Matematik Öğretmen Adaylarının Cebirin Temel Kavramlarına Yönelik Bilgi Düzeyleri

Yıl 2023, Sayı: 56, 949 - 973, 22.06.2023

Mahir Biber

https://doi.org/10.53444/deubefd.1265632

Cited By: 2

Öz

Bu araştırmada, ortaokul matematik öğretmen adaylarının cebir öğrenme alanının temel kavramlarına yönelik bilgi düzeylerini belirlemek ve çeşitli değişkenlere göre incelemek amaçlanmıştır. Araştırma bir devlet üniversitesinin İlköğretim Matematik Öğretmenliği programına devam eden ve kolay örnekleme yöntemine göre belirlenen 151 öğretmen adayı ile yürütülmüştür. Araştırmada durum çalışması deseninden yararlanılmıştır. Araştırmanın verileri araştırmacı tarafından hazırlanan 9 açık uçlu soru ile toplanmıştır. Verilerin analizinde hem nicel hem de nitel analiz tekniklerinden yararlanılmıştır. Elde edilen sonuçlar, ortaokul matematik öğretmen adaylarının cebirin temel kavramlarına ve kavramlar arasındaki ilişkilere yönelik bilgi düzeylerinin yetersiz olduğunu göstermektedir. Öğretmen adaylarının cebir bilgilerinin üst sınıflara doğru geliştiği, buna karşın üst düzey bir cebir bilgisinin oluşturulamadığı anlaşılmaktadır. Ayrıca, cebir bilgi düzeylerinin cinsiyete göre farklılaşmamasına karşın kızların ortalamalarının erkeklerden daha yüksek olduğu sonucuna ulaşılmıştır.

Anahtar Kelimeler

matematik, öğretmen adayları, cebir, bilgi düzeyi

Knowledge Levels of Pre-Service Mathematics Teachers on the Basic Concepts of Algebra

Öz

This study aimed to determine the knowledge levels of secondary school mathematics pre-service teachers about the basic concepts of learning algebra and to examine them according to various variables. The research was carried out with 151 pre-service teachers who attended a state university's Primary Education Mathematics Teaching program and were determined according to the convenience sampling method. The case study technique was used in the research. The data of the study were collected with nine open-ended questions prepared by the researcher. Both qualitative and quantitative analysis techniques were used in data analysis. The results show that the secondary school mathematics pre-service teachers have insufficient knowledge of the basic concepts of algebra and the relationships between the concepts. It is understood that pre-service teachers' algebra knowledge developed towards the upper classes with the effect of the courses they took in their undergraduate education but did not reach the high level. In addition, although the pre-service teachers' algebra knowledge levels did not differ according to gender, it was concluded that the mean algebra scores of girls were higher than boys.

