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

Yıl 2021, Cilt: 17 Sayı: 1, 22 - 40, 15.04.2021
https://doi.org/10.17860/mersinefd.684571

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.

Kaynakça

  • 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.
  • 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.
  • 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., & 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.
  • 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.
  • 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 preservice elementary school teachers. Master Thesis, Middle East Technical University, Ankara, Turkey.
  • 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. Doctoral Thesis, Middle East Technical University, Ankara.
  • 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.
  • 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 Educatıon, 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 Thesis, Middle East Technical University, Ankara, Turkey.
  • 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.
  • Köse, N., Tanışlı, D., Erdoğan, E. Ö, & Ada, T. Y. (2012). İlköğretim matematik öğretmen adaylarinin teknoloji destekli geometri dersindeki geometrik oluşum edinimleri. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 8(3), 102-121.
  • 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.
  • 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. Master Thesis, North Carolina State University, USA.
  • 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 preservice teachers. Journal for Research in Mathematics Education, 14(1), 58- 69.
  • McGlone, C. W. (2009). A case study of preservice teachers’ experiences in a reform geometry course. Doctoral Thesis, 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 behaviour s: 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. (Simon Fraser University Unpublished Master Dissertation). Canada.
  • National Research Council, (2001). Adding it up: Helping children learn mathematics. Kilpatrick J, Swafford J & Finde ll B (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 preservice mathematics teachers. Journal of Research in Education, 21(1), 45-53.
  • Prescott, A., Mitchelmore, M., & White, P. (2002). Students’ difficulties in abstracting angle concepts from physical activities with concrete material. In the Proceedings of the Annual Conference of the Mathematics Education Research Group of Australia Incorporated Eric Digest ED 472950).
  • Reinke, K. S. (1997). Area and perimeter: Preservice teachers’ confusion. School science & mathematics, 97:75.
  • 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.
  • Spear, W. R. (1993). Ideas. Arithmetic teacher, 40, 393-404.
  • Stipek, D. (1998). Motivation to learn: From theory to Practice (3rd ed.). Needham Heights, MA: Allyn and Bacon.
  • 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. In the Proceedings of the 2003 Joint Meeting of PME and PMENA.1.p.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. Lindquist, M. M. and Shulte, A. P. (Eds). Learning and Teaching Geometry, K-12. 1987. Yearbook. Reston, VA: NCTM
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Longman: New York.
  • Van der Sandt, S. (2007). Preservice 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. Acta paedagogica ultrajectina, 1-31.
  • 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 English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, edited by David F., Dorothy G., and Rosamond T. Brooklyn College, Eric Digest. ED 287 697.
  • 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.
  • YOK. (2007). Eğitim ve öğretim. Retrieved May 17, 2007, Web: http:∕ ∕www.yok.gov.tr∕ egitim∕ ogretmen∕ programlar_icerikler.htm.

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

Yıl 2021, Cilt: 17 Sayı: 1, 22 - 40, 15.04.2021
https://doi.org/10.17860/mersinefd.684571

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.

Kaynakça

  • 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.
  • 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.
  • 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., & 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.
  • 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.
  • 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 preservice elementary school teachers. Master Thesis, Middle East Technical University, Ankara, Turkey.
  • 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. Doctoral Thesis, Middle East Technical University, Ankara.
  • 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.
  • 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 Educatıon, 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 Thesis, Middle East Technical University, Ankara, Turkey.
  • 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.
  • Köse, N., Tanışlı, D., Erdoğan, E. Ö, & Ada, T. Y. (2012). İlköğretim matematik öğretmen adaylarinin teknoloji destekli geometri dersindeki geometrik oluşum edinimleri. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 8(3), 102-121.
  • 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.
  • 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. Master Thesis, North Carolina State University, USA.
  • 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 preservice teachers. Journal for Research in Mathematics Education, 14(1), 58- 69.
  • McGlone, C. W. (2009). A case study of preservice teachers’ experiences in a reform geometry course. Doctoral Thesis, 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 behaviour s: 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. (Simon Fraser University Unpublished Master Dissertation). Canada.
  • National Research Council, (2001). Adding it up: Helping children learn mathematics. Kilpatrick J, Swafford J & Finde ll B (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 preservice mathematics teachers. Journal of Research in Education, 21(1), 45-53.
  • Prescott, A., Mitchelmore, M., & White, P. (2002). Students’ difficulties in abstracting angle concepts from physical activities with concrete material. In the Proceedings of the Annual Conference of the Mathematics Education Research Group of Australia Incorporated Eric Digest ED 472950).
  • Reinke, K. S. (1997). Area and perimeter: Preservice teachers’ confusion. School science & mathematics, 97:75.
  • 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.
  • Spear, W. R. (1993). Ideas. Arithmetic teacher, 40, 393-404.
  • Stipek, D. (1998). Motivation to learn: From theory to Practice (3rd ed.). Needham Heights, MA: Allyn and Bacon.
  • 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. In the Proceedings of the 2003 Joint Meeting of PME and PMENA.1.p.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. Lindquist, M. M. and Shulte, A. P. (Eds). Learning and Teaching Geometry, K-12. 1987. Yearbook. Reston, VA: NCTM
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Longman: New York.
  • Van der Sandt, S. (2007). Preservice 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. Acta paedagogica ultrajectina, 1-31.
  • 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 English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, edited by David F., Dorothy G., and Rosamond T. Brooklyn College, Eric Digest. ED 287 697.
  • 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.
  • YOK. (2007). Eğitim ve öğretim. Retrieved May 17, 2007, Web: http:∕ ∕www.yok.gov.tr∕ egitim∕ ogretmen∕ programlar_icerikler.htm.
Toplam 58 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Makaleler
Yazarlar

Tuğba Uygun 0000-0001-5431-4011

Pınar Güner 0000-0003-1165-0925

Yayımlanma Tarihi 15 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 17 Sayı: 1

Kaynak Göster

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. https://doi.org/10.17860/mersinefd.684571

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