Knowledge of mathematics teacher-candidates about the concept of slope / Matematik öğretmeni adaylarının eğim kavramına ilişkin bilgileri

Yıl 2015, Cilt: 11 Sayı: 2, 673 - 693, 01.04.2015

Sefa Dündar

Öz

Eğim kavramı matematikte bazı konuların ön koşullarından birisidir. Kavramsallaştırma yapılabilmesi için ön koşullar önem arz etmektedir. Bu çalışmanın amacı, matematik öğretmeni adaylarının eğim kavramına ilişkin kavram bilgilerini ortaya çıkarmaktır. Araştırma Türkiye’deki bir devlet üniversitesinin matematik öğretmenliği bölümü öğrencileriyle gerçekleştirilmiştir. Öğretmen adaylarının kavram tanımlamaları, kavrama ait anlayışları incelenmiş ve sınıf seviyeleri açısından değerlendirmelerde bulunulmuştur. Elde edilen veriler incelendiğinde matematik öğretmeni adaylarının eğim kavramını daha çok geometriksel yaklaşımla ifade ettikleri, sınıf seviyesi değiştikçe eğim kavramına ilişkin bilgilerinin de değiştiği ortaya çıkmıştır. Sınıf seviyesi arttıkça trigonometrik temsilin kullanımının arttığı, fiziksel temsilin kullanımının ise azaldığı görülmüştür.

