1. Introduction to GeoGebra and Collaborative Learning of Math over the Internet Loretta Grisi-Dicker Doctoral Student Rutgers Graduate School of Education - New Brunswick Department of Urban Education – Newark NJIT C 2 PRISM Free Hands-On Professional Development Teacher Workshop March 21, 2012

2. Agenda Introduction to GeoGebra – Why do it? What is it? How to get it? (5 minutes) – Do some dynamic math in GeoGebra: Using a dynamic worksheet (10 minutes hands on) Doing your own construction (10 minutes hands on) Collaborative Learning of Math over the Internet – NSF eMath Project: Virtual Math Teams with GeoGebra (VMTwG) (5 minutes) Professional Development Courses using VMTwG (5 minutes) Questions and reactions (10 minutes)

3. Why do it? “students consider the available tools [such as] dynamic geometry software… to explore and deepen their understanding of concepts” (Core Curriculum State Standards for Mathematics, p. 7)

4. What is it? dynamic geometry software = dynamic geometry environments (DGEs) Cabri Geometry (France) $ The Geometer’s Sketchpad (USA) $ GeoGebra (Austria) free tools to create geometric images Primitive objects: points, lines, segments, vectors, circles, … Derived tools: midpoint, perpendicular, parallel, … as well as transformations, including reflect, rotate, translate, …

5. Mathematics Using a DGE: GeoGebra Can combine geometry and algebra, or can show each perspective individually

6. Once an image is produced, measurements can be taken of its elements such as length, angle, and area. Measurements can also be used to produce an image or an element thereof. Defining objects of an image can be moved or dragged around the screen, giving these environments their dynamic quality.

7. How to get it? www.geogebra.org GeoGebra Software (Download): http://www.geogebra.org/cms/en/download http://www.geogebra.org/cms/en/download GeoGebra Manual and Tutorials (Help): http://wiki.geogebra.org/en/ http://wiki.geogebra.org/en/ GeoGebra Lessons (Materials): http://www.geogebratube.org/?lang=e http://www.geogebratube.org/?lang=e

8. Do some dynamic math in GeoGebra Using a dynamic worksheet Math: What a drag! Squares, Squares, Squares,... You will see six squares - or do they just look like squares? 1. Drag the vertices of each square with the mouse and write down what you can observe. 2. Try to come up with a conjecture about how each square was created and write it down. Judith Preiner, Created with GeoGebraGeoGebra

10. Do some dynamic math in GeoGebra Drawing a Drawing

11. Do some dynamic math in GeoGebra Doing your own Construction

12. Collaborative Learning of Math over the Internet NSF eMath Project: Virtual Math Teams with GeoGebra (VMTwG) Professional Development Courses using VMTwG

13. Computer-Supported Math Discourse Among Teachers and Students (eMath) NSF-funded research project (DR K-12) Cyber infrastructure: VMT  VMTwG Professional learning for teachers Teachers engage students with VMTwG Student performance data

14. VMTwG Computer Supported Collaborative Learning: Virtual Math Teams with GeoGebra (VMTwG) – Replayer

15. Professional Development Curricular Challenges (Assude, 2005; Cuban, Kirkpatrick, & Peck, 2001; Laborde, 2007)Assude, 2005Cuban, Kirkpatrick, & Peck, 2001Laborde, 2007 There is no time to learn new technology Curriculum is too full to fit another thing

16. Professional Development Cognitive Challenges (Laborde, 2007; Lu, 2008a; Preiner, 2008)Laborde, 2007Lu, 2008aPreiner, 2008 The literature describes a slow, long learning curve for learning DGE’s, going through several stages of development. 1. Static handouts

17. Cognitive Challenges (continued) 2. Dynamic visualizations for presentations Some teachers do not move past the presentation stage

18. Cognitive Challenges (continued) 3. Discovery learning/ Lesson Enrichment Many teachers take several years to transition to discovery learning with significant math discourse.

19. Online, graduate level course Catapult teacher learning Curricular challenges – In-service teachers who have already allotted time for graduate level course. – Choose the least favorite topic that you teach, and replace lessons around that topic with DGE. Cognitive challenges – Directly to preparing teachers to engage their students in learning mathematics using DGE – in a collaborative online environment – With focus on significant mathematical discourse

20. Catapult Pedagogy Simulate classroom procedures of periodically calling the class together to make meaning of an activity Designing each module with Multiple stages: – Asynchronous (preparation and review of prior modules, getting everyone on the same page, noticing and wondering) – Synchronous (reflection on the mathematics, talking about the activity before doing it, describing what will be done, doing the math activity synchronously and collaboratively) – Asynchronous (reflections on the math, the discourse, and the VMTwG system) – Synchronous (reflection on discourse moves, and reflect on what the experience was like for them, and how they will structure it for their students)

21. Significant Math Discourse Successful and unsuccessful discourse moves can be identified and discussed In VMTwG: Discourse is captured, and can be viewed in a spreadsheet log

22. Significant Math Discourse Socialization in math community Language of math & practices Collaborative learning thru discourse Accountability to each other, to math domain, to math community standards Conceptualization & articulation

23. Second online, graduate level course In the second course, teachers will implement what they have learned in their own classrooms, – within the context of their current curriculum; – with mentoring and resources to support this effort.

24. Interesting Questions To Look at Closely How do we assess the transformation that takes place in the teachers? How can we provide optimal scaffolding, – not overwhelmed in the beginning, – yet having sufficient skill and confidence to implement what they have learned with their students and – mentor other teachers, the following school year?

25. More Interesting Questions To Look at Closely How does the development of significant mathematical discourse within VMTwG influence students’ mathematical performance?

26. Arthur B. Powell, Ph. D. Associate Professor & Chair Department of Urban Education – Newark Principal Investigator – NSF eMath project DRL-1118888 Rutgers University powellab@andromeda.rutgers.edu Loretta Grisi-Dicker Doctoral Student Graduate School of Education – New Brunswick Department of Urban Education – Newark Rutgers University loretta.grisi.dicker@rutgers.edu