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

2

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]

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]

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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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