF THE

PEDAGOGICAL EXPERIMENT

During the preparatory stage of experimental work

(2015–2017), educational and methodological sup-

port for using the GeoGebra package as a tool for

implementing the concept of STEM education in the

process of training pre-service mathematics teachers

Implementing GeoGebra as a Tool for STEM Education in Pre-Service Mathematics Teacher Training: Pedagogical Conditions and

Effectiveness

863

in higher education institutions was developed. This

included a textbook for mastering the dynamic math-

ematics GeoGebra package as a tool for implement-

ing the concept of STEM education; sets of research

tasks and educational models for conducting STEM-

oriented research in GeoGebra; a cloud-based com-

plex of interdisciplinary models presented in GeoGe-

bra Book; tasks for individual STEM-oriented re-

search and educational activities of students using Ge-

oGebra modeling; STEM project topics using the Ge-

oGebra package; and working materials for organiz-

ing extracurricular STEM-oriented student work us-

ing GeoGebra modeling in the format of a discus-

sion club (thematic developments, scenarios, presen-

tations, 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 devel-

oped, including motivational-value (the awareness

by pre-service teachers of the value of mathemat-

ical knowledge and the mathematical apparatus as

the basis for computer research on any object; mo-

tivation to learn mathematics; readiness to overcome

difﬁculties), praxiological (the ability of pre-service

teachers to step-by-step plan computer research us-

ing the technology of its implementation; the abil-

ity to use the GeoGebra functional rationally for con-

ducting 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

effectively use various ways of acquiring knowledge;

the desire for constant educational growth; the ability

to apply the GeoGebra package for conducting trans-

disciplinary research).

Each indicator is described at three levels of for-

mation 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 con-

duct independent and collaborative transdisciplinary

research). Tools for their diagnosis have been devel-

oped.

The exploratory and formative stages of the

pedagogical experiment were conducted at the

H. S. Skovoroda Kharkiv National Pedagogical Uni-

versity and Kryvyi Rih State Pedagogical University.

During the exploratory stage (2018), experimental

and control groups were formed; the absence of a sta-

tistically signiﬁcant difference 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), mea-

sures were implemented to introduce reasoned peda-

gogical conditions for using the GeoGebra package as

a tool for implementing STEM education and testing

a complex of educational and methodological materi-

als. The stage’s tasks also included testing a complex

of didactic materials that provide the implementation

of these pedagogical conditions, tracking the dynam-

ics of the process of using the GeoGebra package as

a tool for implementing the concept of STEM educa-

tion in the process of training pre-service mathemat-

ics teachers. The pedagogical experiment was con-

ducted in natural conditions of the educational pro-

cess with the involvement of students in the exper-

imental 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 exper-

imental work, a cloud-oriented educational environ-

ment was created to organize, support, and accom-

pany various types of independent student activity

using the GeoGebra package (educational-cognitive,

educational-research, scientiﬁc-research, project).

To implement the second pedagogical condition,

a practical course on conducting computer STEM-

oriented 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

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 disci-

plines, real objects with the support of a specially

created and constantly updated database of educa-

tional models. To support and direct the indepen-

dent 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 in-

volved in constructing a visual model of the mathe-

matical object in the GeoGebra environment, guided

by instructions for its construction (provided in the

practical course in a table of dynamic drawing con-

struction, which contains a step-by-step description of

construction, comments, and illustrations) and mas-

tering a certain toolkit of GeoGebra in this way. Next,

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

864

Table 1: The distribution of students in the specialty 014.04 Secondary Education (Mathematics) by the level of formation of

the ability to use GeoGebra software as a tool for implementing the STEM education concept after the formative stage of the

pedagogical experiment (in %).

Criteria

Levels Control group Experimental group

Reproductive Partial-equivalent Creative Reproductive Partial-equivalent Creative

Motivational-value 37.7 39.3 23.0 19.4 38.7 41.9

Praxiological 42.6 37.7 19.7 16.1 40.3 43.6

Metacognitive 42.6 36.1 21.3 17.7 37.1 45.2

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 stu-

dent’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 anal-

ysis and understanding of the results obtained, arous-

ing 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 cu-

riosity, stimulate the development of a plan for fur-

ther research, possibly with modiﬁcation of the cre-

ated model.

To implement the third pedagogical condition, a

set of tools to stimulate students to engage in STEM-

oriented GeoGebra modeling was developed and ap-

plied. In particular, extracurricular activities were

organized in the form of a discussion club, where

the leading method of cognitive activity was GeoGe-

bra modeling. Students were also involved in Ge-

oGebra community activities by developing GeoGe-

bra models and presenting their own GeoGebra re-

search as a personal contribution to open world Ge-

oGebra resources, including GeoGebra Book, for the

exchange of ideas and technologies, as well as the

implementation and adaptation of productive interna-

tional experience in the educational process of train-

ing pre-service math teachers to use the GeoGebra

package in STEM education, which played a pow-

erful motivational factor for students. The club for-

mat contributed to the growth of various interactions

between teachers and students on the principles of

mutual respect and trust, the establishment of part-

nership relations between them, the implementation

of individual and group coaching, which found ex-

pression in personalized student counseling, direct-

ing them towards achieving signiﬁcant educational re-

sults, 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 ex-

perimental 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 edu-

cation was determined (table 1).

