Students’ Spatial Abilities, Attitudes Towards Geometry and Van Hiele Geometric Thinking Levels

Öz

The aim of this study was to investigate the relationships between eighth grade students’ spatial abilities, attitudes towards geometry and Van Hiele geometric thinking levels. We conducted the study using exploratory correlational research model with 429 students. The students’ spatial ability and attitudes towards geometry were moderate, and their Van Hiele geometric thinking levels were extremely low. We discovered that the students’ spatial ability scores and Van Hiele geometric thinking levels differed depending on their pre-school attendance status and did not differ according to their gender, and that their attitudes towards geometry were independent from gender and pre-school attendance status. The students’ spatial abilities and Van Hiele geometric thinking levels were positively associated with their attitudes towards geometry.

Anahtar Kelimeler

• spatial ability
• attitude towards geometry
• Van Hiele geometric thinking levels
• eighth grade students

Öğrencilerin Uzamsal Yetenekleri, Geometriye Yönelik Tutumları ve Van Hiele Geometrik Düşünme Düzeyleri

Öz

Bu çalışmanın amacı sekizinci sınıf öğrencilerinin uzamsal yetenekleri, geometriye yönelik tutumları ve Van Hiele geometrik düşünme düzeyleri arasındaki ilişkileri incelemektir. Araştırma keşfedici korelasyonel araştırma modeli ile 429 öğrencinin katılımıyla yürütüldü. Çalışmada öğrencilerin uzamsal yetenekleri ve geometriye yönelik tutumlarının orta düzeyde ve Van Hiele geometrik düşünme düzeylerinin çok düşük olduğu bulunmuştur. Çalışmada ayrıca öğrencilerin uzamsal yetenek puanlarının ve Van Hiele geometrik düşünme düzeylerinin okul öncesi devam durumlarına göre farklılaştığı, cinsiyetlerine göre farklılaşmadığı, geometriye yönelik tutumlarının ise cinsiyet ve okul öncesi devam durumlarından bağımsız olduğu ortaya çıkmıştır. Öğrencilerin uzamsal yetenekleri ve Van Hiele geometrik düşünme düzeyleri, geometriye yönelik tutumlarının pozitif olarak anlamlı bir şekilde ilişkili olduğu da elde edilen sonuçlar arasındadır.

Anahtar Kelimeler

• uzamsal yetenek
• geometriye yönelik tutum
• Van Hiele geometrik düşünme düzeyleri
• sekizinci sınıf öğrencileri

Kaynakça

1. Abdelfatah, H. (2011). A story-based dynamic geometry approach to improve attitudes toward geometry and geometric proof. ZDM – Mathematics Education, 43, 441-450. https://doi.org/10.1007/s11858-011-0341-6 Al-ebous, T. (2016). Effect of the Van Hiele model in geometric concepts acquisition: The attitudes towards geometry and learning transfer effect of the first three grades students in Jordan. International Education Studies, 9(4), 87-98. http://dx.doi.org/10.5539/ies.v9n4p87
2. Bal, A. P. (2012). Teacher candidates’ geometric thinking levels and attitudes to geometry. Journal of Educational Sciences Research, 2(1), 17-34. https://dergipark.org.tr/en/pub/ebader/issue/44650/554613
3. Balacheff, N. (1990). ICME-6 Report of the international group psychology of mathematics education. Educational Studies in Mathematics, 21(2), 193-197. http://www.jstor.org/stable/3482481
4. Batdal Karaduman, G., ve Davaslıgil, Ü. (2019). The effects of differentiated geometry teaching for gifted students on creative thinking, spatial ability level and achievement. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 13(2), 1305-1337. https://doi.org/10.17522/balikesirnef.654451
5. Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21(1), 47-60. https://doi.org/10.2307/749456
6. Ben-Chaim, D., Lappan, G., & Houang, R. T. (1986). Development and analysis of a spatial visualization test for middle school boys and girls. Perceptual and Motor Skills, 63, 659-669. https://doi.org/10.2466/pms.1986.63.2.659
7. Bofferding, L., & Kocabas, S. (2021). Elementary students’ use of spatial thinking strategies in a layered puzzle task. In M. Inprasitha, N. Changsri & N. Boonsena (Eds.). Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Vol 1 (pp. 129). PME. https://pme44.kku.ac.th/home/uploads/volumn/pme44_vol1.pdf
8. Bruce, C. D., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., ..., & Woolcott, G. (2017). Understanding gaps in research networks: Using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics, 95(2), 143-161. https://doi.org/10.1007/s10649-016-9743-2

