Introducing
Dynamic Mathematics Software
to Teachers:
The Case of GeoGebra
Judith Hohenwarter
Markus Hohenwarter
Florida Center for Research in Science,
Technology, Engineering, and Mathematics
Florida State University
Overview
1.
Teacher Professional Development &
Technology Use in Mathematics Education
2.
Description of Research Study
3.
Implementation of Research Outcomes &
Professional Development with GeoGebra
2
Introduction
Integrating technology into teaching and learning mathematics
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Process proved to be rather slow
Many teachers are willing to try out new technology but
are often hindered by initial difficulties and impediments
Common impediments that prevent effective technology
integration into everyday teaching

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lack of access to new technology
lack of basic skills using the technology
lack of knowledge about effective integration of new tools
[Cuban et al., 2001; Lawless and Pellegrino, 2007; Mously et al., 2003;
Niederhauser and Stoddart, 1994; Swain and Pearson, 2002]
3
Introduction
How can we help mathematics teachers to overcome
these difficulties and impediments?
Research shows that professional development plays an
important role to overcome these burdens for
teachers who want to enhance their students’
learning of mathematics by using technology.
[Lawless and Pellegrino, 2007; Mously et al., 2003;
The International Commission on Mathematical Instruction, 2004]
4
Technology Professional Development
Traditional Design
Deficiencies of technology professional development
 Quality is inadequate in general
 Often not appropriate for preparing teachers sufficiently
for a successful technology integration into their
classrooms
[Ansell & Park, 2003; Edwards, 1997]
Doesn’t meet the pedagogical needs of teachers
Content is often disconnected from everyday classroom
practice and teaching methods


[Gross et al., 2001; Moursund, 1989]
5
Technology Professional Development
Research
Hardly any publications deal with potential difficulties that
could occur during the introduction and integration
process of technology into everyday teaching and learning
of mathematics.
[Lagrange et al., 2003]
Research indicates that it is important to know in which
way a software package can be introduced to novices
most effectively.
[Mously et al., 2003]
6
Technology Used in Mathematics Education
Virtual manipulatives

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Small self-contained
learning environments
Focus on specific math topics
Also called applets, mathlets,
or dynamic worksheets
General software tools
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Open and flexible software
Examples
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dynamic geometry software (e.g. Cabri Geometry)
computer algebra systems (e.g. Derive)
spreadsheets (e.g. MS Excel)
dynamic mathematics software (e.g. GeoGebra)
Technology Used in Mathematics Education
Virtual manipulatives

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Convenient for teachers
Available online (often for free)
Don’t require special technology skills to be used
Foster student activity and discovery learning
Why should teachers bother learning how to use
general software tools?

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Virtual manipulatives have obvious limitations of mathematical
experiments to a certain range of activities and topics
General software tools allow visualizing and exploring
mathematical concepts in a more flexible way
[Barzel, 2007]
8
Technology Used in Mathematics Education
Factors for Successful Technology Use
Increased mathematics content knowledge
More complex student questions and mathematical enquiries
More advanced mathematical content can be covered in mathematics
classes

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Increased basic computer literacy
Elevate teachers’ attitude, confidence, and comfort level concerning
computers
See computers and educational software ‘as learning resources and not as
ends in themselves’

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[Mously et al., 2003]
9
Technology Used in Mathematics Education
Factors for Successful Technology Use
Knowledge about basic software use

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Minimize difficulties and impediments during the introduction process
Foster selective use of technology
Knowledge about technology integration
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Integration of new teaching methods into ‘traditional’ classroom settings
Effective but not exclusive use of technology
Design of new learning activities to tap full potential of new technology
Maximize students’ benefit from new technology
[Mously et al., 2003]
10
Research Question
Is it possible to identify common impediments that occur
during the introduction process of dynamic mathematics
software as well as to detect those especially challenging tools
and features of the software GeoGebra in order to
(a) provide a basis for the implementation of more effective
ways of introducing dynamic mathematics software
to secondary school mathematics teachers, and
(b) to design corresponding instructional materials for
technology professional development?
[Preiner, 2008]
11
Purpose of the study

Identification of common impediments that occur
during the introduction process

Establishment of complexity criteria for DGS tools
to determine their general difficulty level

Design of new workshop materials for a more
successful introduction of GeoGebra
12
Implementation of the Study
Context & Environment

