Uncovering the Relation between CK and PCK: An Investigation of Preservice Elementary Mathematics Teachers’ Algebra Teaching Knowledge
Downloads
Abstract
This article discuss the algebra teaching knowledge of preservice elementary mathematics teachers in the context of CK and PCK as well as the relationship between them. The study was conducted with 101 preservice teachers sampled from a state university in Turkey. Rasch analysis was used to interpret the data. The results revealed that preservice teachers performed at mid-level for both CK and PCK tests. It was also found that there was significant correlation between the CK and PCK test scores. Weaknesses of the preservice teachers in terms of knowledge of the learner component of PCK, in comparison with presentation of content, were identified.
Downloads
References
An, S., Kulm, G., & Wu, Z. (2004) The pedagogical content knowledge of middle school, mathematics teacher in China and the U.S. Journal of Mathematics Teacher Education, 7, 145–172.
Google Scholar CrossrefAuthor (2007).
Google Scholar CrossrefAuthor (2016).
Google Scholar CrossrefAziz, J. A., Mohamad, M., Shah, P. M., & Din, R. (2016). Differential item functioning in online learning instrument (EPFun). Creative Education, 7, 180-188. http://dx.doi.org/10.4236/ce.2016.71018
Google Scholar CrossrefBaki, A. (2010). An evaluation of teacher training from undergraduate and postgraduate dimensions. Inonu University, Journal of the faculty of Education, 11(3), 15-31.
Google Scholar CrossrefBaki, A. (2012a, June). Matematik öğretme bilgisi [Mathematics teaching knowledge] Congress of 10th National Science and Mathematics Education. 27-30 June, Nigde University, Nigde.
Google Scholar CrossrefBaki, A. (2012b, September). Matematik öğretme bilgisi [Mathematics teaching knowledge]. Symposium of 11th Mathematicians Association, 19-21 September, Ondokuz Mayıs University, Samsun.
Google Scholar CrossrefBaki, M. ve Baki, A. (2010). Experiences of Turkey in teacher training and teaching knowledge of mathematics teachers. Proceeding of 4th International Symposium of Policies and Issues on Teacher Education, pp. 225-232.
Google Scholar CrossrefBall, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Google Scholar CrossrefBall, D.L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing.
Google Scholar CrossrefBall, D. L., Bass, H., Lewis, J., Sleep, L., Suzuka, K., Babson, A., Jacobs, J., Kim, Y., Thames, M., & Zopf, D. (2008). Designing and using problems to teach mathematical knowledge for teaching. National Council of Teachers of Mathematics Research Presession, Salt Lake City, UT.
Google Scholar CrossrefBerberoğlu, G. (1998). Seçme amacıyla kullanılan testlerde Rasch modelinin katkıları. Yayımlanmamış doktora tezi (Unpublished doctoral dissertation). Hacettepe University, Institue of Social Sciences, Ankara. Retrieved January, 2014 from https://tez.yok.gov.tr/UlusalTezMerkezi.
Google Scholar CrossrefBlömeke, S., Houang, R., & Suhl, U. (2011). TEDS-M: Diagnosing teacher knowledge by applying multidimensional item response theory and multi-group models. IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments. No. 4, pp. 109–126.
Google Scholar CrossrefBond, T.G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd ed.) Mahwah, N.J.: Erlbaum.
Google Scholar CrossrefBurrill, G., Ferrini-Mundy, J., Senk, S. and Chazan, D. (2004). Knowledge of algebra for teaching. In Annual Conference of PME-NA, Toronto, Ontario, Canada.
Google Scholar CrossrefBütün, M. (2005). The study of elementary mathematics teachers’ pedagogical content knowledge. Unpublished master thesis. Karadeniz Technical University, Institue of Pure and Applied Science, Trabzon.
Google Scholar CrossrefCarpenter, T. P., Fennema, E., P. L. Peterson, P. L., & Carey, D. A. (1988). Teachers’ pedagogical content knowledge of student’s problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19, 385–401.
