Author :
Abstract
The present study aims to analyze the pre-service elementary school mathematics teachers’ knowledge for teaching algebra, in the context of algebra pedagogical content knowledge. For this purpose, a test of 20 with validity and reliability on the basis of the conceptual framework of knowledge for teaching algebra, as built by McCrory et al. (2012), was developed, and applied with 101 senior-year pre-service teachers enrolled at a state university. The results reveal that the pre-service teachers exhibit mediocre performance in terms of algebra pedagogical content knowledge. The pre-service teachers were observed to experience difficulties regarding sub-component of algebra pedagogical content knowledge, namely student recognition. They also have difficulty to the "functions and their properties: linear and nonlinear" in algebra content, and the "core concepts and procedures" in domains of mathematical knowledge.
Keywords
Abstract
The present study aims to analyze the pre-service elementary school mathematics teachers’ knowledge for teaching algebra, in the context of algebra pedagogical content knowledge. For this purpose, a test of 20 with validity and reliability on the basis of the conceptual framework of knowledge for teaching algebra, as built by McCrory et al. (2012), was developed, and applied with 101 senior-year pre-service teachers enrolled at a state university. The results reveal that the pre-service teachers exhibit mediocre performance in terms of algebra pedagogical content knowledge. The pre-service teachers were observed to experience difficulties regarding sub-component of algebra pedagogical content knowledge, namely student recognition. They also have difficulty to the "functions and their properties: linear and nonlinear" in algebra content, and the "core concepts and procedures" in domains of mathematical knowledge.
Keywords
- Akkaya, R. ve Durmuş, S. (2006). İlköğretim 6-8. sınıf öğrencilerinin cebir öğrenme alanındaki kavram yanılgıları. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31, 1-12.
- Andrade, H. G. (2001). The effects of instructional rubrics on learning to write. Current Issues in Education, 4(4). Retrieved from http://cie.asu.edu/ojs/index.php/cieatasu/article/view/1630
- Anıl, D., Özer Özkan, Y. ve Demir, E. (2015). PISA 2012 araştırması ulusal nihai rapor. Ankara: MEB..
- Baki, M. ve Baki, A. (2010). Türkiye’nin öğretmen yetiştirme deneyimi ve matematik öğretmeninin alanı öğretme bilgisi. Uluslararası Öğretmen Yetiştirme Politikaları ve Sorunları Sempozyumu II, Hacettepe Üniversitesi, Ankara.
- Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. doi: 10.1177/0022487108324554
- Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.). Teachers’ professional competence. Findings of the COACTIV research program (pp. 25–48). New York: Springer.
- Bekdemir, M., & Işık, A. (2007). Evaluation of conceptual knowledge and procedural knowledge on algebra area of elementary school students. The Eurasian Journal of Educational Research, 28, 9-18.
- Berberoğlu, G. (1998). Seçme amacıyla kullanılan testlerde Rasch modelinin katkıları. Yayımlanmamış doktora tezi. Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara.
- Blömeke, S., Houang, R., & Suhl, U. (2011). Diagnosing teacher knowledge by applying multidimensional item response theory and multi-group models. In Blömeke, S., Hsieh, F. J., Kaiser, G. ve Schmidt, W. H. (Eds.) International perspectives on teacher knowledge, beliefs and opportunities to learn. Advances in mathematics education (pp. 483-501), London: Springer.
- Blömeke, S., & Kaiser, G. (2014). Theoratical framework, study design and main results of TEDS-M. In Blömeke, S., Hsieh, F. J., Kaiser, G. ve Schmidt, W. H. (Eds.) International perspectives on teacher knowledge, beliefs and opportunities to learn. Advances in mathematics education (pp. 19-47), London: Springer:.
- Bond, T.G., & Fox, C. M. (2001) Applying the Rasch model: Fundamental measurement in the human sciences(2nd edition). Mahwah, N.J.: Erlbaum.
- Buschang, R. E., Chung, G. K. W. K., Delacruz, G. C., & Baker, E. L. (2012). Validating measures of algebra teacher subject matter knowledge and pedagogical content knowledge (CRESST Report No. 820). Los Angeles: National Center for Research on Evaluation.
- Bush, W. S. (2009). Diagnostic mathematics assessments for middle school teachers. Retrived on 05.01.2017 from http://louisville.edu/education/centers/crmstd/diag-math-assess-middle.
- Bütün, M. (2005). İlköğretim matematik öğretmenlerinin alan eğitimi bilgilerinin nitelikleri üzerine bir çalışma. Yayınlanmamış yüksek lisans tezi. Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon.
- Büyüköztürk, Ş., Çakan, M., Tan, Ş. ve Atar, H.Y. (2014) TIMSS 2011 ulusal matematik ve fen raporu 8. sınıflar. Ankara: MEB.
- Cepicka, L. (2007). Measuring psychomotor skills : Developing a scale to measure ball-handling skills using the Rasch measurement model. In R. Degregorio, (Ed.). New developments in psychological testing (pp.187-212). New York : Nova Science Publishers.
- Charalambous, C. Y. (2016). Investigating the knowledge needed for teaching mathematics: An exploratory validation study focusing on teaching practices. Journal of Teacher Education, 67(3), 220 –237. doi:10.1177/0022487116634168
- Cohen. L. & Manion. L. (1989). Research methods in education, New York: Routledge.
