GeoGebra IPG Pri 092010

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<p>GeoGebra Institute of Malaysia</p> <p>Introduction We, as mathematics educators, need to teach our students to think critically and to do mathematics as mathematicians do. We need to let them construct their mathematical knowledge themselves. Students need mathematical abilities to solve problem. These abilities include being able to detect patterns, make conjectures, make generalizations, perform inductive and deductive reasoning, and make analogies. These skills can be nurture through tasks that require them to solve problems, engage in exploratory investigation, experience classroom discourse and using the information and communication technology. The multi-platform, open-source dynamic mathematics software GeoGebra (Hohenwarter &amp; Preiner 2007) is one of the mathematics software that can be used to encourage investigation, discovery and experimentation in classrooms and their visualization features can be effectively employed in teaching to generate conjectures (Lavicza 2006, Kreis, 2004). By utilizing Geogebra in our teaching, students learn through exploring, investigating and discovering. GeoGebra enhances students higher order thinking skills in mathematics. It is and effective tool for both teacher and students. Geogebra combines geometry, algebra, calculus, and statistics into a single easy-to-use package for learning and teaching mathematics from elementary through university level. It is available free of charge on the internet and has been translated into 36 languages and is estimated that more than 100 000 educators use this software for teaching and learning in more than 192 countries (Hohenwarter, M., Hohenwarter, J., Kreis &amp; Lavicza, 2008). The open-source nature of the software has important implications both for educators and students. Unlike with commercial products, students are certainly not constrained to use the software only in schools or universities allowed by site licenses, but they can download and install GeoGebra on their private computers.</p> <p>About the Creator: Markus Hohenwarter Markus Hohenwarter created GeoGebra in 2001/2 during his master's thesis project and later PhD thesis in Mathematics Education at the University of Salzburg, Austria. From 2006-2008, his work was supported by an NSF Math &amp; Science Partnership project of Florida Atlantic University and Broward County Schools in Florida. At present, he is leading the GeoGebra project at the Florida Center for Research in Science, Technology, Engineering, and Mathematics Education (FCR-STEM) at Florida State University in Tallahassee, USA.</p> <p>Introduction to GeoGebra A Workshop for GeoGebra Users by Dr. Daniel Leong, GeoGebra Institute of Malaysia, SEAMEO RECSAM on 25 September 2010</p> <p>1</p> <p>GeoGebra Institute of Malaysia</p> <p>Table of Contents1. Installation of GeoGebra .............................................................................................................. 4 Activity 1: Installing GeoGebra .................................................................................................................... 4 Installation WITH Internet access ................................................................................................................. 4 Installation WITHOUT Internet access ......................................................................................................... 4 2. 3. GeoGebras User Interface .......................................................................................................... 4 Basic Use of Tools ....................................................................................................................... 5 Activity 2: Familiarizing with some of the Menu/Tools ............................................................................... 6 Menu ............................................................................................................................................................. 6 Construction Tools ........................................................................................................................................ 7 4. Drawing with GeoGebra ............................................................................................................... 8 Activity 3: Drawing Geometric Figures and Other Objects .......................................................................... 8 Activity 4: What to practice .......................................................................................................................... 9 5. Saving Files ................................................................................................................................. 10 Activity 5: Saving GeoGebra files .............................................................................................................. 10 Activity 6: Opening GeoGebra Files ........................................................................................................... 10 6. Drawings, Constructions, and Drag Test ................................................................................. 10 Discussion ................................................................................................................................................... 10 7. Rectangle Construction ............................................................................................................. 11 Activity 7: Constructing a rectangle ............................................................................................................ 11 8. Navigation Bar and Construction Protocol ............................................................................. 12 Activity 8: Checking your construction ...................................................................................................... 12 9. GeoGebras Properties Dialog .................................................................................................. 12 How to access the Properties Dialog ........................................................................................................... 12 Activity 9: What to practice ........................................................................................................................ 13 10. Square Construction .................................................................................................................. 13 Activity 10: Constructing squares ............................................................................................................... 13 11. Create custom tool ...........................................................................Error! Bookmark not defined. Activity 11: Creating a Square tool ............................................................................................................. 14 12. 13. Measuring Length, Area and Angles ........................................................................................ 14 Equilateral Triangle Construction ............................................................................................. 15 Activity 12: Constructing an Equilateral Triangle ...................................................................................... 15 14. Export of Pictures to the Clipboard .......................................................................................... 16 Activity 13: Exporting Pictures to the Clipboard ........................................................................................ 