Google Scholar CrossrefCepicka, L. (2007). Measuring psychomotor skills: Developing a scale to measure ball-handling skills using the Rasch measurement model. In Degregorio, R. (Eds) New developments in psychological testing (pp. 187-212). New York: Nova Science Publishers.
Google Scholar CrossrefChick, H. L., & Harris, K. (2007). Pedagogical content knowledge and the use of examples for teaching ratio. Paper presented at conference of the Australian Association for Research in Education. 25 - 28 November, Fremantle, WA.
Google Scholar CrossrefÇıkla, O. (2004). The effects of multiple representations based instruction on seventh grade students’ algebra performance, attitude toward mathematics and representation preference. Unpublished doctoral dissertation, Middle East Technical University, Ankara.
Google Scholar CrossrefDeMarois, P., & Tall, D. O. (1996). Facets and layers of the function concept. Proceedings of PME 20, Valencia, 2, 297–304.
Google Scholar CrossrefDoğan, N. (2002). Comparison of classical test theory and latent traits theory by samples. Unpublished Doctoral dissertation, Hacettepe University, Institute of social sciences, Ankara). Online at: https://tez.yok.gov.tr/
Google Scholar CrossrefDönmez, G. (2009). Assessment of pre- service mathematics teachers’ pedagogical content knowledge about limit and continuity. Unpublished master thesis, Marmara University, Institue of Educational Sciences, İstanbul.
Google Scholar CrossrefDubinsky, E., & Harel, G. (1992). Forward. In G. Harel and E. Dubinsky (Eds.), The concept of function: aspects of epistemology and pedagogy, MAA Notes, Number 25 (pp. 7-9). Washington, DC: Mathematical Association of America.
Google Scholar CrossrefEven, 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.
Google Scholar CrossrefFennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact. In: D.A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (New York: Macmillan Publishing).
Google Scholar CrossrefFerrini-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.
Google Scholar CrossrefFerrini-Mundy, J., Floden, R., McCrory, R., Burrill, G., & Sandow, D. (2005). A conceptual framework for knowledge for teaching school algebra. East Lansing, MI: Authors.
Google Scholar CrossrefFerrini-Mundy, J., McCrory, R., & 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.
Google Scholar CrossrefFloden, R. E., Ferrini-Mundy, J., McCrory, R., Senk, S. and Reckase, M. (2005). KAT item development matrix. http://www.educ.msu.edu/kat/ adresinden 20 Kasım 2013 tarihinde edinilmiştir.
Google Scholar CrossrefGrossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Google Scholar CrossrefGrossman, P. L. (1995). Teachers' knowledge. In L. W. Anderson (Ed.), International encyclopedia of teaching and teacher education (2nd ed., pp. 20-24). Tarrytown, NY: Pergamon.
Google Scholar CrossrefHaciomeroglu, G. (2006). Prospective secondary teachers’ subject matter knowledge and pedagogical content knowledge of the concept of function. (Unpublished doctoral dissertation) Florida State University, USA.
Google Scholar CrossrefHadjidemetriou, C. and Williams, J.S. (2002). Children’s graphical conceptions. Research in Mathematics Education, 4, 69-87.
Google Scholar CrossrefHeaton, 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.
Google Scholar CrossrefHeinze, A., Star J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41(5), 535–540.
Google Scholar CrossrefHill H. C., Blunk M. L., Charalambous C. Y., Lewis J. M., Phelps G. C., Sleep L., & Ball D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511.
Google Scholar CrossrefIşık, C., Kar, T., İpek, A. S., & Işık, A. (2012). Difficulties encountered by pre-service classroom teachers in constructing stories about line graphs. International Online Journal of Educational Sciences, 4(3), 644-658.
