Exploring the Creation of Mathematical Fractals Utilizing Euclidian Construction in a Pre-Service Teacher Environment: A New Perspective to Integrate Contemporary Mathematics into School Curriculum
Abstract: Fractal images are very beautiful and stunning. Fractal Geometry presents a different geometry than classical geometry. Classical or Euclidean geometry has been utilized in the development of mathematics, science, and engineering for centuries. But, it has failed to model and formulize many of the ordinary events and shapes surrounding us. Natural objects such as ferns, coastlines, and mountains have formed of more complicated geometric figures. We developed some curriculum materials infusing the concepts of fractal geometry in middle and high school mathematics curriculum. These materials consist of a number of hands-on activities and mathematics software such as CABRI-II. Students were asked to explore various objects in nature which are not seemed to be formed of lines, circles, squares or triangles. Students were engaged, motivated, persevered, and made connections between mathematics and real life events during these activities.