Kuvvetli Desteğe Dayanan Bir Geometri Öğretimi İçin Sunulan Etkinliklerin Etkilerinin İncelenmesi

Matematik eğitiminde tüm öğrencilerden yüksek başarının beklenmesi ve kuvvetli desteğin verilmesini temel alan bu çalışmada, çeşitli etkinliklerle zenginleştirilmiş bir geometri öğretiminin öğrencilerin Van Hiele Geometrik Düşünme Düzeyleri ve uzamsal yeteneklerine etkisi incelenmiştir. Zayıf deneysel desenin benimsendiği mevcut çalışmanın katılımcıları, Türkiye’nin orta ölçekli bir ilinde dezavantajlı bölgelerde yaşayan ve o bölgelerdeki devlet okulların öğrenim gören, 6. sınıftan 7. sınıfa geçen 22 öğrenciden oluşturmaktadır. Araştırmada Van Hiele Geometri Testi ve Uzamsal Yetenek Testi ön test ve son test olarak kullanılmıştır. Ön test ile son test arasında verilen eğitimde, geometrik deneyimler sunan yaratıcı drama, dijital hikâye yazımı, origami, geometrik inşa, GeoGebra, GeoCadabra, SketchUp, eğitsel oyun ve Small Basic etkinliklerine yer verilmiştir. Van Hiele Geometrik Düşünme Testinden alınan puanlarda ön test ile son test arasında anlamlı bir fark saptanmazken; Uzamsal Yetenek Testinden alınan puanlarda son test lehine anlamlı bir fark olduğu belirlenmiştir. Bu testte etki büyüklüğü değeri 0.591 olup, etkinin büyük oranlı olduğu görülmüştür. Çalışma, geometri öğretiminde kuvvetli bir destek sağlamak için farklı türde etkinliklerin sunulmasının olumlu etkilerini vurgulamaktadır.

Anahtar Kelimeler:

Geometri, van hiele geometrik düşünme düzeyi, uzamsal yetenek, kuvvetli destek

Examining the Effects of Presented Activities for a Strong Supported Geometry Instruction

In this study, based on the expectation of high achievement and the need for strong support from all students in mathematics education, the effect of geometry instruction enriched with various activities on students' Van Hiele Geometric Thinking Levels and spatial abilities was examined. The participants of the present study, in which the weak experimental design was adopted, consisted of 22 students, who passed from the 6th grade to the 7th grade, living in disadvantaged areas in a medium-sized province of Turkey and studying at public schools in those regions. In the research, Van Hiele Geometry Test and Spatial Ability Test were used as pre-test and post-test. In the training given between the pre-test and the post-test, creative drama, digital story writing, origami, geometric construction, GeoGebra, GeoCadabra, SketchUp, educational games, and Small Basic activities were included. While no significant difference was found between the pre-test and post-test in the scores obtained from the Van Hiele Geometric Thinking Test. It was determined that there was a significant difference in favour of the post-test in the scores obtained from the Spatial Ability Test. In this test, the effect size value was 0.591, and it was seen that the effect was large. The study emphasizes the positive effects of presenting different types of activities in order to provide strong support in geometry instruction.

Keywords:

