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AN INVESTIGATION INTO EFFECTS OF DYNAMIC GEOMETRY SOFTWARE (DGS) ON STUDENTS’ THINKING PREFERENCES: SOLVING GEOMETRY PROBLEMS WITH AND WITHOUT DGS

Year 2015, Volume: 2 , 215 - 225, 01.09.2015

Abstract

Researchers suggest that students have preferences (visual and
non-visual) when solving mathematics problems. Many times students have
difficulties in solving problems because of one-sided thinking and weakly
associating other representations. Reform efforts support connecting visual
representations with non-visual representations in order to develop deeper
understanding.  This study investigates
how prospective teachers with different preferences for visual, non-visual, and
harmonic thinking solve geometry problems with and without using DGS. The study aims to explore whether
students’ use of DGS when solving geometry problems is related to their
preferences. Suwarsono’s mathematical processing instrument (MPI) was
administered to determine their preferences for visual and non-visual thinking.
Based on MPI instrument’s results and their performances of geometry problems
solved with and without DGS, three students were selected to be
interviewed.  Multiple case studies were
conducted to conduct a deeper analysis. The reason for selecting three students
was to take at least one person from each group based on their thinking preferences
so that different cases can be compared and contrasted. The results reveal that
regardless of students’ preferences preservice teachers preferred to use visual
solutions when they are asked to use DGS. When their solutions of DGS and
paper-and-pencil were compared, students’ solutions with DGS demonstrated more
conceptual understanding of the task than paper-and-pencil.

References

  • Bretscher, N. (2009). Dynamic geometry software: The teacher's role in facilitating instrumental genesis. Research in Mathematics Education, 11(2), 187-188. Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339-352. Coskun, S. (2011). A multiple case study investigating the effects of technology on students‘ visual and nonvisual thinking preferences: comparing paper-pencil and dynamic software based strategies of algebra word problems (Unpublished Doctoral Dissertation). University of Central Florida, Florida, USA. de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68, 179-201. Drijvers, P., & Gravemeijer, K. (2005). Computer algebra as an instrument: Examples of algebraic schemes. In The didactical challenge of symbolic calculators (pp. 163-196). Springer US. Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234. Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: necessity of intrumental orchestrations. Zentralblatt für Didaktik der Mathematik, 34(5), 204-211. Habre, S. (2009). Geometric conjecture in Dynamic Geometry Software environment. Mathematics & Computer Education, 43(2), 151-164. Habre, S. & Grundmeier, T.A. (2011). Prospective Mathematics Teachers' Views on the Role of Technology in Mathematics Education. Issues in the Undergraduate Mathematics Preparation of School Teachers, 3. Hanna, G., & de Villiers, M. (2012). Proof and proving in mathematics education. Springer. Hähkiöniemi, M., & Leppäaho, H. (2012). Prospective Mathematics Teachers' Ways of Guiding High School Students in GeoGebra-Supported Inquiry Tasks. International Journal for Technology in Mathematics Education, 19(2). Harskamp, E., Suhre, C., & Van Streun, A. (2000). The graphics calculator and students’ solution strategies. Mathematics Education Research Journal, 12(1), 37-52. Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256. Healy, L., & Lagrange, J. B. (2010). Introduction to section 3. In Mathematics Education and Technology-Rethinking the Terrain (pp. 287-292). Springer, US. Hegedus, S. J. (2004). Dynamic Representations: A New Perspective on Instrumental Genesis. Working Group 9, Tools and technology in mathematical didactics, 1031. Hollebrands, K. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22(1), 55-72. Hoyles, C., & Lagrange, J. B. (2010). Mathematics education and technology: rethinking the terrain: the 17th ICMI study (Vol. 13). Springerverlag Us. Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations–a case study. International Journal of Computers for Mathematical Learning, 6(1), 63-86. Huntley, M. A., Rasmussen, C. L, Villarubi, R. S., Sangtong, J., & Fey, J. T. (2000). Effects of Standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand. Journal for Research in Mathematics Education, 31(3), 328-361. Iranzo-Domenech, N. (2009). Influence of dynamic geometry software on plane geometry problem solving strategies (Doctoral Dissertation). Universitat Autonoma de Barcelona, Spain. Jones, K. (2000). Providing a foundation for deductive reasoning: students' interpretations when using Dynamic Geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-2), 55-85., Johnston-Wilder, S., & Mason, J. (Eds.). (2005). Developing thinking in geometry. Sage. Koehler, M. J., & Mishra, P. (2005). Teachers learning technology by design. Journal of Computing in Teacher Education, 21(3), 94–102. Kokol-Voljc, V. (2007) Use of mathematical software in pre-service teacher training: The case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 55-60. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press. Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In Second international handbook of mathematics education(pp. 237-269). Springer Netherlands. Leung, A. (2008). Dragging in dynamic geometry environment through the lens of variation, International Journal of Computers for Mathematical Learning, 13, 135–157. Mariotti, M. A. (2002). Influence of technologies advances on students’ math learning. In L. English, M.G. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 695–723). LEA. Merriam, S.B. (1998). Qualitative Research and Case Study Applications in Education. San Fransisco: Jossey-Bass Publishers.
 Pandisco, A. E. (2010). Exploring the link between pre-service teachers‘ conception of proof and the use of dynamic geometry software. School Science and Mathematics, 102(5), 216-221. Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh-grade students. Unpublished doctoral dissertation, Monash University. Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for mathematical learning, 9(3), 281-307. Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software. Journal for Research in Mathematics Education, 37(5), 356-387.
Year 2015, Volume: 2 , 215 - 225, 01.09.2015

