Farklı Düzeyde Sayı Duyusu Becerisine Sahip İlköğretim Matematik Öğretmen Adaylarına İlişkin Durum Çalışması

Year 2018, Volume: 12 Issue: 2, 276 - 305, 31.12.2018

Özge Dayı Mehmet Ali Kandemir

https://doi.org/10.17522/balikesirnef.506441

Abstract

Bu çalışmada
ilköğretim matematik öğretmen adaylarının sayı duyularının incelenmesi
amaçlanmıştır. Çalışmada farklı sayı duyusu başarı düzeyindeki iki öğretmen
adayının  sayı duyusu becerileri kendi
içlerinde derinlemesine incelendikten sonra karşılaştırma yaparak mevcut durum  incelendiği için durum çalışması deseni
kullanılmıştır. Araştırmada seçilen iki ilköğretim matematik öğretmen adayı
aykırı durum örneklemesi ile seçilmiştir. Veri toplamak amacıyla sayı duyusu testi
ve klinik mülakat sayı duyusu testi kullanılmıştır. Elde edilen nitel veriler
içerik analizine ve doküman  incelemesine
tabi tutulmuştur. Araştırmanın sonucunda öğretmen  adaylarının soruların çözümünde kullandıkları
stratejiler, sayı duyusu kullanma düzeyleri, sayı duyusu bileşenleri ve sayı
duyusu arasındaki ilişkiye ilişkin bulgular elde edilmiştir. Bu çalışma,  sayı duyusu
özelliklerinin kullanımında yüksek ve düşük sayı duyularına sahip iki öğretmen
adayı arasında keskin farklılıklar olduğunu ortaya koymuştur. Elde edilen
sonuçlara göre öğretmen adaylarının çözüm süreçleri incelendiğinde kural
kullanma, yanlış hesaplamalar yapma, açıklama olmayan cevaplar, sezgisel
fikirler, zihinsel hesaplamalar, tahmin stratejilerini kullanma gibi
çeşitlenmiştir.

Keywords

Sayı duyusu, sayı duyusu bileşenleri, çözüm yolu stratejileri, matematik öğretmen adayları

Case Study of Elementary School Mathematics Teacher Candidates with Number Sense Skills at Different Levels

Abstract

In
this study, it is aimed to examine the number senses of primary school
mathematics teacher candidates. In the study, the number sense skills of two
teachers candidates at different levels of number sense success were examined  in-depth and the case study design was used by
making comparisons since the current situation was examined. Two elementary
school mathematics teacher candidates who participated in the study were
selected by using the extreme (deviant) case sampling. Number sense test and
clinical interview number sense test were used to collect data. The qualitative
data were subjected to content analysis and document review. As a result of the
research, the findings regarding the strategies used by the teacher candidates to
solve problems, the number sense use levels, the number sense components, and
their relationships with number sense were obtained. As a result of this study,
there were sharp differences between two teacher candidates with high and low
number sense levels in the use of number sense characteristics. According to
the results, when the problem solving processes of the teacher candidates were
examined, their strategies were diversified such as using rules, making
incorrect calculations, answers without explanations, intuitive ideas, mental
calculations, and estimating strategies.

Keywords

Number sense, number sense components, strategies for problem solving, mathematics teacher candidates

