Ortaokul Öğrencilerinin Kesir ve Geometrik Alan Ölçme Bilgisini Birbirine Bağlama Becerisinin Belirlenmesi

Yıl 2023, Cilt: 17 Sayı: 2, 963 - 993, 02.01.2024

Fatma Nur Öztürk , Nejla Gürefe

https://doi.org/10.17522/balikesirnef.1319889

Cited By: 1

Öz

Bu çalışmada ortaokul öğrencilerinin kesir bilgisi ve geometrik alan ölçme Bilgisi ortaya çıkarılarak kesri belirlerken alan ölçme bilgisini nasıl kullandığı belirlenmiştir. Durum çalışması şeklinde tasarlanan bu çalışma 6, 7 ve 8. sınıflardan belirlenen dokuz öğrenci ile yürütülmüştür. Birebir görüşmeler yoluyla toplanan veriler betimsel analiz kullanılarak analiz edilmiştir. Bulgular sonucunda katılımcıların kesir ve alan ölçme bilgisinin ön içselleştirme, içselleştirme, yoğunlaştırma ve yenidenleştirme profillerinden çoğunlukla ön içselleştirme profilinde olduğu belirlenmiştir. Öğrencilerin farklı bölümlendirilmiş kesir alan modellerinde, değişik stratejiler ve yöntemler kullandıklarını, farklı zihinsel şemalar ortaya çıkardıklarını ve öğrencilerin görevlere verdiği yanıtların kesir bilgisi ve alan ölçme bilgisini ortaya çıkardığı görülmüştür. Araştırmanın sonucunda kesir kavramı gibi önemli bir kavramı öğreten matematik öğretmenlerinin ve sınıf öğretmenlerinin temel matematiksel kavramları bütünleştirebilen görevler tasarlamaları ve farklı alanlar arasında bağ kurmaları konusunda öneride bulunulabilir.

Anahtar Kelimeler

Kesir, alan ölçme, ortaokul öğrencileri

Destekleyen Kurum

Yok

Proje Numarası

Yok

Teşekkür

Yok

How do Middle School Students Use Their Knowledge of Geometric Area Measurement When Determining Fractions?

Öz

In this study, the objective was to assess students' proficiency in utilizing their knowledge of geometric area measurement and fractions, and to examine how they apply this knowledge in determining fractions. The research, structured as a case study, encompassed nine students from the 6th, 7th, and 8th grades. Data gathered through individual interviews were analyzed using content analysis. The findings revealed that participants predominantly exhibited a preliminary internalization profile in terms of their understanding of fractions and area measurement. This profile encompasses stages such as pre-internalization, internalization, condensation, and reification. It was observed that students employed diverse strategies and methods within various segmented fraction area models, thereby unveiling distinct mental schemes. The responses provided by students to the tasks illustrated their comprehension of fractions and area measurement. Based on the research results, it is recommended that mathematics teachers and classroom instructors, tasked with imparting crucial concepts like fractions, devise tasks that integrate fundamental mathematical principles and establish connections across different domains.

