Introduction to GeoGebra andCollaborative Learning of Math

over the Internet

Loretta Grisi-DickerDoctoral Student

Rutgers Graduate School of Education - New BrunswickDepartment of Urban Education – Newark

NJIT C2PRISM Free Hands-On Professional Development Teacher Workshop

March 21, 2012

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)

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)

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, …

Mathematics Using a DGE: GeoGebra

Can combine geometry and algebra, or can show each perspective individually

• 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.

How to get it?

www.geogebra.org

• GeoGebra Software (Download): http://www.geogebra.org/cms/en/download

• GeoGebra Manual and Tutorials (Help): http://wiki.geogebra.org/en/

• GeoGebra Lessons (Materials): http://www.geogebratube.org/?lang=e

Do some dynamic math in GeoGebraUsing 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 GeoGebra

Do some dynamic math in GeoGebraDrawing a Drawing

Do some dynamic math in GeoGebraDoing your own Construction

Collaborative Learning of Math over the Internet

NSF eMath Project:

• Virtual Math Teams with GeoGebra (VMTwG)

• Professional Development Courses using VMTwG

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

VMTwG

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

Professional DevelopmentCurricular Challenges

(Assude, 2005; Cuban, Kirkpatrick, & Peck, 2001; Laborde, 2007)

• There is no time to learn new technology

• Curriculum is too full to fit another thing

Professional DevelopmentCognitive Challenges

(Laborde, 2007; Lu, 2008a; Preiner, 2008)

• The literature describes a slow, long learning curve for learning DGE’s, going through several stages of development.1. Static handouts

Cognitive Challenges(continued)

2. Dynamic visualizations for presentations

Some teachers do not move past the presentation stage

Cognitive Challenges(continued)

3. Discovery learning/ Lesson Enrichment

Many teachers take several years to transition to discovery learning with significant math discourse.

Online, graduate level courseCatapult 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

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)

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

Significant Math Discourse

• Socialization in math community

• 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

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.

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?

More Interesting Questions To Look at Closely

• How does the development of significant mathematical discourse within VMTwG influence students’ mathematical performance?

Arthur B. Powell, Ph. D.Associate Professor & ChairDepartment of Urban Education – NewarkPrincipal Investigator – NSF eMath project DRL-1118888Rutgers Universitypowellab@andromeda.rutgers.edu

Loretta Grisi-DickerDoctoral StudentGraduate School of Education – New BrunswickDepartment of Urban Education – NewarkRutgers University loretta.grisi.dicker@rutgers.edu