Exploring of Students' Ability to Solve Geometry Problems Based on Van Hiele's Level of Thinking

Ayu Andira 1 Indonesia , Muhammad Darwis M 2 Indonesia , Haerul Syam 3 Indonesia
1 Mathematics Education Program, University of Muhammadiyah Makassar, Indonesia
2 Mathematics Education Program, State University of Makassar, Indonesia
3 Mathematics Education Program, University of Muhammadiyah Makassar
Link Copied!
Published 2022-03-27
Vol. 1 No. 2 (2022) PAGES 192-200
DOI 10.51574/ijrer.v1i2.181
Views / Downloads 724 1755

Based on Van Hiele's level of thinking, this study intends to investigate students' ability to solve geometric problems. Polya's heuristic of problem-solving steps is used to assess problem-solving ability. A qualitative, descriptive study is the form of research used in this case. The Van Hiele Geometry Test (VHGT), problem-solving aptitude assessments, and interviews were used. Based on Van Hiele's level of thinking, researchers chose three students from a group of 27 students in grade VIII high junior school Terpadu Sheikh Muhammad Ja'far as research subjects. Data collection methods include tests and interviews. Data condensation, data presentation, conclusion drafting, and verification are all research data analysis approaches. The validity of the data is verified using a triangulation of techniques and sources. The findings of the study are: subjects at the pre 0 level only have visual, verbal, and drawing skills. Subjects at level 0 (visualization) were not able to solve the four problem-solving heuristics by Polya. Subjects at level 1 (analysis) were able to reach the second stage of the problem-solving heuristic by Polya. Subjects at level 2 (informal deduction reached the third stage of the problem-solving heuristic by Polya.

Andira, A., Darwis M, M., & Syam, H. (2022). Exploring of Students’ Ability to Solve Geometry Problems Based on Van Hiele’s Level of Thinking. ETDC: Indonesian Journal of Research and Educational Review , 1(2), 192–200. https://doi.org/10.51574/ijrer.v1i2.181
More Citation Formats
Download Citation

