Solving of reverse constructions with GeoGebra in mathematics teacher training

1. Solving of reverse constructions with GeoGebra in mathematics teacher training RNDr. Kitti Vidermanová, PhD. PaedDr. Janka Melušová, PhD. Department of Mathematics Constantine the Philosopher University in Nitra

2. Idea • while checking homework • Students sent their solutions in GeoGebra and Cabri II by e-mail • Mistake of one student – she used wrong given data in construction task – time consuming and demanding

3. The Constructional Tasks • Belong to most difficult tasks in school geometry, because they cannot be solved/taught by any algorithm, they have to be solved by deduction …should be taught because • they offer space for independent creative activity of students, • they help to development of creativity and visualization, • Logical thinking, • Sence for aesthetics.

4. The Reverse Constructions • Teach how to read from figure, • While the solving process, students do not construct but inquire and explain separate steps of the construction, • Transformation of wording to symbolic language, • Deeper understanding.

5. Study – brief description • 3 tasks (2 planar, 1 spatial) – constructions done in GeoGebra, • 8 student working independently with the computer and wrote their reasoning on the paper, • Tasks: „Based on given construction, try to find out, what shape should be constructed and which objects were given.“

6. Task 1 • Given • length of base AB, • size of angle by A, • height of the trapezoid. Task Draw the isosceles trapezoid ABCD.

7. Task 1 - results

8. Task 2 • Given • lengths of medians. Task Draw the triangle ABC.

9. Task 2 -results

10. Task 3 • Given data • length of side of the base • altitude. Task Draw the regular pyramid with triangle base in sloping parallel projection

11. Task 3 - results

12. Students’ opinions (future teachers) ICT in geometry • It is interesting and motivating, but it should be used more for revising, it is important to get the skills in drawing on the paper, • Students spend too much time sitting by a computer, I prefer the standard (pen and paper) way to teach. Reverse constructions • Interesting, new and demanding, • Like a puzzle, so they can be motivating • I would use this kind of task because students usually do not like classic drawing with pencil, it may be useful to alternate this task with classic ones • I would implement them at upper secondary and tertiary education, students should develop the drawing skills.

13. Survey of in-service teachers Surveyin 2007 (129 respondents,average length of practice 17, 8 years) • 66% of teacher have the possibility to use the computers in mathematics lessons • Only 40 % of these really use it. Reasons: • Lack of time for innovative methods (teach students to work with program), • Lot of teachers is not able to use the software.

14. Additional information Since 2008/09 – curricular reform • Less content, less time. Project MVP - design of teachers book aimed to use of ICT in school mathematics (including the training of teachers)

15. Thank you for your attention