1. Andreas Philippou and Costantinos Christou University of Cyprus

2.  Academic year 2008-09  The University of Cyprus is responsible for the preservice education of teachers of secondary education.  Prepare math teachers to use integrate computers into their teaching in the mathematics classrooms. Sample of activities.  Concept : limits, derivative, integrals etc.  Main aim of the program  facilitate preservice mathematics teachers incorporate technology in their teaching

3.  The program was organized and run by the University of Cyprus in cooperation with the ministry of Education and Culture.  104 preservice teachers attended this course.  5 classes of approximately 20 students.  Purpose of this article is to present how we used Geogebra both as a teaching tool and to create interactive web pages for students from middle school up to lyceum.

4.  Two sessions were devoted to an introduction of Geogebra.  Two sessions developed the concepts of dynamic geometry  Eight sessions were focused on functions, graphs, differentiation and integration.  Tutors demonstrated the basic GeoGebra operations  Problems from the module’s worksheets linked to mathematics lectures.  Tutors notes amplified or explained important points, and provided additional answers or suggestions.

5.  Equations and functions  Preservice teachers  investigated ideas about the linear, quadratic and cubic equations and functions.  plotted graphs of a cubic, a piecewise function, trigonometric, exponential and logarithmic functions, inverses of functions and graphs over a finite range.  created interactive graphs utilizing sliders.  Differentiation – Integration  introduced to GeoGebra’s dash notation and derivative command.  linked algebra and geometry for the first derivative of a quadratic.  developed ideas on tangents, second Derivative, concavity, local maxima and minima of polynomials, GeoGebra’s extremum function, local maxima and minima for non-polynomials and points of inflection.

6.  Dynamic geometry and trigonometry  introduced to Geogebra geometrical tools and initially constructed basic shapes such as squares, rectangles, parallelograms, rhombuses and after that they continued with the construction of several geometrical theorems such as Thales’ theorem, inscribed angles.  constructed the trigonometric circle and developed relevant activities.

7.  Examples from the worksheets prepared by tutors.  Purpose of the activities was to provide an to illustrate a mathematical concept or problem with GeoGebra and mainly to describe how they would teach their lesson.  Specifically, they were asked to discuss teacher’s actions and possible questions to be asked, and student’s actions and possible responses (Haciomeroglu, Bu, Schoen & Hohenwarter, 2009).  Enable multiple representations and visualization of the mathematical concepts.

12.  Various opportunities that dynamic mathematics software like Geo-Gebra can offer for the teaching of mathematics in secondary education.  Our work with prospective teachers has shown that:  developing and presenting lessons with GeoGebra improved not only teachers’ mathematical content knowledge but  also their abilities to develop effective lessons for their students in various content areas of secondary mathematics.

13.  Haciomeroglu, E., Bu,L., Schoen, R., & Hohenwarter, M. (2009). Learning to Develop Mathematics Lessons with GeoGebra. MSOR Connection, 9 (2), 24-26.  GeoGebra. Available via: http://www.geogebra.org [Accessed 27 June 2009].http://www.geogebra.org  Kelly, A.E., Lesh, RA., and Beak, J. Y. (2008) Handbook of innovative Design Research in Science, Technology, Engineering, Mathematics (STEM) Education. New York: Taylor & Francis.