selected issues of digital technology usage in

Mária Mišútová Martin Mišút

SELECTED ISSUES OF DIGITAL TECHNOLOGY USAGE IN MATHEMATICS EDUCATION OF ENGINEERS

Trnava

August

2014

ii

ABSTRACT The monograph submitted provides an overview of scientific knowledge as well as an overview of theoretical and experimental results related to the information technologies implementation into mathematical preparation of future engineers at the Slovak University of Technology, Faculty of Materials Science and Technology in Trnava (hereinafter referred to as STU MTF). The common objective of the several years´ lasting efforts was to make the main educational process more efficient via the information and communication technologies (hereinafter only ICT) application with focus on achieving the required level of students´ knowledge and skills described in the graduate profile by the simultaneous more efficient work of the teacher and the positive change of students´ attitude to mathematical subjects by means of creative thinking development so that it satisfies not only the teacher but the students as well providing thus the required results at the same time. The creative thinking development obviously results in the improved probability of students´ implementation in the job market as the adaptation capability of a graduate as well as the knowledge interpretation and its creative application are the highlighted prerequisites of the university graduate qualifications. In addition, it is more than probable that the importance of these features will still increase. The monograph is divided into three main parts. The first part provides an overview of the theoretical background, means, used methods and tools. The second part introduces the experimentally obtained results of the several years’ lasting research focused on the information and

iii communication technologies implementation aimed at improving the educational process quality and efficiency. Regarding the conditions and the environment, the experiments were executed within the mathematical education of the future technical intelligence. The third part is oriented on the generalization of the obtained knowledge. KEY WORDS information

and communication

technologies,

learning, creativity, emerging technologies

mathematics,

e-

iv SCIENTIFIC CONTRIBUTION The current society is under pressure of the fast development of technologies. Modern digital technologies have significantly increased our possibility to communicate, improved the importance and role of knowledge, have made the production more efficient as well as they have enhanced the offer of services provided. The transfer of information is very fast, huge almost in all continents and in the outer space as well. The technologies allow opening and keeping work, interest or study communities, they considerably influence the attitude of people to knowledge, i.e. to the institutions with the mission to build, preserve and provide new knowledge – to universities. Tertiary institutions experience significant changes caused by information technologies. Not only the administrative as well as the managerial processes almost completely depend on the technological tools utilization requiring high investments for their implementation but also both main university processes experience the changes, i.e. the field of research and education. It is the result of the fact that the information or better to say knowledge have become the factor that decides about their success in the environment with the continuously growing competition. It was not so long ago that the rate of utilizing the digital technologies either in the form of electronic information sources, experimental simulation tools, analytical or statistical tools was beyond our imagination. Obviously, the new technologies not only influence the origin of new knowledge, they also bring considerable changes into education eliminating thus the physical limitations represented mainly by time and space of its application while enhancing its possibilities at the same time. The application of digital

v technologies has the power to bring higher quality to the educational process; nevertheless, it has some drawbacks as well. On one hand, this is the reason for the thorough research in optimal conditions of utilizing the technologies in the education, analysing their structure, form and technical implementation, and on the other hand, also the reason for learning about the mutual relations and regularities of the various factors of digital technologies implementation and effects on the educational process result and quality. Regarding the aforementioned, the monograph submitted aims at presenting the state of knowledge we have in the field of ICT implementation in the university environment within the mathematical preparation of engineers. The knowledge has been systemized on the basis of several years´ lasting research resulted not only into well documented and verified practical recommendations for the efficient use in the tertiary education but it also resulted into the thorough elaboration of

the

theoretical principles, methods and tools allowing for the replication of our positive experience on one side, and building the basis for the minimization of possible difficulties related to the various aspects of digital technologies utilization on the other side. Mapping the technological support of teaching mathematics includes the various areas such as the research of existing best experience, theoretical and applied models of computer-aided teaching of mathematics, investigation of the emerging technologies and mathematical software as well as the analysis of the changes in the mathematical education caused by the technologies utilization and on-line education. The models presented here were not only proposed on the basis of the state of knowledge in the

vi time given but they were all experimentally verified and adapted with the aim to optimize the characteristics investigated. From the practical point of view, the authors focused on two aims in the monograph: 

provide an insight into and comprehension of the current and future trends related to the support of the digital technologies within the mathematical preparation of engineers;



provide an insight into and comprehension of practical, technical and methodological issues related to e-education in mathematics; The ambition of the submitted monograph is to provide the current

state of knowledge in the field of ICT utilization within the mathematical preparation of engineers as well as provide the overview of selected trends, tools, methods and possibilities offered by digital technologies for the mathematical preparation improvement. The authors assume that the university teachers will find useful information and inspiration to improve their own teaching via the appropriately chosen technology and on-line sources.

vii

Introduction.................................................................... 5 1.

