Solution Strategies of a Teacher Candidate: Rediscovering Numbers in Base Eight

Yıl 2016, , 0 - 0, 24.05.2016

Didem Akyüz

https://doi.org/10.17679/iuefd.17283573

Öz

Up to today, many of the studies mostly investigated students' understanding of natural numbers rather than preservice teachers’. This study conducts a case study in order to investigate a preservice teacher's understanding of natural numbers and operations on them. The preservice teachers, who were enrolled in a senior year course in an elementary mathematics education department, used materials for natural numbers that aimed to teach the concepts and operations using base eight instead of customarily used base ten for a period. This way, preservice teachers had a chance to develop different strategies for the operations that they memorized in base ten and their thinking ways are investigated during the solution of operations. The results reveal that using different base supports preservice teachers to change their thinking style and interpret the problems from a different perspective without doing any memorization.

Anahtar Kelimeler

natural numbers, prospective teachers, base 8, number operations

Bir Öğretmen Adayının Çözüm Stratejileri: Sayıları Sekizlik Tabanda Yeniden Keşfetme

Öz

Bugüne kadar yapılan çalışmalar çoğunlukla öğrencilerin doğal sayıları nasıl anladıklarını incelemiş fakat öğretmen adaylarının doğal sayıları nasıl anladıkları ve öğrettikleri üzerine yeterince yoğunlaşmamıştır. Bu çalışmada öğretmen adaylarının doğal sayılar kavramını ve  doğal sayılardaki işlemleri nasıl anladığını araştırmak için bir durum çalışması yapılmıştır. Çalışmada ilköğretim matematik eğitimi bölümünde okuyan öğretmen adayları, 4. sınıf zorunlu ders kapsamında doğal sayılar ve doğal sayılar üzerindeki işlemleri onluk taban yerine sekizlik tabanda hazırlanan içerik ile işlemiştir. Böylece öğretmen adaylarına onluk tabanda ezbere yaptığı birçok işlem için stratejiler geliştirme fırsatı verilmiş ve bu süreçte nasıl düşündükleri detaylı olarak araştırılmıştır. Araştırmanın sonucu farklı bir taban kullanmanın öğretmen adaylarının düşünce şeklini değiştirdiğini, ezberden çıkarak farklı bir bakış açısıyla soruları yorumladıklarını göstermektedir

Anahtar Kelimeler

doğal sayılar, öğretmen adayları, sekizlik taban, dört işlem

Kaynakça

• Andreasen, J. B. (2006). Classroom mathematical practices in a preservice elementary mathematics education course using an instructional sequence related to place value and operations. Unpublished Doctoral Dissertation, University of Central Florida.
• Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction (8th ed.). Upper Saddle River, NJ: Merrill Prentice Hall.
• Ball, D., Bass, H., & Hill, H. (2004). Knowing and using mathematical knowledge in teaching: Learning what matters. In Proceedings for the 12th Annual Conference of the South African Association for Research in Mathematics, Science and Technology Education. Durban. SAARMSTE.
• Cobb, P. (2001). Supporting the improvement of learning and teaching in social and institutional context. Cognition and instruction: Twenty-five years of progress, 455-47.
• Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational psychologist, 31(3-4), 175-190.
• Conner, A. (2007). Student teachers' conceptions of proof and facilitation of argumentation in secondary mathematics classrooms. Unpublished Doctoral Dissertation, The Pennsylvania State University, PA.
• Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: Sage Publications.
• Denzin, N. K., & Lincoln, Y. S. (2000). Handbook of qualitative research (2nd ed.). Thousand Oaks, CA: Sage Publications.
• Franke, M. L., Carpenter, T., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers' self-sustaining, generative change in the context of professional development1. Teaching and Teacher Education, 14(1), 67-80.
• Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. Second handbook of research on mathematics teaching and learning, 1, 371-404.
• Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American educational research journal, 42(2), 371-406.
• Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington, D.C.: National Academy Press.
• Lerman, S. (2000). A case of interpretations of social: A response to Steffe and Thompson. Journal for Research in Mathematics Education, 31(2), 210-227.
• Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in china and the united states. Mahwah, NJ: Lawrence Erlbaum and Associates.
• Maxwell, J. A. (1996). Qualitative research design: An interactive approach. Applied social research methods series, v. 41. Thousand Oaks, CA: Sage Publications.
• McClain, K. (2003). Supporting preservice teachers' understanding of place value and mulitdigit arithmetic. Mathematical Thinking and Learning, 5(4), 281-306.
• Menon, R. (2004). Preservice teachers' number sense. Focus on Learning Problems in Mathematics, 26(2), 49-61.
• Merriam, S. B. (1988). Case study research in education: A qualitative approach (1st ed.). San Francisco, CA: Jossey-Bass.
• Ross, S. H. (2001). Pre-service elementary teachers and place value: Written assessment using a digit-correspondence task. In C. N. Walter (Ed.), Proceedings of the twenty-third annual meeting of the north American chapter of the international group for the psychology of mathematics education (pp. 897-906) Snowbird, UT: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• Roy, G. (2008). Prospectıve Teachers’ Development Of Whole Number Concepts And Operatıons Durıng A Classroom Teachıng Experıment. Unpublished Doctoral Dissertation, University of Central Florida.
• Safi, F. (2009). Explorıng The Understandıng Of Whole Number Concepts And Operatıons: A Case Study Analysıs Of Prospectıve Elementary School Teachers. Unpublished Doctoral Dissertation, University of Central Florida.
• Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1-23.
• Stake, R. E. (2006). Multiple case study analysis. New York, NY: The Guilford Press.
• Stephan, M., & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428-464.
• Thanheiser, E. (2009). Preservice elementary school teachers‘ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251-281.
• Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 5-25.
• Uçar, Z. T. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education, 2(2), 87-102.
• Toulmin, S. E. (1969). The uses of argument. Cambridge, The University Press.
• Yin, R. K. (2003). Applications of case study research (2nd ed.). Thousand Oaks, CA: Sage Publications.
• Zazkis, R., & Khoury, H. A. (1993). Place value and rational number representations: Problem solving in the unfamiliar domain of non-decimals. Focus on Learning Problems in Mathematics, 15(1), 38-51.