Investigation Of The Relationship Between The Eighth Grade Students’ Spatial Abilities And Their Geometry Achievements
Yıl 2024,
Cilt: 10 Sayı: 2, 99 - 111, 23.08.2024
Hüseyin Demirkan
,
Adem Duru
Öz
The main goal of this study is to determine the relationship between the eighth-grade students’ spatial abilities and their geometry achievement considering the variables of gender, preschool education and type of school. This research study was carried out by applying correlational survey model. 400 eighth-grade students taking education at different type of middle schools participated in Göksun, Kahramanmaraş. Demographic information form, Transformational Geometry and Geometric Objects Achievement Test developed by the researcher and Spatial Ability Practice Test developed by Newton and Bristoll (2011) and translated to Turkish by the researcher were used as data collection instruments in the study. The data were analysed via SPSS 17.0 package software by using descriptive statistics, independent samples t-test, one way ANOVA and Pearson correlation coefficient. According to the findings of the research; it was determined that there was positively significant and moderate correlation between students’ spatial ability and their geometry achievement scores. In respect to the students’ spatial abilities; a significant difference was determined on the side of girls, the students taking education in day school and the students received preschool education.
Kaynakça
- Abay, S., Tertemiz, N., and Gökbulut, Y. (2018). Öğretmen adaylarının uzamsal yeteneklerinin çeşitli değişkenler açısından incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12(1), 45- 62.
- Arı, A. (2003). Taşımalı ilköğretim uygulaması (Uşak Örneği). Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 23(1), 101-115.
- Baki, A. (2015). Kuramdan uygulamaya matematik eğitimi (6.baskı). Ankara: Harf Eğitim Yayıncılığı.
- 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). Charlotte, NC: NCTM/Information Age
Publishing.
- Ben-Chaim, D., Lappan, G., and Houang, R. T. (1989). Adolescents’ ability to communicate spatial information:
Analyzing and effecting students’ performance. Educational Studies in Mathematics, 20, 121-146. Berberoğlu, G. (2007). Türk bakış açısından PISA araştırma sonuçları, Konrad Adenauer Stiftung Vakfı, [Online]:
http://www.konrad.org.tr/Egitimturk/07girayberberoglu.pdf.
- Boulter, D. R. (1992). The effects of instruction on spatial ability and geometry performance. Unpublished master thesis, Queen’s University, Ontario.
- Burnett, S. A. and Lane, D. M. (1980). Effects of academic instruction on spatial visualization. Intelligence, 4(3), 233-242.
- Büyüköztürk, Ş. (2002). Sosyal bilimler için veri analizi el kitabı. Ankara: Pegem Yayıncılık.
- Büyüköztürk, Ş., Çakan, M., Tan, Ş., and Atar, H. Y. (2014). TIMSS 2011 ulusal matematik ve fen raporu: 8. Sınıflar [TIMSS 2011 national mathematics and science report: 8th grade]. Ankara, Turkey: Milli Eğitim Bakanlığı.
- Carnoldi, C. and Vecchi, T. (2003). Visuo-spatial working memory and individual differences. New York:
Psychology Press.
- Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York, NY: Cambridge
University Press.
- Chao, J. Y. and Liu, C. H. (2017). A case study on the spatial conceptualization abilities for sixth grade elementary students from urban, suburban and remote schools. EURASIA Journal of Mathematics Science and
Technology Education, 13(6), 1675-1686.
- Colom, R., Contreras, M. J., Botella, J. and Santacreu, J. (2001). Vehicles of spatial ability. Personality and
Individual Differences,32, 903-912.
- Coxford, A. F. (1995). The Case for connections. In P. A. House and A. F. Coxford (Eds.), Connecting Mathematics
across the Curriculum, pp. 3-12. Reston, VI: National Council of Teachers of Mathematics.
- Çavuşoğlu, D. and Dönmez, B. (2018). Transported education application in pazarcik according to the views of the managers, teachers, students and parents. Kuramsal Eğitimbilim Dergisi (Journal of Theoretical
Educational Science), 11(4), 646-675.
