Research Article
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Year 2022, Volume: 9 Issue: 5, 183 - 203, 01.09.2022
https://doi.org/10.17275/per.22.110.9.5

Abstract

References

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual knowledge and procedural knowledge. In A. J. Baroody & A. Dowker. The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise (pp.1-33). Mahwah, NJ: Erlbaum.
  • Baroody, A.J., & Dowker, A. (Eds.) (2003). The development of arithmetic concepts and skills: Recent research and theory. Mahwah: Erlbaum.
  • Blite, A. W., Van der Burg, E., & Klein, A. S. (2001). Students' flexibility in solving two-digit addition and subtraction problems: Instruction effects. Journal of Educational Psychology, 93, 627-638.
  • Cai, J. (2003). Singaporean students’ mathematical thinking ın problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34 (5). 719-737.
  • Cangelosi, J.S. (1996). Teaching mathematics in secondary and middle school: An interactive approach (2nd ed.). Englewood Cliffs, NJ: Merrill/Prentice Hall.
  • Carlson, M. P., & Bloom, I. (2005). The cycle nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45–75.
  • de Bock, D., Verschaffel, L., and Janssens, D. (1998). The predominance of the linear model in secondary school students' solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathetmatics, 35, 65–83.
  • Demetriou, A. (2004). Mind intelligence and development: A cognitive, differential, and developmental theory of intelligence. In A. Dementriou & A. Raftopoulos (Eds.), Developmental change: Theories, models and measurement (pp. 21-73). Cambridge, UK: Cambridge University Press.
  • De Villiers, M. D. (2003). Rethinking Proof: with the geometer’s sketchpad. Emeryville, CA: Key Curriculum Press.
  • Elchuck, L. M. (1992). The effects of software type, mathematics achievement, spatial visualization, locus of control, independent time of ınvestigation, and van Hiele level on geometric conjecturing ability. Unpublished doctoral disssertation. Pennsylvia State University, USA.
  • Elia, I., Heuvel–Panhuizen, M. V., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605-618.
  • Engstro¨m, L. (2004). Examples from teachers’ strategies using a dynamic geometry program in upper secondary school. Paper presented at ICME-10.
  • Fey, J. T., Hollenbeck, R. M., & Wray, J. A. (2010). Technology and the mathematics curriculum. In B. J. Reys, R. E. Reys & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 41–49). Reston, VA: National Council of Teachers of Mathematics.
  • Gawlick, T. (2004). Towards a theory visualization by dynamic geometry software. Paper presented at the 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark, 4-11 July 2004.
  • Gutierrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22, 237-25l.
  • Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535–540.
  • Hölzl, R. (2001). Using dynamic geometry software to add constrast to geometric situations-A case study. International Journal of Computers for Mathematical Learning, 6(1), 63-86.
  • Idris, N. (1999). Linguistic aspects of mathematical education: How precise do teachers need to be? In M. A. Clemet (Ed), Cultural and language aspects of Science, Mathematics, and technical education (pp. 280 – 289). Brunei: Universiti Brunei Darussalam.
  • Idris, N. (2009). The impact of using Geometers’ Sketchpad on Malaysian students’ achievement and van Hiele geometric thinking. Journal of Mathematics Education, 2(2), 94-107.
  • Jonassen, D.H. (2000). Integrating problem solving into instructional design. In R.A. Reiser & J. Dempsey (Eds.), Trends and issues in instructional design and technology. Upper Saddle River, NJ: Prentice-Hall.
  • Leikin, R. & Levav-Waynberg, A. (2009). Development of teachers’ conceptions through learning and teaching: meaning and potential of multiple–solution tasks. Canadian Journal of Science, Mathematics and Technology Education, 9(4), 203–223.
  • Meng, C. C. & Idris, N. (2012). Enhancing students’ geometric thinking and achievement in solid geometry. Journal of Mathematics Education, 5(1), 15-33.
  • Muir, T., & Beswick, K. (2005). Where did I go wrong? Students’ success at various stages of the problem-solving process. Accessed August 13, 2008.
  • National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press
  • Olive, J., & Makar, K., with, Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer R. (2010). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology – Rethinking the terrain. The 17th ICMI Study (pp. 133–177). New York: Springer.
  • Rittle-Johnson, B. & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561–574.
  • Rittle-Johnson, B., Star, J. R., & Durkin, K. (2012). Developing procedural flexibility: are novices prepared to learn from comparing procedures? British Journal of Educational Psychology, 82 (3), 436–455.
  • Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A Study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51, 297–317.
  • Scher, D. (2000). Lifting the curtain: the evolution of the geometer’s sketchpad. The Mathematics Educator, 10(2), 42-48.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411
  • Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18, 565–579
  • Steele, D. & Widman, T. (1997). Practitioner's research: A study in changing preservice teacher's conceptions about mathematics and mathematics teaching and learning. School Science and Mathematics, 97, 184-191.
  • Strasser, R. (2002). Research on dynamic geometry software (DGS) — An introduction. ZDM, 34(3), 65-65.
  • Sullivan, P., Zevenbergen, R., & Mousley, J. (2006). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. International Journal for Science and Mathematics Teaching, 4, 117–143.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry: Final report of the cognitive development and achievement in secondary school geometry project. Chicago: University of Chicago Press.
  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Greenwich, CT: Information Age Publishing.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & van Dooren, W. (2007). Developing adaptive expertise: A feasible and valuable goal for (elementary) mathematics education? Ciencias Psicologicas, 1, 27–35.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335–359.
  • Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 57– 77). New York: Macmillan.
  • Zaslavsky, O., & Sullivan, P. (2011). Constructing knowledge for teaching secondary mathematics. London, United Kingdom: Springer.

