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Apr 27, 2021
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Abstract

A look into students’ misconceptions help explain the very low geometric thinking and may assist teachers in correcting errors to aid students in reaching a higher van Hiele geometric thinking level. In this study, students’ geometric thinking was described using the van Hiele levels and misconceptions on triangles. Participants (N=30) were Grade 9 students in the Philippines. More than half of the participants were in the van Hiele’s visualization level. Most students had imprecise use of terminologies. A few had misconceptions on class inclusion, especially when considering isosceles right triangles and obtuse triangles. Very few students correctly recognized the famous Pythagorean Theorem. Implications for more effective geometry teaching are considered.

Keywords

Geometric thinking Misconception Triangles Van Hiele levels

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Author Biographies

Joanne Ramirez Casanova, De La Salle University - Manila

Science Education DepartmentGraduate Student

Minie Rose Caramoan Lapinid, De La Salle University - Manila

Science Education DepartmentChairpersonAssociate Professor

References

  1. Atebe, H. U. (2008). Student's van Hiele levels of geometric thought and conception in plane geometry: a collective case study of Nigeria and South Africa. Doctoral dissertation. Makhanda: Rhodes University.

  2. [Google Scholar]

  3.  

  4. Atebe, H. U., & Schafer, M. (2010). Beyond teaching language: towards terminological primacy in learners' geometric conceptualisation. Pythagoras, 2010(71), 53-64. doi:10.4102/pythagoras.v0i71.7

  5. [Article]     [Google Scholar]

  6.  

  7. Bamberger, H. J., Oberdorf, C., & Schultz-Ferrell, K. (2010). Math misconceptions: PreK-grade 5: From misunderstanding to deep understanding. Portsmouth: Heinemann.

  8. [Google Scholar]

  9.  

  10. Banerjee, R., & Subramaniam, K. (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 80(3), 351-367. doi:10.1007/s10649-011-9353-y

  11. [Article]     [Google Scholar]


  12. Barrett, J. E., & Clements, D. H. (2003). Quantifying path length: Fourth-grade children's developing abstractions for linear measurement. Cognition and Instruction, 21(4), 475-520. doi:10.1207/s1532690xci2104_4

  13. [Article]     [Google Scholar]

  14.  

  15. Brandell, J. L. (1994). Helping students write paragraph proofs in geometry. The Mathematics Teacher, 87(7), 498-502. doi:10.5951/MT.87.7.0498

  16. [Article]     [Google Scholar]

  17.  

  18. Confrey, J. (1990). Chapter 1: A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16(1), 3-56. doi:10.3102/0091732X016001003

  19. [Article]     [Google Scholar]

  20.  

  21. Contreras, R. S. (2009). Investigating the van hiele levels of geometric understanding of high school students on quadrilaterals. Masteral Thesis. Manila: De La Salle University. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/3787

  22. [Article]     [Google Scholar]

  23.  

  24. Crawford, M. L. (2001). Teaching contextually. Research, Rationale, and Techniques for Improving Student Motivation and Achievement in Mathematics and Science. Texas: Cord.

  25. [Article]     [Google Scholar]

  26.  

  27. de Villiers, M. (2010). Algumas reflexões sobre a teoria de van Hiele. Educação matemática pesquisa: Revista do programa de estudos pós-graduados em educação matemática, 12(3), 400-431.

  28. [Google Scholar]

  29.  

  30. Drews, D., Dudgeon, J., Hansen, A., Lawton, F., & Surtees, L. (Eds.). (2005). Children′ s errors in mathematics: Understanding common misconceptions in primary schools. London: SAGE.

  31. [Google Scholar]

  32.  

  33. Edwards, T. G. (2000). Some big ideas of algebra in the middle grades. Mathematics Teaching in the Middle school, 6(1), 26-31. doi:10.5951/MTMS.6.1.0026

  34. [Article]     [Google Scholar]

  35.  

  36. Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’ geometric thinking based on van Hiele’s theory. Infinity Journal, 7(1), 55-60. doi:10.22460/infinity.v7i1.p55-60

  37. [Article]     [Google Scholar]

  38.  

