This document describes an online mathematics course called "Mathematics-Reactivation" for secondary level education in Poland. The course was developed by three people between 2010-2014 and provided online materials to support in-class teaching for over 250 schools and 13,000 students. It included interactive content to explain mathematical concepts, Geogebra applets for experimentation, practice exercises, and exams. The goal was to enhance traditional classroom teaching by allowing teachers to display content digitally and have students actively experiment with mathematics online and in computer labs. The course aimed to promote new styles of self-directed learning and more engaging experimentation-based teaching.

1. Geogebra in online teaching
A complete e-course
in secondary level mathematics
Przemysław Kajetanowicz
Institute of Mathematics and Computer Science
Wrocław University of Technology

2. Contents
• Recent challenges in Polish education
system
• „Mathematics-Reactivation” in a nutshell
• Outline of content’s functionality
• Geogebra in action

3. Structure of Polish education system
• Before 1999
– Elementary (=primary) – 8 years
– Secondary – 4 years
• Since 1999
– Elementary (=primary) – 6 years
– Grammar (=junior high=gymnasium) – 3 years
– Secondary (=senior high=lyceum) – 3 years
• Graduation math exam
– Obligatory until 1984 and since 2010

4. • Project start: 14th
January 2010
– 13 people involved
– Content developers:
• Agnieszka Herczak-Ciara
• Przemysław Kajetanowicz
• Jędrzej Wierzejewski (additionally: project coordinator)
– 250 schools, over 13 000 students
– Goal: to provide a large number of secondary schools with
online support of in-class teaching
• Comprehensive interactive materials
• Material exposition (reading)
• Java-driven sophisticated e-exercises and exams (practicing)
• Geogebra applets (experimentation)
• Electronic testing (self-assessment and in-lab exams)
„Mathematics – Reactivation”

5. MR Web page

6. MR Moodle platform

7. Functionality logic
• Discussion of concepts/methods/theorems
(reading and practicing)
• Interactive simulators (experimenting)
• Exercise pages addressing a portion of
material
• Practice exam at the end of a chapter
Show
Show
Show
Show

8. Introducing concepts
Dynamic behaviour of UE

9. Explaining „why...”

10. Explaining math phenomena

11. Deriving formulae

12. Presenting formulae

13. Explaining quarter identification

14. Tool for self-experimentation

15. Boring algorithms made fun

16. Boring algorithms made fun (2)

17. Boring algorithms made fun (3)

18. Boring algorithms made fun (4)

19. Showing the beauty
(no, no, we don’t teach it)

20. Experimenting with interpolation

21. From experiment to proof (1)

22. From experiment to proof (2)

23. From experiment to proof (3)
No derivatives!

24. Announcing higher math...

25. Section segments theorem (1)

26. Section segments theorem (2)

27. Section segments theorem (3)

28. Section segments theorem (4)

29. Section segments theorem (5)

30. Content-assisted teaching
• In class
– Definitions displayed rather than written
– Solving e-exercises
– Playing with mathematics (Geogebra)
• In computer lab (students’ active
participation)
• Homework
– Portions of material left for self-study
– Selected exercises given for solving at home

31. Learning and teaching - new styles
• Learning - unbounded self-assessment and
experimentation opportunity
• Teaching – new classroom style
– Exposition by teacher (no more writing
definitions)
– Geogebra-driven experiments (what do you think
will happen if we change the sign of the parameter
a ?)

32. Thank you for your attention