Preservice Middle School Mathematics Teachers’ Development of Flexibility and Strategy Use by Geometric Thinking in Dynamic Geometry Environments

Year 2022, Volume: 9 Issue: 5, 183 - 203, 01.09.2022
https://doi.org/10.17275/per.22.110.9.5

Abstract

The current study, aimed to examine the development of flexibility and strategy use through instructional sequence encouraging the preservice middle school mathematics teachers’ geometric thinking and problem-solving performance on dynamic geometry environment. Mixed-method research design was used in the study. The study was conducted with 46 preservice middle school mathematics teachers selected by criterion sampling strategy. The data were collected through the tests including open-ended and multiple-choice questions. In the quantitative part of the study, it was attempted to identify whether the tasks affect problem solving skills and geometric thinking. The said individuals participated in six-week instructional sequence designed by the tasks of geometric constructions performed by GeoGebra. For the qualitative part, document analysis technique was used in order to illustrate the ways of this effect in detail and illustrate the development of flexibility and strategy use. It was observed that tasks by DGE improved the preservice middle school mathematics teachers’ scores of problem-solving and geometric thinking. Also, they solved the problems by representing the properties of higher thinking levels than the levels they had before participating in the instructional sequence enacted by GeoGebra. It is believed that this could encourage the improvement of their flexibility and strategy use.