- Çilingir Altıner, E. (2018). İlkokul öğrencilerinin uzamsal düşünme ile yapboz oyunlarındaki becerileri arasındaki
ilişki. International Online Journal of Educational Sciences, 10(1), 75-87.
- Del Grande, J. (1990). Spatial sense. Arithmetic Teacher, 37(6), 14-20.
- Elliot, J. and Smith, I. M. (1983). An international directory of spatial tests. Windsor, Berkshire: NFER-Nelson.
- Guzel, N. and Sener, E. (2009). High school students’ spatial ability and creativity in geometry. Procedia: Social and Behavioral Sciences, 1(1), 1763-1766.
- Gül, Y. Ç. ve Karataş, İ. (2015). 8.sınıf öğrencilerinin dönüşüm geometrisi başarılarının uzamsal becerileri, geometri anlama düzeyleri ve matematiğe yönelik tutumları arasındaki ilişkinin incelenmesi. Karaelmas Eğitim Bilimleri Dergisi, 3, 36-48.
- Hacıömeroğlu, G. ve Hacıömeroğlu, E. S. (2017). Cinsiyet, uzamsal beceri, mantıksal düşünme becerisi ve çözüm tercihleri arasındaki ilişkinin incelenmesi. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 7(1), 116-131.
- Hannafin, R. D., Truxaw, M. P., Vermillion, J. R. and Liu, Y. (2008). Effects of spatial ability and instructional program on geometry achievement. The Journal of Educational Research, 101(3), 148-156.
- Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior,22, 55-72.
- İrioğlu, Z. ve Ertekin, E. (2012). İlköğretim ikinci kademe öğrencilerinin zihinsel döndürme becerilerinin bazı değişkenler açısından incelenmesi, Dünya’daki Eğitim ve Öğretim Çalışmaları Dergisi, 2(1), 75-81.
- Jo, I., Hong, J. E., and Verma, K. (2016). Facilitating spatial thinking in world geography using Web-based GIS, Journal of Geography in Higher Education, 40(3), 442-459.
- Karaman, T., and Toğrol, Y. A. (2009). Relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and performance related to plane geometry subjects among sixth grade students. Boğaziçi University Journal of Education, 26(1), 1-26.
- Gay, L. R. and Mills, G. E. (2014). Educational research: Competencies for analysis and applications, Global Edition: Edition 10. Pearson Education Limited.
- Kaufman, S. B. (2007). Sex differences in mental rotation and spatial visualization ability: Can they be accounted for by differences in working memory capacity? Intelligence,35, 211-223.
- Kayhan, E.B. (2005). Investigation of high school students’ spatial ability. MSc Dissertation, Ankara: Middle East Technical University.
- Kayri, M. (2009). Araştırmalarda gruplar arası farkın belirlenmesine yönelik çoklu karşılaştırma (post-hoc) teknikleri. Fırat Üniversitesi Sosyal Bilimler Dergisi, 19(1), 51-64.
- Kösa, T. (2016). Matematik eğitiminde teoriler. Erhan Bingölbali, Salahattin Arslan, İsmail Özgür Zembat (Eds.), Uzamsal Yetenek: Tanımı ve Bileşenleri (s.325-339). Ankara.
- Kösa, T. ve Kalay, H. (2018). 7. sınıf öğrencilerinin uzamsal yönelim becerilerini geliştirmeye yönelik tasarlanan öğrenme ortamının değerlendirilmesi. Kastamonu Eğitim Dergisi, 26(1), 83-92.
- Kurt, M. (2002). Görsel-uzamsal yeteneklerin bileşenleri. Klinik Psikiyatri, 5(2), 120-125.
- Lehmann, J. and Jansen, P. (2019). The relationship between theory of mind and mental rotation ability in
preschool-aged children. Cogent Psychology, 6(1), 1-8.