9. Cansız Aktaş, A. ve Aktaş, Y. D. (2013). The development of a current attitude scale towards geometry. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 7, 225- 247. https://dergipark.org.tr/tr/pub/balikesirnef/issue/3377/46608
10. Choo, S., Park, S., & Nelson, N. J. (2021). Evaluating spatial thinking ability using item response theory: Differential item functioning across math learning disabilities and geometry instructions. Learning Disability Quarterly, 44(2), 68-81. https://doi.org/10.1177/0731948720912417
11. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
12. Conceição, J., & Rodrigues, M. (2021). 3D decomposition as a spatial reasoning process: A window to 1st grade students’ spatial structuring. In M. Inprasitha, N. Changsri & N. Boonsena (Eds.). Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Vol 1 (pp. 136). PME. https://pme44.kku.ac.th/home/uploads/volumn/pme44_vol1.pdf
13. Duatepe, A. (2000). An investigation of the relationship between Van Hiele geometric level of thinking and demographic variable for pre-service elementary school teacher [Unpublished master’s thesis]. Middle East Technical University. https://tez.yok.gov.tr/UlusalTezMerkezi/
14. 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. https://tez.yok.gov.tr/UlusalTezMerkezi/
15. Duatepe-Paksu, A., & Ubuz, B. (2009). Effects of drama-based geometry instruction on student achievement, attitudes, and thinking levels. The Journal of Educational Research, 102(4), 272-285. https://doi.org/10.3200/JOER.102.4.272-286
16. Fitriyani, H., Kusumah, Y. S., & Turmudi (2021). Spatial reasoning: A survey on the 8th grader students’ gain in online learning. International Journal on Emerging Mathematics Education, 5(1), 51-60. http://dx.doi.org/10.12928/ijeme.v5i1.20140
17. Forsythe, S. K. (2015). Dragging maintaining symmetry: Can it generate the concept of inclusivity as well as a family of shapes? Research in Mathematics Education, 17(3), 198-219. https://doi.org/10.1080/14794802.2015.1065757
18. Fraenkel, J. R., & Wallen, N. E. (2012). How to design and evaluate research in education (8th ed.). McGraw-Hill.
19. Gal, H., & Lew, H. C. (2008). Is a rectangle a parallelogram? Towards a bypass of Van Hiele level 3 decision making. Paper presented at Topic Study Group 18, ICME-11 Monterrey, Mexico, July 2008. https://www.researchgate.net/publication/344351933_Is_a_Rectangle_a_Parallelogram_-Towards_a_Bypass_of_Van_Hiele_Level_3_Decision_Making
20. Ganley, C. M., & Vasilyeva, M. (2011). Sex differences in the relation between math performance, spatial skills, and attitudes. Journal of Applied Developmental Psychology, 32(4), 235-242. https://doi.org/10.1016/j.appdev.2011.04.001
21. Ghasemi, A., & Zahediasl, S. (2011). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology Metabolism, 10(2), 486-489. https://doi.org/10.5812/ijem.3505
22. 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. https://doi.org/10.5951/jresematheduc.22.3.0237
23. Guven, B., & Okumus, S. (2011). 8th Grade Turkish students’ van Hiele levels and classification of quadrilaterals. Proceedings of PME 35, 2, 473-480. https://www.igpme.org/wp-content/uploads/2019/05/PME35-2011-Ankara.zip
24. Hannula, M. S., & Toivanen, M. (2019). Making and observing visual representations during problem solving: An eye tracking study. In Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education. https://researchportal.helsinki.fi/files/129964849/Hannula_RR.docx
25. Jones, K., & Tzekaki, M. (2016). Research on the teaching and learning of geometry. In: Á. Gutiérrez, G. C. Leder & P. Boero (Eds) The second handbook of research on the psychology of mathematics education. Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_4
26. Kılıç, Ç., Köse, Y. N., Tanışlı, D., & Özdaş, A. (2007). The fifth grade students’ Van Hiele geometric thinking levels in tessellation. Elementary Education Online, 6(1), 1305-1337. http://www.ilkogretim-online.org/fulltext/218-1596620431.pdf?1635191185
27. Kline, R. B. (2016). Principles and practice of structural equation modelling (4th ed.). The Guilford Press.
28. Kösa, T., & Kalay, H. (2018). Evaluation of the learning environment designed for developing 7th grade students’ spatial orientation skills. Kastamonu Education Journal, 26(1), 83-92. https://dergipark.org.tr/tr/pub/kefdergi/issue/31578/348100
