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Geometrik Şekiller Üzerine Akıl Yürütme Becerisi Geometri Performansının Bir Yordayıcısı mıdır?

Year 2020, Volume: 49 Issue: 2, 651 - 689, 28.10.2020

Abstract

Bu çalışmada matematik öğretmen adaylarının geometrik şekiller üzerine akıl yürütme becerileri ile geometri performansları arasındaki ilişki incelenmiştir. Çalışmanın katılımcılarını Doğu ve Güneydoğu Anadolu bölgelerinde bulunan iki üniversitenin eğitim fakültelerinde 2016-2017 öğretim yılı güz döneminde öğrenim gören 252 Bayan, 132 Erkek toplam 384 matematik öğretmen adayı oluşturmaktadır. Araştırmada zaman ve işgücü koşulları açısından var olan sınırlılıklar sebebiyle örneklem belirlenirken uygun örnekleme yöntemi tercih edilmiştir. Çalışmanın uygulamalarının yapıldığı bölümde ilişkisel tarama modeli kullanılmıştır. Çalışmanın verileri araştırmacılar tarafından geliştirmiş olan geometrik şekiller üzerine akıl yürütme beceri testi ve geometri performans testi ile toplanmıştır. Araştırma verileri betimsel istatistikler, t-testi, ANOVA Testi, Cohen’s f, Cohen’s d etki büyüklüğü değerleri, korelasyon analizi ve regresyon analizi yardımıyla analiz edilmiştir. Araştırmada geometrik şekiller üzerine akıl yürütme becerisi ve geometri performansı verileri cinsiyet değişkenine göre karşılaştırıldığında erkeklerin ortalamalarının bayanlardan yüksek olduğu tespit edilmiştir. Ayrıca geometri performans puanları incelendiğinde üçüncü sınıfların en yüksek ortalamaya sahip olduğu görülürken geometrik şekiller üzerine akıl yürütme becerisi puanları incelendiğinde en yüksek ortalamaya ikinci sınıfların sahip olduğu görülmektedir. Araştırmada matematik öğretmen adaylarının ölçek ve test puanları cinsiyet değişkenine göre incelendiğinde, geometrik şekiller üzerine akıl yürütme becerisi ve geometri performansı puanlarının aralarında anlamlı bir farklılık göstermediği bulunmuştur. Çalışmada yapılan ANOVA testi sonucunda geometrik şekiller üzerine akıl yürütme becerisi ve geometri performansı için sınıflar arası farklılığın anlamlı olduğu tespit edilmiştir. Hesaplanan Cohen’s f etki büyüklüğü değerleri sınıflar arası farklılıkların düşük düzeyde olduğunu göstermiştir. Bu farklılık sınıflar arasında araştırıldığında bazı sınıflar arasında anlamlı farklılığın olduğu tespit edilmiştir. Bu farklılıkların Cohen’s d etki büyüklüğü değerleri incelendiğinde de sınıflar arasında düşük düzeyde anlamlı etkilerin bulunduğu görülmektedir. Çalışmada değişkenler arasındaki korelasyon değerleri incelendiğinde geometrik şekiller üzerine akıl yürütme becerisi ile geometri performansı arasında yüksek düzeyde ilişki bulunmuştur. Ayrıca, geometrik şekiller üzerine akıl yürütme becerisinin geometri performansının anlamlı bir yordayıcısı olduğu tespit edilmiştir. Araştırmada elde edilen bulgular neticesinde geometrik şekiller üzerine akıl yürütme becerisi ve geometri performansı kavramlarının akademik alan ve matematik öğretiminde kullanımına ilişkin önerilerde bulunulmuştur.

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Are Reasoning Skills on Geometric Shapes Predictors of Geometry Performance?