Google Scholar CrossrefIşıksal, M. (2006). A study on pre-service elementary mathematics teachers’ subject matter knowledge and pedagogical content knowledge regarding the multiplicatıon and division of fractions. Unpublished doctoral dissertation, Middle East Technical University, Ankara.
Google Scholar CrossrefIzard, J., Haines, C., Crouch, R., Houston, S., & Neill, N. (2003). Assessing the impact of the teaching of modelling: Some implications. In S. Lamon, W. Parker, K. Houston (Eds.), Mathematical Modelling: A Way of Life. ICTMA 11, (165–177). Chichester: Horwood Publishing.
Google Scholar CrossrefKazima, M., Pillay, V., & Adler, J. 2008. Mathematics for teaching: observations of two case studies. South African Journal of Education, 28, 283–299.
Google Scholar CrossrefKoparan, T. (2012). The effect of project based learning approach on the statistical literacy levels and attitude towards statistics of student. Unpublished doctoral dissertation. Karadeniz Technical University, Institue of Educational Sciences, Trabzon
Google Scholar CrossrefLesh, R. and Doerr, H. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh ve H. Doerr (Eds.) Beyond constructivism (pp. 3-34). Hillsdale, NJ: Erlbaum.
Google Scholar CrossrefLi, 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. Retrived November, 2012 from http://hdl.handle.net/2152/3337
Google Scholar CrossrefMa, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum Associates.
Google Scholar CrossrefMathematics Study Panel (2003). Mathematics proficiency for all students. Santa Monica CA: RAND.
Google Scholar CrossrefMarks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
Google Scholar CrossrefMcCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S, L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584-614.
Google Scholar CrossrefMcMillan, J. H., & Schumacher, S. (2001). Research in education: A conceptual introduction (5th ed.). New York: Longman.
Google Scholar CrossrefMinistry of National Education [MoNE] (2013). Ortaokul öğretim matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı [Curriculum of elementary mathematics for 5th,6th,7th and 8th grades]. Ankara: MEB Yayınları.
Google Scholar CrossrefMisailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Journal of Mathematical Behaviour, 22, 335–368.
Google Scholar CrossrefMoses, R. (1995). Algebra, the new civil right. In C. B. Lacampagne, W. Blair, & J. Kaput (Eds.), The algebra initiative colloquium (Vol. 2) (pp. 53-67). Washington, DC: U.S. Department of Education, Office of Educational Research and Improvement.
Google Scholar CrossrefNational Council of Teachers of Mathematics [NCTM] (2000). Professional standards for teaching mathematics. Reston, VA: Author.
Google Scholar CrossrefOzden, M. (2008). The effect of content knowledge on pedagogical content knowledge: The case of teaching phases of matters. Educational Sciences: Theory and Practice, 8(2), 633-645.
Google Scholar CrossrefÖğrenci Seçme ve Yerleştirme Merkezi [ÖSYM] (2014). 2014 Kamu Personeli Seçme Sınavı A Grubu ve Öğretmenlik Sonuçları. [[Results of Teacher Selection Examination of 2014] Retrieved January, 2015 from http://dokuman.osym.gov.tr/pdfdokuman/2014/KPSS/OABT-SORUYANIT/KPSS-2014-OABTsayisal25072014.pdf
Google Scholar CrossrefÖğrenci Seçme ve Yerleştirme Merkezi [ÖSYM] (2015). 2015 Kamu Personeli Seçme Sınavı Öğretmenlik Sonuçları [Results of Teacher Selection Examination of 2015] . Retrieved December, 2015 from http://dokuman.osym.gov.tr/pdfdokuman/2015/KPSS/2015KPSS_SAYISABILGILER28082015.pdf
Google Scholar CrossrefÖğrenci Seçme ve Yerleştirme Merkezi [ÖSYM] (2016). 2016 Kamu Personeli Seçme Sınavı Öğretmenlik Sonuçları [Results of Teacher Selection Examination of 2015] . Retrieved September, 2016 from http://dokuman.osym.gov.tr/pdfdokuman/2016/KPSS/OABT/OABTSonucSayisalBilgiler02092016.pdf
Google Scholar CrossrefÖzmantar, M.F., Bingölbali, E. ve Akkoç, H. (Ed.) (2008). Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem Akademi.
