 Ball, D. L. (2000). Intertwining Content and Pedagogy in Teaching and Learning to Teach. Journal of Teacher Education, 51, 241247. [Google Scholar]
 Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it so special? Journal of Teacher Education, 59, 389407. [Google Scholar]
 Billstein, R., Libeskind, S., & Lott, J. (2010). A problem solving approach to mathematics for elementary school teachers (10th ed.). Redding: AddisonWesley. [Google Scholar]
 Birenbaum, M., & Tatsuoka, K. (1981). Effect of different instructional methods on error types and the underlying dimensionality of the test, part I (No. CERLRR83): Illinois University. [Google Scholar]
 Bofferding, L. (2014). Negative integer understanding: Characterizing first graders' mental models. Journal for Research in Mathematics Education, 45, 194245. [Google Scholar]
 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 Unpublished Dissertation, George Mason University, Fairfax, VA.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]
 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]
 Creswell, J. W. (1994). Research design: qualitative and quantitative approaches. Sage Publications. [Google Scholar]
 Davidson, P. M. (1987). Precursors of nonpositive integer concepts. Paper presented at the Biennial meeting of the Society for Research in Child Development, Baltimore, MD. [Google Scholar]
 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), 171197 [Google Scholar]
 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]
 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]
 Edwards, L. D. (1998). Embodying mathematics and science: Microworld as representations. The Journal of Mathematical Behavior, 17(1), 5378. [Google Scholar]
 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. 147164. NY: Macmillan Publishing Co. [Google Scholar]
 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]
 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]
 Greenberg, J., &Walsh, K. (2008). No common denominator: The preparation of elementary teachers in mathematics. Washington, DC: National Council on Teacher Quality. [Google Scholar]
 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), 371406. [Google Scholar]
 Hill, H. C., Ball, D. L. & Schilling, S. (2008). Unpacking “pedagogical content knowledge”: conceptualizing and measuring teachers' topicspecific knowledge of students, Journal for Research in Mathematics Education, 39 (4) , pp. 372400 [Google Scholar]
 Janvier, C. (1983). The understanding of directed numbers. Paper presented at the Psychology of MathematicsEducation  North America5, Montreal. [Google Scholar]
 Lewis, C. (1988). Why and how to learn why: analysisbased generalization of procedures. Cognitive Science, 12, 211–256. [Google Scholar]
 Liebeck, P. (1990). Scores and forfeits: An intuitive model for integer arithmetic. Educational Studies in Mathematics, 21, 221 – 239. [Google Scholar]
 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]
 Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. [Google Scholar]
 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, 3760. doi:10.1007/s1085701392534. [Google Scholar] [Crossref]
 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]
 Mukhopadhyay, S., Resnick, L. B., &Schauble, L. (1990). Social sensemaking 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]
 Nunes, T. (1993). Learning mathematics: Perspectives from everyday life. In R. B. Davis [Google Scholar]
 & C. A. Maher (Eds.), Schools, mathematics, and the world of reality (pp. 61 78). Boston, MA: Allynand Bacon. [Google Scholar]
 Petrou, M., & Goulding, M. (2011). Conceptualising teachers' mathematical knowledge in teaching. T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 925). Springer. [Google Scholar]
 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]
 Shawyer, R. (1985). Positive, Negative, Plus, Minus, Add, Subtract. Ontario Mathematics Gazette, 23(3), 34  35. [Google Scholar]
 Shore, F. S. (2005). Operating with integers. Ohio Journal of School Mathematics, Autumn, 2005, 711. [Google Scholar]
 Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 414. [Google Scholar]
 Silverman, J. &Thompson, P. W. (2008). Toward a framework for the development of Mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 499511. [Google Scholar]
 Skemp, R. R. (1987). The psychology of learning mathematics. London, England: PsychologyPress. [Google Scholar]
 Steiner, C. (2009). A study of preservice elementary teachers’ conceptual understanding of integers. Unpublished doctoral dissertation, Kent State University, Kent, Ohio. [Google Scholar]
 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]
 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. 583588). Macau, China: University of Macau. [Google Scholar]
 Widjaja, W., Stacey, K., & Steinle, V. (2011). Locating decimals on the number line: Insights into the thinking of preservice primary teachers. Journal of Mathematical Behavior, 30(1), 80–91. doi: 10.1016/j.jmathb.2010.11.004 [Google Scholar] [Crossref]
 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]
 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]