References

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual knowledge and procedural knowledge. In A. J. Baroody & A. Dowker. The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise (pp.1-33). Mahwah, NJ: Erlbaum.
  • Baroody, A.J., & Dowker, A. (Eds.) (2003). The development of arithmetic concepts and skills: Recent research and theory. Mahwah: Erlbaum.
  • Blite, A. W., Van der Burg, E., & Klein, A. S. (2001). Students' flexibility in solving two-digit addition and subtraction problems: Instruction effects. Journal of Educational Psychology, 93, 627-638.
  • Cai, J. (2003). Singaporean students’ mathematical thinking ın problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34 (5). 719-737.
  • Cangelosi, J.S. (1996). Teaching mathematics in secondary and middle school: An interactive approach (2nd ed.). Englewood Cliffs, NJ: Merrill/Prentice Hall.
  • Carlson, M. P., & Bloom, I. (2005). The cycle nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45–75.
  • de Bock, D., Verschaffel, L., and Janssens, D. (1998). The predominance of the linear model in secondary school students' solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathetmatics, 35, 65–83.
  • Demetriou, A. (2004). Mind intelligence and development: A cognitive, differential, and developmental theory of intelligence. In A. Dementriou & A. Raftopoulos (Eds.), Developmental change: Theories, models and measurement (pp. 21-73). Cambridge, UK: Cambridge University Press.
  • De Villiers, M. D. (2003). Rethinking Proof: with the geometer’s sketchpad. Emeryville, CA: Key Curriculum Press.
  • Elchuck, L. M. (1992). The effects of software type, mathematics achievement, spatial visualization, locus of control, independent time of ınvestigation, and van Hiele level on geometric conjecturing ability. Unpublished doctoral disssertation. Pennsylvia State University, USA.
  • Elia, I., Heuvel–Panhuizen, M. V., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605-618.
  • Engstro¨m, L. (2004). Examples from teachers’ strategies using a dynamic geometry program in upper secondary school. Paper presented at ICME-10.
  • Fey, J. T., Hollenbeck, R. M., & Wray, J. A. (2010). Technology and the mathematics curriculum. In B. J. Reys, R. E. Reys & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 41–49). Reston, VA: National Council of Teachers of Mathematics.
  • Gawlick, T. (2004). Towards a theory visualization by dynamic geometry software. Paper presented at the 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark, 4-11 July 2004.
  • Gutierrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22, 237-25l.
  • Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535–540.
  • Hölzl, R. (2001). Using dynamic geometry software to add constrast to geometric situations-A case study. International Journal of Computers for Mathematical Learning, 6(1), 63-86.
  • Idris, N. (1999). Linguistic aspects of mathematical education: How precise do teachers need to be? In M. A. Clemet (Ed), Cultural and language aspects of Science, Mathematics, and technical education (pp. 280 – 289). Brunei: Universiti Brunei Darussalam.
  • Idris, N. (2009). The impact of using Geometers’ Sketchpad on Malaysian students’ achievement and van Hiele geometric thinking. Journal of Mathematics Education, 2(2), 94-107.
  • Jonassen, D.H. (2000). Integrating problem solving into instructional design. In R.A. Reiser & J. Dempsey (Eds.), Trends and issues in instructional design and technology. Upper Saddle River, NJ: Prentice-Hall.
  • Leikin, R. & Levav-Waynberg, A. (2009). Development of teachers’ conceptions through learning and teaching: meaning and potential of multiple–solution tasks. Canadian Journal of Science, Mathematics and Technology Education, 9(4), 203–223.
  • Meng, C. C. & Idris, N. (2012). Enhancing students’ geometric thinking and achievement in solid geometry. Journal of Mathematics Education, 5(1), 15-33.
  • Muir, T., & Beswick, K. (2005). Where did I go wrong? Students’ success at various stages of the problem-solving process. Accessed August 13, 2008.
  • National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press
  • Olive, J., & Makar, K., with, Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer R. (2010). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology – Rethinking the terrain. The 17th ICMI Study (pp. 133–177). New York: Springer.
  • Rittle-Johnson, B. & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561–574.
  • Rittle-Johnson, B., Star, J. R., & Durkin, K. (2012). Developing procedural flexibility: are novices prepared to learn from comparing procedures? British Journal of Educational Psychology, 82 (3), 436–455.
  • Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A Study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51, 297–317.
  • Scher, D. (2000). Lifting the curtain: the evolution of the geometer’s sketchpad. The Mathematics Educator, 10(2), 42-48.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411
  • Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18, 565–579
  • Steele, D. & Widman, T. (1997). Practitioner's research: A study in changing preservice teacher's conceptions about mathematics and mathematics teaching and learning. School Science and Mathematics, 97, 184-191.
  • Strasser, R. (2002). Research on dynamic geometry software (DGS) — An introduction. ZDM, 34(3), 65-65.
  • Sullivan, P., Zevenbergen, R., & Mousley, J. (2006). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. International Journal for Science and Mathematics Teaching, 4, 117–143.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry: Final report of the cognitive development and achievement in secondary school geometry project. Chicago: University of Chicago Press.
  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Greenwich, CT: Information Age Publishing.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & van Dooren, W. (2007). Developing adaptive expertise: A feasible and valuable goal for (elementary) mathematics education? Ciencias Psicologicas, 1, 27–35.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335–359.
  • Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 57– 77). New York: Macmillan.
  • Zaslavsky, O., & Sullivan, P. (2011). Constructing knowledge for teaching secondary mathematics. London, United Kingdom: Springer.
There are 41 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Tuğba Uygun 0000-0001-5431-4011

Publication Date September 1, 2022
Acceptance Date May 29, 2022
Published in Issue Year 2022 Volume: 9 Issue: 5

Cite

APA Uygun, T. (2022). Preservice Middle School Mathematics Teachers’ Development of Flexibility and Strategy Use by Geometric Thinking in Dynamic Geometry Environments. Participatory Educational Research, 9(5), 183-203. https://doi.org/10.17275/per.22.110.9.5