Presentation shared by author at the 2015 EDEN Open Classroom Conference "Open Discovery Space: Transforming schools into innovative learning organisations" held on 18-21 September 2015, in Athens, Greece. Find out more on #OCCAthens here: http://www.eden-online.org/eden-events/open-classroom-conferences/athens2015.html

1. Konstantinidis Ioannis,
School of Pedagogical and Technological Education of Athens, Greece
AN INTRODUCTION TO THE
GEOMETRY OF FRACTALS IN
PRIMARY AND
SECONDARY EDUCATION

2. • lines,
• circles,
• squares,
• cubes,
• cylinders and
• Spheres
• In nature, however, other shapes prevail around us:
• clouds,
• lightning,
• ice crystals,
• sponges and
• Shoreline
• exhibit a complexity that looks nothing like the simple
geometric objects of "classical" Geometry [1].
In the course of classical geometry in school we learn about:

3. • We took the idea (exemplified by the so-called "Pythagorean
tree") to describe the world using a geometry more complex
than the one usually presented in schools, because such a
geometry represents the true reality around us.
• Such a knowledge about the surrounding world will hopefully
render the pupil's perception of the world better and more
complete.
• Therefore, we propose that the notion of complex geometry will
render our students more creative, open new pathways of
thinking, and motivate new activities in life.
The Idea:

4. • The lesson scenario presented in ISE (Inspiring Science Education
- http://portal.opendiscoveryspace.eu/el/edu-object/mia-
eisagogi-stin-morfoklasmatiki-geometria-fractals-829770) is an
attempt to introduce a way of thinking more "complex" than the
one students are so far exposed to in school.
• As a teaching method, we apply the so-called Inquiry Based
Learning [4], consisting of five stages.
Description of Lesson's Plan

5. • The "Pythagorean tree" [3] is a fractal geometrical set devised by
the Dutch mathematician Albert E. Bosman in 1942 [2].
• The simulation which we developed is called
Pythagorean_tree.jar. Its use helps the student to experiment
dynamically and form a student's own opinion about the
concept of fractal geometry, studying the Pythagorean Tree. The
image given in next slide shows an example of a pattern formed
after running the simulation.
Description of the Simulation

6. An example of a pattern formed after running
the simulation

7. • Step 1: Create an initial rectangle.
• Step 2: In the upper ends of the initial rectangle build two new
rectangular blocks with fixed angles (specified by the user).
• Step 3: Repeat steps 2 and 3 for all new rectangles until a Tree is
formed.
• The figures below show further examples of Pythagorean Trees.
Algorithm of construction of the Tree of Pythagoras

8. • In conclusion, we believe that after this course the student will
have another view of the surrounding nature.
• The student will be able to understand and describe a more
"real" way the reality around him.
Conclusions

9. Konstantinidis Ioannis,
School of Pedagogical and Technological Education of Athens, Greece
The End