Anahtar Kelimeler

mathematics, pre-service teachers, algebra, knowledge level

Kaynakça

• Ahuja, O. P. (2008). Importance Of Algebraic Thinking For Preservice Primary Teachers. https://www.semanticscholar.org/paper/Importance-Of-Algebraic-Thinking-For-Preservice-P./efbbdf2470a15d479749d9673aa8b1e0cbbb255c
• Akgün, L. (2009). Eight-grade students’ connection skills between word problems and the concept of variable. Mersin University Journal of the Faculty of Education, 5(2), 275–284. https://doi.org/10.17860/efd.00303
• Asante, K. O. (2010). Sex differences in mathematics performance among senior high students in Ghana. Gender and Behaviour, 8(2), Article 2. https://doi.org/10.4314/gab.v8i2.61947
• Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272. https://doi.org/10.1080/10986060701360910
• Aydin, M., & Köğce, D. (2008). Preservice teachers’ perceptions of “equation and function” conceptions. Journal of Yüzüncü Yıl University Education Faculty, 5(1), Article 1.
• Ball, D. L. (1988). Research on teaching mathematics: Making subject matter knowledge part of the equation. National Center for Research on Teacher Education, 116 Erickson Hall, College of Education, Michigan State University, East Lansing, MI 48824-1034 ($5. https://eric.ed.gov/?id=ED301467
• Birgin, O., & Demi̇rören, K. (2020). Investigation of 7th and 8th grade students’ performance about algebraic expressions. Pamukkale University Journal of Education, 50, Article 50. https://doi.org/10.9779/pauefd.567616
• Çelik, D. (2007). Analytical examination of the preservice teachers’ algebraic thinking skills [Doctoral Thesis]. Karadeniz Technical University.
• Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46. https://doi.org/10.1177/001316446002000104
• Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage Publications.
• Dede, Y., Bayazi̇t, İ., & Soybaş, D. (2010). Prospective teachers’ understanding of equation, function, and polynomial concepts. Kastamonu Education Journal, 18(1), Article 1.
• Demir, H., & Tuğrul, K. (2021). The Reasons For Failure In The Teaching Content Knowledge Test Of Pre-Service Elementary Mathematics Teachers. Social Sciences Studies Journal, 7(84), 2672–2687. https://doi.org/10.26449/sssj.3243
• Didiş Kabar, M. G., & Amaç, R. (2018). Investigating pre-service middle-school mathematics teachers’ knowledge of student and instructional strategies: An algebra case. Journal of Abant İzzet Baysal University Education Faculty, 18(1), 157–185.
• Dougherty, B., Bryant, D. P., Bryant, B. R., Darrough, R. L., & Pfannenstiel, K. H. (2015). Developing concepts and generalizations to build algebraic thinking: The reversibility, flexibility, and generalization approach. Intervention in School and Clinic, 50(5), 273–281. https://doi.org/10.1177/1053451214560892
• Dubinsky, E., & Harel, G. (1992). The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America.
• Duru, A., & Savaş, E. (2005). Gender difference in mathematics teaching. Erzincan University Journal of Education Faculty, 7(1), Article 1.
• Even, R. (1990). Subject Matter Knowledge for Teaching and the Case of Functions. Educational Studies in Mathematics, 21(6), 521–544.
• Graham, A. T., & Thomas, M. O. J. (2000). Building a Versatile Understanding of Algebraic Variables with a Graphic Calculator. Educational Studies in Mathematics, 41(3), 265–282.
• Huang, R., & Kulm, G. (2012). Prospective Middle Grade Mathematics Teachers’ Knowledge of Algebra for Teaching. Journal of Mathematical Behavior, 31(4), 417–430. https://doi.org/10.1016/j.jmathb.2012.06.001
• Kabael, T. U. (2010). Concept of the function: Historical development, understanding process, misconceptions and the teaching strategies. TÜBAV Science Journal, 3(1), Article 1.
• Kalaycı, Ş. (2008). Spss uygulamalı çok değişkenli istatistik teknikleri [Multivariate statistical techniques with spss applications]. Asil Publication.
• Karakuş, F. (2018). Investigation of primary pre-service teachers’ concept images on cylinder and cone. Elementary Education Online, 17(2), 1033–1050.
• Kartal, B., & Çinar, C. (2017). Examining pre-service mathematics teachers’ geometry knowledge of polygons. Journal of Ahi Evran University Kırşehir Education Faculty, 18(2), Article 2.
• Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. https://doi.org/10.2307/2529310
• Lima, R. N., & Tall, D. (2006). The concept of equations: What have students met before? PME, 4, 233–241.
• Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32. https://doi.org/10.1007/BF03217543
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook, 2nd ed (pp. xiv, 338). Sage Publications, Inc.
• MoNE. (2018). İlkokul ve ortaokul matematik dersi öğretim programı [Primary and secondary school mathematics curriculum]. Ministry of National Education. http://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
• MoNE. (2019). PISA 2018 Türkiye ön raporu [PISA 2018 Turkey preliminary report] (No. 10; Eğitim Analiz ve Değerlendirme Raporları Serisi [Training Analysis and Evaluation Reports Series]). http://www.meb.gov.tr/meb_iys_dosyalar/2019_12/03105347_PISA_2018_Turkiye_On_Raporu.pdf
• MoNE. (2020). TIMMS 2020 Türkiye ön raporu [TIMSS 2020 Turkey preliminary report] (No. 15; Eğitim Analiz ve Değerlendirme Raporları Serisi). http://odsgm.meb.gov.tr/meb_iys_dosyalar/2020_12/10175514_TIMSS_2019_Turkiye_On_Raporu_.pdf
• Moskal, B. M., & Leydens, J. A. (2000). Scoring Rubric Development: Validity and Reliability. Practical Assessment, Research & Evaluation, 7(10).
• NCTM. (1989). Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics. https://www.nctm.org/Standards-and-Positions/More-NCTM-Standards/
• Norman, D. A. (1992). Design principles for cognitive artifacts. Research in Engineering Design, 4(1), 43–50. https://doi.org/10.1007/BF02032391
• Serbin, K. S. (2021). Prospective teachers’ knowledge of secondary and abstract algebra and their use of this knowledge while noticing students’ mathematical thinking. https://vtechworks.lib.vt.edu/handle/10919/104563
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching -. Educational Researcher, 15(2), 4–14. https://doi.org/10.2307/1175860
• Sitrava, R. T. (2017). Prospective mathematics teachers’ concept images of algebraic expressions and equations. Cumhuriyet International Journal of Education, 6(2), Article 2. https://doi.org/10.30703/cije.331098
• Tavşancıl, E., & Aslan, A. E. (2001). Sözel, yazılı ve diğer materyaller için içerik analizi ve uygulama örnekleri [Content analysis and application examples for oral, written and other materials]. Epsilon Publishing.
• Toheri, T., & winarso, widodo. (2017, April 17). Improving Algebraic Thinking Skill, Beliefs And Attitude For Mathematics Throught Learning Cycle Based On Beliefs [MPRA Paper]. https://mpra.ub.uni-muenchen.de/78290/
• Zuya, H. E. (2017). Prospective teachers’ conceptual and procedural knowledge in mathematics: The case of algebra. American Journal of Educational Research, 5(3), Article 3. https://doi.org/10.12691/education-5-3-12