- Lohman, D. F. (1996). Spatial ability and g. In I. Dennis ve P. Tapsfield (Eds.), Human Abilities: Their Nature and
Assessment (pp. 97–116). Hillsdale, NJ: Erlbaum.
- Maier, P. H. (1996). Spatial geometry and spatial ability – how to make solid geometry solid? In E. Cohors-
Fresenberg, H. Maier, K. Reiss, G. Toerner ve H. G. Weigand (Eds.), Selected Papers from the Annual
Conference on Didactics of Mathematics 1996, Osnagrueck, 69-81.
- Mazman, G. Z. and Altun, A. (2013). Individual differences in spatial orientation performances: an eye tracking
study. World Journal on Educational Technology, 5(2), 266-280.
- McGee, M. G. (1979). Human spatial abilities: psychometric studies and environmental, genetic, hormonal, and
neurological influences. Psychological Bulletin, 86(5), 889-918.
- Ministry of National Education [MoNE].(2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. T.C. Milli
Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
- National Council of Teachers of Mathematics [NCTM].(2000). Principles and standards for school mathematics. Reston, VA: Author.
- National Research Council. (2006). Learning to think spatially: GIS as a support System in the K-12 curriculum.
Washington, DC: National Academies Press.
- Newton, P. and Bristoll, H. (2011). Spatial ability practice test 1. Retrieved from http://www.psychometric-
success.com
- Ogunkola, B. and Knight, C. (2019). Technical drawing course, video games, gender, and type of school on spatial ability. The Journal of Educational Research, 112(5), 575-589.
- Olkun, S. ve Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki. The TurkishOnline Journal of Educational Technology, 2(4), 1-7.
- O’Brien, T. (1989). Some thoughts on treasure keeping. Kappan, 70, 360-364.
Panaoura, G., Gagatsis, A. and Lemonides C. (2007). Spatial abilities in relation to performance in geometry tasks. Proceedings of CERME 5, 1062-1071.
- Pellegrino, J. W., Alderton, D. L. and Shutle, V. J. (1984). Understanding spatial ability. Educational Psychologist,
19(3), 239-253.
- Pittalis, M., Mousoulides, N. and Christou, C. (2007). Spatial ability as a predictor of students’ performance in
geometry. Proceedings of CERME 5, 1072-1081.
- Polat, M., Gönen, E., Parlak, B., Yıldırım, A. ve Özgürlük, B. (2016). TIMMS 2015 ulusal matematik ve fen ön raporu:
4. ve 8. sınıflar [TIMMS 2015 national mathematics and science preliminary report: Grades 4 and 8].
Ankara, Turkey: Milli Eğitim Bakanlığı.
- Postma, A., Jager, G., Kessels, R. P. C., Koppeschaar, H. P. F. and van Honk, J. (2004). Sex differences for selective
forms of spatial memory. Brain and Cognition, 54, 24-34.
- Schattschneider, D. (2010). The mathematical side of M. C. Escher. Notices of the AMS, 57(6), 706-718.
- Shamsuddin, N. A. A. and Din, S. C. (2016). Spatial ability skills: A correlation between Augmented Reality (AR)
and conventional way on wayfinding system. Environment-Behaviour Proceedings Journal, 1(2), 159-167. Stillwell, J. (2010). Mathematics and its history (3rd ed.). New York: Springer.
- Tartre, L. A. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in
Mathematics Education, 21(3), 216-229.
- Toptaş, V., Çelik, S., and Karaca, E. T. (2012). Improving 8th grades spatial thinking abilities through a 3D modeling program. The Turkish Online Journal of Educational Technology, 11(2), 128-134.
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and visual/spatial intelligence capabilities of sixth grade students. International Journal of Instruction,
8(1), 189-204.