References

• Akkaya, R. (2015). An investigation into the number sense performance of secondary school students in Turkey. Journal of Education and Training Studies, 4(2), 113-123.
• Almeida, R., Bruno, A., & Perdomo-Díaz, J. (2016). Strategies of number sense in pre-service secondary mathematics teachers. International Journal of Science and Mathematics Education, 14(5), 959-978.
• Baki, M. (2013). Sınıf öğretmeni adaylarının bölme işlemi ile ilgili matematiksel bilgileri ve öğretimsel açıklamaları. Eğitim ve Bilim, 38(167).
• Barchard, K. A., & Hakstian, A. R. (1997). The effects of sampling model on inference with coefficient alpha. Educational and Psychological Measurement, 57(6), 893-905.
• Bayram, G. (2013). 8. sınıf öğrencilerinin üslü ifadelere ilişkin sayı duyuları ve başarıları arasındaki ilişki, Yayımlanmamış Doktora Tezi, Pamukkale Üniversitesi Eğitim Bilimleri Enstitüsü, Denizli.
• Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2016). Örnekleme Yöntemleri. Ş. Büyüköztürk, E. Kılıç Çakmak, Ö. E. Akgün, Ş. Karadeniz, & F. Demirel içinde, Bilimsel Araştırma Yöntemleri (s. 83-92). Ankara: Pegem Akademi
• Clark, C. M., & Peterson, P. L. (1986). Teachers' thought processes. In M. C. Wittrock (Ed.), Handbook of Research on Teaching (3rd ed., pp. 255-296). New York, NY: Macmillan
• Courtney-Clarke, M., & Wessels, H. (2014). Number sense of final year pre-service primary school teachers: Original research. Pythagoras, 35(1), 9 pages.
• Creswell, J. W. (2016). Karma Yöntem Desenlerinin Çeşitleri. S. B. Demir içinde, Research Desıgn Qualitative, Quantitative and Mixed Methods Approaches (s. 219-240). Ankara: Eğiten Kitap.
• Dede, H. G., & Şengül, S. (2016). İlköğretim ve Ortaöğretim Matematik Öğretmen Adaylarının Sayı Hissinin İncelenmesi 1. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(2), 285-303.
• . Ergin, D.,Y., (1995). Ölçeklerde Geçerlik ve Güvenirlik. M.Ü. Atatürk Eğitim Fakültesi Eğitim Bilimleri Dergisi, 7,125-148
• Fraenkel, J. R., & Wallen, N. E. How to design and evaluate research in education 2006. Mc Grawall Hill.
• Gay, S. A. ve Aichele, D. B. (1997). Middle school students' understanding of number sense related to percent. School Science and Mathematics, 97 (1), 27–36.
• Gay, A. S. (1990). A study of middle school students’ understanding of number sense related to percent (Doctor of Education, Oklahoma State University, 1990). Dissertation Abstracts International, UMI No. 9119873.
• Gliner, G.(1991). Factors contributing to success in mathematical estimation in preservice teachers : Types of problems and previous mathematics experience. Educational Studies in Mathematics. 22(6), 595-606.
• Greer, B. (1997). Modelling Reality in Mathematics classroom: The Case of Word Problems, Learning and Instruction, 7 (7), 293- 307.
• Harç, S. (2010). 6. Sınıf öğrencilerinin sayı duyusu kavramı açısından mevcut durumlarının analizi, Yayınlanmış Yüksek Lisans Tezi, Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
• Hiebert, J. (1984). Children’s mathematics learning: The struggle to link form and understanding. The Elementary School Journal, 84, 496-513.
• Hiebert, J., Carpenter, T. P., & Moser, J. M. (1982). Cognitive development and children's solutions to verbal arithmetic problems. Journal for research in mathematics education, 83-98.
• Hinton, V. (2011). Pre-service teachers’ computational knowledge, efficacy, and number sense skills (Doctoral dissertation).
• Hungerford, T. W. (1994). Future elementary teachers: The neglected Constituency. The American Mathematical Monthly. 101 (1), 15-21.
• Iymen, E., & Paksu, A. D. (2015). Analysis of 8th Grade Students' Number Sense Related to the Exponents in Terms of Number Sense Components. Egitim ve Bilim, 40(177).
• İymen. E, (2012). 8. Sınıf Öğrencilerinin Üslü Ifadeler ile Ilgili Sayı Duyularının Sayı Duyusu Bileşenleri Bakımından Incelenmesi. Yayımlanmamış yüksek lisans tezi, Pamukkale Üniversitesi, Denizli.
• Kamii, C. & Lewis. B. A. (1991). Achievement tests in primary mathematics: Perpetuating lower-order thinking. Arithmetic Teacher, 39(9). 4-9.
• Kaminski, E. (1997). Teacher education students’ number sense: Initial explorations. Mathematics Education Research Journal, 9(2), 225-235. doi: 10.1007/BF03217312
• Kartal, A. (2016). 8. Sınıf Öğrencilerinin Kesirlerde Sayı Duyularının İncelenmesi (Yayımlanmamış Doktora Tezi) . Recep Tayyip Erdoğan Üniversitesi, Sosyal Bilimler Enstitüsü, Rize.
• Kayhan-Altay, M. (2010). İlköğretim İkinci Kademe Öğrencilerinin Sayı Duyularının; Sınıf Düzeyine, Cinsiyete Ve Sayı Duyusu Bileşenlerine Göre İncelenmesi, Yayınlanmamış Doktora Tezi, Hacettepe Üniversitesi, Ankara.
• Kayhan-Altay, M. ve Umay, A. (2011). Sınıf Öğretmeni Adayların Hesaplama Becerileri ve Sayı Duyuları Arasındaki İlişkinin İncelenmesi. e-Journal of New World Sciences Academy, 6(1), 1277-1283.
• Lin, Y. C. (2016). Diagnosing Students' Misconceptions in Number Sense via a Web-Based Two-Tier Test. Eurasia Journal of Mathematics, Science & Technology Education, 12(1).
• Linn, R.L., & Gronlund, N.E. (1995). Measuring and assessment in teaching (7th ed.). Englewood Cliffs, NJ: Prentice-Hall.