- Çelik, D. (2007). Öğretmen adaylarının cebirsel düşünme becerilerinin analitik incelenmesi. Yayımlanmamış doktora tezi. Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon.
- Çelik, D. ve Güneş, G. (2013). Farklı sınıf düzeyindeki öğrencilerin harfli sembolleri kullanma ve yorumlama seviyeleri. Kuram ve Uygulamada Eğitim Bilimleri Dergisi, 13(2), 1168-1186.
- Dede, Y., Bayazit, İ. ve Soybaş, D. (2010). Öğretmen adaylarının denklem, fonksiyon ve polinom kavramlarını anlamaları. Kastamonu Eğitim Dergisi, 18(1), 67-88.
- Doerr, H. M. (2004). Teachers’ knowledge and the teaching of algebra. In K. Stacey, H. Chick & M. Kendal (Eds), The Future of the teaching and learning of algebra. The 12th ICMI Study (pp. 267-290). Norwood, MA: Kluwer Academic Publishers.
- Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116. doi: 10.2307/749215
- Ferrini-Mundy, J., Burrill, G., Floden, R., & Sandow, D. (2003). Teacher knowledge for teaching school algebra: Challenges in developing an analytical framework. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
- Ferrini-Mundy, J., & Senk, S. (2006). Knowledge of algebra for teaching: Framework, item development and pilot results. Research symposium at the research presession of NCTM annual meeting. St. Louis, MO.
- Guler, M., & Celik, D. (2016). A research on future mathematics teachers' instructional explanations: The case of algebra. Educational Research and Reviews, 11(16), 1500-1508. doi: 10.5897/ERR2016.2823
- Haciomeroglu, G. (2006). Prospective secondary teachers’ subject matter knowledge and pedagogical content knowledge of the concept of function. Unpublished doctoral dissertation. Florida State University, Florida.
- Hambleton, R., Jones, R., & Rogers, H. (1993). Influence of item parameter estimation errors in test development. Journal of Educational Measurement, 30, 143-155. doi: 10.1111/j.1745-3984.1993.tb01071.x
- Heaton, R. M. (1992). Who is minding the mathematics content? A case study of a fifth-grade teacher. The Elementary School Journal, 93(2), 153–162. doi: 10.1086/461719
- Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371–406. doi:10.3102/00028312042002371
- Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of function, The Journal of Mathematical Behavior, 17, 123–134. doi: 10.1016/S0732-3123(99)80064-9
- Koparan, T. (2012). Proje tabanlı öğrenme yaklaşımının öğrencilerin istatistiksel okuryazarlık seviyelerine ve istatistiğe yönelik tutumlarına etkisi. Yayımlanmamış doktora tezi. Karadeniz Teknik Üniversitesi, Eğitim Bilimleri Enstitüsü, Trabzon.
- Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM Mathematics Education, 40(5), 873-892.
- Kruyen, P. M. (2012). Using short tests and questionnaires for making decisions about individuals: When is short too short. Ridderkerk: Ridderprint.
- Li, X. (2007). An investigation of secondary school algebra teachers' mathematical knowledge for teaching algebraic equation solving. Unpublished doctoral dissertation. The University of Texas at Austin.
- Lin, C. Y., Kuo, Y. C., & Ko, Y. Y. (2015). Pre-Service teachers’ perceptions and beliefs of technological pedagogical content knowledge on algebra. Journal of Computers in Mathematics and Science Teaching, 34(3), 327-344.
- McCrory, R., Floden, R., Ferrini-Mudy, J., Reckase,M.D., & Senk., S.L.(2012). Knowledge algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(4), 584-615. doi: 10.5951/jresematheduc.43.5.0584
- McCrory, R., & Smith, J. P. (2005, April). Teachers' knowledge in practice: Analysis of video of algebra teaching. Paper presented at the Annual meeting of the American Educational Research Association, Montreal, CA.
- McNeill, K. L., González‐Howard, M., Katsh‐Singer, R., & Loper, S. (2016). Pedagogical content knowledge of argumentation: Using classroom contexts to assess high‐quality PCK rather than pseudoargumentation. Journal of Research in Science Teaching, 53(2), 261-290. doi: 10.1002/tea.212542
- Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Journal of Mathematical Behaviour, 22, 335-368. doi: 10.1016/S0732-3123(03)00025-7
- Özmantar, M.F., Bingölbali, E. ve Akkoç, H. (Ed.) (2008). Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem Akedemi.
- Santos, J.R.A. (1999). Cronbach’s alpha: A tool for assessing the reliability of scales. Journal of extension, 37(2), 1-5.
- Schmidt, W. H., Tatto, M. T., Bankov, K., Blömeke, S., Cedillo, T., Cogan, L., et al. (2007). The preparation gap: Teacher education for middle school mathematics in six countries (MT21 Report). East Lansing: MSU.
- Shulman, L.S. (1986). Those who understand; Knowledge growth in teaching. Educational Researcher, 15(2), 4- 14.
- Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
- Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra: A challenge at the crossroads of policy and practice. Review of Educational Research, 81, 453–492. doi:10.3102/0034654311423025
- Talim Terbiye Kurulu Başkanlığı [TTKB](2013a). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
- Talim Terbiye Kurulu Başkanlığı [TTKB](2013b). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim
- Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
- Usiskin, Z. (2001). Teachers’ mathematics: A collection of content deserving to be a field. The Mathematics Educator, 6(1), 86-98.