International Association of Educators   |  ISSN: 2834-7919   |  e-ISSN: 1554-5210

Original article | International Journal of Progressive Education 2018, Vol. 14(4) 70-84

Pre-Service Elementary Mathematics Teachers' Specialized Content Knowledge: The Case of Integer Addition and Subtraction

Ali Sabri İpek

pp. 70 - 84   |  DOI:   |  Manu. Number: MANU-1805-15-0001.R2

Published online: September 11, 2018  |   Number of Views: 361  |  Number of Download: 900


Pre-service mathematics teachers’ content knowledge is an important issue. Therefore, detailed studies are needed to be conducted on mathematical topics. The study examines preservice elementary mathematics teachers’ (PEMTs) special content knowledge (SCK) of integer addition and subtraction in the context of using multiple representations, explaining mathematical reasons lying behind the concepts and justifying them. The findings obtained from the written responses of 42 PEMTs reveal that preservice teachers do not have sufficient and balanced special content knowledge. This is especially more so in the case of addition and subtraction of numbers with opposite signs. The preservice teachers were observed to have more difficulty in using the number line model compared to the use of other representations. The findings offer some indicators about how PEMTs understand integer addition and subtraction through multiple representations and why more emphasis on the SCK components

Keywords: Specialized content knowledge, Integer addition and subtraction, Pre-service elementary mathematics teachers

How to Cite this Article?

APA 6th edition
Ipek, A.S. (2018). Pre-Service Elementary Mathematics Teachers' Specialized Content Knowledge: The Case of Integer Addition and Subtraction. International Journal of Progressive Education, 14(4), 70-84. doi: 10.29329/ijpe.2018.154.6

Ipek, A. (2018). Pre-Service Elementary Mathematics Teachers' Specialized Content Knowledge: The Case of Integer Addition and Subtraction. International Journal of Progressive Education, 14(4), pp. 70-84.

Chicago 16th edition
Ipek, Ali Sabri (2018). "Pre-Service Elementary Mathematics Teachers' Specialized Content Knowledge: The Case of Integer Addition and Subtraction". International Journal of Progressive Education 14 (4):70-84. doi:10.29329/ijpe.2018.154.6.