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Sekizinci Sınıf Öğrencilerinin Uzamsal Yetenekleri ile Geometri Başarıları Arasındaki İlişkinin İncelenmesi
Yıl 2024,
Cilt: 10 Sayı: 2, 99 - 111, 23.08.2024
Hüseyin Demirkan
,
Adem Duru
Öz
Bu çalışmanın temel amacı, sekizinci sınıf öğrencilerinin uzamsal yetenekleri ile geometri başarıları arasındaki ilişkiyi cinsiyet, okul öncesi eğitim ama durumul ve okul türü değişkenlerini dikkate alarak belirlemektir. Bu araştırma ilişkisel tarama modeli uygulanarak gerçekleştirilmiştir. Kahramanmaraş ili Göksun ilçesinde farklı ortaokul türlerinde öğrenim gören 400 sekizinci sınıf öğrencisi katılmıştır. Araştırmada veri toplama aracı olarak demografik bilgi formu, araştırmacı tarafından geliştirilen Dönüşümsel Geometri ve Geometrik Cisimler Başarı Testi ile Newton ve Bristoll (2011) tarafından geliştirilen ve araştırmacı tarafından Türkçeye uyarlanan Uzamsal Yetenek Uygulama Testi kullanılmıştır. Veriler SPSS 17.0 paket programı ile betimsel istatistikler, bağımsız örneklemler için t-testi, tek yönlü ANOVA ve Pearson korelasyon katsayısı kullanılarak analiz edilmiştir. Araştırma bulgularına göre; öğrencilerin uzamsal yetenekleri ile geometri başarı puanları arasında pozitif yönde anlamlı ve orta düzeyde bir ilişki olduğu tespit edilmiştir. Öğrencilerin uzamsal yetenekleri açısından; kız öğrenciler, gündüzlü okullarda eğitim alan öğrenciler ve okul öncesi eğitim alan öğrenciler lehine anlamlı bir farklılık tespit edilmiştir.
Kaynakça
- Abay, S., Tertemiz, N., and Gökbulut, Y. (2018). Öğretmen adaylarının uzamsal yeteneklerinin çeşitli değişkenler açısından incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12(1), 45- 62.
- Arı, A. (2003). Taşımalı ilköğretim uygulaması (Uşak Örneği). Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 23(1), 101-115.
- Baki, A. (2015). Kuramdan uygulamaya matematik eğitimi (6.baskı). Ankara: Harf Eğitim Yayıncılığı.
- 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). Charlotte, NC: NCTM/Information Age
Publishing.
- Ben-Chaim, D., Lappan, G., and Houang, R. T. (1989). Adolescents’ ability to communicate spatial information:
Analyzing and effecting students’ performance. Educational Studies in Mathematics, 20, 121-146. Berberoğlu, G. (2007). Türk bakış açısından PISA araştırma sonuçları, Konrad Adenauer Stiftung Vakfı, [Online]:
http://www.konrad.org.tr/Egitimturk/07girayberberoglu.pdf.
- Boulter, D. R. (1992). The effects of instruction on spatial ability and geometry performance. Unpublished master thesis, Queen’s University, Ontario.
- Burnett, S. A. and Lane, D. M. (1980). Effects of academic instruction on spatial visualization. Intelligence, 4(3), 233-242.
- Büyüköztürk, Ş. (2002). Sosyal bilimler için veri analizi el kitabı. Ankara: Pegem Yayıncılık.
- Büyüköztürk, Ş., Çakan, M., Tan, Ş., and Atar, H. Y. (2014). TIMSS 2011 ulusal matematik ve fen raporu: 8. Sınıflar [TIMSS 2011 national mathematics and science report: 8th grade]. Ankara, Turkey: Milli Eğitim Bakanlığı.
- Carnoldi, C. and Vecchi, T. (2003). Visuo-spatial working memory and individual differences. New York:
Psychology Press.
- Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York, NY: Cambridge
University Press.
- Chao, J. Y. and Liu, C. H. (2017). A case study on the spatial conceptualization abilities for sixth grade elementary students from urban, suburban and remote schools. EURASIA Journal of Mathematics Science and
Technology Education, 13(6), 1675-1686.
- Colom, R., Contreras, M. J., Botella, J. and Santacreu, J. (2001). Vehicles of spatial ability. Personality and
Individual Differences,32, 903-912.
