Abstract
Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. Chaos theory is the qualitative study of unstable periods in deterministic nonlinear dynamical systems, chaos theory looks at how things evolve. Fractal geometry is a subject that has established connections with many areas of mathematics (including number theory, probability theory and dynamical systems). Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century; this paper investigate the concepts of chaos theory and fractal geometry as a conceptual transformation at secondary school level. This paper reports a study of the effects of teaching chaos theory and fractal geometry on geometric reasoning skills in geometry. Thirty of the tenth grade students of basic education participated in an experimental group, which was involved in working with chaos theory and fractal geometry activities, pre-treatment measures the geometric Reasoning skills. Teaching fractal geometry properties and examples were focused in the teaching activities. At the end of the teaching measures geometric reasoning skills were again obtained. Since the study was an exploration, the effectiveness of teaching chaos theory and fractal geometry, the exploratory data collected by the researcher was also considered to be an important part of the study.Â
Highlights
Geometry is integrated in an inclusive mathematics curriculum in Oman secondary stage. Clements and Battista (1992) have claimed that school geometry refers almost universally to Euclidian geometry, even though there are numerous approaches to the study of a topic, such as synthetic, analytical, transformational, and vector- not to mention nonEuclidian approaches
The question dealt with cognitive aspects of chaos theory and fractal geometry, these aspects were chosen from the work of (Benson et al, 1993& and Barnes, 1993), The selection, and adoption of some of the question, was done in consultation with four colleagues in math department in college of Science and math education in college of Education at SQU, it was refereed by three experts who are working in the field of fractal geometry in USA
The Treatment in the Experimental Group. This is a quasi-experimental study of one sample group, in which topics of chaos theory and fractal geometry activities in addition to school geometry has presented for the experimental group
Summary
Geometry is integrated in an inclusive mathematics curriculum in Oman secondary stage. Clements and Battista (1992) have claimed that school geometry refers almost universally to Euclidian geometry, even though there are numerous approaches to the study of a topic, such as synthetic, analytical, transformational, and vector- not to mention nonEuclidian approaches. The study of fractal geometry is appropriate in high school for many reasons: students have the opportunity to investigate traditional mathematics topics from a new approach, to make connections both within mathematics and between mathematics and natural and human worlds, and to explore mathematics in non-analytic ways (Lornell&Wesberg, 1999, 265). In terms of description, the notion of scale independence and self-similarity are useful for making sense of the leveled and embedded natures of individuals, social collectives, bodies of knowledge, cultures and societies, O’Daffer and Thorquist (1993; 43) have pointed out that mathematical reasoning is part of mathematical thinking that involves forming generalizations and drawing valid conclusions about ideas and how they are related. Fractal geometry is a natural place for the development of students reasoning skills; it offers ways to describe physical environments and natural geometric figures
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