November 10-13, 1999

Department of Mathematics

University of California, Los Angeles

Los Angeles, CA90095

There are three main components of technology in education: 1) organization and management of some educational system (from a school to the system of education of the whole country); 2) satisfaction of some supplementary needs of education systems and educators (e.g., information supply, communication facilities, word processing, etc.); 3) realization of a teaching/learning process. The latter type is called educational technology. It has three aspects. First, the most obvious one, is technology as a discipline for teaching and learning. The second aspect is the technology of learning, and the third one is the technology of teaching. Technologies of the both latter types are called instructional [1] or pedagogical technologies [2]. Contemporary understanding of technology in education is, as a rule, connected with them. However, modern education is mostly aimed not at technologies as integral systems but limited to the utilization of computers and other electronic devices.

Computers and its software are being integrated into the educational process with increasing speed. The main areas of application are [3]: computer literacy, classroom management, and direct involvement with student instruction. The first are relates to technology as a discipline. The second application area is directed at the organizational problems of teaching and has to be treated in the context of technology of teaching. The third area refers both to teaching and learning technologies.

The computer-based technologies, which use computers as a teaching and/or learning tool, form a specific class of educational technologies. Consequently, it is more effective to consider computers as a part of an integral technology.

Now efficiency of computer utilization in education is comparatively low with respect to the diverse facilities provided by modern computers. The reason is that there are no, as a rule, integral computer-based technologies. Only methods and instructions for learning by means of computers are developed. However, it is insufficient due to the diversity of side effects. These effects are neglected on the level of methods and instructions but are taken into account on the level of technology. That is why, it is so urgent to implement a technological approach to learning and, especially, to teaching.

Consequently, it is necessary to develop integral educational technologies and to apply them to different levels of education: from preschools to universities. It is essential that teachers possess not only the art of teaching but also the technology of teaching as a foundation for this art.

Basing on an advanced model of a general technology [4-6] and creativity approach to learning and teaching [2], it is possible to provide a variety of new facilities in education making it more adequate to the contemporary tasks than the education we have now. Problems of elaboration and utilization of educational technologies are analyzed from methodological and theoretical points of view.

To work efficiently with educational technologies (i.e., to investigate, design, implement, and utilize them), it is necessary to understand technology as a social phenomenon. Today, many people think that technology has appeared only in the XX century and associate technology with a quantity of sophisticated machines and devices (such as computers) utilized in modern society. However, there are technologies without benefit of tools or machines [7].

Thus to obtain an adequate definition of technology, it is necessary to analyze existing definitions. However, the quantity of such definition is so huge that it is possible to do this only in a book. Consequently, here we consider only some of them that are the most appropriate:

(1) Technology is a systematic application of scientific knowledge to some practical purpose or activity. [7]

(2) Technology is a systematic knowledge and action, usually of industrial processes but applicable to any recurrent activity. [8]

(3) Technology is [9]:

• a technical language;
• the science of application of knowledge to practical purposes;
• application of scientific knowledge to practical purposes;
• the totality of means employed by people to provide itself with the objects of material culture

(4) Technology is the application of scientific and other knowledge to practical tasks by ordered systems that involve people, organizations, living things and machines. [10,11]

(5) Technology is any systematized practical knowledge, based on experimentation and/or scientific theory, which enhances the capacity of society to produce goods and services, and which is embodied in productive skills, organization, or machinery. [12]

It is possible to demonstrate that all these and the majority of other definitions are not constructive being incomplete, ambivalent, and, in some cases, even inconsistent. For example, while in the definition (5), technology is defined as some kind of knowledge, the definitions (1) and (4) treat technology as an application (i.e., as a process). The definitions (2) and (3) contain both versions and more.

However, these discrepancies are not contradictions. They only demonstrate that technology is a complex phenomenon and different definitions reflect dissimilar aspects of technology. In such a way, an analysis of existing definitions and the phenomenon itself demonstrates [5] that technology has three components: structural, mental, and material. Thus knowledge corresponds to the mental component while application is a material projection (materialization) of this knowledge.