- Coxford, A. F. (1995). The Case for connections. In P. A. House and A. F. Coxford (Eds.), Connecting Mathematics
across the Curriculum, pp. 3-12. Reston, VI: National Council of Teachers of Mathematics.
- Çavuşoğlu, D. and Dönmez, B. (2018). Transported education application in pazarcik according to the views of the managers, teachers, students and parents. Kuramsal Eğitimbilim Dergisi (Journal of Theoretical
Educational Science), 11(4), 646-675.
- Çilingir Altıner, E. (2018). İlkokul öğrencilerinin uzamsal düşünme ile yapboz oyunlarındaki becerileri arasındaki
ilişki. International Online Journal of Educational Sciences, 10(1), 75-87.
- Del Grande, J. (1990). Spatial sense. Arithmetic Teacher, 37(6), 14-20.
- Elliot, J. and Smith, I. M. (1983). An international directory of spatial tests. Windsor, Berkshire: NFER-Nelson.
- Guzel, N. and Sener, E. (2009). High school students’ spatial ability and creativity in geometry. Procedia: Social and Behavioral Sciences, 1(1), 1763-1766.
- Gül, Y. Ç. ve Karataş, İ. (2015). 8.sınıf öğrencilerinin dönüşüm geometrisi başarılarının uzamsal becerileri, geometri anlama düzeyleri ve matematiğe yönelik tutumları arasındaki ilişkinin incelenmesi. Karaelmas Eğitim Bilimleri Dergisi, 3, 36-48.
- Hacıömeroğlu, G. ve Hacıömeroğlu, E. S. (2017). Cinsiyet, uzamsal beceri, mantıksal düşünme becerisi ve çözüm tercihleri arasındaki ilişkinin incelenmesi. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 7(1), 116-131.
- Hannafin, R. D., Truxaw, M. P., Vermillion, J. R. and Liu, Y. (2008). Effects of spatial ability and instructional program on geometry achievement. The Journal of Educational Research, 101(3), 148-156.
- Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior,22, 55-72.
- İrioğlu, Z. ve Ertekin, E. (2012). İlköğretim ikinci kademe öğrencilerinin zihinsel döndürme becerilerinin bazı değişkenler açısından incelenmesi, Dünya’daki Eğitim ve Öğretim Çalışmaları Dergisi, 2(1), 75-81.
- Jo, I., Hong, J. E., and Verma, K. (2016). Facilitating spatial thinking in world geography using Web-based GIS, Journal of Geography in Higher Education, 40(3), 442-459.
- Karaman, T., and Toğrol, Y. A. (2009). Relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and performance related to plane geometry subjects among sixth grade students. Boğaziçi University Journal of Education, 26(1), 1-26.
- Gay, L. R. and Mills, G. E. (2014). Educational research: Competencies for analysis and applications, Global Edition: Edition 10. Pearson Education Limited.
- Kaufman, S. B. (2007). Sex differences in mental rotation and spatial visualization ability: Can they be accounted for by differences in working memory capacity? Intelligence,35, 211-223.
- Kayhan, E.B. (2005). Investigation of high school students’ spatial ability. MSc Dissertation, Ankara: Middle East Technical University.
- Kayri, M. (2009). Araştırmalarda gruplar arası farkın belirlenmesine yönelik çoklu karşılaştırma (post-hoc) teknikleri. Fırat Üniversitesi Sosyal Bilimler Dergisi, 19(1), 51-64.
- Kösa, T. (2016). Matematik eğitiminde teoriler. Erhan Bingölbali, Salahattin Arslan, İsmail Özgür Zembat (Eds.), Uzamsal Yetenek: Tanımı ve Bileşenleri (s.325-339). Ankara.
- Kösa, T. ve Kalay, H. (2018). 7. sınıf öğrencilerinin uzamsal yönelim becerilerini geliştirmeye yönelik tasarlanan öğrenme ortamının değerlendirilmesi. Kastamonu Eğitim Dergisi, 26(1), 83-92.