Google Scholar CrossrefSantagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. Zdm, 43(1), 133-145.
Google Scholar CrossrefSantos, J.R.A. (1999). Cronbach’s alpha: A tool for assessing the reliability of scales. Journal of extension, 37(2), 1-5.
Google Scholar CrossrefSchmidt, H. W., Tatto, M. T., Bankov, K., Blömeke, S., Cedillo, T., Cogan, L., Han, S., Houang, R., Hsieh, F. J., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: Teacher education for middle school mathematics in six countries. Mathematics Teaching in the 21st Century, Center for Research in Mathematics and Science Education, Michigan State University.
Google Scholar CrossrefSelden, A. and Selden, J. (2003). Errors and misconceptions in college level theorem proving. Tennessee Technological University Department of Mathematics Tech Report No. 2003-3. Retrived December, 2013 from http://math.tntech.edu/techreports/TR_2003_3.pdf
Google Scholar CrossrefShulman, L.S. (1986). Those who understand; Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Google Scholar CrossrefShulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57 (1), 1-22.
Google Scholar CrossrefStump, S. L. (1999). Secondary mathematics teachers' knowledge of slope. Mathematics Education Research Journal, 11(2), 124–144.
Google Scholar CrossrefŞahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551.
Google Scholar CrossrefTatto, A., Teresa, M., Schwille Prof, J., Senk Prof, S., Lawrence, C., Peck Mr, R., & Rowley Dr, G. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M) (pp. 1-297). International Association for the Evaluation of Educational Achievement (IEA).
Google Scholar CrossrefTatto, 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.
Google Scholar CrossrefThompson, P. W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. H. Schoenfeld, and J. J. Kaput (Eds.), Research in Collegiate Mathematics Education, 1 (Issues in Mathematics Education Vol. 4, pp. 21-44). Providence, RI: American Mathematical Society.
Google Scholar CrossrefUsiskin, Z. (1988). Conceptions of school algebra and uses of variable. In A. F. Coxford and A. P. Shulte (Eds.), The ideas of algebra, K-12 (1988 Yearbook of the National Council of Teachers of Mathematics, pp. 8-19). Reston, VA: NCTM.
Google Scholar CrossrefWarburton, R. (2013a) ‘Mathematical Knowledge for Teaching’: Do you need a mathematics degree? Proceedings of the British Society for Research into Learning Mathematics, 33(2), 61-66.
Google Scholar CrossrefWatson, J., Kelly, B., & Izard, J. (2004). Student change in understanding of statistical variation after instruction and after two years: An application of Rasch analysis. AARE Conference, Melbourne, Url: http://www.aare.edu.au (search code WAT04867).
Google Scholar CrossrefWolfe, EW, & Smith Jr, EV. (2007a). Instrument development tools and activities for measure validation using Rasch models: part I-instrument development tools. Journal of applied measurement, 8(1), 97-123.
Google Scholar CrossrefWolfe, EW, & Smith Jr, EV. (2007b). Instrument development tools and activities for measure validation using Rasch models: part II--validation activities. Journal of Applied Measurement, 8(2), 204-234.
Google Scholar CrossrefWright, B. D. (1977). Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14(2), 97 – 116.
Google Scholar CrossrefYüksek Öğretim Kurumu [YÖK] (2016). İlköğretim matematik öğretmenliği lisans programı [Bachelor curriculum of elementary school mathematics education department]. Retrived August, 2016 from http://www.yok.gov.tr/documents/10279/49665/ilkogretim_matematik/cca48fad-63d7-4b70-898c-dd2eb7afbaf5
Google Scholar CrossrefDownloads
Published
Almetric
Dimensions
Issue
Section
License
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
