Abstract
The classical idea of an instructional process is to create some new knowledge, skills and abilities, so-called KSAs. If a student has a set of KSAs at the beginning of a learning process and if he or she has a new set of them at the end of a learning period we can say the instructional activity transforms the student from the starting state (state number 1) to the final state (state number 2). One can define such transformation as an effective action. It is possible to describe each action as a set of external impacts. In the case when this set is a series of standard actions, which usually give a predicted result, we can say it is a traditional education technology in so-called triad form: object number 1 transfers into object number 2. It is possible to present this in the form of a matrix equation. This equation is the main one in the general theory of technologies. The main idea of this article is to analyze the effectiveness of an instructional process based on mathematical descriptions, which was developed in the general theory of technologies.
TopHistorical Background
Despite the complexity of the universe, its perception by humans is possible as a result of modeling. One defines modeling as a simplified description takes into account some properties. The loss of a number of important properties in the description of nature is the payment for simplification of studied problems. Therefore, a number of different models is necessary for study of each serious problem. The process of learning is tied to several models that take into account different theoretical points of view (Frigg & Hartman, 2011; Romanenko & Nikitina, 2009). The best known of them are theory of systems (Bertalanaffy, 1974), theory of human activity (Vygotsky, 1978; Vygotsky, 1986), theory of global evolution (Gould, 1981; Chaykovsky, 2008). The general theory of technologies is one of them. There are two important questions in the field of education, natural sciences, and sociology. The first question is what it is, and the second is how to do it (Romanenko & Nikitina, 2012b). The answer to the first question is given in physics and engineering. The answer to the second one can find in the field of chemistry and other types of processing. Processing is defined as a path of fabrication or transformation of different objects we need. One can transform objects by different ways. If the object under transformation is a person or a group of humans, such transformations cover areas of medicine, policy, and education as well. The processing can sometimes create objects we really need. Human knowledge develops unevenly over the time, and in different areas.
Key Terms in this Chapter
Transformation: In general it is a result of an effect of environment that changes an object. In everyday practice it is a set of actions that change the state or properties of different materials, goods, services or knowledge.
Logistical Curve: S-shape line that describes the time dependence for development of competences and some other behaviors.
Technology: A strictly determined sequence of operations that guarantees a desirable result. The base of technology is an algorithm of the sequence of operations that can strictly predict a final result.
Human Activity: A set of human operations and actions that have real predicted goal.
Reflection: A weak interaction between an object and the external world that does not change the principal properties of the object.
Object: In general it is each independent part of universe.
Competence: A comprehensive description of capability that includes knowledge, skills and abilities and sometimes behaviors. It usually denotes as KSA or KSAO.
Processing: A set of actions which are defined as a path of fabrication or transformation of different objects needed to create new goods, knowledge and services on the basis of different items.
Mastering Index: Quantitative value for measuring average student group achievements after a standard set of exercises.
Universal Curriculum Core: The pack of basic skills and knowledge required of each individual for a professional qualification.
Abilities: The possibility to achieve a goal or find a solution to a problem.
Skills: The learned pack of actions to carry out predetermined results.
Hidden Process: Some competences are created without special open learning. This process is a typical side effect of each instructional strategy.
Modeling: A simplified description of an object or situation that takes into account only some its behaviors.