A presentation on how to make strict compass and straightedge constructions with GeoGebra.

1. The 7th International Conference for Informatics and Information Technology - CIIT 2010 Feb 24-27, 2011, Bitola, FYR Macedonia Compass & Straightedge with GeoGebra Linda Fahlberg-Stojanovska Vitomir Stojanovski University St. Clement of Ohrid - Bitola

2. Effective technology The most effective educational technologies are the ones that require little or no behavioral change on the part of the teacher or the learner. They should not increase cognitive load, nor should they require extensive training or technical support. Dr. Andrew Van Schaack, Vanderbilt U.

3. Goal: Mathematics Education One of our main goals in mathematics education is teaching logical thinking skills. That is, the ability to look at a problem and see what is given, what is required and the steps neededto get from the given to the required. And how to check the result.

4. Why Compass & Straightedge? We have very, very small set of tools. The problems state specifically what is given and what is required. Every construction is based on previous constructions – previous learning. The construction is visible and measurable. We can see it; we can check it physically to see whether it is correct.

5. Why Compass & Straightedge? Creativity and Thinking Construct a 30° angle. How many ways? Draw an equilateral triangle and bisect one of the angles? Draw a right-triangle with hypotenuse double the length of a side? …

6. Why Compass & Straightedge? Teaches logical thinking skills Fun and creative Usually is required learning

7. What tools in C&S? A pencil A compass and A straightedge.

8. What can we do with these tools? With a pencil draw points and GeoGebra New Point Tool mark intersectionpoints. GeoGebra Intersection Tool

9. What can we do with these tools? With a straightedge draw line through 2 points GeoGebra Line Tool draw segment between 2 points GeoGebra Segment Tool draw ray from 1 point through 2nd point GeoGebra Ray Tool

10. What can we do with these tools? With a compass measure a length between 2 points for a radius and then draw a circle with centered at a 3rd point with that radius. GeoGebra Compass Tool

11. Our toolbar in GeoGebra for C&S

12. Construction worksheet The BasicConstruct.ggb Ready-to-use worksheet with the GeoGebra toolbar for C&S Available online (post it freely) at: http://mathcasts.org/gg/construct/BasicConstruct.html Download and open it with GeoGebra http://mathcasts.org/gg/construct/BasicConstruct.ggb

13. First construction # 1 Copy a line segment geogebrawiki.pbworks.com/Segment-Copy YouTube Screencast - Show and Tell Online interActivity with GeoGebra Printable and online materials Online DIY worksheet for making construction Metadata

14. First construction # 1 Copy a line segment Given a line segment AB and a line with a point P on it. Copy the line segment AB onto the line so that P corresponds to A. We can start with blank and have kiddies draw the line segment and line or We can put AB and line on BasicConstruct.ggb

15. Second construction # 2 Copy a triangle Given a triangle ABC and a line with a point P on it. Copy the triangle so that P corresponds to A and the base of the triangle is on the line. We can start with blank and have kiddies draw the triangle and line or We can ΔABC and line on BasicConstruct.ggb

16. FOSS (Free and open source software) Can be used on school LANs Can be used offline Many, many applications Ready to use applets are available Is easy to use, powerful and dynamic Teachers and students can work anywhere Students can build animations, simulators, … Why GeoGebra?

17. References http://math247.pbworks.com/(mathcasts, pencasts, GeoGebra,…) http://www.mathopenref.com/ (compass and straightedge) GeoGebra YouTube Channel http://www.youtube.com/user/GeoGebraChannel http://geogebrawiki.wikispaces.com- english http://geogebramkd.wikispaces.com - macedonian Linda Fahlberg-Stojanovska: emath@emathforall.com

18. Getting Started with C&S http://geogebrawiki.wikispaces.com/Construct+with+GeoGebra Printable materials Online interActivity with GeoGebra and/or Download Links to pages on the 7 basic constructions http://geogebramkd.wikispaces.com/Конструкции+со+Геогебра На македонски