During the control stage, the results of the con-

ducted experiment were analyzed. The obtained re-

sults allowed us to conclude about the positive ef-

fect of implementing the developed pedagogical con-

ditions on the level of formation of pre-service math-

ematics teachers’ ability to use GeoGebra software

as a tool for implementing the STEM education con-

cept. The veriﬁcation was carried out using the Pear-

son correlation coefﬁcient, which conﬁrmed that the

difference factor in the distributions of the students of

control and experimental groups is statistically signif-

icant at the 0.05 level. Therefore, the research hypoth-

esis was conﬁrmed that the use of GeoGebra software

as a tool for implementing the STEM education con-

cept in the process of training pre-service mathemat-

ics teachers will be effective under the implementa-

tion of justiﬁed pedagogical conditions.

6 CONCLUSIONS

1. The research proposes a solution to the scientiﬁc

problem of substantiating the pedagogical condi-

tions for using GeoGebra as a tool for implement-

ing 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 con-

clusions to be made.

2. The analysis of psychological and pedagogical lit-

erature showed that STEM education is an inno-

vative approach that is being implemented and de-

veloped jointly by scientists and educators from

many countries of the world who are interested

in the development of science-intensive produc-

tion and high technologies. STEM education is

being spread at all educational levels, which de-

termines its special importance in the system of

Implementing GeoGebra as a Tool for STEM Education in Pre-Service Mathematics Teacher Training: Pedagogical Conditions and

Effectiveness

865

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 con-

tent component of the model is determined (the

selection and structuring of the content of edu-

cation is carried out), the procedural component

is tested (the forms, methods, means of teaching,

the speciﬁcity of organizing the educational pro-

cess in its speciﬁc aspects are used), and the con-

ceptual component is reﬁned (terminology, basic

principles, etc.).

Integrated, activity-based, and technological ap-

proaches are highlighted as key components of

STEM education. Increasing the volume and sig-

niﬁcance of independent research requires its ra-

tional organization on technological principles.

The potential of mathematics as a STEM disci-

pline 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 appara-

tus, its widespread use, the mathematization of

various ﬁelds of knowledge; the signiﬁcant im-

pact of mathematical education on the intellectual,

moral, and aesthetic development of the individ-

ual; and the exceptional importance of mathemat-

ical modeling and computational experimentation

based on it as the leading method of scientiﬁc, en-

gineering, and practical human activity.

The problems in training mathematics teachers for

the implementation of STEM learning are out-

lined, which necessitate the need for theoretical

justiﬁcation and research regarding the modern-

ization of higher education in the context of effec-

tive implementation of the STEM concept.

4. The educational and developmental potential as

well as deﬁning features of the GeoGebra pack-

age as a tool for implementing the STEM educa-

tion 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 pack-

age 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.), sci-

entiﬁc and practical activities of different direc-

tions. 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 devel-

oped and theoretically substantiated. These in-

clude creating a cloud-oriented educational envi-

ronment that contains software, informational, di-

dactic, and methodological resources for organiz-

ing, 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. Us-

ing 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 in-

dividual and group coaching.

6. A pedagogical experiment was conducted to ver-

ify the effectiveness 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 teach-

ers. Criteria and indicators were developed for

the formation of the ability of pre-service math-

ematics teachers to use the GeoGebra package as

a tool for implementing the concept of STEM ed-

ucation: motivational-value (pre-service teachers’

awareness of the value of mathematical knowl-

edge and the mathematical apparatus as the ba-

sis for computer research of any objects; moti-

vation to learn mathematics; readiness to over-

come difﬁculties); praxiological (ability of pre-

service teachers to step-by-step plan computer re-

search using the technology of its conduct; abil-

ity 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

effectively use various ways of acquiring knowl-

edge; desire for continuous educational growth;

ability to use the GeoGebra package for conduct-

ing transdisciplinary research). The reproductive,

partially exploratory, and creative levels of forma-

tion were characterized for each criterion, scales

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

866

were developed for their measurement, and diag-

nostic tools were determined and selected. The

experimental data were processed using mathe-

matical statistics methods. The results obtained

conﬁrmed the effectiveness of the reasoned ped-

agogical 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 FUTURE WORK

The research conducted does not exhaust all aspects

of the analyzed problem. We consider the devel-

opment of a model of professional training of pre-

service mathematics teachers on the basis of an in-

tegrative 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.

ACKNOWLEDGEMENTS

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 Method-

ological Foundations of Using Mobile Informa-

tion 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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