Year 2020, Volume: 49 Issue: 2, 651 - 689, 28.10.2020

Abstract

In this study, the relationship between the pre-service mathematics teachers’ reasoning skills on geometric shapes and geometry performances were investigated. The participants of the study consisted of 384 pre-service mathematics teachers, 252 females, 132 males who studied at the faculties of education of two universities in Eastern and Southeastern Anatolia in the fall semester of 2016-2017 academic year. In the study, due to the limitations in terms of time and labor conditions, appropriate sampling method was preferred when determining the sample. In the section where the applications of the study were done, relational survey model was used. The data of the study were collected by reasoning skills on geometric shapes test and geometry performance test developed by the researchers. The data were analyzed using descriptive statistics, t-test, ANOVA test, Cohen’s f, Cohen’s d effect size values, correlation analysis and regression analysis. In the study, when the reasoning skills on geometric shapes and geometry performance data were compared according to gender variable, it was found that the average of men was higher than women. In addition, when the geometry performance scores are examined, it is seen that the third grade has the highest average, while reasoning skills on geometric shapes scores have the highest average in the second grade. When the scale and test scores of pre-service mathematics teachers were examined according to gender variable, it was found that reasoning skills on geometric shapes ability and geometry performance scores did not show a significant difference between them. As a result of ANOVA test, it was found that the differences between the classes were significant reasoning skills on geometric shapes ability and geometry performance. The calculated Cohen’s effect size values showed that the differences between the classes were low. When this difference was investigated between the classes, it was found that there was a significant difference between some classes. When the Cohen’s effect size values of these differences are examined, it is seen that there are low significant effects between the classes. When the correlation values between the variables were examined, a high-level relationship was found between the reasoning skills on geometric shapes ability and the geometry performance. In addition, it was found that reasoning skills on geometric shapes ability is a significant predictor of geometry performance. As a result of the findings obtained in the study, suggestions were made about the use of the concepts of reasoning skills on geometric shapes and geometry performance in academic field and mathematics teaching.

