### Addressing Transitional Challenges in Learning Dynamic Geometry

```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 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) \$
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 Manual and Tutorials (Help):
http://wiki.geogebra.org/en/
• GeoGebra Lessons (Materials):
http://www.geogebratube.org/?lang=e
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 GeoGebra
Do some dynamic math in GeoGebra
Drawing a Drawing
Do some dynamic math in GeoGebra
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 Development
Curricular 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 Development
Cognitive 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.
Catapult teacher learning
• Curricular challenges
– In-service teachers who have already allotted time for
– 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
In VMTwG:
Discourse is
captured, and can
be viewed in a
Successful and
unsuccessful
discourse moves
can be identified
and discussed
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
• 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 & Chair
Department of Urban Education – Newark
Principal Investigator – NSF eMath project DRL-1118888
Rutgers University
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Loretta Grisi-Dicker
Doctoral Student
Graduate School of Education – New Brunswick
Department of Urban Education – Newark
Rutgers University
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