NSF MSP project between
Florida Atlantic University and
the Broward County School District
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44 middle/high school math teachers in 3 groups
Beginning of 2 week summer institute
4 introductory GeoGebra workshops on consecutive days
Structure of workshops:
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Guided workshop activities, discussions, home exercises
13
Implementation of the Study
Evaluation Tools
Day
1
1
1
2
2
3
3
4
4
5
10
14
Name
Survey I
Workshop I
Home Exercise I
Workshop II
Home Exercise II
Workshop III
Home Exercise III
Workshop IV
Home Exercise IV
Survey II
Survey III
Helper Cards
When / Where
Beginning of WS I
End of WS I
At home
End of WS II
At home
End of WS III
At home
End of WS IV
At home
Beginning of next day
End of institute
Every workshop
Content
Computer literacy
Activities and tools
Exercise and tools
Activities and tools
Exercise and tools
Activities and tools
Exercise and tools
Activities and tools
Exercise and tools
GeoGebra features
Math content knowledge
Problems/difficulties
Summary of Findings
Workshops in General

General attitude of participants towards workshops
88% of participants stated that they ‘liked the workshops’

Workshops were rated rather easy
average rating of 1.64
on a scale from 0 (‘very easy’) to 5 (‘very difficult’)
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Conclusions
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15
Workshop content seemed relevant for teachers
Difficulty level seemed appropriate
Teachers were motivated / eager to learn more
Summary of Findings
GeoGebra
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GeoGebra was characterized as
user friendly / intuitive / enjoyable / helpful / useful / …
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Teachers appreciated GeoGebra’s potential for
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fostering better understanding of ‘difficult’ concepts
applications in a wide range of mathematical topics
facilitating their role as a teacher
Conclusions
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16
Teachers experienced GeoGebra as a useful tool
General style of software introduction was appropriate
Summary of Findings
GeoGebra
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Algebraic input and commands
more challenging than use of DGS tools
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No impact of external variables on difficulty ratings
gender / age / teaching experience / math content knowledge /
computer skills / operating system
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Use of touchpad vs. external computer mouse
touchpad users had more difficulties than mouse users
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Conclusions
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Thorough introduction of keyboard input necessary
Workshops / GeoGebra appropriate for all user types
Participants should use a mouse when operating GeoGebra
Summary of Findings
Complexity Analysis of DGS Tools
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Participants’ ratings showed different difficulty of DGS tools
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Complexity analysis of introduced DGS tools
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dependence / influence on existing objects
number / types of objects involved
number / order of actions
keyboard input required
Establishment of complexity criteria for DGS tools
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2 criteria for ‘easy to use’ tools
2 criteria for ‘middle’ tools
1 criterion for ‘difficult to use’ tools
Summary of Findings
Classification of all GeoGebra DGS Tools

‘Easy to use’ tools
Requires 2 existing points which can also be created ‘on the fly’
specifying the position and direction of the line
Directly affects lines and requires just one action

‘Middle’ tools
Requires 2 points and order of selection / creation is relevant
Involves objects of different types
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‘Difficult to use’ tools
Order of actions is relevant and keyboard input is required
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Summary of Findings
Complexity Criteria for DGS Tools
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Conclusions
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‘Easy to use’ and ‘middle’ tools appropriate for beginning of workshops
‘Difficult to use’ tools should be introduced later on
More thorough introduction of ‘difficult to use’ tools necessary
Similarities and differences of certain tools need to be addressed
(e.g. parallel / perpendicular lines; segment / line)
Prevent unnecessary difficulties related to complexity of tools
Complexity criteria also applicable for tools of
dynamic geometry software
Cabri Geometry and Geometer’s Sketchpad
20
Implementation of Research Outcomes
Design of New Workshop Materials
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Series of 9 workshops that cover about 2 to 3 hours each
Workshop handouts and files for participants
Workshop guide and presentations for presenters
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New materials cover
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use of basic tools and features of GeoGebra
ways of integrating GeoGebra into everyday teaching
creation of instructional materials with GeoGebra
use of advanced GeoGebra features (e.g. sequences)
Use for self-dependent introduction possible
21
Implementation of Research Outcomes
Design of New Workshop Materials
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Structure
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Detailed instructions / tips and tricks
Guided activities / practice activities
Presentations / discussions
‘Back to school’ activities
Best practice examples
Challenge activities
Objectives
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Increase awareness of most common mistakes/difficulties novices face
Prevention of common impediments in future workshops
Make introduction process easier for novices
Implementation of Research Outcomes
New Workshop Materials

Basic workshops
cover a total of 10 to15 workshop hours
 WS 1: Introduction, Installation & Drawings vs. Geometric Constructions
 WS 2: Geometric Constructions & Use of Commands
 WS 3: Algebraic Input, Functions & Export of Pictures to the Clipboard
 WS 4: Inserting Pictures into the Graphics Window
 WS 5: Inserting Static and Dynamic Text

