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Article Excerpt
The system approach in science and technology education is concerned mainly with continuous systems, whose behavior is described by differential and difference equations. However, in the digital era, the use of discrete systems becomes more and more popular. In particular, the design of hybrid systems--which combines digital and analog (continuous) subsystems--is receiving attention through computer-embedded systems and decision-controlled systems.
This article studies a way to integrate hybrid systems in science and technology classes. It proposes a new class of hybrid systems called Algorithmic Hybrid Systems, which are based on algorithmic notation. An argument in favor of introducing such hybrid systems in science and technology lessons is presented. A method for modeling and simulating hybrid systems using system dynamics simulation software is proposed, and several examples are presented and discussed.
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System dynamics is a methodology for studying and managing complex systems (Forrester, 1961). Incorporating constructivist-learning principles (Piaget, 1971), it has been applied to education through a computer-based environment aimed at K-12 classes and beyond (Forrester, 1994). Students study the behavior of simple and complex systems in various subjects, by constructing computer models and running simulations. They acquire system-thinking skills, develop a panoramic multidisciplinary outlook, and learn about specific systems (Chen & Stroup, 1993). The approach has already been applied around the world in science, math, social sciences, business and the humanities. For examples visit the Creative Learning Exchange site at http://www.clexchange.org
The focus of system dynamics in general, and education in particular, has been mainly on continuous systems, whether these are physical, biological, or social systems (Labinaz, Bayoumi & Rudie, 1997). Variables of continuous systems are defined as continuous sets, and modeled by means of differential and difference equations. The behavior of such systems is mainly determined by feedback loops that describe direct and indirect causal relations among elements (Forrester, 1968).
However, in recent years the importance of systems in which continuous and discrete elements interact has been recognized. Particular attention has been given to hybrid systems, in which a discrete logical part controls a continuous part of the system (Branicky, 1995). The logical controller is usually modeled as a finite automaton, also called Finite State Machine (FSM). This concept is widely used in computer embedded systems design.
This article studies the potential of hybrid system modeling in the context of learning science and technology. It shows the relevance of hybrid systems to high school education, and describes uses of system dynamics software tools for constructing and exploring hybrid systems in schools.
The main contribution of the article is in introducing a novel approach to the representation of hybrid systems, which is especially suitable for educational needs. This approach is based on the concept of algorithmic hybrid systems, in which the controlling part of the system is represented in the form of an algorithm. The algorithmic model of hybrid systems uses fundamental concepts taken from the computer science curriculum (algorithm) on the one hand, and from the classical science curriculum (differential equation) on the other hand.
The article is organized as follows: a section that defines hybrid systems, and describes their relevancy to science and technology education. A section that presents the Algorithmic Hybrid System. This is followed by a section that proposes how to implement the model using system dynamics software (STELLA). Two examples are given in the next section. The final section is the conclusion.
HYBRID SYSTEMS
Much recent research has been devoted to explore the mathematical framework for hybrid systems, towards developing a general theory of hybrid systems (Branicky, 1995; Labinaz, Bayoumi, & Rudie, 1997; Mosterman & Biswas, 2000). Nevertheless, the potential role of hybrid systems in science and technology education has not been studied. To do so, a clarification of the nature of such systems is required.
Analog and digital Systems
Systems are generally described as complex objects whose components are inter-related (Bunge, 1974). By dynamic systems we mean systems wherein processes are developing over time. Dynamic systems may be classified into continuous and discrete, depending on their type of variables. By analog systems we mean systems that...
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