References

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  • Akyüz, G. and Pala, N. M. (2010). The effect of student and class characteristics on mathematics literacy and problem solving in PISA 2003. Elementary Education Online, 9(2), 668-678.
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  • Alptekin, S., Vural, M., & Aksoy, Y. (2016). A sample activity for improving the addition fluency of students with poor mathematics performance: cover-copy-compare Çanakkale Ondokuz Mayıs University Journal of Faculty of Education, 35(1), 105-117.
  • Altun, A. (2014). Determining the views of students attended to entrance examination for academic personnel and postgraduate education (eeappe) on the factors causing local item dependency. Qualitative Studies, 9(2), 19-31.
  • Areepattamannil, S. (2014). International Note: What factors are associated with reading, mathematics and science literacy of Indian adolescents? A multilevel examination. Journal of Adolescence, 37(2014), 367–372.
  • Arıcı, S. (2009). The effect of origami-based instruction on spatial visualization, geometry achievement and geometric reasoning of tenth-grade students. Published Master’s Thesis, Boğaziçi University, Educational Sciences Program, İstanbul.
  • Arıcı, S. & Aslan Tutak, F. (2015). Using origami to enhance geometric reasoning and achievement. International Journal of Science and Mathematics Education, 13(1), 179–200.
  • Arıkan, S. (2016). The relationship between opportunity to learn and mathematics performance in Turkey. Mustafa Kemal University Journal of Graduate School of Social Sciences, 13(36), 47-66.
  • Aunio P. & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(1), 427-435.
  • Aunola, K., Leskinen, E., & Nurmi, J. E., (2006). Developmental dynamics between mathematical performance, task motivation, and teachers’ goals during the transition to primary school. British Journal of Educational Psychology, 76(1), 21-40.
  • Aygüner, E. (2016). A comparison of eight grade students' self-efficacy perception of visual mathematics literacy and their actual performance. Published Master’s Thesis, Eskişehir Osmangazi University, Institute of Education, Eskişehir.
  • Bal A. P. (2012). Primary school students’ views and challenges on performance task preparation process in mathematics course. Pegem Journal of Education and Instruction, 2(1), 11-23.
  • Bal-İncebacak, B. & Ersoy, E. (2016). Analysis of mathematical reasoning ability of the grade 7 students according to TIMSS. The Journal of International Social Research, 9(46), 474-481.
  • Brown, M., Jones, K., Taylor, R., & Hirst, A. (2004). Developing geometrical reasoning. In: Ian Putt, Rhonda Faragher & Mal McLean (Eds), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA27), 27-30 June 2004, Townsville, Queensland, Australia, 127-134.
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  • Buckley, J., Seery, N., & Canty, D. (2018). Investigating the use of spatial reasoning strategies in geometric problem solving. International Journal of Technology and Design Education, 2018(1), 1-22.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz Ş., & Demirel, F. (2012). Scientific research methods. Ankara: Pegem Academy Publishing.
  • Büyüköztürk, Ş. (2015). Manual of data analysis for social sciences (10nd ed.). Ankara: Pegem Academy Publishing.
  • Cankoy, O. & Ozder, H. (2011). The influence of visual representations and context on mathematical word problem solving. Pamukkale University Journal of Education, 30(2), 91-100.
  • Chamberlin, M. T. (2011). The potential of prospective teachers experiencing differentiated instruction in a mathematics course. International Electronic Journal of Mathematics Education, 6(1), 135-156.
  • Chacón, I. M. G., Albaladejo, I. M. R., & López, M. M. G. (2016). Zig-zagging in geometrical reasoning in technological collaborative environments: a mathematical working space-framed study concerning cognition and affect. ZDM Mathematics Education, 48(1), 909-924.
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  • Çubukçu, Z. (2004). The effect of thinking styles of pre-service teachers on learning style preferences. İnönü University Journal of the Faculty of Education, 1(1), 19-36.
  • Duatepe, A., Akkuş-Çıkla, O., & Kayhan, M. (2005). An investigation on students’ solution strategies for different proportional reasoning items. Hacettepe University Journal of Education, 28(1), 73-81.
  • Ellis, H. C. & Hunt, R. R. (1993). Fundamentals of cognitive psychology. The United States of America: Oxford Brown and Benchmark.
  • Erkek, Ö. & Işıksal-Bostan, M. (2015). The role of spatial anxiety, geometry self-efficacy and gender in predicting geometry achievement. Elementary Education Online, 14(1), 164-180.
  • Erdal, H. (2007). The investigation of measurement & evaluation parts in the new elementary school mathematics curriculum. Non-published Master’s Thesis, Afyon Kocatepe University, Institute of Social Sciences, Afyon.
  • Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude. Non-published PhD Dissertation, Atatürk University Institute of Education Sciences, Erzurum.
  • Erdoğan, T., Akkaya, R., & Çelebi-Akkaya, S. (2009). The effect of Van Hiele model based instruction on the creative thinking levels of 6th grade primary school students. Educational Sciences Theory & Practice, 9(1), 161-194.
  • Ergül, A. & Artan, İ. (2015). Determining early mathematical reasoning skills. Journal of Theoretical Educational Science, 8(4), 454-485.
  • Ersoy, A., Gürdoğan-Bayır, Ö., & Güvey, E. (2010). Project works in primary education: classroom teachers’ expectations of parents. Anadolu University Journal of Social Sciences, 10(3), 157-170.
  • Field, A. (2005). Discovering statistics using SPSS (2nd ed.). London: Sage.
  • Fischbein, E. & Nachlieli, T. (1998). Concepts and figures in geometrical reasoning. International Journal of Science Education, 20(10), 1193-1211.
  • Fujita, T. & Jones, K. (2002). Opportunities for the development of geometrical reasoning in current textbooks in the UK and Japan. British Society for Research into Learning Mathematics, 22(3), 79-84.
  • Funkhouser, C. (2002). The effects of computer-augmented geometry instruction on student performance and attitudes. Journal of Research on Technology in Education, 35(2), 163-175.
  • Geer, E. A., Quinn, J. M., & Ganley, C. M. (2018). Relations between spatial skills and math performance in elementary school children: A longitudinal investigation. Developmental Psychology, 54(12), 1-22.
  • Gerald, L. M. (2002). An evolutionary theory of knowledge and conceptual evolution in science. Global Bioethics Journal, 15(3), 73-80.
  • Gökkaya-Çoban, F. B. (2001). The Effect of computer assisted instruction on mathematics performance of seventh graders. Published Master’s Thesis, Boğaziçi University, Graduate Studies in Science and Engineering, İstanbul.
  • Hall, W., Davis, N. B., Bolen, L. M., & Chia, R. (1999). Gender and racial differences in mathematical performance. The Journal of Social Psychology, 139(6), 677-689.
  • İlhan, A. (2015). Development of visual mathematics literacy scale towards elementary school mathematics teacher candidates and investigation of the relationship between success in geometry and visual mathematics literacy. Published Master’s Thesis, Fırat University Institute of Education, Elazığ.
  • İlhan, A. (2019). Investigation of the relationship of elementary mathematics teacher candidates between visual mathematics literacy perception level, reasoning skill on geometry and performance levels. Published PhD Dissertation, Inönü University, Graduate School of Education, Malatya.
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There are 75 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Article
Authors

Aziz İlhan 0000-0001-7049-5756

Recep Aslaner 0000-0003-1037-6100

Publication Date October 28, 2020
Submission Date July 22, 2019
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA İlhan, A., & Aslaner, R. (2020). Are Reasoning Skills on Geometric Shapes Predictors of Geometry Performance?. Cukurova University Faculty of Education Journal, 49(2), 651-689. https://doi.org/10.14812/cuefd.595333

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