Advanced workshops
cover a total of 8 to 12 workshop hours (future extensions planned)
 WS 6: Creating Dynamic Worksheets
 WS 7: Custom Tools & Customizing the Toolbar
 WS 8: Conditional Visibility & Sequences
 WS 9: Spreadsheet View & Basic Statistics Concepts
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Implementation of Research Outcomes
New Workshop Materials
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Presenter materials
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Workshop guide
overview, pace chart, suggested instructional methods
Presentations
ready to use, can be modified by presenter
Workshop files
GeoGebra constructions, dynamic worksheets, and images
Handouts
in doc–format to allow adaptations and modifications
All materials are available online
http://www.geogebra.org/en/wiki/index.php/Workshop_materials
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Conclusion

Remember the common impediments that prevent effective
technology integration into everyday teaching?

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Lack of access to new technology
Lack of basic skills using the technology
Lack of knowledge about effective integration of new tools
How can we tackle these impediments?
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Open-source dynamic mathematics software GeoGebra
Knowledge of how to introduce software more effectively
Offering corresponding workshop materials and best practice examples
Offering effective professional development and support
Coordinating research activities related to effective integration of
GeoGebra into everyday teaching
Download this presentation
http://www.geogebra.org/talks
Contacts
Markus@geogebra.org – Developer of GeoGebra, IGI information
Judith@geogebra.org – Workshop materials, GeoGebra translations
Thanks for your attention!
Questions and discussion
References

Ansell, S. E. and Park, J. (2003). Technology counts 2003: Tracking tech trends. Education Week,
22(35):43 – 44.

Barzel, B. (2007). “New technology? New ways of teaching – No time left for that!”.
International Journal for Technology in Mathematics Education, 14(2):77 — 86.

Cuban, L., Kirkpatrick, H., and Peck, C. (2001). High access and low use of technologies in high
school classrooms: Explaining an apparent paradox. American Educational Research Journal,
38(4):813 — 834.

Edwards,V. B. (1997). Technology counts 1997: Schools and reform in the information age.
Education Week, 27(11).

Gross, D., Truesdale, C., and Bielec, S. (2001). Backs to the wall: Supporting teacher
professional development with technology. Educational Research and Evaluation, 7(2):161 – 183.
27
References

Hohenwarter, M. and Lavicza, Z. (2007). Mathematics teacher development with ICT: Towards
an International GeoGebra Institute. In Küchemann, D., editor, Proceedings of the British Society
for Research into Learning Mathematics, volume 27, pages 49 — 54, University of Northampton, UK.
BSRLM.

Lagrange, J.-B., Artigue, M., Laborde, C., and Trouche, L. (2003). Technology and mathematics
education: A multidimensional study of the evolution of research and innovation. In Bishop, A.
J., Clements, M. A., Keitel, C., Kilpatrick, J., and Leung, F. K. S., editors, Second International
Handbook of Mathematics Education, pages 237 — 269. Kluwer Academic Publishers,
Dordrecht.

Lawless, K. and Pellegrino, J. W. (2007). Professional development in integrating technology into
teaching and learning: Knowns, unknowns, and ways to pursue better questions and answers.
Review of Educational Research, 77(4):575 — 614.

Moursund, D. (1989). Effective inservice for integrating computer-as-tool into the curriculum.
International Society for Technology in Education, Eugene, OR.
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References

Mously, J., Lambdin, D., and Koc, Y. (2003). Mathematics teacher education and technology. In
Bishop, A. J., Clements, M. A., Keitel, C., Kilpatrick, J., and Leung, F. K. S., editors, Second
International Handbook of Mathematics Education, pages 395 — 432. Kluwer Academic
Publishers, Dordrecht.

Niederhauser, D. and Stoddart, T. (1994). Teachers’ perspectives on computer assisted
instruction: Transmission versus construction of knowledge. Paper presented at the annual
meeting of the American Educational Research Association.

Preiner, J. (2008). Introducing Dynamic Mathematics Software to Mathematics Teachers: the
Case of GeoGebra. PhD thesis, 264 pages, University of Salzburg, Austria

Swain, C. and Pearson, T. (2002). Educators and technology standards: Influencing the digital
divide. Journal of Research on Technology in Education, 34(3):326 – 335.

The International Commission on Mathematical Instruction (2004). The fifteenth ICMI study:
The professional education and development of teachers of mathematics. Educational Studies
in Mathematics, 56(2/3):359 – 377.
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