Yıl: 2021 Cilt: 17 Sayı: 1 Sayfa Aralığı: 22 - 40 Metin Dili: İngilizce DOI: 10.17860/mersinefd.684571 İndeks Tarihi: 29-07-2022

Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices

Öz:
This study aimed to establish the relationship between pre-service elementary mathematics teachers’ (PEMTs) van Hiele geometric thinking levels and their constructivist-based teaching practices. In order to address the research questions framing this study, data related to the PEMTs’ van Hiele geometry reasoning stages were gathered through the van Hiele Geometry Test (VHGT). In addition, constructivist-based teaching practice was examined by conducting the observation protocol named as Reformed Teaching Observation Protocol (RTOP) to the 108 PEMTs. Moreover, interviews were conducted to 15 Turkish PEMTs in order to obtain detailed information about the research question. The results of the data analysis represented that there was a statistically significant positive correlation between the PEMTs’ constructivist-based teaching practice and their van Hiele geometry reasoning levels. As a conclusion, the PEMTs having high level of van Hiele geometry thinking were likely to enact their teaching practices more appropriately to the constructivist approach.
Anahtar Kelime: geometry teaching preservice treachers van Hiele geometric thinking level constructivist-based teaching

Van Hiele Geometrik Düşünme ve Yapılandırmacı Temelli Öğretim Uygulamaları

Öz:
Bu çalışmanın amacı matematik öğretmen adaylarının van Hiele geometrik düşünme düzeyleri ve öğretim uygulamalarının ne derece yapılandırmacı yaklaşımı temel alarak gerçekleştirebildikleri arasındaki ilişkinin araştırılmasıdır. Bu çalışmayı yönlendiren araştırma problemlerini cevaplamak amacıyla, veriler matematik öğretmen adaylarının van Hiele geometrik düşünme düzeylerini belirlemek için van Hiele Geometri Testi kullanılmıştır. Ayrıca, öğretmen adaylarının yapılandırmacı yaklaşım temel alınarak gerçekleştirilen öğretim uygulaması için de Yenilenen Öğretimi Gözlem Protokolü’nün 108 matematik öğretmen adayına uygulanmasıyla toplanmıştır. Ayrıca, araştırma problemine ilişkin daha detaylı veriye ulaşmak için 15 matematik öğretmen adayıyla görüşme yapılmıştır. Araştırmanın bulguları, matematik öğretmen adaylarının yapılandırmacı yaklaşımı temel alarak gerçekleştirdikleri öğretim uygulamaları ile van Hiele geometrik düşünme düzeyleri arasında pozitif yönde anlamlı bir ilişki olduğunu göstermektedir. Sonuç olarak, van Hiele geometrik düşünme düzeyleri yüksek olan öğretmen adaylarının yapılandırmacı yaklaşımı temel alarak öğretim uygulamalarını daha etkili şekilde gerçekleştirebildikleri görülmüştür.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Atebe, H. U. (2008). Students’ Van Hiele levels of geometric thought and conception in plane geometry: a collective case study of Nigeria and South Africa. Doctoral dissertation. Rhodes University, South Africa.
  • Aubrey, C. (1997). Mathematics teaching in the early years: An investigation of teachers’ subject knowledge. London: Falmer Press.
  • Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241.
  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 14-46.
  • Ball, D.L., Lubienski, S. T. & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In: Rich ardson V (ed .). Handbook of research on teaching.4th Edition. New York: Macmillian.
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 843-908). Charlotte, NC: Information Age.
  • Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268.
  • Betiku, O. F. (1999). Resources for the effective implementation of the 2- and 3- dimensional mathematics topics at the junior and senior secondary school levels in the Federal Capital Territory, Abuja. Nigerian Journal of Curriculum Studies, 6(2), 49–52.
  • Browning, C., Edson, A. J., Kimani, P., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 333-383.
  • Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31-48.
  • Carpenter, T. P., Fennema, E., Peterson, P.L., & Carey, D.A.(1988). Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19, 385-401.
  • Clements, D. H. (1999). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5-11.
  • Clements, D. H. (2003). Teaching and Learning Geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), Research Companion to Principles and Standards for School Mathematics (pp. 151-178). Reston, VA: NCTM.
  • Clements, D., & Battista, M. (1990). The effects of logo on children’s conceptualizations of angle and polygons. Journal for Research in Mathematics Education, 21(5), 356-371.
  • Crowley, M. L. (1987). The Van Hiele model of the development of geometric thought. NCTM: Reston.
  • Duatepe, A., (2000). An investigation on the relationship between van Hiele geometric level of thinking and demographic variables for pre-service elementary school teachers. (Unpublished master’s thesis). Middle East Technical University, Ankara.
