I. Introduction

This presentation is based on the type of research defined as Instructional Development Research Model. An integral part of this kind of research is determining requirements for the instructional media developed, which, according to J. Willis (Willis, 1993), deal with the "determination of need (perhaps a good package has already been developed), learners analysis, task and concept analysis, and specification of instructional objects".

Developing the concepts of this type of research described by W. Dick, L. Carey , S.Thiagarajan, M. Semmell, D. Semmel, J. Willis ( Dick & Carey, 1985; Thiagarajan, Semmell & Semmell, 1974; Willis, 1993), it should be pointed out that the requirements for the developed instruction material must reflect : 1.the specifics of the studied discipline (or group of disciplines); 2. the psychological theory used to describe the process of teaching and learning, the type of the developed instructional materials and the role and place of educational software in the course of instruction.

Thus, if we deal with design of instructional materials of a certain type, based on a certain psychological theory, applied for a study of a certain group of disciplines using a certain methodology for solving the same type of problems, then these instructional materials should meet certain common requirements. This is theoretical assumption on which this research is based. Proceeding from this assumption, a goal of this research can be defined as design of Computer Based Instructional Model of teaching advanced mathematics at undergraduate level. The psychological theory on which the instruction is based is the theory of stage-by-stage development of mental actions.

This research is based on the following empirical and experimental data obtained in:

• design and development of "Raduga" (Bouniaev, Kovtun, et al.,1991) a popular educational software in Russia for creating instructional material in math that meets the described above requirements;
• research on determining the math content for student math teachers which is reflected in "Reforms in the Education of Teachers of Mathematics" (Bouniaev, 1986).
• data obtained through practical experience of teaching abstract math both in Russia and the US using new technologies and in a more traditional environment;
• experiments in design and use of instructional material in abstract math w ith Hypercard, Authorware Pro, Linkway, etc.

The theoretical foundation of this research is:

1. Psychological theory of stage-by-stage development of mental actions elaborated by the Russian school of psychology (Leontiev, 1975; Talyzina, 1975) and further worked out and applied to the computer oriented training in "Development of multi functional dialogue CAT programs " (Bouniaev,1991) and "Databases in training process" (Bouniaev, 1994). Since this experimentally proven and universally accepted theory in Russia is practically unknown outside of the country, it will be discussed in greater details further on including its basic assumptions and resulting prescriptions for the organization of instructional process.

   The stage-by-stage development of mental actions theory also determines methods of analysis of the instructional process and selection of appropriate strategies. The analysis is based on specifics of the studied material, teaching goals for this discipline and its place in the curriculum, as well as specific characteristics of the group of students taking this course. The fundamentals of this method as developed and applied for computer oriented instruction (Bouniaev, 1991) are used in this research.

2. As theoretical and experimental research shows (Bouniaev, 1994) databases and bases of knowledge (complete with a designed interface) can serve as construct frameworks for implementation of basic theses and prescriptions of the stage-by-stage theory of developing mental actions in organizing interactive computer oriented instruction. Therefore, theories of artificial intelligence and data and knowledge representation were used (Durkin, 1994; Haes-Roth, et al, 1983) in this research. D.Newman (Newman, et al., 1989) emphasized that Intelligent Tutoring systems can not substitute teacher's performance which is certainly indisputable. However, a current tendency to present knowledge in Artificial Intelligence format makes a substantial impact on instructional software design which does not formally belong to Artificial Intelligence Systems. We consider the frame structure of knowledge presentation very useful for our purposes.

   At the same time, in order to present general possibilities of studying abstract mathematics in a computer assisted environment based on the theory of stage-by-stage development of mental actions it will be sufficient to deal with databases primarily. Top priority in this case (from pedagogical stand point not information technology stand point) is not solving the problem of presenting knowledge but that of an adequate interface. In this case we fully support B. Shneiderman (Shneiderman , 1982 & 1992) who wrote about importance of interface in a computer based instruction.

Go on to the next section of this paper.

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Mikhail Bouniaev
Southern Utah University
Math/CS Department
351 W. Center
Cedar City, Utah, USA, 84720

E-mail: BOUNIAEV@SUU.EDU

Moscow Pedagogical State University
Department of Mathematical Analysis
Moscow, Russia