PRE-SERVICE TEACHERS’ UNDERSTANDING OF SELECTED CONCEPTS OF FRACTIONS
Abstract
The case study investigated prospective teachers’ understanding of concepts of fractions following the IOE’s chief examiners’ reports that have raised concerns about the persistent abysmal performance of the pre-service teachers on items on fractions in mathematics examinations in the colleges of education in Ghana. The case study was conducted in one college of education in the Central Region of Ghana with a sample of 26 pre-service teachers using a mixed method of sequential explanatory design approach. The participants took an achievement test followed by interview with the view to gaining insights into their understanding of specific concepts of fractions. The results indicated that although almost all of the prospective teachers demonstrated high levels of computational competence, none of them was able to demonstrate an understanding of why the algorithm for the division of a fraction by a fraction works. With regard to their Pedagogical Content Knowledge (PCK) of fractions, almost half of the participants could not generate any approach of teaching division of fractions to demonstrate an effective PCK. It was recommended that a new approach of teaching fractions in which connections are made between topics related to fractions be adopted by mathematics tutors in the colleges of education to guide prospective teachers to acquire a deeper conceptual understanding of fractions and their applications.
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Addy, C. K. K. (2006). Primary school teachers’ and pupils’ attitudes
toward mathematics and their effects on pupils’ achievement in Manyo Krobo District. Unpublished master’s thesis, University of Cape Coast, Cape Coast.
Agbenyega, J. (2010, August). Teaching and working with large classes. A presentation at the 1st International Workshop on Strategies for Effective Research and Teaching Quality in Education, University of Cape Coast, Cape Coast.
Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: examining what prospective teachers bring to teacher education. A doctoral dissertation submitted to the Department of Teacher Education, Michigan State University.
Ball, D. L. (1990). Pre-service elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Ball, D. L., Bass, H., & Hill, H. (2004). Knowing and using mathematical knowledge in teaching: Learning what matters. Paper presented at the Southern African Association for Research in Mathematics, Science, and Technology Education, Cape Town: South Africa.
Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed.), (pp. 433–456). New York: Macmillan.
Banturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31, 235–268.
Baumert, J., Kunker, M., Blum, W., Brunner, M., Voss, T., JorCharity, A., Klusman, U., Krauss, S., Nembrand M., & Tsai, Y. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180.
Cohen, L., Manion, L., & Morrison, K., (2006). Research methods in education, (6th ed), London: Routledge Falmer.
Davis, E. K., Bishop, A. J. & Seah, W. T. (2010). Cultural influences on students. conception of fractions. Ghana Journal of Education; Issues and Practice 2(1), 70-82
Davis, E. K., & Ampiah, J. G. (2009). Ghanaian primary school teacher trainees’ conception of addition of two unlike fractions. Journal of Science and Mathematics Education, 4(1), 64–83.
DfES, (2006). ‘Functional’ skills – Your questions answered. London: DfES
Delaney, S., Charalambous, C. Y., Hsu, H., & Mesa, V. (2007). The treatment of addition and subtraction of fractions in Cypriot, Irish, and Taiwanese text books. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 2, 193–200.
Enfield, M. (1998). Content and pedagogy: Intersection in the National Science Teachers Association (NSTA) standards for science teacher education. Retrieved August 10, 2010 from http://www.msu.edu/~dugganha/PCK.htm?iframe=true&width
Fletcher J. A. (2005) Constructivism and mathematics education in Ghana. Mathematics Connection 5, 29-36.
Fletcher J. A. (2001) Appraisal of mathematics teachers in Ghana' African Journal of Educational Studies in Mathematics and Sciences, 1, 81-102
Fletcher, J. A. (2000). Constructivism and mathematics education. Journal of the Mathematical Association of Ghana, 12, 27–33.
Forrester, T., & Chinnappan, M. (2010). The Predominance of Procedural Knowledge in Fractions. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle: Merga, 185–192.
Hauk, S., Jackson, B., & Noblet, K. (2010). No teacher left behind: Assessment of secondary mathematics teachers’ pedagogical content knowledge. Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education, University of Northern Colorado.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics, (pp. 1-27), Hillsdale: Earlbaum.
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.
Huang, T., Liu, S., & Lin, C. (2009). Preservice teacher’ mathematical knowledge of fractions. Research in Higher Education Journal, 5, 1-8.