  1. Ball, D. L. (2000). Intertwining Content and Pedagogy in Teaching and Learning to Teach. Journal of Teacher Education, 51, 241-247. [Google Scholar]
  2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it so special? Journal of Teacher Education, 59, 389-407. [Google Scholar]
  3. Billstein, R., Libeskind, S., & Lott, J. (2010). A problem solving approach to mathematics for elementary school teachers (10th ed.). Redding: Addison-Wesley. [Google Scholar]
  4. Birenbaum, M., & Tatsuoka, K. (1981). Effect of different instructional methods on error types and the underlying dimensionality of the test, part I (No. CERL-RR-8-3): Illinois University. [Google Scholar]
  5. Bofferding, L. (2014). Negative integer understanding: Characterizing first graders' mental models. Journal for Research in Mathematics Education, 45, 194-245. [Google Scholar]
  6. Bolyard, J. (2005). A comparison of the impact of two virtual manipulatives on student achievement and conceptual understanding of integer addition and subtraction. Unpublished Dissertation, George Mason University, Fairfax, VA. [Google Scholar]
  7. Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1981). Results from the second mathematics assessment of the national assessment of educational progress. Reston, VA: NCTM. [Google Scholar]
  8. Creswell, J. W. (1994). Research design: qualitative and quantitative approaches. Sage Publications. [Google Scholar]
  9. Davidson, P. M. (1987). Precursors of non-positive integer concepts. Paper presented at the Biennial meeting of the Society for Research in Child Development, Baltimore, MD. [Google Scholar]
  10. Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., and Zopf, D. (2008). Mathematical knowledge for teaching: Adapting US measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197 [Google Scholar]
  11. Diezmann, C. M., Lowrie, T., & Sugars, L. A. (2010). Primary students’ success on the structured number line. Australian Primary Mathematics Classroom, 15(4), 24–28. [Google Scholar]
  12. Ding, M. (2016). Developing preservice elementary teachers’ specialized content knowledge for teaching fundamental mathematical ideas: The case of the associative property. International Journal of STEM Education, 3(9), 1–19. [Google Scholar]
  13. Edwards, L. D. (1998). Embodying mathematics and science: Microworld as representations. The Journal of Mathematical Behavior, 17(1), 53-78. [Google Scholar]
  14. Fennema, E. and Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, pp. 147-164. NY: Macmillan Publishing Co. [Google Scholar]
  15. Ferguson, V. L. (1993). Developing mathematical conceptions. A study of conceptual, skill, and pedagogical differences in integer conceptions of preservice teachers: An expository approach vs. a constructivist approach. Unpublished Dissertation, University of Oklahoma. [Google Scholar]
  16. Fuson, K. C. (1992). Research on learning and teaching addition and subtraction of whole numbers. In G.Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp.53–187). Hilldale, NJ: Lawrence Erlbaum Associates Inc. [Google Scholar]
  17. Greenberg, J., &Walsh, K. (2008). No common denominator: The preparation of elementary teachers in mathematics. Washington, DC: National Council on Teacher Quality. [Google Scholar]
  18. 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. [Google Scholar]
  19. Hill, H. C., Ball, D. L.  & Schilling, S.  (2008). Unpacking “pedagogical content knowledge”: conceptualizing and measuring teachers' topic-specific knowledge of students, Journal for Research in Mathematics Education, 39 (4) , pp. 372-400 [Google Scholar]
  20. Janvier, C. (1983). The understanding of directed numbers. Paper presented at the Psychology of MathematicsEducation - North America-5, Montreal. [Google Scholar]
  21. Lewis, C. (1988). Why and how to learn why: analysis-based generalization of procedures. Cognitive Science, 12, 211–256. [Google Scholar]
  22. Liebeck, P. (1990). Scores and forfeits: An intuitive model for integer arithmetic. Educational Studies in Mathematics, 21, 221 – 239. [Google Scholar]
  23. Lin, Y. C., Chin, C. & Chiu, H.Y. (2011). Developing an instrument to capture high school mathematics teachers’ specialized content knowledge: An exploratory study. In Ubuz, B. (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 353. Ankara, Turkey: PME. [Google Scholar]
  24. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. [Google Scholar]
  25. Mitchell, R., Charalambous, C. Y., Hill, C. H. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17, 37-60. doi:10.1007/s10857-013-9253-4. [Google Scholar] [Crossref] 
  26. Morris, A, Heibert, J, & Spitzer, S. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: what can preservice teachers learn? Journal for Research in Mathematics Education, 2009(40), 491–529 [Google Scholar]
  27. Mukhopadhyay, S., Resnick, L. B., &Schauble, L. (1990). Social sense-making in mathematics: Children’s ideas of negative numbers. In G. Booker, J. Cobb, & T. N. de Mendicuti (Eds.), Proceedings of the 14th Conference of the International Group for the Psychology of MathematicsEducation (Vol. 3, pp. 281–288). Oaxtapec, Mexico: PME. [Google Scholar]
  28. Nunes, T. (1993). Learning mathematics: Perspectives from everyday life. In R. B. Davis [Google Scholar]
  29. & C. A. Maher (Eds.), Schools, mathematics, and the world of reality (pp. 61 -78). Boston, MA: Allynand Bacon. [Google Scholar]
  30. Petrou, M., & Goulding, M. (2011). Conceptualising teachers' mathematical knowledge in teaching. T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9-25). Springer. [Google Scholar]
  31. Schwarz, B. B., Hershkowitz, R. & Prusak, N. (2010). Argumentation and mathematics. In C. Howe & K. Littleton (Eds.), Educational dialogues: Understanding and promoting productive interaction (pp. 115–141). London: Routledge. [Google Scholar]
  32. Shawyer, R. (1985). Positive, Negative, Plus, Minus, Add, Subtract. Ontario Mathematics Gazette, 23(3), 34 - 35. [Google Scholar]
  33. Shore, F. S. (2005). Operating with integers. Ohio Journal of School Mathematics, Autumn, 2005, 7-11. [Google Scholar]
  34. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. [Google Scholar]
  35. Silverman, J. &Thompson, P. W. (2008). Toward a framework for the development of Mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 499-511. [Google Scholar]
  36. Skemp, R. R. (1987). The psychology of learning mathematics. London, England: PsychologyPress. [Google Scholar]
  37. Steiner, C. (2009). A study of pre-service elementary teachers’ conceptual understanding of integers. Unpublished doctoral dissertation, Kent State University, Kent, Ohio. [Google Scholar]
  38. Stephan, M., & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428–464. [Google Scholar]
  39. Venkat, H. (2015). Representational approaches to primary teacher development in South Africa. In X. Sun, B. Kaur, & J. Novotná (Eds.). Conference proceedings of ICMI study 23: Primary mathematics study on whole numbers (pp. 583-588). Macau, China: University of Macau. [Google Scholar]
  40. Widjaja, W., Stacey, K., & Steinle, V. (2011). Locating decimals on the number line: Insights into the thinking of pre-service primary teachers. Journal of Mathematical Behavior, 30(1), 80–91. doi: 10.1016/j.jmathb.2010.11.004 [Google Scholar] [Crossref] 
  41. Wilkins, J. R. (1996). Students' use of informal strategies and representation in solving addition and subtraction integer problems. Unpublished Dissertation, University of California at Los Angeles, Los Angeles [Google Scholar]
  42. Yackel, E. & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 227–236). Reston, VA: National Council of Teachers of  Mathematics. [Google Scholar]