• Markovits, Z. & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25 (1), 4–29.
• McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12 (3), 2–9.
• Mcmillan, J. H. (2000). Educational Research: Fundamentals fort he consumer. New York: Longman.
• MEB (Milli Eğitim Bakanlığı), (2018). İlköğretim Matematik Dersi 5-8. Sınıflar Öğretim Programı ve Kılavuzu. Ankara: MEB.
• Miles, M. B., Huberman, A. M., Huberman, M. A., & Huberman, M. (1994). Qualitative data analysis: An expanded sourcebook: Sage.
• Mohamed, M. ve Johnny, J. (2010). Investigating number sense among students. Procedia Social and Behavioral Sciences, 317-324.
• National Council of Teachers of Mathematics (NCTM) (2000). Principles and standars for school mathematics. Reston, VA: Author.
• Rasch, K. (1992). Mathematical Literacy To Empower Teacher Education Students in the 21st Century: How Can This Become Reality? Paper presented at the National Forum of the Association of Independent Liberal Arts Colleges for Teacher Education, June 5-8, 1992,Maryville University of Saint Louis, Missouri,USA. ERIC Document : ED 351 291.
• Resnick, L. B. (1989). Defining, assessing and teaching number sense. In Establishing foundations for research on number sense and related topics: Report of a conference (pp. 35-39). San Diego State University, Center for Research in Mathematics and Science Education.
• Resnick, L. B. (1983). Mathematics and science learning: A new conception. Science, 220(4596), 477-478. http://dx.doi.org/10.1126/science.220.4596.477
• Reys, R. E. ve Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth- grade students in Taiwan, Journal for Research in Mathematics Education, 29 (2), 225–237.
• Reys. R.E.. Reys. B. J.. Nohda. N.. & Emori. H. (1995). Mental computation performance and strategy use of Japanese students in grade 2.4.6. and 8. Journal for Research in Mathematics Education, 26. 204-326.
• Reys R. E., Reys, B. J., Nohda, N. lshidda, J., Yoshikawa, S., & Shimizu. K. (1991). Computational estimation performance and strategies used by fifth- and eighth-grade Japanese students. Journal for Research in Mathematics Education, 22(1 ), 39-58.
• Sengul, S. (2013). Identification of Number Sense Strategies used by Pre-service Elementary Teachers. Educational Sciences: Theory and Practice, 13(3), 1965-1974.
• Singh, P. (2009). An Assessment of Number Sense among Secondary School Students. International Journal for Mathematics Teaching and Learning. http://www.cimt.org.uk/journal/singh.pdf adresinden ulaşılmıştır. Erişim Tarihi: 10/06/2016.
• Sowder, J. T. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 371-389). New York, NY, England: Macmillan Publishing Co, Inc.
• Stemler, S. (2001). An overview of content analysis. Practical assessment, research & evaluation, 7(17), 137-146.
• Şengül, S. ve Gülbağcı Dede, H. (2014). The strategies of mathematics teachers when solving number sense problems. Turkish Journal of Computer and Mathematics Education, 5(1), 73-88.
• Tekin, H. (2000). Eğitimde Ölçme ve Değerlendirme. (14. Baskı). Yargı Yayınevi, Ankara.
• Tirosh, D., & Graeber, A. O. (1991). The effect of problem type and common misconceptions on preservice elementary teachers' thinking about division. School Science and Mathematics, 91(4), 157-163.
• Tsao, Y. L. (2004). Exploring the Connections among Number Sense, Mental Computation Performance, and the Written Computation Performance of Elementary Preservice School Teachers. Journal of College Teaching & Learning, 1(12), 71-90.
• Yaman, H. (2015). Sınıf düzeylerine göre öğretmen adaylarının sayı duyusu performansları. Kastamonu Eğitim Dergisi, 23(2), 739-754.
• Yang, D. C. (1997). Number sense performance and strategies possessed by sixth- and eighth-grade students in Taiwan. Doctoral dissertation, University of Missouri, Columbia, 1995. Dissertation Abstracts International, 57, 3.
• Yang, D. C. (2005). Number sense strategies used by 6th-grade students in Taiwan. Educational Studies, 31, 317-333.
• Yang, D. C. (2007). Investigating the strategies used by pre-service teachers in Taiwan when responding to number sense questions. School Science and Mathematics, 107(7), 293-301.
• Yang, D. C., & Li, M. F. (2008). An investigation of 3rd grade Taiwanese students’ performance in number sense. Educational Studies, 34(5), 443-455. doi: 10.1080/03055690802288494
• Yang, D. C., & Li, M. N. (2013). Assessment of Animated Self-Directed Learning Activities Modules for Children's Number Sense Development. Journal of Educational Technology & Society, 16(3).
• Yang, D. C., & Lin, Y. C. (2015). Assessing 10-to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test. Educational Research, 57(4), 368-388.
• Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7(2), 383-403.
• Yapıcı, A. (2013). 5, 6 ve 7. sınıf öğrencilerinin yüzdeler konusunda sayı duyularının incelenmesi, Yayımlanmamış Yüksek Lisans Tezi, Hacettepe Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
• Zanzali, N. A. A., & Ghazali, M. (1999). Assessment of school children’s number sense. Proceedings of the International Conference on Mathematics Education into the 21st Century: Societal Challenges: Issues and Approaches. Cairo, Egypt.