- Kurt, M. (2002). Görsel-uzamsal yeteneklerin bileşenleri. Klinik Psikiyatri, 5(2), 120-125.
- Lehmann, J. and Jansen, P. (2019). The relationship between theory of mind and mental rotation ability in
preschool-aged children. Cogent Psychology, 6(1), 1-8.
- Lohman, D. F. (1996). Spatial ability and g. In I. Dennis ve P. Tapsfield (Eds.), Human Abilities: Their Nature and
Assessment (pp. 97–116). Hillsdale, NJ: Erlbaum.
- Maier, P. H. (1996). Spatial geometry and spatial ability – how to make solid geometry solid? In E. Cohors-
Fresenberg, H. Maier, K. Reiss, G. Toerner ve H. G. Weigand (Eds.), Selected Papers from the Annual
Conference on Didactics of Mathematics 1996, Osnagrueck, 69-81.
- Mazman, G. Z. and Altun, A. (2013). Individual differences in spatial orientation performances: an eye tracking
study. World Journal on Educational Technology, 5(2), 266-280.
- McGee, M. G. (1979). Human spatial abilities: psychometric studies and environmental, genetic, hormonal, and
neurological influences. Psychological Bulletin, 86(5), 889-918.
- Ministry of National Education [MoNE].(2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. T.C. Milli
Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
- National Council of Teachers of Mathematics [NCTM].(2000). Principles and standards for school mathematics. Reston, VA: Author.
- National Research Council. (2006). Learning to think spatially: GIS as a support System in the K-12 curriculum.
Washington, DC: National Academies Press.
- Newton, P. and Bristoll, H. (2011). Spatial ability practice test 1. Retrieved from http://www.psychometric-
success.com
- Ogunkola, B. and Knight, C. (2019). Technical drawing course, video games, gender, and type of school on spatial ability. The Journal of Educational Research, 112(5), 575-589.
- Olkun, S. ve Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki. The TurkishOnline Journal of Educational Technology, 2(4), 1-7.
- O’Brien, T. (1989). Some thoughts on treasure keeping. Kappan, 70, 360-364.
Panaoura, G., Gagatsis, A. and Lemonides C. (2007). Spatial abilities in relation to performance in geometry tasks. Proceedings of CERME 5, 1062-1071.
- Pellegrino, J. W., Alderton, D. L. and Shutle, V. J. (1984). Understanding spatial ability. Educational Psychologist,
19(3), 239-253.
- Pittalis, M., Mousoulides, N. and Christou, C. (2007). Spatial ability as a predictor of students’ performance in
geometry. Proceedings of CERME 5, 1072-1081.
- Polat, M., Gönen, E., Parlak, B., Yıldırım, A. ve Özgürlük, B. (2016). TIMMS 2015 ulusal matematik ve fen ön raporu:
4. ve 8. sınıflar [TIMMS 2015 national mathematics and science preliminary report: Grades 4 and 8].
Ankara, Turkey: Milli Eğitim Bakanlığı.
- Postma, A., Jager, G., Kessels, R. P. C., Koppeschaar, H. P. F. and van Honk, J. (2004). Sex differences for selective
forms of spatial memory. Brain and Cognition, 54, 24-34.
- Schattschneider, D. (2010). The mathematical side of M. C. Escher. Notices of the AMS, 57(6), 706-718.
- Shamsuddin, N. A. A. and Din, S. C. (2016). Spatial ability skills: A correlation between Augmented Reality (AR)
and conventional way on wayfinding system. Environment-Behaviour Proceedings Journal, 1(2), 159-167. Stillwell, J. (2010). Mathematics and its history (3rd ed.). New York: Springer.
- Tartre, L. A. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in
Mathematics Education, 21(3), 216-229.
- Toptaş, V., Çelik, S., and Karaca, E. T. (2012). Improving 8th grades spatial thinking abilities through a 3D modeling program. The Turkish Online Journal of Educational Technology, 11(2), 128-134.
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