Dynamical Systems

Dynamical Systems Are Self-Organizing

Dynamic implies synergistic, changing, and chaotic (i.e., underlying order that appears random). System denotes an assemblage of interacting components whose essential properties arise from the relationships between its parts. Students, teachers, classrooms, schools, and school districts make up dynamical systems in education.

Students and teachers are individuals made up of diverse systems—biological, affective, and cognitive. There is also diversity based on race, ethnicity, gender, disability, and socioeconomic status—other systems that are an integral part of students and teachers. All of these systems contribute to individual differences in rate of learning, level of thinking, memory, and motivation. Pedagogically, teachers need to be aware of the dynamic complexity of their students and themselves [Page 286]in order to more effectively understand what occurs in the teaching-learning process. For example, an African American student who has lived in a rural town will perceive information differently from an African American student who has been raised in an inner-city ghetto. Even though both students are African American, the differences in the systems that make up who they are will contribute to diverse outcomes. If both are learning the word field, their understanding of the meaning of this word will reflect their different experiences. The same teaching strategy may not work for both of them. For one, a trip to a field might be necessary whereas the other will have experience with fields and can easily make a connection. A view of students as dynamic systems emphasizes the individuality and complexity of all students.

Each dynamic system, in addition to being fluid and integrative, exists in a state space, which is an abstract construct depicting the range of behavior open to a system and constrained by the degrees of freedom available to the elemental components of the system. Each student has his or her own state space or possible behaviors. For example, a student whose family speaks Spanish at home is going to be constrained by English being a second language. His or her state space will be different from that of a student for whom English is a primary language. In order to be effective, a teacher needs to be sensitive to the different state spaces of his or her students. Some students may be incapable of carrying out certain behaviors because of the limits of their state space. The student with Spanish as the primary language may be incapable of understanding certain English idioms until he or she has learned other words first and changed his or her state space through self-organization.

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