Kennedy, M. (1997). Defining optimal knowledge for teaching science and mathematics. National Institute for Science Education. University of Wisconsin-Madison.
Institute of Education (2008). Chief examiners’ report FDC 122, FDC 122C, Cape Coast: University of Cape Coast.
Institute of Education (2011). Chief examiners’ report on mathematics methods, Cape Coast: University of Cape Coast.
Lamon, S. J. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
Lee, J. K. (2002). Teacher knowledge: Transforming content knowledge into pedagogical knowledge. Retrieved September 20, 2010, from http://www.msit.gsu.edu/socialstudies/courses/7540_02/pck.doc
Lin, C. (2009). A comparative study of web-based and traditional instruction on preservice teachers’ knowledge of fractions. Contemporary Issues in Technology and Teacher Education [Online serial], 9(3), 257–279.
Li, Y., & Smith, D. (2007). Prospective middle school teachers’ knowledge in mathematics and pedagogy for teaching – the case of fraction division. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 3, 185–192.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum Associates.
Mereku, K. (2000). School mathematics in Ghana: 1960 – 2000. Mathematics Connection, 1(1), 18-24.
Ministry of Education [MOE]. (2001). Teaching syllabus for mathematics junior secondary schools. Accra: Curriculum Research and Development Division.
Ministry of Education [MOE]. (2007). Teaching syllabus for mathematics junior secondary schools. Accra. Curriculum Research and Development Division.
Mitchell, A., & Horne, M. (2008). Fraction number line tasks and the additivity concept of length measurement. In M. Goos, R. Brown, & K. Makar (Eds.). Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australia, 353–360.
Piccolo, D. (2008). Views of content and pedagogical knowledge for teaching mathematics. School Science and Mathematics Journal, 108(2), 46-48.
Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. Retrieved September 13, 2010 from http://www.cimt.plymouth.ac.uk/Journal/rizvi.pdf
Roche, A., & Clarke, D. (2009). Making sense of partitive and quotative division: A snapshot of teachers’ pedagogical content knowledge. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia, 2. Palmerston North, NZ: Merga.
Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192.
Sidhu, K. S. (2001). Methodology of research in education. New Delhi: Sterling Publishers Pvt. Ltd.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conception: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 2 -25.
Tirosh, D., Fischein, E., Graeber, A. O., & Wilson, J. W. (1998). Prospective elementary teachers’ conception of rational numbers. Retrieved August 25, 2010, from http://jwilson.coe.uga.edu/Texts.Folder/Tirosh/Pros.El.Tchrs.html
Trochim, W. M. K. (2007). Social research methods book. Retrieved July 15, 2010, from http://www.socialresearchmethods.net/kd/index.php
Tsay, J. J., & Hauk, S. (2009). Prospective elementary teachers’ multiplication schema for fractions. Online publication. Retrieved September 7, 2010, from www.mathed.asu.edu/crume2009/Tsay_LONG1.Pdy.Pdf
Turnuklu, B. E., & Yesildere, S. (2007). The pedagogical content knowledge in mathematics: Preservice primary mathematics teachers’ perspectives in Turkey. IUMPST: The Journal, 1.
Veal, W, R & MaKinster, J. G. (1999). Pedagogical Content Knowledge Taxonomies, Electronic Journal of Science Education, 3(4) (online publication).
West African Examinations Council (2011, 2012) Mathematics Chief Examiners’ reports on core mathematics. Accra: WAEC.
Wilmot, E. M. (2009). Teacher knowledge and student performance: Begle revisited in Ghana. Journal of Science and Mathematics Education, 4(1), 13–30.
Young, E. (2002). Unpacking mathematical content through problem solving. Retrieved September 12, 2010, from http://www.math.youngzones.org/dissertation.html
Zakaria, E., & Zaini, N. (2009). Conceptual and procedural knowledge of rational numbers in trainee teachers. European Journal of Social Sciences, 9(2), 202-217.
Zulbiye, T. U. (2010). Mathematics teachers’ pedagogical content knowledge: Where do explanations come from? European Educational Research Association (ECER) Conference 2010. Retrieved October 13, 2010, from http://www.eera-ecer.eu/ecer-programmes/conference/ecer.../1725-2.
DOI: http://dx.doi.org/10.46827/ejes.v0i0.2941
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