Downloads

Download data is not yet available.
  1. Abramovich, S., & Grinshpan, A. Z. (2008). Teaching mathematics to non-mathematics majors through applications. Primus, 18(5), 411-428. https://doi.org/10.1080/10511970601182772 DOI: https://doi.org/10.1080/10511970601182772
  2. Alabdulaziz, M. S., & Higgins, S. (2021). The Compatibility of Developed Mathematics Textbook Content in Saudi Arabia with NCTM Standards: A Critical Review. International Journal of Instruction, 14(2), 461-482. https://doi.org/10.29333/iejme/11103 DOI: https://doi.org/10.29333/iji.2021.14226a
  3. Anwar, R. B., & Rahmawati, D. (2017). Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem Based Polya's Stages. International Education Studies, 10(10), 20-28. https://eric.ed.gov/?id=EJ1156292 DOI: https://doi.org/10.5539/ies.v10n10p20
  4. Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of mathematics teacher education, 14(2), 133-148. https://doi.org/10.1007/s10857-011-9173-0 DOI: https://doi.org/10.1007/s10857-011-9173-0
  5. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
  6. D’Ambrosio, U. (2007). The role of mathematics in educational systems. ZDM, 39(1), 173-181. https://doi.org/10.1007/s11858-006-0012-1 DOI: https://doi.org/10.1007/s11858-006-0012-1
  7. Daulay, K. R., & Ruhaimah, I. (2019). Polya theory to improve problem-solving skills. Journal of Physics: Conference Series (Vol. 1188, No. 1, p. 012070). IOP Publishing. https://doi.org/10.1088/1742-6596/1188/1/012070/meta DOI: https://doi.org/10.1088/1742-6596/1188/1/012070
  8. Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational studies in mathematics, 61(3), 293-319. https://doi.org/10.1007/s10649-006-2372-4 DOI: https://doi.org/10.1007/s10649-006-2372-4
  9. Deal, L. J., & Wismer, M. G. (2010). NCTM principles and standards for mathematically talented students. Gifted Child Today, 33(3), 55-65. https://doi.org/10.1177/107621751003300313 DOI: https://doi.org/10.1177/107621751003300313
  10. Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM, 41(5), 605-618. https://doi.org/10.1007/s11858-009-0184-6 DOI: https://doi.org/10.1007/s11858-009-0184-6
  11. Ersoy, M., İlhan, O. A., & Sevgi, S. (2019). Analysis of the Relationship between Quadrilaterals Achievement Levels and Van Hiele Geometric Thinking Levels of the Seventh Grade Students. Higher Education Studies, 9(3), 1-11. DOI: https://doi.org/10.5539/hes.v9n3p1
  12. Gal, H. (2019). When the use of cognitive conflict is ineffective—problematic learning situations in geometry. Educational Studies in Mathematics, 102(2), 239-256. https://doi.org/10.1007/s10649-019-09904-8 DOI: https://doi.org/10.1007/s10649-019-09904-8
  13. Graham, K. J., & Fennell, F. (2001). Principles and standards for school mathematics and teacher education: Preparing and empowering teachers. School Science and Mathematics, 101(6), 319-327. https://doi.org/10.1111/j.1949-8594.2001.tb17963.x DOI: https://doi.org/10.1111/j.1949-8594.2001.tb17963.x
  14. Haataja, E., Moreno-Esteva, E. G., Salonen, V., Laine, A., Toivanen, M., & Hannula, M. S. (2019). Teacher's visual attention when scaffolding collaborative mathematical problem solving. Teaching and Teacher Education, 86, 102877. https://doi.org/10.1016/j.tate.2019.102877 DOI: https://doi.org/10.1016/j.tate.2019.102877
  15. Halat, E. (2006). Sex-related differences in the acquisition of the van Hiele levels and motivation in learning geometry. Asia Pacific education review, 7(2), 173-183. https://doi.org/10.1007/BF03031541 DOI: https://doi.org/10.1007/BF03031541
  16. Hasbi, M., Lukito, A., & Sulaiman, R. (2019). Mathematical Connection Middle-School Students 8th in Realistic Mathematics Education. In Journal of Physics: Conference Series (Vol. 1417, No. 1, p. 012047). IOP Publishing. https://doi.org/10.1088/1742-6596/1417/1/012047/meta DOI: https://doi.org/10.1088/1742-6596/1417/1/012047
  17. Hilbert, T. S., Renkl, A., Kessler, S., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18(1), 54-65. https://doi.org/10.1016/j.learninstruc.2006.10.008Huinker, D. (2018). Principles to Actions: Moving to a framework for teaching mathematics. Teaching Children Mathematics, 25(3), 133-136. https://doi.org/10.5951/teacchilmath.25.3.0133 DOI: https://doi.org/10.1016/j.learninstruc.2006.10.008
  18. Jäder, J., Lithner, J., & Sidenvall, J. (2020). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51(7), 1120-1136. https://doi.org/10.1080/0020739X.2019.1656826 DOI: https://doi.org/10.1080/0020739X.2019.1656826
  19. Kusuma, M. A., Yuliati, N., Maharani, P., & Hasanah, N. (2021). Thinking process of 7th class students in understanding quadrilateral concepts based on Van Hiele theory. In Journal of Physics: Conference Series (Vol. 1839, No. 1, p. 012012). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1839/1/012012