Geometry, van hiele geometric thinking level, spatial ability, strong support,

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Allexsaht-Snider, M., & Hart, L. E. (2001). "Mathematics for all": How do we get there? Theory into Practice, 40(2), 93-101. https://doi.org/10.1207/s15430421tip4002_3
Battista, M. T. (2007). The development of geometric and spatial thinking. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). NCTM.
Battista, M. T., & Clements, D. H. (1988). A case for a Logo-based elementary school geometry curriculum. The Arithmetic Teacher, 36(3), 11-17. https://doi.org/10.5951/AT.36.3.0011
Battista, M. T., & Clements, D. H. (1996). Students' understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258-292. https://doi.org/10.5951/jresematheduc.27.3.0258
Bayrak, M. E. (2008). Investigation of effect of visual treatment on elementary school student’s spatial ability and attitude toward spatial ability problems. Unpublished master’s thesis, Middle East Technical University.
Boakes, N. J. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. RMLE Online, 32(7), 1-12. https://doi.org/10.1080/19404476.2009.11462060
Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge University Press.
Chrysanthou, I. (2008). The use of ICT in primary mathematics in Cyprus: The case of GeoGebra. Unpublished master’s thesis, University of Cambridge.
Chua, G. L. L., Tengah, K. A., Shahrill, M., Tan, A., & Leong, E. (2017). Analysing students’ perspectives on geometry learning from the combination of van hiele phase-based instructions and Geogebra. In Proceeding of the 3rd International Conference on Education (Vol. 3, pp. 205-213).
Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151-178). National Council of Teachers of Mathematics.
Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D.H. Clements, J. Sarama, & A.M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 267-297). Lawrence Erlbaum Associates.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). Macmillan Publishing Co, Inc.
Contero, M., Naya, F., Company, P., Saorin, J. L., & Conesa, J. (2005). Improving visualization skills in engineering education. IEEE Computer Graphics and Applications, 25(5), 24-31. https://doi.org/10.1109/MCG.2005.107
Croom, L. (1997). Mathematics for all students. In J. Trentacosta & M. J. Kenney (Eds.), Multicultural and gender equity in the mathematics: the gift of diversity (pp. 1-9). National Council of Teachers of Mathematics.
Delialioğlu, Ö., & Aşkar, P. (1999). Contribution of students' mathematical skills and spatial ability of achievement in secondary school physics. Hacettepe University Journal of Education, 16, 34-39. Retrieved from https://dergipark.org.tr/en/download/article-file/88085
Duatepe, A. (2000). An investigation of the relationship between Van Hiele geometric level of thinking and demographic variables for pre-service elementary school teachers. Published master’s thesis, Middle East Technical University.
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.
Duatepe-Paksu, A. (2016). van Hiele geometrik düşünme düzeyleri [van Hiele Geometric Thinking Levels]. In E. Bingolbali, S. Arslan, İ. O. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in mathematics education] (pp. 265-275). Pegem Akademi.
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), 272-286. https://doi.org/272-286. 10.3200/JOER.102.4.272-286
Ekstrom, R. B. (1976). Kit of factor-referenced cognitive tests. Educational Testing Service.
Eme, P. E., & Marquer, J. (1999). Individual strategies in a spatial task and how they relate to aptitudes. European Journal of Psychology of Education, 14(1), 89-108. Retrieved from https://link.springer.com/content/pdf/10.1007/BF03173113.pdf
Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education (6th edition). McGraw-Hill.
Furner, J. M., Yahya, N., & Duffy, M. L. (2005). Teach mathematics: Strategies to reach all students. Intervention in School and Clinic, 41(1), 16-23. https://doi.org/10.1177/10534512050410010501
Gluck, J., & Fitting, S. (2003). Spatial strategy selection: Interesting incremental information. International Journal of Testing, 3(3), 293-308. https://doi.org/10.1207/S15327574IJT0303_7
Gutiérrez, Á. (1992). Exploring the links between Van Hiele Levels and 3-dimensional geometry. Structural Topology, 18, 31-48. Retrieved from https://upcommons.upc.edu/bitstream/handle/2099/1073/st18-07-a3-ocr.pdf?sequence=1&isAllowed=y
Gutstein, E. (2002). Roads towards equity in mathematics education: Helping students develop a sense of agency. In Annual Meeting of the American Educational Research Association, New Orleans.
Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37-73. https://doi.org/10.2307/30034699
Heid, M. K. (2005). Technology in mathematics education: Tapping into visions of the future. In W. J. Masalski & P. C. Elliot (Eds.), Technology-Supported Mathematics Learning Environments, (pp. 345–366). NCTM.
Hohenwarter, M., & Jones, K. (2007). Ways of linking geometry and algebra, the case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 126-131.
Hsi, S., Linn, M. C., & Bell, J. E. (1997). The role of spatial reasoning in engineering and the design of spatial instruction. Journal of Engineering Education, 86(2), 151-158.
Jones, K., & Mooney, C. (2003). Making space for geometry in primary mathematics. In I. Thompson (Ed.), Enhancing primary mathematics teaching, (pp. 3-15). Open University Press.
Karaman, T. (2000). The relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and the performances related to plane geometry subject of the sixth grade students. Unpublished master’s thesis, Boğaziçi University.