16 15. 16. Inserting pictures into a text processing document............................................................... 16 Inserting Pictures into the Graphics Window ......................................................................... 17</p> <p>Introduction to GeoGebra A Workshop for GeoGebra Users by Dr. Daniel Leong, GeoGebra Institute of Malaysia, SEAMEO RECSAM on 25 September 2010</p> <p>2</p> <p>GeoGebra Institute of MalaysiaActivity 14: Drawing Tools for Symmetric Figures.................................................................................... 17 17. Basic Algebraic Input, Commands, and Functions ................................................................ 18 Activity 15: Tips and Tricks ....................................................................................................................... 18 Activity 16: Visualizing Integer Addition on the Number Line .................................................................. 19 18. Static and Dynamic Text ............................................................................................................ 20 Activity 17: Inserting Static Text ................................................................................................................ 20 Activity 18: Inserting Dynamic Text .......................................................................................................... 20 19. Conditional Formatting .............................................................................................................. 21 Activity 19: Conditional Formatting Inserting Checkboxes................................................................... 21 20. Fraction with Circles .................................................................................................................. 22 Activity 20: Constructing Circular Sectors with sliders .............................................................................. 22 21. Visualizing Multiplication of Natural Numbers ........................................................................ 24 Activity 21: Constructing a Model for Visualizing Multiplication ............................................................. 24 22. Reconstruct ggb files ................................................................................................................. 26 Activity 22: Reconstructing Thumb-up.ggb ............................................................................................ 26 23. Creating Dynamic Worksheets ................................................................................................. 26 Activity 23: Exporting a Dynamic Worksheet ............................................................................................ 27 Activity 24: Enhancing Dynamic Worksheets ............................................................................................ 27 24. 25. Providing Dynamic Worksheets to Students .......................................................................... 28 GeoGebras Spreadsheet View ................................................................................................. 28 Spreadsheet Cells Input ............................................................................................................................... 29 Activity 25: Recording to Spreadsheet Feature ........................................................................................... 29 Activity 26: Relative Copy and Linear Equations ....................................................................................... 30 Activity 27: Creating a histogram ............................................................................................................... 31 26. Useful Web Links........................................................................................................................ 32 GeoGebra Homepage .................................................................................................................................. 32 GeoGebraWiki ............................................................................................................................................ 32 GeoGebra User Forum ................................................................................................................................ 32 GeoGebra Documentation ........................................................................................................................... 32 GeoGebra Institute of Malaysia .................................................................................................................. 33</p> <p>Introduction to GeoGebra A Workshop for GeoGebra Users by Dr. Daniel Leong, GeoGebra Institute of Malaysia, SEAMEO RECSAM on 25 September 2010</p> <p>3</p> <p>GeoGebra Institute of Malaysia</p> <p>1. Installation of GeoGebra Activity 1: Installing GeoGebra Preparations Create a new folder called GeoGebra_your name on your desktop. Hint: During the session, save all files into this folder so they are easy to find later on. Installation WITH Internet access Install GeoGebra WebStart Open your Internet browser and go to http://www.geogebra.org/cms/en/download Click on the button called GeoGebra WebStart. Note: The software is automatically installed on your computer. You only need to confirm all messages that might appear with OK or YES. Hint: Using GeoGebra WebStart has several advantages for you provided that you have an Internet connection available for the initial installation: You dont need to have special user permissions in order to use GeoGebra WebStart, which is especially useful for computer labs and laptop computers in schools. Once GeoGebra WebStart was installed you can use the software off-line as well. Provided you have Internet connection after the initial installation, GeoGebra WebStart frequently checks for available updates and installs them automatically. Thus, you are always working with the newest version of GeoGebra. Installation WITHOUT Internet access Your workshop presenter will provide the GeoGebra installer files via USB drives or CDs. Copy the installer file from the storage device into the created GeoGebra_your name folder on your computer. Hint: Make sure you have the correct version for your operating system Examples: MS Windows: GeoGebra_3_0_0_0.exe MacOS: GeoGebra_3_0_0_0.zip Double-click the GeoGebra installer file and follow the instructions of the installer assistant. 2. GeoGebras User Interface The GeoGebras basic interface is divided into four sections: a graphics view, an algebra view, an input bar and a spreadsheet view. On the one hand you can operate the provided geometry tools with the mouse in order to create geometric constructions on the drawing pad of the graphics window. On the other hand, you can directly enter algebraic input, commands, and functions into the input field by using the keyboard or data into the spreadsheet view. While the graphical representation of all objects is displayed in the graphics window, their algebraic numeric representation is shown in the algebra window. The user interface of GeoGebra is flexible and can be adapted to the needs of your students. If you want to use GeoGebra in the elementary or early middle school, you might want to hide the algebra window, input field, worksheet view and coordinate axes and just work with the drawing pad and geometry tools. Later on, you might want to introduce the coordinate system using a grid to...</p>