  20. Maharani, A., Sulaiman, H., Aminah, N., & Rosita, C. D. (2019). Analyzing the student’s cognitive abilities through the thinking levels of geometry van hiele reviewed from gender perspective. In Journal of Physics: Conference Series (Vol. 1188, No. 1, p. 012066). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1188/1/012066
  21. Morino, L. (2021). Basic Analytic Geometry. In Mathematics and Mechanics-The Interplay (pp. 255-296). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-63207-9_7 DOI: https://doi.org/10.1007/978-3-662-63207-9_7
  22. Nusaibah, N., Pramudya, I., & Subanti, S. (2021). Geometric Thinking Skills of Seventh Grade Students on the Topic of Triangle and Quadrilateral Based on Van Hiele Geometry Learning Theory. In Journal of Physics: Conference Series (Vol. 1776, No. 1, p. 012020). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1776/1/012020
  23. Ramlan, A. M. (2016). The effect of Van Hiele learning model toward geometric reasoning ability based on self-efficacy of senior high school students. JME (Journal of Mathematics Education), 1(2), 62-71. https://doi.org/10.31327/jomedu.v1i2%20July.54 DOI: https://doi.org/10.31327/jme.v1i2.54
  24. Rahayuningsih, S., Hasbi, M., Mulyati, M., & Nurhusain, M. (2021). The effect of self-regulated learning on students’problem-solving abilities. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(2), 927-939. http://dx.doi.org/10.24127/ajpm.v10i2.3538 DOI: https://doi.org/10.24127/ajpm.v10i2.3538
  25. Rellensmann, J., Schukajlow, S., & Leopold, C. (2020). Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems. ZDM, 52(1), 97-110. https://doi.org/10.1007/s11858-019-01085-1 DOI: https://doi.org/10.1007/s11858-019-01085-1
  26. Serin, H. (2018). Perspectives on the Teaching of Geometry: Teaching and Learning Methods. J. Educ. Train, 5(1), 131-137. DOI: https://doi.org/10.5296/jet.v5i1.12115
  27. Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on the current state-of-the-art. ZDM, 50(1), 5-18. https://doi.org/10.1007/s11858-018-0933-5 DOI: https://doi.org/10.1007/s11858-018-0933-5
  28. Sulistiowati, D. L., Herman, T., & Jupri, A. (2019). Student difficulties in solving geometry problem based on Van Hiele thinking level. In Journal of Physics: Conference Series (Vol. 1157, No. 4, p. 042118). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1157/4/042118
  29. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say?. Procedia-Social and Behavioral Sciences, 8, 142-151. https://doi.org/10.1016/j.sbspro.2010.12.020 DOI: https://doi.org/10.1016/j.sbspro.2010.12.020
  30. Taneo, P. N., & Kusumah, Y. S. (2021). Analysis of Students' Mathematical Problem-Solving Ability Based on Category Levels Through Polya Steps. (JIML) JOURNAL OF INNOVATIVE MATHEMATICS LEARNING, 4(2), 87-95. http://dx.doi.org/10.22460/jiml.v4i2.p87-95 DOI: https://doi.org/10.22460/jiml.v4i2.p87-95
  31. Tarim, K. (2009). The effects of cooperative learning on preschoolers’ mathematics problem-solving ability. Educational studies in mathematics, 72(3), 325-340. https://doi.org/10.1007/s10649-009-9197-x DOI: https://doi.org/10.1007/s10649-009-9197-x
  32. Yalley, E., Armah, G., & Ansah, R. K. (2021). Effect of the VAN Hiele Instructional Model on Students’ Achievement in Geometry. Education Research International, 2021. DOI: https://doi.org/10.1155/2021/6993668
  33. Watan, S. (2018). Exploring the relationship between teachers’ instructional and students’ geometrical thinking levels based on van Hiele theory. In Journal of Physics: Conference Series (Vol. 1097, No. 1, p. 012122). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1097/1/012122
  34. Wijaya, Y. Y., Margaretha, P. M., & Wijayanti, N. P. A. A. (2019). Senior high school student’s visual-spatial intelligence according to van hiele geometric thinking theory. In IOP Conference Series: Earth and Environmental Science (Vol. 243, No. 1, p. 012055). IOP Publishing. DOI: https://doi.org/10.1088/1755-1315/243/1/012055
  35. Whitney, H. (2015). Geometric integration theory. Princeton university press.
  36. Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038 DOI: https://doi.org/10.1016/j.tate.2020.103038
  37. Yudianto, E., Sugiarti, T., & Trapsilasiwi, D. (2018). The identification of van Hiele level students on the topic of space analytic geometry. In Journal of Physics: Conference Series (Vol. 983, No. 1, p. 012078). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/983/1/012078
  38. Zhou, D., Du, X., Hau, K. T., Luo, H., Feng, P., & Liu, J. (2020). Teacher-student relationship and mathematical problem-solving ability: mediating roles of self-efficacy and mathematical anxiety. Educational Psychology, 40(4), 473-489. https://doi.org/10.1080/01443410.2019.1696947 DOI: https://doi.org/10.1080/01443410.2019.1696947

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.

Dimension Badge

Downloads

Downloads
Crossmark Badge
Crossmark Badge
Section
Articles
Keywords
Problem-Solving Geometry Problems Van Hiele Level Thinking