Kariadinata, R., Yaniawati, R. P., Susilawati, W., & Banoraswatii, K. (2017, July). The implementation of GeoGebra software-assited DDFC instructional model for improving students' Van-Hiele geometry thinking skill. In Proceedings of the 2017 International Conference on Education and Multimedia Technology (pp. 58-62). https://doi.org/10.1145/3124116.3124129
Kayhan, E. B. (2012). Strategies and difficulties in solving spatial visualization problems: A case study with adults, Unpublished doctoral dissertation, Middle East Technical University.
Kehoe, J. (1995). Basic item analysis for multiple-choice tests. ERIC/AE Digest Series EDO-TM-95-11. Retrieved from http://ericae.net/digests/tm9511.htm
Klemer, A., & Rapoport, S. (2020). Origami and GeoGebra activities contribute to geometric thinking in second graders. Eurasia Journal of Mathematics, Science and Technology Education, 16(11), 1-12. https://doi.org/10.29333/ejmste/8537
Kösa, T. (2011). Ortaöğretim öğrencilerinin uzamsal berecilerinin incelenmesi [An investigation of secondary school students’ spatial skills]. Unpublished doctoral dissertation, Karadeniz Technical University.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56(6), 1479-1498. https://doi.org/10.2307/1130467
Liao, Y. T., Yu, C. H., & Wu, C. C. (2015, April). Learning geometry with augmented reality to enhance spatial ability. In 2015 international conference on learning and teaching in computing and engineering (pp. 221-222). IEEE.
Lohman, D. F. (1979). Spatial ability: A review and reanalysis of the correlational literature (No. TR-8). Stanford Univ Calif School of Education.
Maier, P. H. (1996, March). Spatial geometry and spatial ability–How to make solid geometry solid. In Selected papers from the Annual Conference of Didactics of Mathematics (pp. 63-75).
Manizade, A. G., & Mason, M. (2010, July). Choosing GeoGebra Applications Most Appropriate for Teacher’s Current Geometry Classroom: Pedagogical Perspective. In First North American GeoGebra Conference (p. 214).
Martin, D. B. (2003). Hidden assumptions and unaddressed questions in mathematics for all rhetoric. The Mathematics Educator, 13(2), 7-21. Retrieved from https://openjournals.libs.uga.edu/tme/article/view/1856/1764
McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86(5), 889-918. https://doi.org/10.1037/0033-2909.86.5.889
MoNE. (2018). Mathematics Course Curriculum (1st-8th Grades). Ankara: MEB.
National Council for Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. VA: Author.
Naraine, B. (1989). Relationships among eye fixation variables on task-oriented viewings of angles, van Hiele levels, spatial ability, and field dependence. Unpublished doctoral dissertation, The Ohio State University.
Okagaki, L., & Frensch, P. A. (1994). Effects of video game playing on measures of spatial performance: Gender effects in late adolescence. Journal of Applied Developmental Psychology, 15(1), 33-58. https://doi.org/10.1016/0193-3973(94)90005-1
Olkun, S. (2003). Making connections: Improving spatial abilities with engineering drawing activities. International Journal of Mathematics Teaching and Learning, 3(1), 1-10. Retrieved from https://www.cimt.org.uk/journal/sinanolkun.pdf
Olkun, S., & Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki [The relationship between primary school students' computer experiences and their achievement in spatial thinking and geometry]. The Turkish Online Journal of Educational Technology, 2(4), 86-91. Retrieved from https://www.proquest.com/openview/b21bab5a15f743b13a6116f461abfade/1?pq-origsite=gscholar&cbl=1576361
Paksu, A. D. (2009). Factors that predict geometry self-efficacy of pre-service elementary teachers. In proceedings of PME, 33, 1, 368.
Prigge, G. R. (1978). The differential effects of the use of manipulative aids on the learning of geometric concepts by elementary school children. Journal for Research in Mathematics Education, 9(5), 361-367. https://doi.org/10.5951/jresematheduc.9.5.0361
Saads, S., & Davis, G. (1997). Spatial abilities, van Hiele levels & language use in three-dimensional geometry. In proceedings of PME, 4, 4-104.
Schultz, K. (1991). The contribution of solution strategy to spatial performance. Canadian Journal of Psychology, 45(4), 474-491. https://doi.org/10.1037/h0084301
Şener-Akbay, P. (2012). Cross-sectional study on grades, geometry achievemnt and van Hiele geometric thinking levels. Unpublished master’s thesis, Boğaziçi University.
Tartre, L. A. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in Mathematics Education, 21(3), 216-229. https://doi.org/10.5951/jresematheduc.21.3.0216
Turğut, M. (2010). Teknoloji destekli lineer cebir öğretiminin ilköğretim matematik öğretmen adaylarının uzamsal yeteneklerine etkisi [The effect of technology assisted linear algebra instruction on pre-service primary mathematics teachers’ spatial ability]. Unpublished doctoral dissertation, Dokuz Eylül University.
Tutkun, O. F., & Ozturk, B. (2013). The effect of GeoGebra mathematical software to the academic success and the level of Van Hiele geometrical thinking. International Journal of Academic Research, 5(4), 22-28. https://doi.org/10.7813/2075-4124.2013/5-4/B.3
Usiskin, Z. (1982). van Hiele levels and achievement in secondary school geometry. University of Chicago. ERIC Document Reproduction Service no. ED220 288.
Uzun, Z. B. (2019). Ortaokul öğrencilerinin geometrik düşünme düzeyleri, uzamsal yetenekleri ve geometriye yönelik tutumları [Middle school students geometric thinking levels, spatial abilities and attitudes towards geometry]. Unpublished master’s thesis, Balıkesir University.
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., & Wray, J. (2010). Elementary and middle school mathematics: Teaching developmentally. Pearson Education.
Zeybek, N. (2016). Ortaokul matematik öğretmen adaylarının uzamsal stratejilerinin belirlenmesi [Identifying the spatial strategies of pre-service middle school mathematics teachers]. Unpublished master’s thesis,