Anahtar Kelimeler

Fraction, Area Measurement, Middle School Students

Proje Numarası

Yok

Kaynakça

• Acar, N. (2010). Kesir çubuklarının ilköğretim 6. sınıf öğrencilerinin kesirlerde toplama ve çıkarma işlemlerindeki başarılarına etkisi [The effect of fraction rulers on the addition and subtraction of fraction abilities of 6th grade students of elementary school]. [Unpublished master’s thesis]. Selçuk University.
• Akbaba-Dağ, S. (2014). Mikroöğretim ders imecesi modeli ile sınıf öğretmeni adaylarının kesir öğretim bilgilerinin geliştirilmesine yönelik bir uygulama [A microteaching lesson study practice to improve pre-service teachers' knowledge of teaching fractions] [Unpublished doctoral dissertation]. Dumlupınar University.
• Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal Of Experimental Child Psychology, 113(3), 447-455. https://doi.org/10.1016/j.jecp.2012.06.004
• Baştürk, S. (2016). Primary student teachers’ perspectives of the teaching of fractions. Acta Didactica Napocensia, 9(1), 35-44.
• Battista, M. T. (2003). Understanding students’ thinking about area and volume measurement. In D. H. Clements (Ed.), 2003 yearbook, learning and teaching measurement (122-142). National Council of Teachers of Mathematics.
• Cavanagh, M. (2008). Area measurement in year 7. Educational Studies in Mathematics, 33, 55- 58.
• Chappell, M. F., & Thompson, D. R. (1999). Perimeter or area? Which measure is it?. Mathematics Teaching in the Middle School, 5(1), 20-23. https://doi.org/10.5951/MTMS.5.1.0020
• Ciosek, M., & Samborska, M. (2016). A false belief about fractions-What is its source?. The Journal of Mathematical Behavior, 42, 20-32. https://doi.org/10.1016/j.jmathb.2016.02.001
• Cramer, K., & Henry, A. (2002). Using manipulative models to build number sense for addition of fractions. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 yearbook (pp. 41-48). National Council of Teachers of Mathematics,
• Cramer, K., Monson, D., Whitney, S., Leavitt, S., & Wyberg, T. (2010). Dividing fractions and problem solving. Mathematics Teaching in the Middle School, 15(6), 338-346. https://doi.org/10.5951/MTMS.15.6.0338
• Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches. Sage.
• Denzin, N. K., & Lincoln, Y. S. (Eds.). (2011). The Sage handbook of qualitative research. Sage.
• Doğan Temur, Ö. (2011). Dördüncü ve beşinci sınıf öğretmenlerinin kesir öğretimine ilişkin görüşleri: Fenomenografik araştırma [Opinions of teachers of fourth and fifth grade about teaching fractions: A phenomographic research]. Dumlupınar University, Journal of Social Sciences, 29, 203-212. https://dergipark.org.tr/tr/download/article-file/55686
• Dougherty, B. J., & Slovin, H. (2004). Generalized diagrams as a tool for young children's problem solving. 28th Conference of the International Group for the Psychology of Mathematics Education.
• Gürefe, N. (2018). Ortaokul öğrencilerinin alan ölçüm problemlerinde kullandıkları stratejilerin belirlenmesi [Determining strategies used in area measurement problems by middle school students]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 33(2), 417-438. https://doi.org/10.16986/HUJE.2017032703.
• Hackenberg, A. J., & Lee, M. Y. (2015). Relationships between students’ fractional knowledge and equation writing. Journal for Research in Mathematics Education, 46(2), 196-243. https://doi.org/10.5951/jresematheduc.46.2.0196
• Kavuncu, T. (2019) Investigation of 5th grade student's skills of problem solving and posing problems suitable for fraction models [Unpublished master’s thesis]. Osmangazi University.
• Kieren, T. E. (1976, April). On the mathematical, cognitive and instructional. In R. A. Lesh & D. A. Bradbard (Eds.), Number and measurement. Papers from a research workshop (pp. 101). National Science Foundation.
• Kordaki, M., & Balomenou, A. (2006). Challenging students to view the concept of area in triangles in a broad context: Exploiting the features of Cabri-II. International Journal of Computers for Mathematical Learning, 11, 99-135. https://doi.org/10.1007/s10758-005-5380-z
• Kurt, G. (2006). Middle grade students’ abilities in translating among representations of fractions (Unpublished master’s thesis). Middle East Technical University.
• Lee, M. Y. (2017). Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96(3), 327-348. https://doi.org/10.1007/s10649-017-9771-6
• Lee, M. Y., & Hackenberg, A. J. (2014). Relationships between fractional knowledge and algebraic reasoning: The case of Willa. International Journal of Science and Mathematics Education, 12(4), 975-1000. https://doi.org/10.1007/s10763-013-9442-8
• Lee, M. Y., & Lee, J. E. (2020). Spotlight on area models: Pre-service teachers’ ability to link fractions and geometric measurement. International Journal of Science and Mathematics Education, 1-24. https://doi.org/10.1007/s10763-020-10098-2
• Lehrer, R., Jaslow, L., & Curtis, C. L. (2003). Developing an understanding of measurement in the elementary grades. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 100-121). National Council of Teachers of Mathematics.
• Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates.
• Mitchell, A. E. (2011). Interpreting students’ explanations of fraction tasks, and their connections to length and area knowledge Doctoral dissertation]. Australian Catholic University.
• Olive, J., & Steffe, L. P. (2010). The construction of fraction schemas using the generalized number sequence. In Children's fractional knowledge (pp. 277-314). Springer.
• Olkun, S., & Uçar, Z. T. (2014). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics teaching in primary education] (6th ed.). Eğiten Kitap.
• Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36. https://doi.org/10.1007/BF00302715
• Siebert, D., & Gaskin, N. (2006). Creating, naming, and justifying fractions. Teaching Children Mathematics, 12(8), 394-400. https://doi.org/10.2307/41198803
• Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13-19. https://doi.org/10.1016/j.tics.2012.11.004
• Şen, C. (2021). Assessment of A Middle-school mathematics teacher’s knowledge for teaching the 5th-grade subject of fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 12(1), 96-138. https://doi.org/10.16949/turkbilmat.742136
• Tan Şişman, G., & Aksu, M. (2009). Yedinci sınıf öğrencilerinin alan ve çevre konularındaki başarıları [Seventh grade students’ success on the topics of area and perimeter]. Elementary Education Online, 8(1), 243-253. https://dergipark.org.tr/en/download/article-file/90905
• Toptaş, V., Han, B., & Akın, Y. (2017). Primary school teachers’ opinions about different meanings of fractions and models of fractions. Sakarya University Journal of Education Faculty, 33, 49-67. https://dergipark.org.tr/tr/download/article-file/332047
• Uslu, C. Ş. (2006). İlköğretim 1. ve 2. kademesi ile ortaöğretim 10. sınıf öğrencilerinin matematiğin temel kavramlarındaki eksik ve yanlış öğrenmelerinin karşılaştırılması [Comparison of the deficiencies and misconceptions on the basic concepts of mathematics in the 1st and 2nd grade of primary education with 10th class students of the secondary education] [Unpublished master’s thesis]. Selçuk University.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim [Primary and secondary school mathematics: Teaching with a developmental approach] (S. Durmuş, Trans. Ed.). Nobel.
• Yakar, G. (2019). Investigating middle school inclusive students' learning process of basic fraction concepts with fraction models [Unpublished master’s thesis], Tokat Gaziosmanpaşa University.
• Yavuz Mumcu, H. (2018). Using mathematical models in fraction operations: A case study. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 12(1), 122-151. https://doi.org/10.17522/balikesirnef.437721
• Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. Seçkin Yayıncılık.
• Zeybek, Z., & Cross Francis, D. (2017). Let’s cut the cake. Teaching Children Mathematics, 23(9), 542-548. https://doi.org/10.5951/teacchilmath.23.9.0542