29. Lenhard, W., & Lenhard, A. (2016). Calculation of effect sizes. Psychometrica. https://doi.org/10.13140/RG.2.2.17823.92329
30. Lusyana, E., & Setyaningrum, W. (2018). Van Hiele instructional package for vocational school students’ spatial reasoning. Beta: Jurnal Tadris Matematika, 11(1), 79-100. https://doi.org/10.20414/betajtm.v11i1.146
31. Ma, H. L., Lee, D. C., Lin, S. H., & Wu, D. (2015). A study of Van Hiele of geometric thinking among 1st through 6th. Eurasia Journal of Mathematics, Science & Technology Education, 11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a
32. McCoun, P. K. C. (1993). Gender differences in attitudes, spatial visualization ability, and learning styles of remedial mathematics students [Unpublished master’s thesis]. Texas Tech University.
33. Misnasanti, & Mahmudi, A. (2018). Van Hiele thinking level and geometry visual skill towards field dependent-independent students in junior high school. Journal of Physics: Conference Series, 1097, 012133. https://doi.org/10.1088/1742-6596/1097/1/012133
34. Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29-43. https://www.aft.org/sites/default/files/periodicals/Newcombe_1.pdf
35. Newman, S. D., Hansen, M. T., & Gutierrez, A. (2016). An fMRI study of the impact of block building and board games on spatial ability. Frontiers Psychology, 7, 1278. https://doi.org/10.3389/fpsyg.2016.01278
36. Okamoto, Y., Weckbacher, L. M., & Hallowell, D. (2014). How is spatial reasoning related to mathematical thinking and how important is early exposure to spatial activities? In P. Liljedahl, C. Nicol, S. Oesterle & D. Allan, (Eds.). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, Vol 1 (pp. 177). PME. https://www.pmena.org/pmenaproceedings/PMENA%2036%20PME%2038%202014%20Proceedings%20Vol%201.pdf
37. Owens, K. (2014). Diversifying our perspectives on mathematics about space and geometry: An ecocultural approach. International Journal of Science and Mathematics Education, 12, 941-974. https://doi.org/10.1007/s10763-013-9441-9
38. Owens, K. (2015). Visuospatial reasoning: An ecocultural perspective for space, geometry and measurement education. Springer. https://doi.org/10.1007/978-3-319-02463-9
39. Owens, K. (2020a). Transforming the established perceptions of visuospatial reasoning: Integrating an ecocultural perspective. Mathematics Education Research Journal, 32, 257-283. https://doi.org/10.1007/s13394-020-00332-z
40. Owens, K. (2020b). Noticing and visuospatial reasoning. Australian Primary Mathematics Classroom, 25(1), 11-15. https://link.gale.com/apps/doc/A655088074/AONE?u=anon~385de04a&sid=googleScholar&xid=755b3235
41. Özsoy, N., Yağdıran, E., & Öztürk, G. (2004).Tenth grade students’ learning styles and their geometric thinking levels. Eurasian Journal of Educational Research, 16, 50–63. http://dspace.balikesir.edu.tr/handle/20.500.12462/5203
42. Polat, K., Oflaz, G., & Akgün, L. (2019). The relationship of visual proof skills with Van Hiele levels of geometric thinking and spatial ability. Erciyes Journal of Education, 3(2), 105-122. https://doi.org/10.32433/eje.604126
43. Pujawan, I. G. N., Suryawan, I. P. P., & Prabawati, D. A. A. (2020). The effect of Van Hiele learning model on students’ spatial abilities. International Journal of Instruction, 13(3), 461-474. https://doi.org/10.29333/iji.2020.13332a
44. Resnick, I., Harris, D., Logan, T., & Lowrie, T. (2020). The relation between mathematics achievement and spatial reasoning. Mathematics Education Research Journal, 32, 171-174. https://doi.org/10.1007/s13394-020-00338-7
45. Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321. https://doi.org/10.5951/jresematheduc.20.3.0309
46. Septia, T., Prahmana, R. C. I., Pebrianto, & Wahyu, R. (2018). Improving students spatial reasoning with course lab. Journal on Mathematics Education, 9(2), 327-336. https://doi.org/10.22342/jme.9.2.3462.327-336
47. Sevgi, S., & Gürtaş, K. (2020). Analysis of attitude and self-efficacy of middle school students towards geometry. Ahi Evran University Journal of Kırşehir Education Faculty, 21(1), 416-455. https://doi.org/10.29299/kefad.2020.21.01.012
48. Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM – Mathematics Education, 48, 1-29. https://doi.org/10.1007/s11858-016-0796-6
49. Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2017). Geometry education, including the use of new technologies: A survey of recent research. In G. Kaiser (Ed.). Proceedings of the 13th International Congress on Mathematical Education (pp. 277-287). Springer, Cham. https://doi.org/10.1007/978-3-319-62597-3_18
50. Sunzuma, G., Masocha, M., & Zezekwa, N. (2012). Secondary school students’ attitudes towards their learning of geometry: A survey of Bindura urban secondary schools. Greener Journal of Educational Research, 3(8), 402-410. https://doi.org/10.15580/GJER.2013.8.051513614
51. Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
52. Topraklıkoğlu, K., & Öztürk, G. (2019). Seventh grade students' spatial ability and their attitudes towards geometry. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 13(2), 564-587. https://doi.org/10.17522/balikesirnef.539402
53. Topraklıkoğlu, K., & Öztürk, G. (2021). Teaching geometry through augmented reality activities using three-dimensional modelling. International Online Journal of Educational Sciences, 13(5), 1325-1342. https://doi.org/10.15345/iojes.2021.05.003
54. Tso, T. Y., & Liang, Y. N. (2001). The study of interrelationship between spatial abilities and Van Hiele levels of thinking on geometry of eight-grade student. Journal of Research in Education Sciences, 46(1&2), 1-20. https://doi.org/10.6300/JNTNU.2001.46.01
55. Turğut, M. (2007). Investigation of 6, 7 and 8 grade students’ spatial ability [Unpublished master’s thesis]. Dokuz Eylül University. https://tez.yok.gov.tr/UlusalTezMerkezi/
56. Turğut, M., & Yılmaz, S. (2012). Investigation of 7. and 8. grade students’ spatial ability. Journal of Dicle University Ziya Gökalp Education Faculty, 19, 69-79. https://dergipark.org.tr/tr/download/article-file/786964 Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. CDASSG Project, Chicago University. https://eric.ed.gov/?id=ED220288
57. Van Putten, S. (2008). Levels of thought in geometry of pre-service mathematics educators according to the van Hiele Model [Unpublished master’s thesis]. University of Pretoria.
58. Wahab, R. A., Abdullah, A H., Mokhtar, M., Atan, N. A., & Abu, M. S. (2017). Evaluation by experts and designated users on the learning strategy using SketchUp make for elevating visual spatial skills and geometry thinking. Bolema: Boletim de Educação Matemática, 31(58), 819-840. https://doi.org/10.1590/1980-4415v31n58a15
59. Watan, S., & Sugiman (2018). Exploring the relationship between teachers’ instructional and students’ geometrical thinking levels based on van Hiele theory. Journal of Physics: Conference Series 1097 012122. https://doi.org/10.1088/1742-6596/1097/1/012122
60. Woolcott, G., Logan, T., Marshman, M., Ramful, A., Whannell, R., Lowrie, T. (2020). The re-emergence of spatial reasoning within primary years mathematics education. In J. Way, C. Attard, J. Anderson, J. Bobis, H. McMaster & K. Cartwright (Eds). Research in Mathematics education in Australasia 2016-2019. Springer. https://doi.org/10.1007/978-981-15-4269-5_10
61. Wu, D., & Ma, H. (2005). A study of the geometric concepts of the elementary school students who are assigned to the Van Hiele level one. Proceedings of PME 29, 4, 329-336. https://www.emis.de/proceedings/PME29/PME29RRPapers/PME29Vol4WuMa.pdf
62. Wu, D., & Ma, H. (2006). The distributions of Van Hiele levels of geometric thinking among 1st through 6th graders. Proceedings of PME 30, 5, 409-416. https://www.emis.de/proceedings/PME30/5/409.pdf
63. Xie, F., Zhang, L., Chen, X., & Xin, Z. (2019). Is spatial ability related to mathematical ability: A meta-analysis. Educational Psychology Review, 32, 113-155. https://doi.org/10.1007/s10648-019-09496-y
64. Yıldırım Gül, Ç., & Karataş, İ. (2015). Investigation of correlation among the 8th grade students’ achievement on transformation geometry, spatial ability, levels of geometry understanding and attitudes towards mathematics. Karaelmas Journal of Educational Sciences, 3(1), 36-48. http://ebd.beun.edu.tr/index.php/KEBD/article/view/63