transform certain concepts from them (Duit and Komorek 1997; Duit et al. 1997,
1998).
The reasons for this aforementioned tendency are multiple. Firstly, Chaos is a
branch of modern Physics which concerns the average-size scales of Nature—the
ones in which we live—and thus has phenomena that are relatively easy to notice
and observe. This is in contrast to Relativity, which usually concerns very large
scales, and to Quantum Mechanics, which mainly describes events in the microscopic world.
Secondly, Chaos, as a concept for instruction, could bring significant changes to
the ideas about and the perceptions of everyday phenomena that the learning subjects
may have. For instance, involvement with Chaos Theory abolishes the learner’s
belief that small causes have small effects and that, as the cause increases in size and
significance, so does the effect (Lorenz 2005a; Smith 2007). Additionally, Chaos
Theory deals a severe blow to the certainty that the same system, with the same or
similar pre-existing conditions, will evolve totally similarly (identically) in time
(Lorenz 1963, 1969; Prigogine 1997; Stewart 2002).
Thirdly, Chaos can easily be produced and studied in a school Physics laboratory.
It requires only simple activities and equipment, such as a Chaos Pendulum
(Skordoulis et al. 2014; PASCO 2017), that exists in many high schools.
Additionally, Complex Systems and Complexity, in a variety of their aspects, as
well as the ideas that stem from these fields, such as cellular automata (Wolfram
2002), arise in more and more scientific fields and in an increasing number of events
in daily life (Kaufmann 1995; Mitchell 2009; Holland 2014). The same is true of
Fractals, the mathematical representation of chaotic systems (Mandelbrot 1982;
Bountis 2004).
It is obvious that, if knowledge of Chaos, chaotic natural systems, Complexity
and Complex Systems is to be diffused into school classrooms (mainly high school
classrooms, but also primary), a necessary prerequisite is to teach future teachers, as
well as in-service Science teachers, about these issues. This is the reason why the
current research and the teaching methodology stemming from it focus mainly on
undergraduate primary school teachers. The concepts related to Chaos and Complex
Systems that are intended to be taught to prospective primary school teachers must,
by necessity, be discharged from heavy mathematical formalism, and bring out
mainly conceptual aspects of these fields of Physics. Such aspects are: the sensitive
dependence on initial conditions, the limited predictability, the existence of rules in
apparently chaotic natural systems (Kellert 1994), the emergence of complex patterns based on simple rules, the fact that “the whole is larger than the sum of its
parts”, the critical state (a small change in the cause can cause a great or—at least—
an unpredictable change in the results), etc.
252
A. Gkiolmas et al.
1998).
The reasons for this aforementioned tendency are multiple. Firstly, Chaos is a
branch of modern Physics which concerns the average-size scales of Nature—the
ones in which we live—and thus has phenomena that are relatively easy to notice
and observe. This is in contrast to Relativity, which usually concerns very large
scales, and to Quantum Mechanics, which mainly describes events in the microscopic world.
Secondly, Chaos, as a concept for instruction, could bring significant changes to
the ideas about and the perceptions of everyday phenomena that the learning subjects
may have. For instance, involvement with Chaos Theory abolishes the learner’s
belief that small causes have small effects and that, as the cause increases in size and
significance, so does the effect (Lorenz 2005a; Smith 2007). Additionally, Chaos
Theory deals a severe blow to the certainty that the same system, with the same or
similar pre-existing conditions, will evolve totally similarly (identically) in time
(Lorenz 1963, 1969; Prigogine 1997; Stewart 2002).
Thirdly, Chaos can easily be produced and studied in a school Physics laboratory.
It requires only simple activities and equipment, such as a Chaos Pendulum
(Skordoulis et al. 2014; PASCO 2017), that exists in many high schools.
Additionally, Complex Systems and Complexity, in a variety of their aspects, as
well as the ideas that stem from these fields, such as cellular automata (Wolfram
2002), arise in more and more scientific fields and in an increasing number of events
in daily life (Kaufmann 1995; Mitchell 2009; Holland 2014). The same is true of
Fractals, the mathematical representation of chaotic systems (Mandelbrot 1982;
Bountis 2004).
It is obvious that, if knowledge of Chaos, chaotic natural systems, Complexity
and Complex Systems is to be diffused into school classrooms (mainly high school
classrooms, but also primary), a necessary prerequisite is to teach future teachers, as
well as in-service Science teachers, about these issues. This is the reason why the
current research and the teaching methodology stemming from it focus mainly on
undergraduate primary school teachers. The concepts related to Chaos and Complex
Systems that are intended to be taught to prospective primary school teachers must,
by necessity, be discharged from heavy mathematical formalism, and bring out
mainly conceptual aspects of these fields of Physics. Such aspects are: the sensitive
dependence on initial conditions, the limited predictability, the existence of rules in
apparently chaotic natural systems (Kellert 1994), the emergence of complex patterns based on simple rules, the fact that “the whole is larger than the sum of its
parts”, the critical state (a small change in the cause can cause a great or—at least—
an unpredictable change in the results), etc.
252
A. Gkiolmas et al.