  • Duatepe, A. (2004). The effects of drama based instruction on seventh grade students’ geometry achievement, van Hiele geometric thinking levels, attitude toward mathematics and geometry (Unpublished doctoral dissertation). Middle East Technical University, Ankara.
  • Du Plooy, E. (1998). Kurrikulum 2005:’n Uitdaging vir alle wisku nde-op voeders. Die Un ie, 94, 14-15.
  • Ferguson, R. F. (1991). Paying for public education: New evidence on how and why money matters. Harvard Journal on Education, 28, 465-498.
  • French, D. (2004). Teaching and learning geometry. London: Continuum.
  • Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462.
  • Fuys, D., Geddes, D., & Tischler, R. (1988). Journal of research in mathematics education monograph 3: The van Hiele model of thinking in geometry among adolescents. Reston: National Council of Teachers of Mathematics.
  • Geddes, D., & Fortunato, I. (1993). Geometry: Research and classroom activities. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 199-225). New York: Macmillan Publishing Company.
  • Graham, K. J., & Fennell, F. (2001). Principles and standards for school mathematics and teacher education: Preparing and empowering teachers. School Science and Mathematics, 101, 319-327.
  • 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(3), 237-251.
  • Gul-Toker, Z. (2008). The effect of using dynamic geometry software while teaching by guided discovery on students’ geometric thinking levels and achievement (Unpublished master’s thesis). Middle East Technical University, Ankara.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
  • Hoffer, A. (1988). Geometry and visual thinking. In T. R. Post (Ed.), Teaching mathematics in grades K-8: Research based methods (pp. 233-261). Newton, MA: Allyn & Bacon.
  • Kanes, C., & Nisbet, S. (1996). Mathematics-teachers’ knowledge bases: Implications for teacher education. Asia-Pacific journal of teacher education, 24(1), 5-9.
  • Kennedy, M. M. (1998). Educational reform and subject matter knowledge. Journal of research in science teaching, 35, 249-263.
  • Kirby, S. N. (2005). Developing a strategic research and development program in mathematics education. RAND Research Brief, 1–3. Retrieved fromhttp://www.rand.org/content/ dam/rand/pubs/research_briefs/2005/RB8023.pdf.
  • Köse, N., Tanışlı, D., Erdoğan, E. Ö. ve Ada, T. Y. (2012). İlköğretim matematik öğretmen adaylarinin teknoloji destekli geometri dersindeki geometrik oluşum edinimleri. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 8(3), 102-121.
  • Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179-192). Reston, VA: National Council of Teachers of Mathematics.
  • Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology, 77, 247-271.
  • Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
  • MacIssac, D., & Falconer, K. (2002). Reforming physics instruction via RTOP. The Physics Teacher, 4, 479-485.
  • Mansi, K.E. (2003). Reasoning and geometric proof in mathematics education a review of the literature (Unpublished master’s thesis). North Carolina State University, United States of America.
  • Marshall, C. & Rossman, G. B. (1999). Designing qualitative research (3rd Ed.). Thousand Oaks: Sage Publications.
  • Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate pre-service teachers. Journal for Research in Mathematics Education, 14(1), 58- 69.
  • McGlone, C. W. (2009). A case study of pre-service teachers’ experiences in a reform geometry course (Unpublished doctoral dissertation). University of North Carolina, United States of America.
  • Mitchelmore, M. C. (1997). Children’s informal knowledge of physical angle situations. Cognition and Instruction, 7(1) 1-19.
  • Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction and generalization. Educational Studies in Mathematics, 41(3), 209-238.
  • Moody, A., (1997). Discreteness of the van Hiele levels of student insight into geometry. Dissertation Abstracts Index, 57(08) 3451A.
  • Moran, G. J. W., (1993). Identifying the van Hiele levels of geometric thinking is seventh-grade students through the use of journal writing. Dissertation Abstracts Index, 54(2) 464A.
  • Muijs, D., & Reynolds, D. (2002). Teachers’ beliefs and behaviours: What really matters? Journal of classroom interaction, 37, 3-15.
  • NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
  • Napitupulu, B. (2001). An exploration of students’ understanding and van Hiele levels of thinking on geometric constructions (Unpublished master’s thesis). Simon Fraser University, Canada.
  • National Research Council, (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, & B. Findell (eds). Mathematics learning study committee, Center for education, division of behavioral and social sciences and education. Washington, DC: National Academy Press.
  • Pandiscio, E. A., & Knight, K. C. (2011). An investigation into the van Hiele levels understanding geometry of pre-service mathematics teachers. Journal of Research in Education, 21(1), 45-53.
  • Reinke, K. S. (1997). Area and perimeter: Pre-service teachers’ confusion. School science & mathematics, 97(2), 75-77.