Theoretical Background of ICT Utilization ............... 7

1.1.

Determination Of Terminology ................................ 7

1.2.

Object Of Research ................................................ 14

1.2.1.

Short Overview Of Approaches To Ict Utilization In Education 14

1.2.2.

Ict In Teaching Mathematics .............................................. 22

1.2.3.

Issues Of Mathematical Education At Universities And In Preparation Of Engineers ................................................... 29

1.2.4.

Issue Of Gender Diversity ................................................... 34

1.2.5.

Technology-Based Knowledge Assessment......................... 34

1.2.6.

Efficiency Of Education With Ict ......................................... 38

1.3.

Overview Of Current Training Methods And Forms Focused On Creativity ............................................. 41

1.3.1.

Creative Training ................................................................ 42

1.3.2.

Problem Situation And Creative Tasks ................................ 45

1.3.3.

Methods Of Creative Thinking Development ...................... 48

2. 2.1.1.

Experimental – Results Of Research Projects ......... 52 Personable Profile Of Ict Users Focused On Creativity In International Context ......................................................... 52

viii 2.1.2.

Personable Characteristics And Creativity ...........................62

2.2.

Innovation In Mathematical Subjects Of TechnologyBased Preparation Of Engineers .............................. 66

2.2.1.

Innovation Of The Concept Of Mathematical Subjects Training (Curriculum Analysis) .............................................66

2.2.2.

Technology-Based Methods Of Learning And Abilities Developing ..........................................................................73

2.2.3.

Methods Of Knowledge And Skills Assessment....................82

2.2.4.

Analysis Of Materials Determined For Knowledge Assessment 90

2.2.5.

Survey Of Students´ Interest And Possibilities To Utilize The Internet In Study .................................................................98

2.2.6.

Utilization Of Creativity Principles In Ict Implementation .. 101

2.3.

Increase of the Quality and Flexibility in the Training In Mathematics Via Information Technologies ....... 113

2.3.1.

Preparation Of Interactive Study Materials ....................... 119

2.3.2.

Increase Of Quality And Flexibility In Subjects Of Geometry 124

2.3.3.

Increase Of Quality And Flexibility In Mathematical Subjects 133

2.3.4.

Knowledge Assessment Supported By Ict .......................... 141

2.3.5.

Students´ Success In Technology-Based Tests According To The Graduated Secondary School Type ............................. 149

ix

3.

Acquired Knowledge in ICT Application in Mathematical Subjects ....................................... 155

4. 5.

Conclusion .......................................................... 161 References

163

INTRODUCTION Modern

information

and

communication

technologies

bring

considerable changes into education. The educational system has to educate the people to be prepared for life, work and learning in the current society where the ability to manage the technologies has continuously growing significance. Currently, it is necessary to prepare the students as the information users who can manage the search of necessary information as well as its processing and creative utilization. The teacher is obliged to build these students´ abilities helping them to study successfully and implement in the job market. Therefore, the result of the educational process should not be represented only by the students´ knowledge as it can get old but mainly by the abilities in the form of the students´ competence. The pedagogical and psychological research shows that if the students have to obtain more than the vague knowledge, they need to be involved in the education. They do not have to be only the passive recipients of new pieces of information. The creative individual with a high flexibility in thinking can proceed to better and original results in the tasks solution even with the smaller amount of information than the individual who is very well informed and whose thinking cannot flexibly operate with the material available. The teacher is an important factor as s/he is no longer the source of information and becomes the assistant in the student´s learning. This new and more demanding role requires deeper understanding of the subject matter, the will to teach experimentally, and not perform as an authority. The competition in the international job market requires that the education is more efficient. The education efficiency is influenced by the

organization of the educational process having two mutually eliminating objectives: keep the costs for the education as low as possible whereas the society requirements have to be met at their possible maximum as well. As a result, it is necessary innovate the educational process in terms of its content, methods and forms. In the education of engineers Mathematics plays a key role especially in the first years of study. The course is frequently the reason of the students’ study prolongation or study cessation. The results of the investigation in the field of technologies utilization in teaching Mathematics can initiate the changes increasing the chances of the university students to accomplish the study successfully. The information about the potential influence of the technology-based training ensures also the better utilization of the lower amount of sources the Slovak universities have at their disposal. What is more, relevant information can lead to further investigation which students´ characteristics contribute to the best results achievement in various types of education at their most.

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