Post on 23-Dec-2015
Introducing Dynamic Mathematics Software
to Teachers: The Case of GeoGebra
Judith HohenwarterMarkus Hohenwarter
Florida Center for Research in Science, Technology, Engineering, and MathematicsFlorida 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
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Introduction
Integrating technology into teaching and learning mathematics 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 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]
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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]
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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]
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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]
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Technology Used in Mathematics Education
Virtual manipulatives Small self-contained
learning environments Focus on specific math topics Also called applets, mathlets,
or dynamic worksheets
General software tools Open and flexible software Examples
dynamic geometry software (e.g. Cabri Geometry) computer algebra systems (e.g. Derive) spreadsheets (e.g. MS Excel) dynamic mathematics software (e.g. GeoGebra)
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Technology Used in Mathematics Education
Virtual manipulatives 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? 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]
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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
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’
[Mously et al., 2003]
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Technology Used in Mathematics Education
Factors for Successful Technology Use
Knowledge about basic software use Minimize difficulties and impediments during the introduction
process Foster selective use of technology
Knowledge about technology integration 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]
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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]
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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
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Implementation of the Study
Context & Environment
NSF MSP project between Florida Atlantic University and the Broward County School District
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:
Guided workshop activities, discussions, home exercises
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Day Name When / Where Content1 Survey I Beginning of WS I Computer literacy1 Workshop I End of WS I Activities and tools
1Home Exercise I At home Exercise and tools
2 Workshop II End of WS II Activities and tools
2Home Exercise II At home Exercise and tools
3 Workshop III End of WS III Activities and tools
3Home Exercise III At home Exercise and tools
4 Workshop IV End of WS IV Activities and tools
4Home Exercise IV At home Exercise and tools
5 Survey IIBeginning of next day GeoGebra features
10 Survey III End of instituteMath content knowledge
Helper Cards Every workshop Problems/difficulties
Implementation of the Study
Evaluation Tools
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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’)
Conclusions Workshop content seemed relevant for teachers Difficulty level seemed appropriate Teachers were motivated / eager to learn more
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Summary of Findings
GeoGebra
GeoGebra was characterized as user friendly / intuitive / enjoyable / helpful / useful / …
Teachers appreciated GeoGebra’s potential for fostering better understanding of ‘difficult’ concepts applications in a wide range of mathematical topics facilitating their role as a teacher
Conclusions Teachers experienced GeoGebra as a useful tool General style of software introduction was
appropriate16
Summary of Findings
GeoGebra
Algebraic input and commandsmore challenging than use of DGS tools
No impact of external variables on difficulty ratingsgender / age / teaching experience / math content knowledge / computer skills / operating system
Use of touchpad vs. external computer mousetouchpad users had more difficulties than mouse users
Conclusions Thorough introduction of keyboard input necessary Workshops / GeoGebra appropriate for all user types Participants should use a mouse when operating GeoGebra
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Summary of Findings
Complexity Analysis of DGS Tools
Participants’ ratings showed different difficulty of DGS tools
Complexity analysis of introduced DGS tools dependence / influence on existing objects number / types of objects involved number / order of actions keyboard input required
Establishment of complexity criteria for DGS tools 2 criteria for ‘easy to use’ tools 2 criteria for ‘middle’ tools 1 criterion for ‘difficult to use’ tools
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Summary of Findings
Classification of all GeoGebra DGS Tools
‘Easy to use’ toolsRequires 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’ toolsRequires 2 points and order of selection / creation is
relevant
Involves objects of different types
‘Difficult to use’ toolsOrder of actions is relevant and keyboard input is required
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Summary of Findings
Complexity Criteria for DGS Tools
Conclusions ‘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
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Implementation of Research Outcomes
Design of New Workshop Materials
Series of 9 workshops that cover about 2 to 3 hours each
Workshop handouts and files for participants Workshop guide and presentations for presenters
New materials cover 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 possible21
Implementation of Research Outcomes
Design of New Workshop Materials
Structure Detailed instructions / tips and tricks Guided activities / practice activities Presentations / discussions ‘Back to school’ activities Best practice examples Challenge activities
Objectives Increase awareness of most common mistakes/difficulties
novices face Prevention of common impediments in future workshops Make introduction process easier for novices
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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
Presenter materials 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? 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? 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 teaching25
Thanks for your attention!
Questions and discussion
Download this presentation http://www.geogebra.org/talks
Contacts Markus@geogebra.org – Developer of GeoGebra, IGI information Judith@geogebra.org – Workshop materials, GeoGebra translations
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.
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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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