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Rationale GeoGebra: Free and Dynamic Potentials of GeoGebra Concluding Remarks
Exploring GeoGebra: A Dynamic
Mathematics Software
Ateng’ Ogwel
Centre for Mathematics, Science and Technology Education in Africa
Special dedication to TCTP 14 Participants: Oct. 2010
OGWEL, JCA (CEMASTEA): "Exploring GeoGebra with TCTP 14"
TCTP14: Explore through the Mind, Hands and Heart

Outline
1 Rationale
Rationale and Objectives
ICT Integration in Education
2 GeoGebra: Free and Dynamic
Constructing Objects: Toolbar
Constructing Objects: Symbolic Approach
3 Potentials of GeoGebra
Object Properties
Technologies and Pedagogy
4 Concluding Remarks
Remarks
Feedback

Rationale
Inadequate Modeling: There is persistent urge to align school
education with the fast changing needs of the society. Education
appears to be predominantly characterized by individualistic
learning of isolated facts and skills for examinations.
There is pressure to incorporate ICT in education. Emergence
of Courseware and tools are driven by technologists,
programmers and mathematicians as educationists show laxity
and resistance to techno-revolution in education
ICT is not a panacea for quality and efﬁcient education, unless
properly integrated and accepted. Therefore, there is need to
develop a community of educators who collaborate in the use
and integration of ICT in education.

Objectives
By the end of the interactive session, a participant should
be able to
Download and install a Dynamic Mathematics
Software, GeoGebra
Explore and use Menus and basic tools of GeoGebra
to construct mathematical objects
Evaluate the potential of GeoGebra as a tool for
integrating ICT in mathematics education, and its
potential towards stimulating higher order thinking
skills

ICT Integration in Education

GeoGebra
A Dynamic Mathematics Software, that integrates
Geometry, Algebra (GeoGebra) and Calculus. It has
elements of Dynamic Geometry Software (DGS) and
Computer Algebra Systems (CAS). Runs on any
platform that supports Java.
It is freely available for online installation from
http://www.geogebra.org/cms/en/download or
downloadable for local installation at
http://www.geogebra.org/cms/en/installers
Examples at www.geogebra.org/book/intro-en.zip and
at the wiki
http://www.geogebra.org/en/wiki/index.php/Main_Page.
Thoughts, help and queries are shared at the forum
www.geogebra.org/forum

Menus: File; Edit; View; Options; Window; Help
Tools: Move; Points; Lines; Loci/Constructions;
Polygons; Circles and Circular arcs; Conics;
Measurements; transformation; �ݺ�ߣr; Visibility;
Toolbar Help
Views:
Graphics/ Geometry View: Default view and drawing
pad on which geometrical objects are constructed.
Algebra View: Algebraic representation of objects.
Spreadsheet View: Every cell has a speciﬁc name
and names of objects match the spreadsheet cells
Input Bar: Gives algebraic command as alternative to
the geometrical tools on the toolbar.

Activity 1: Menus, Tools and Views
1 Download, install and open GeoGebra application.
2 Using Menus
Select the point style to a cross ("x") and labelling to
"All New Objects"
Activate only the "Algebra View".
3 Using Tools
Place any three points "A", "B" and "C" on the
Drawing pad and observe the "Algebra View". Use
the "Move" tool to manipulate the points and observe
changes in the "Algebra View"
Use the "Drop Down Arrow" to change the tools
appearing on the toolbar

Spreadsheet View
1 Save current file as "Menu1.ggb" in a folder "JCA25"
Open a "New Window" and select "Spreadsheet
View"
2 Type/ input the texts enclosed by quotation marks in
the given cells (ENTER to confirm input):
"1" (A1); "(2,5)" (A2); "b=5" (B1); "p=(3,1)" (B2);
"(-1,0)" (C1);
"Segment[A2,C1]" (C2)
3 Manipulate objects and describe your observations
4 In the "Algebra View", click on, and manipulate A1.
5 Save the current file as "Spreadsheet1.ggb"

Constructing Objects: Symbolic Approach
Algebraic Input Bar
1 Open a New Window and activate the "Input Bar".
Deactivate the "Spreadsheet View"
2 Type/ input the following verbatim in the "Input Bar":
a=12
A=(1,2)
b=Segment[A,a]
B=(4,7)
p=Polygon[A,B,5]
"Area of polygon p =" +p
3 Manipulate the objects and describe your
observations. Save the current ﬁle as "Input1.ggb"

Object Properties
Object Properties
1 Open the file "Input1.ggb"
2 Type c=Polygon[A,B,a] in the Input Bar
3 Right Click
a in the Geometry window and select "Animation On"
(first, highlight a in the Algebra Window)
p, select "Object Properties" and change the color
and style of the object
Change the color and font size of the text "Area of
polygon ..."
4 Select "View" and activate "Construction Protocol"
Observations?
5 Save the current file as "Activity1.ggb"

Semiotic Tools
Collaboration: The previous activity introduced you to
basics of GeoGebra. Competence and confidence is
gained through practice, explorations, review of
examples and readiness to seek help and share with
the GeoGebra community.
GeoGebra, like any other tool, mediates the learning
process. In themselves, they don’t directly
communicate the mathematical concepts.
Novelty of GeoGebra, like other mathematical tools,
may be exciting and fascinating at first. However,
didactical use requires a reflection on the curriculum
content, objectives and trends in education .

GeoGebra as a Pedagogical Tool
Presentation Tool (Multiple representation)
Graphical/Geometric Representation
Algebraic/ Functional Representation
Dynamic Visualizations
Making Connections
Modeling Tool
Dynamic Constructions
Experiments and Discovery learning
Authoring Tool
Exporting Images
Creation, use and sharing of materials with an on-line
community (exporting web worksheets)
Research on teaching and learning using GeoGebra

Activity 2: GeoGebra and School Curriculum
1 Use GeoGebra to design activities that may be used
to address any of the previous curriculum objectives
2 Contextual Application
Identify areas/topics in your local curriculum, where
GeoGebra may be used as a pedagogical tool
What would be the advantages of using GeoGebra
rather than the existing media and or teaching
methods in the identiﬁed content areas?
3 Outline steps, tools and objects that you will need in
order to address the identiﬁed local curriculum
content, possibly indicating a time-frame for the
activity.

Remarks
Remarks: Curriculum
Higher order thinking: The previous activities are all
linked and indicate mathematical connectedness.
Solving some of them require analysis, synthesis and
evaluation – elements of HOTS
New knowledge: GeoGebra affords generality of
concepts and reveal mathematical structures with
efﬁciency, unlike paper and pencil scenarios.
Learning Need: GeoGebra has the potential to create
learning need, by stimulating situations in which
current knowledge is inadequate in solving a
problem. ⇒ discovery of mathematics, its processes
or versatility of applications in real life

Remarks
Remarks: Educational Trends
Evidence: Use of information and communication
technologies in education requires evidence on their
efﬁcacy to overcome the threshold of mistrust by
practitioners.
Collaboration: The widespread trend of collaboration
in educational research, and in design of tools and
courseware need to be reﬂected in school education
by enhancing collaborative and cooperative learning.
Assessment reform: Assessment of learning with and
using ICT needs to be an immediate agenda of
educational innovation in most countries

Feedback
Feedback
Please give us some feedback by
completing the given questionnaire. Kindly share your
experiences and thoughts on use of GeoGebra as a
Dynamic Mathematics Software with others.
Thanks

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