  39. French, D. (2004). Teaching and learning geometry. London: Continuum International Publishing Group.

  40. [Google Scholar]

  41.  

  42. Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education. Monograph, 3, i-196. doi:10.2307/749957

  43. [Article]     [Google Scholar]

  44.  

  45. Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102. doi:10.2307/749100

  46. [Article]     [Google Scholar]

  47.  

  48. Groth, R. E. (2005). Linking theory and practice in teaching geometry. The Mathematics Teacher, 99(1), 27-30. doi:10.5951/MT.99.1.0027

  49. [Article]     [Google Scholar]

  50.  

  51. Gutiérrez, 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. doi:10.2307/749076

  52. [Article]     [Google Scholar]

  53.  

  54. Johnston-Wilder, S., & Mason, J. (2005). Developing thinking in geometry. London: Paul Chapman Publishing.

  55. [Google Scholar]

  56.  

  57. Jones, K. (2003). Issues in the teaching and learning of geometry. In L. Haggarty (Ed.). Aspects of teaching secondary mathematics: Perspectives on practice (pp. 121–139). London: Routledge.

  58. [Article]     [Google Scholar]

  59.  

  60. Lim, S. K. (2011). Applying the van Hiele theory to the teaching of secondary school geometry. Teaching and Learning, 13(1), 32–40.

  61. [Article]     [Google Scholar]

  62.  

  63. Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11. doi:10.4102/pythagoras.v36i1.261

  64. [Article]     [Google Scholar]

  65.  

  66. Ma, H. L., Lee, D. C., Lin, S. H., & Wu, D. B. (2015). A study of van Hiele of geometric thinking among 1st through 6th graders. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1181-1196. doi:10.12973/eurasia.2015.1412a

  67. [Article]     [Google Scholar]

  68.  

  69. Mason, M. (1998). The van Hiele levels of geometric understanding. The professional handbook for teachers: Geometry, 4, 4-8.

  70. [Article]     [Google Scholar]

  71.  

  72. Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for research in mathematics education, 14(1), 58-69. doi:10.5951/jresematheduc.14.1.0058

  73. [Article]     [Google Scholar]

  74.  

  75. Metila, R. A., Pradilla, L. A. S., & Williams, A. B. (2016). The challenge of implementing mother tongue education in linguistically diverse contexts: The case of the Philippines. The Asia-Pacific Education Researcher, 25(5), 781-789. doi:10.1007/s40299-016-0310-5

  76. [Article]     [Google Scholar]

  77.  

  78. Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in mathematics Education, 10(3), 163-172. doi:10.5951/jresematheduc.10.3.0163

  79. [Article]     [Google Scholar]

  80.  

  81. Sarama, J., Clements, D. H., Parmar, R. S., & Garrison, R. (2011). Geometry. In F. Fennell (Ed.). Achieving fluency: Special education and mathematics (pp. 163–196). Reston, Va: National Council of Teachers of Mathematics.

  82. [Article]     [Google Scholar]

  83.  

  84. Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for research in mathematics education, 20(3), 309-321. doi:10.2307/749519

  85. [Article]     [Google Scholar]

  86.  

  87. Solaiman, N. P., Magno, S. N., & Aman, J. P. (2017). Assessment of the third year high school students’ van Hiele levels of geometric conceptual understanding in selected secondary public schools in Lanao del Sur. Journal of Social Sciences (COES&RJ-JSS), 6(3), 603-609. doi:10.25255/jss.2017.6.3.603.609

  88. [Article]     [Google Scholar]

  89.  

  90. Swan, M. (2001). Dealing with misconceptions in mathematics. In P. Gates (Ed.). Issues in Mathematics Teaching (pp. 147–165). London: Routledge. doi:10.4324/9780203469934

  91. [Article]     [Google Scholar]

  92.  

  93. van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). London: Pearson Education UK.

  94. [Article]

  95.  

  96. van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers' and prospective teachers' content knowledge of geometry. South African Journal of Education, 23(3), 199-205.

  97. [Article]     [Google Scholar]

  98.