At the same time, further development of educational technology demands more exact and effective definition, which will provide conditions for elaboration of new technologies and better utilization of the existing ones. To achieve this goal, new definitions have been introduced basing on the assumption that it is necessary to distinguish concrete and general technologies [4-6].

Definition 1. A concrete technology T is a system of completely specified methods and procedures for representation of a definite kind of processes of obtaining a specific result.

Remark. Here and in what follows, we consider only structural and mental components relating to the material component as the realization of a technology or a technological process.

Definition 2. A method (procedure) M is called technologically specified if conditions and means for its realization are included in its description.

Consequently, technology is not an arbitrary description of some (even the most practical) process. Technology, as a description, has to satisfy specific conditions that transform abstract knowledge to a practical one. These conditions (formulated and analyzed in [5,6]) separate technology from other kinds of process descriptions which constitute the following sequence:

It is necessary to remark that all other kinds of process descriptions are used in education. As a matter of fact, now programs and procedures are used more frequently than technologies (in the correct meaning of this concept). Moreover, all three kinds of descriptions as well as others (e.g., algorithms) are useful for pedagogical goals. It is only important to choose the relevant kind of description basing on the existing conditions.

Definition 3. A general technology GT is a cluster of knowledge about concrete technologies from some class.

In other words, while concrete technology is a description of some process (e.g., technology of geometry teaching), general technology is an amalgamation of concrete technologies related to some field or problem and knowledge about these technologies (e.g., teaching technology).

Definition 4. A technological process is a process that is realized as it is prescribed in some technology.

Deficiency in a good definition of technology has resulted in a high level of confusion in the diverse collection of definitions of instructional or pedagogical technology. While some definitions are excessively narrow, particularly those confined to devices and hardware, others are much too broad and bear little relevance to the real world of academia. There are contradictory and ambivalent definitions. Many examples of such definitions are analyzed in [7].

One of the best definitions was elaborated by the Commission on Instructional Technology [1]. In it, instructional technology is treated as a systematic way of designing, carrying out, and evaluating the total process of learning and teaching in terms of specific objectives, based on research in human learning and communication, and employing a combination of human and nonhuman resources to bring about more effective instruction. Technology is considered in this definition from the structural perspective. Historical experience and definitions 1 and 3 from the previous part show that two conditions (of basing on research and of bringing about more effective instruction) are superficial and it is necessary to delete them. Thus we obtain a constructive definition of technology providing a base for elaboration of a mathematical model.

There are three general categories of technologies: production, service, and utilization technologies. So the question arises, what is the type of pedagogical technologies. It is not a simple question because the answer depends on educational paradigm. If it is a student-oriented paradigm, then pedagogical technology is a service technology. If it is a teacher-oriented paradigm, then pedagogical technology is an utilization technology. If it is a society-oriented paradigm, then pedagogical technology is a production technology. Consequently, each approach emphasizes specific criteria for technology evaluation influencing in such a way design, implementation, and utilization of pedagogical technologies.

The main problem concerning pedagogical technology is their efficiency. It is caused by several objectives. The main one is that pedagogical technology exists in structural and material forms while explicit knowledge about these structures is scarce and poorly systematized. Instructions and rules provide incomplete reflection of pedagogical processes. It is possible to conjecture that this has been one of essential reasons for the consistent failure of technological innovations through the years. As it is stressed in [14], different technical devices met only marginally most problems that teachers define as important. Besides, the mere existence of technological tools is not sufficient to assure their adoption and use.

Other objectives are consequences of the main one. Thus, incomplete representation of technological knowledge results in a variety of difficulties and obstacles to the development, evaluation, and utilization of pedagogical technologies. For example, technical devices (such as computers, tape recorders, TV sets, etc.) are not, as a rule, naturally included in pedagogical process being unable to enhance, supplement, and support school activities, instead of just filling in time and supplying student busywork. Consequently, the prospects for advancing education through information technology require, for their success, a great deal in the way of nontechnical developments basing on collaborative attention of technologists and educators [16].

