Introducing Dynamic Mathematics Software to Teachers: The Case of GeoGebra

1. Introducing Dynamic Mathematics Software to Teachers: The Case of GeoGebra Florida Center for Research in Science, Technology, Engineering, and Mathematics Florida State University Judith HohenwarterMarkus Hohenwarter

2. Overview • Teacher Professional Development & Technology Use in Mathematics Education • Description of Research Study • Implementation of Research Outcomes & Professional Development with GeoGebra

3. 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]

4. 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]

5. Technology Professional DevelopmentTraditional 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]

6. Technology Professional DevelopmentResearch 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]

7. 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)

8. 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]

9. 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]

10. 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]

11. 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]

12. 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

13. Implementation of the StudyContext & 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

14. Implementation of the StudyEvaluation Tools

15. Summary of FindingsWorkshops 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

16. Summary of FindingsGeoGebra • 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 appropriate

17. Summary of FindingsGeoGebra • Algebraic input and commands more challenging than use of DGS tools • No impact of external variables on difficulty ratings gender / age / teaching experience / math content knowledge / computer skills / operating system • Use of touchpad vs. external computer mouse touchpad 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

18. Summary of FindingsComplexity 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

19. Summary of FindingsClassification 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 • ‘Difficult to use’ tools Order of actions is relevant and keyboard input is required

20. Summary of FindingsComplexity 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

21. Implementation of Research OutcomesDesign 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 possible

22. Implementation of Research OutcomesDesign 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

23. Implementation of Research OutcomesNew 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

24. Implementation of Research OutcomesNew Workshop Materials • Presenter materials • Workshop guide overview, pace chart, suggested instructional methods • Presentationsready 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

25. 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 teaching

26. 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

27. 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.

28. 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.

29. 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.