Anahtar Kelimeler

eğim, matematik öğretmen adayı, matematik eğitimi

Kaynakça

• Altun, A. (2011). The european community’s the vision of media literacy education within the frame of the recommendations, Yüzüncü Yıl University, Journal of Education Faculty, 8(1), 58-86.
• Atasayar, A. (2008). Design and usability of a content development tool for concept teaching process. (Master Thesis), Hacettepe University, Ankara.
• Baştürk, S. (2009). Perspectives of student teachers of secondary mathematics education on mathematics teaching in faculty of arts and science. Inonu Unıversıty Journal of The Faculty of Educatıon, 10(3), 137-160.
• Bilgin, N. (2000). İçerik Analizi. İzmir: Ege Üniversitesi Edebiyat Fakültesi Yayınları.
• Brown, T. (1996). The phenomenology of the mathematics classroom. Educational Studies in Mathematics, 31(1-2), 115-150.
• Cankoy, O. (2010). Mathematics teachers’ topic-specific pedagogical content knowledge in the context of teaching a0 , 0! And a ÷ 0. Educational Sciences: T eory & Practice, 10(2).
• Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education, 33(5), 352-378. doi: 10.2307/4149958
• Carlson, M., Oehrtman, M., & Engelke, N. (2010). The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings. Cognition and Instruction, 28(2), 113-145. doi: 10.1080/07370001003676587
• Chi Kit, C. (2006). The use of variation theory to improve secondary three students’ learning of the mathematical concept of slope University of Hong Kong, Master Thesis. Retrieved from http://hub.hku.hk/bitstream/10722/51380/6/FullText.pdf?accept=1
• Clarke, B. (1995). Expecting the unexpected: Critical incidents in the mathematics classrooms. Unpublished doctoral dissertation, University of Wisconsin-Madison.
• Cohen, D. K., McLaughlin, M. W., and Talbert, J. E. (1993). Teaching for Understanding: Challenges for Policy and Practice. San Francisco: Jossey-Boss.
• Cross, T. L., & Stewart, R. A. (1995). A Phenomenological Investigation of the" Lebenswelt" of Gifted Students in Rural High Schools. Journal of Secondary Gifted Education, 6(4), 273-280.
• De Villiers, M. (1998). To teach definitions in geometry or teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the twenty-second international conference for the Psychology of Mathematics Education (Vol. 2, pp. 248–255). Stellenbosch: Program Committee.
• Dreyfus, T. (1991). Advanced Mathematical Thinking Processes. In D. Tall (Ed.), Advanced Mathematical Thinking (Vol. 11, pp. 25-41): Springer Netherlands.
• Dündar, S., Yaman, H., & Ağar, Ö. (2015). An invesatigation of 5th and 6th grade students’ success rates in solving fraction problems having different representation formats. Journal of Emerging Trends in Educational Research and Policy Studies, 6(1), 18-26.
• Ersoy, A., & Türkkan, B. (2009). Perceptions about Internet in elementary school children’s drawings. Elementary Education Online, 8(1), 57-73.
• Erşen, Z. B., & Karakuş, F. (2013). Evaluation of preservice elementary teachers’ concept ımages for quadrilaterals. Turkish Journal of Computer and Mathematics Education, 4(2), 124-146.
• Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for research in mathematics education, 94-116.
• Fennema, E., & Franke, M. L. (1992). Teacher’s knowledge and its impact. In Douglas A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Simon and Schuster Macmillan.
• Green, A. J. (1995). Experiential learning and teaching: A critical evaluation of an enquiry which used phenomenological method. Nurse Education Today, 15(6), 420-426.
• Hattikudur, S., Prather, R. W., Asquith, P., Alibali, M. W., Knuth, E. J., & Nathan, M. (2012). Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y-intercept. School Science and Mathematics, 112(4), 230-240. doi: 10.1111/j.1949-8594.2012.00138.x
• Hitchinson, E. (1996). Pre-service teachers knowledge: A contrast of beliefs and knowledge of ratio and proportion. Unpublished doctoral thesis, University of Wisconsin-Madison.
• Johnson, B., & Christensen, L. (2013). Educational research: Quantitative, qualitative, and mixed approaches (5th ed.). Thousand Oaks, CA: Sage Publications.
• Lampert, M. (1988). T e teacher’s role in reinventing the meaning of mathematical knowing in the classroom. In M. J. Behr et al. (Eds.), Proceedings of the 10th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 433-480). DeKalb, IL: Northern Illinois University.
• Leikin, R., & Winicki-Landman, G. (2001). Defining as a vehicle for professional development of secondary school mathematics teachers. Mathematics Education Research Journal, 3, 62-73.
• Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of educational psychology, 77(3), 247.
• Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Review of Educational Research, 60(1), 1-64. doi: 10.3102/00346543060001001
• Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. The Journal of Mathematical Behavior, 21(1), 87-116. doi: http://dx.doi.org/10.1016/S0732-3123(02)00105-0
• Lobato, J., & Thanheiser, E. (2002). Developing understanding of ratio as measure as a foundation for slope. Making sense of fractions, ratios, and proportions, 162-175.
• Konyalıoğlu, A.C., Özkaya, M., & Damla Gedik, S. (2012). Investigation of Pre-Service Mathematics Teachers’ SubjectMatter Knowledge in terms of Their Approaches to Errors. Iğdır University Journal of the Institute of Science and Technology, 2(2), 27-32.
• McMillan, J.H., & Schumacher, S. (2010). Research in education: evidence-based inquiry (7th Edition). Boston : Pearson.
• Miles, M. B., & Huberman, A. M. (1994). An expanded sourcebook qualitative data analysis (2th ed.). California: Sage Pablications, Inc.
• Milli Eğitim Bakanlığı [MEB], (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara
• Moore-Russo, D., Conner, A., & Rugg, K. (2011). Can slope be negative in 3-space? Studying concept image of slope through collective definition construction. Educational Studies in Mathematics, 76(1), 3-21. doi: 10.1007/s10649-010-9277-y
• Munby, H., Russel, T., & Martin, A. K. (2001). Teacher knowledge and how it develops. In V. Richardson (Ed.), Handbook of research on teaching (4th Edt., pp. 877–904). Washington, DC: American Educational Research Association.
• Nagle, C., & Moore-Russo, D. (2014). Slope Across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards. The Mathematics Educator, 23(2), 40-59.
• Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. (2013). Calculus students’ and instructors’ conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491-1515. doi: 10.1007/s10763-013-9411-2
• National Council of Teachers of Mathematics [NCTM], (2000). Principles and Standards for School Mathematics. VA: Reston.
• Neubrand, M. (2008). Knowledge of teachers–knowledge of students: Conceptualizations and outcomes of a mathematics teacher education study in Germany. Paper presented at the Symposium on the Occasion of the 100th Anniversary of ICMI (Rome, March 5-8, 2008) Workıng Group 2: The professional formation of teachers, Carl-von-Ossietzky-University, Oldenburg, Germany.
• Noble, T., Nemirovsky, R., Wright, T., & Tierney, C. (2001). Experiencing Change: The Mathematics of Change in Multiple Environments. Journal for Research in Mathematics Education, 32(1), 85-108. doi: 10.2307/749622
• Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A., & Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. International Journal of Science and Mathematics Education, 10(6), 1393-1414. doi: 10.1007/s10763-012-9344-1
• Reys, R. E. (1974). Division and Zero-An Area of Needed Research. Arithmetic Teacher, 21(2), 153-156.
• Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4-14. doi: 10.2307/1175860
• Shulman, L. S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57(1), 1-22.
• Simon, M. A, & Blume, G. W. (1994). Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 13(2), 183-197.
• Smith, D. C., & Neale, D. C. (1989). The construction of subject matter knowledge in primary science teaching. Teaching and teacher Education, 5(1), 1-20.
• Spence, M. (1996). Psychologizing algebra: Case studies of knowing in the moment. Unpublished doctoral dissertation, University of Wisconsin-Madison.
• Stanton, M., & Moore-Russo, D. (2012). Conceptualizations of Slope: A Review of State Standards. School Science and Mathematics, 112(5), 270-277. doi: 10.1111/j.1949-8594.2012.00135.x
• Stein, M. K., Baxter, J. A., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27(4), 639-663.
• Stump, S. L. (1997). Secondary mathematics teachers' knowledge of the concept of slope. Paper presented at the American Educational Research Association, Chicago, Illinois.
• Stump, S. L. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11(2), 124-144. doi: 10.1007/BF03217065
• Stump, S. L. (2001a). Developing preservice teachers' pedagogical content knowledge of slope. The Journal of Mathematical Behavior, 20(2), 207-227. doi: http://dx.doi.org/10.1016/S0732-3123(01)00071-2
• Stump, S. L. (2001b). High School Precalculus Students' Understanding of Slope as Measure. School Science and Mathematics, 101(2), 81-89. doi: 10.1111/j.1949-8594.2001.tb18009.x
• Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. doi: 10.1007/BF00305619
• Teuscher, D., & Reys, R. E. (2010). Slope, Rate of Change, and Steepness: Do Students Understand These Concepts? Mathematics Teacher, 103(7), 519-524.
• Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 181-234). Albany, NY: SUNY Press.
• Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293-305.
• Vinner, S. (1991). The Role of Definitions in the Teaching and Learning of Mathematics. In Tall, D. (Ed.), Advanced Mathematical Thinking (pp. 65-81). Boston: Kluwer.
• Wilson, M. R. (1994). One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 346-370.
• Wilson, S. & Floden, R. E. (2003). Creating eff ective teachers: Concise answers for hard questions. An addendum to the report “Teacher Preparation Research: Current Knowledge, Gaps, and Recommendations.” Denver, CO: Education Commission of the States. (ERIC Document Reproduction Service No. ED 476366)
• Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin yayınevi.