Abstract

References

  • Bretscher, N. (2009). Dynamic geometry software: The teacher's role in facilitating instrumental genesis. Research in Mathematics Education, 11(2), 187-188. Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339-352. Coskun, S. (2011). A multiple case study investigating the effects of technology on students‘ visual and nonvisual thinking preferences: comparing paper-pencil and dynamic software based strategies of algebra word problems (Unpublished Doctoral Dissertation). University of Central Florida, Florida, USA. de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68, 179-201. Drijvers, P., & Gravemeijer, K. (2005). Computer algebra as an instrument: Examples of algebraic schemes. In The didactical challenge of symbolic calculators (pp. 163-196). Springer US. Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234. Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: necessity of intrumental orchestrations. Zentralblatt für Didaktik der Mathematik, 34(5), 204-211. Habre, S. (2009). Geometric conjecture in Dynamic Geometry Software environment. Mathematics & Computer Education, 43(2), 151-164. Habre, S. & Grundmeier, T.A. (2011). Prospective Mathematics Teachers' Views on the Role of Technology in Mathematics Education. Issues in the Undergraduate Mathematics Preparation of School Teachers, 3. Hanna, G., & de Villiers, M. (2012). Proof and proving in mathematics education. Springer. Hähkiöniemi, M., & Leppäaho, H. (2012). Prospective Mathematics Teachers' Ways of Guiding High School Students in GeoGebra-Supported Inquiry Tasks. International Journal for Technology in Mathematics Education, 19(2). Harskamp, E., Suhre, C., & Van Streun, A. (2000). The graphics calculator and students’ solution strategies. Mathematics Education Research Journal, 12(1), 37-52. Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256. Healy, L., & Lagrange, J. B. (2010). Introduction to section 3. In Mathematics Education and Technology-Rethinking the Terrain (pp. 287-292). Springer, US. Hegedus, S. J. (2004). Dynamic Representations: A New Perspective on Instrumental Genesis. Working Group 9, Tools and technology in mathematical didactics, 1031. Hollebrands, K. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22(1), 55-72. Hoyles, C., & Lagrange, J. B. (2010). Mathematics education and technology: rethinking the terrain: the 17th ICMI study (Vol. 13). Springerverlag Us. Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations–a case study. International Journal of Computers for Mathematical Learning, 6(1), 63-86. Huntley, M. A., Rasmussen, C. L, Villarubi, R. S., Sangtong, J., & Fey, J. T. (2000). Effects of Standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand. Journal for Research in Mathematics Education, 31(3), 328-361. Iranzo-Domenech, N. (2009). Influence of dynamic geometry software on plane geometry problem solving strategies (Doctoral Dissertation). Universitat Autonoma de Barcelona, Spain. Jones, K. (2000). Providing a foundation for deductive reasoning: students' interpretations when using Dynamic Geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-2), 55-85., Johnston-Wilder, S., & Mason, J. (Eds.). (2005). Developing thinking in geometry. Sage. Koehler, M. J., & Mishra, P. (2005). Teachers learning technology by design. Journal of Computing in Teacher Education, 21(3), 94–102. Kokol-Voljc, V. (2007) Use of mathematical software in pre-service teacher training: The case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 55-60. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press. Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In Second international handbook of mathematics education(pp. 237-269). Springer Netherlands. Leung, A. (2008). Dragging in dynamic geometry environment through the lens of variation, International Journal of Computers for Mathematical Learning, 13, 135–157. Mariotti, M. A. (2002). Influence of technologies advances on students’ math learning. In L. English, M.G. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 695–723). LEA. Merriam, S.B. (1998). Qualitative Research and Case Study Applications in Education. San Fransisco: Jossey-Bass Publishers.
 Pandisco, A. E. (2010). Exploring the link between pre-service teachers‘ conception of proof and the use of dynamic geometry software. School Science and Mathematics, 102(5), 216-221. Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh-grade students. Unpublished doctoral dissertation, Monash University. Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for mathematical learning, 9(3), 281-307. Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software. Journal for Research in Mathematics Education, 37(5), 356-387.
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Journal Section Articles
Authors

Didem Akyüz This is me

Publication Date September 1, 2015
Published in Issue Year 2015 Volume: 2

Cite

APA Akyüz, D. (2015). AN INVESTIGATION INTO EFFECTS OF DYNAMIC GEOMETRY SOFTWARE (DGS) ON STUDENTS’ THINKING PREFERENCES: SOLVING GEOMETRY PROBLEMS WITH AND WITHOUT DGS. The Eurasia Proceedings of Educational and Social Sciences, 2, 215-225.