  • Sawada, D., Piburn, M., Turley, J., Falconer, K., Benford, R., Bloom, I., et al. (2000). Reformed teaching observation protocol (RTOP). Tempe: Arizona State University.
  • Senk, S. L. (1985). How Well do the Students Write Geometry Proofs?. Mathematics Teacher, 78(6), 448-456.
  • Senk, S. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20, 309-321.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review 57(1), 1-22.
  • Spear, W. R. (1993). Ideas. Arithmetic teacher, 40, 393-404.
  • Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16, 245-268.
  • Stipek, D. (1998). Motivation to learn: From theory to Practice (3rd ed.). Needham Heights, MA: Allyn and Bacon.
  • Strom, D., Kemeny, V., Lehrer, R., & Forman, E. A. (2001). Visualizing the emergent structure of children’s mathematical argument. Cognitive Science, 25, 733-773.
  • Swafford, J. O., Jones, G. A., & Thornton, C. A. (1997). Increased knowledge in geometry and instructional practice. Journal for Research in Mathematics Education, 28(4), 467-483.
  • Topcu, M. S. (2011). Turkish elementary student teachers’ epistemological beliefs and moral reasoning. European Journal of Teacher Education, 34(1), 99-125.
  • Ubuz, B., & Ustun, I. (2003). Figural and conceptual aspects in identifying polygons. Proceedings of the 2003 Joint Meeting of PME and PMENA., Honolulu, HI, 1, 328.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry: Cognitive development and achievement in secondary school geometry project. Chicago: University of Chicago Press.
  • Usiskin, Z. (1987). Resolving the Continuing Dilemmas in School Geometry. In M. M. Lindquist, & A. P. Shulte (Eds). Learning and Teaching Geometry, K-12. Reston, VA: NCTM
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Longman: New York.
  • Van der Sandt, S. (2007). Pre-service geometry education in South Africa: A typical case? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-9.
  • Van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education, 22(1), 199-205.
  • Van Hiele, P. M. (1959). Development and learning process: a study of some aspects of Piaget’s psychology in relation with the didactics of mathematics. In J. B. Walters (ed.) Acta paedagogica ultrajectina. University of Utrecht: Groningen.
  • Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando: Academic Press.
  • Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310-317.
  • Van Hiele-Geldof, D. (1984). The didactics of geometry in the lowest class of secondary school. In D. Fuys, D. Geddes, & R. Tisch (Eds.) English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele. Brooklyn College: Brooklyn.
  • Von Minden, A. M., Wallis, R.T., & Nardie, A.H. (1998). Charting the links between mathematics content and pedagogy concepts: Cartographies of cognition. Journal of Experimental Education, 66(3), 3-9.
  • YÖK. (2007, 17 Mayıs). Eğitim ve öğretim. http:∕ ∕www.yok.gov.tr∕ egitim∕ ogretmen∕ programlar_icerikler. htm. adresinden edinilmiştir.
APA uygun t, Güner P (2021). Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. , 22 - 40. 10.17860/mersinefd.684571
Chicago uygun tuğba,Güner Pınar Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. (2021): 22 - 40. 10.17860/mersinefd.684571
MLA uygun tuğba,Güner Pınar Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. , 2021, ss.22 - 40. 10.17860/mersinefd.684571
AMA uygun t,Güner P Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. . 2021; 22 - 40. 10.17860/mersinefd.684571
Vancouver uygun t,Güner P Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. . 2021; 22 - 40. 10.17860/mersinefd.684571
IEEE uygun t,Güner P "Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices." , ss.22 - 40, 2021. 10.17860/mersinefd.684571
ISNAD uygun, tuğba - Güner, Pınar. "Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices". (2021), 22-40. https://doi.org/10.17860/mersinefd.684571
APA uygun t, Güner P (2021). Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 17(1), 22 - 40. 10.17860/mersinefd.684571
Chicago uygun tuğba,Güner Pınar Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi 17, no.1 (2021): 22 - 40. 10.17860/mersinefd.684571
MLA uygun tuğba,Güner Pınar Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi, vol.17, no.1, 2021, ss.22 - 40. 10.17860/mersinefd.684571
AMA uygun t,Güner P Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi. 2021; 17(1): 22 - 40. 10.17860/mersinefd.684571
Vancouver uygun t,Güner P Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi. 2021; 17(1): 22 - 40. 10.17860/mersinefd.684571
IEEE uygun t,Güner P "Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices." Mersin Üniversitesi Eğitim Fakültesi Dergisi, 17, ss.22 - 40, 2021. 10.17860/mersinefd.684571
ISNAD uygun, tuğba - Güner, Pınar. "Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices". Mersin Üniversitesi Eğitim Fakültesi Dergisi 17/1 (2021), 22-40. https://doi.org/10.17860/mersinefd.684571