However, even such incomplete knowledge has not been acquired by the majority of teachers. Consequently, one more problem is connected with teacher skills and knowledge in utilization of educational technology (or more exactly, technical means of this technology). Recently, a group of 20 business and education leaders at the CEO Forum on Education and technology examined and analyzed utilization of computers in American schools. The study finds that although more then six million computers are in nation's schools, most teachers still lack the training to use them in a way that truly helps children. Simply using computers as a tool to "drill" students does not raise achievement. The CEO Forum suggests in its report that teacher training in technology should be mandatory by 2002.

Mathematical theory of technology provides various means for eliminating these and some other shortcomings of the modern pedagogical technology. For example, the model of technology elaborated in this theory contains a description of all necessary components of concrete technology and, consequently, it guides how to design integral technologies in education. This model is also aimed at the development of a framework for learning different of concrete technologies, i.e., for achieving teacher technological literacy. For example, it is necessary to teach teacher not only how to use computer but how to utilize pedagogical technology based on computer facilities. In addition to this, mathematical theory of technology offers means for computer modeling, evaluation, and optimization of both existing and proposed pedagogical mathematical theory of technologies.

The technological approach to education is inevitable if we want to have the majority of population being integrated in modern culture and society with its sophisticated technical devices and complicated social structures. Recent research demonstrates advantages of the technological approach [17]. Consequently, we come to the necessity to apply scientific methods to design, evaluation, and utilization of educational technology. The mathematical theory of technology provides educators with such methods. It is only necessary to adapt the general structures and results of this theory to the problems of education.

However, it is important to understand what place must be occupied by the pedagogical technology in the professional activity of teacher. Now teaching is an art on the highest level, craftsmanship in a general case, a fakery in the worst case. Utilization of pedagogical technology must not transform teacher into an element of an educational "assembly line" as a worker in industry is an element of an assembly line at some plant. On the contrary, pedagogical technology is aimed at developing teacher creativity and enhancing his abilities to achieve higher level in his professional activity. Teacher has to use pedagogical technology for developing students' intellect, skills, and knowledge as architect uses building blocks for construction of a many-storey buildings.

1. A report by the Commission on Instructional Technology, To Improve Learning, v. 1 and 2, New York, 1970
2. Burgin, M., "Pedagogical technology as a base for teacher creativity", Creativity and Pedagogy, pt. 2, Moscow, 1988, pp. (in Russian)
3. Dall, C., "Evaluating Educational software", Chicago and London, 1987
4. Burgin, M., "System Functioning and Technological Processes", Abstracts presented to the American Mathematical Society, 1992, v.13, N3
5. Burgin, M., "Mathematical Theory of Technology", Methodological Problems of Mathematics and Information Sciences, Kiev, 1997, pp. 91-100 (in Russian)
6. Burgin, M., "A Technological Approach to the System Science-Industry-Consumption" , Science and Science of Science, 1997, No. 3/4, pp. 73-88 (in Russian)
7. Saettler, P., "The Evolution of American Educational Technology", Englewood, 1990
8. Encyclopedia of Physical Science and Technology, v. 13.- New York - London - Tokyo: Academiс Press, Inc., 1992
9. McGraw-Hill Concise Encyclopedia of Science and Technology. - New York - London - Tokyo, 1989
10. Webster's Third new International Dictionary, 1993
11. Street, J., "Politics and Technology", 1992
12. Pacey, A., "The Culture of Technology", 1983
13. Gendron, B., "Technology and Human Condition", New York, 1977
14. Cuban, L., "Teachers and Machines: The Classroom Use of Technology since 1920", New York, 1986
15. Cohen, D.K., "Educational Technology and School Organization", Technology in Education: Looking toward 2020, Hillsdale, N.J., 1988
16. Nickerson, R.S., "Technology in Education: Possible Influences on Context, Purposes, Content, and Methods", Technology in Education: Looking toward 2020, Hillsdale, N.J., 1988
17. Chung, C.A., Abu Huda, "An Interactive Multimedia Training Simulator for Responding to Bomb Threats", Simulation, 1999, v. 72, N2, pp. 68-77