A Pedagogical Overview of Relevant Literature

Chapter

Abstract

This literature reviewed in this chapter is an examination of conceptual and empirical studies in the area of elementary teachers’ knowledge for teaching mathematics; it includes a discussion of the implications and implementations emerging from the review. The literature review is divided into four major sections: sociocultural theory, a history of research on teachers’ knowledge for teaching mathematics, studies about elementary teachers’ knowledge for teaching mathematics, and an interpretive summary and critical analysis. Taken together, these sections of literature provide a historical and theoretical context for this study.

Keywords

Mathematical knowledge Elementary teachers Teachers’ knowledge Language Sociocultural theory Vygotsky Pedagogical content knowledge Pedagogical knowledge Content knowledge Vertical curriculum knowledge Lateral Curriculum knowledge Representations Zone of proximal development Student mathematical background Mathematics instruction Schema Internalization Mathematical learning South Korea National Mathematics Curriculum Teaching Learning Mathematical understanding Process–product Mathematics Category Achievement Standards CCSS South Korean government Specialized mathematical knowledge Subject matter knowledge Education context 

References

  1. Albert, L. R. (2000). Outside in, inside out: Seventh grade students mathematical thought processes. Educational Studies in Mathematics, 41, 109–142.CrossRefGoogle Scholar
  2. Albert, L. R. (2012). Rhetorical ways of thinking: Vygotskian theory and mathematical learning . New York: Springer.CrossRefGoogle Scholar
  3. An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in china and the U.S. Journal of Mathematics Teacher Education, 7, 145–172.CrossRefGoogle Scholar
  4. Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373–397.Google Scholar
  5. Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspective on mathematics teaching and learning (pp. 83–104). Westport: Ablex.Google Scholar
  6. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.CrossRefGoogle Scholar
  7. Bass, H. (2005). Mathematics, mathematicians and mathematics education. Bulletin of the American Mathematical Society, 42, 417–430.CrossRefGoogle Scholar
  8. Barnett, J., & Hodson, D. (2000). Pedagogical context knowledge: Toward a fuller understanding of what good science teachers know. Science Teacher Education, 85, 426–453.Google Scholar
  9. Borko, H., & Putnam, R. T. (1996) Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 637–708). New York: Macmillan.Google Scholar
  10. Borman, G., & Dowling, M. (2010). Schools and inequality: A multilevel analysis of Coleman’s equality of educational opportunity data. Teachers College Record, 112, 1201–1246.Google Scholar
  11. Bruner, J. (1986). Actual minds, possible worlds. Cambridge: Harvard University Press.Google Scholar
  12. Bullough, R. V. (2001). Pedagogical content knowledge circa 1907 and 1987: A study in the history of an idea. Teaching and Teacher Education, 17, 655–666.CrossRefGoogle Scholar
  13. Chaiklin, S. (1986). Constructing productions and producing constructions. The American Psychologist, 41, 590–593.CrossRefGoogle Scholar
  14. Chapman, O. (2004). Facilitating peer interactions in learning mathematics: Teachers’ practical knowledge. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 191–198.Google Scholar
  15. Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/Math/ September 9, 2012. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf/.
  16. Darling Hammond, L. (2000). Teacher quality and student achievement: A Review of state policy evidence. Education Policy Analysis Archives, 8, 1–44.CrossRefGoogle Scholar
  17. Dee, T. S., & Jacob, B., Brain, A. (2011). The impact of no child left behind on student achievement. Journal of Policy Analysis and Management, 30, 418–446.CrossRefGoogle Scholar
  18. Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complicities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24, 8–40.CrossRefGoogle Scholar
  19. Even, R. (1993). Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concepts. Journal for Research in Mathematics Education, 24, 94–116.CrossRefGoogle Scholar
  20. Fennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning . New York: Macmillan.Google Scholar
  21. Fernyhough, C. (2008). Getting Vygotskian about theory of mind: Mediation, dialogue, and the development of social understanding. Developmental Review, 28, 225–262.CrossRefGoogle Scholar
  22. Gearhart, M. (2007). Mathematics knowledge for Teaching: Questions about Constructs. Measurement: Interdisciplinary Research and Perspectives, 5, 173–180.Google Scholar
  23. Graham, K. J. (2001). Principles and standards for school mathematics and teacher education: Preparing and empowering teachers. School Science and Mathematics, 101, 319–327.CrossRefGoogle Scholar
  24. Graham, C., Burgoyne, N., Cantrell, P., Smith, L., Clair, L., & Harris, R. (2009). TPACK development in science teaching: Measuring the TPACK confidence of inservice science teachers. Tech Trends, 53, 70–79.CrossRefGoogle Scholar
  25. Grossman, P. L., & Richert, A. E. (1988). Unacknowledged knowledge growth: A re-examination of the effects of teacher education. Teaching and Teacher Education, 4, 53–62.CrossRefGoogle Scholar
  26. Grossman, P. L., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. Reynolds (Ed.), The knowledge base for beginning teachers (pp. 23–36). New York: Pergamon.Google Scholar
  27. Grouws D. A. & Schultz, K. A. (1996). Mathematics teacher education. In J. Sikula (Ed.), Handbook of research on teacher education (2nd ed., pp. 442–458). New York: Association of Teacher Educators.Google Scholar
  28. Hanushek, E. A. (1998). Conclusions and controversies about the effectiveness of school resources. Economic Policy Review Federal Reserve Bank of New York, 4, 11–27.Google Scholar
  29. Hardie, C. D. (1942). Truth and fallacy in educational theory . Cambridge: Cambridge University Press.Google Scholar
  30. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., & Human, P. (1998). Making sense: Teaching and learning mathematics with understanding. Portsmouth: Heinemann.Google Scholar
  31. Hill, H. C. (2004). Professional development standards and practices in elementary school mathematics. Elementary School Journal, 104, 345–363.CrossRefGoogle Scholar
  32. Hill, H. C., Schilling, S. G., & Ball, D. L (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11–30.CrossRefGoogle Scholar
  33. 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.CrossRefGoogle Scholar
  34. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372–400.Google Scholar
  35. Jang, S. J., & Tsai, M. F. (2012). Exploring the TPACK of Taiwanese elementary mathematics and science teachers with respect to use of interactive whiteboards. Computers & Education, 59, 327–338.CrossRefGoogle Scholar
  36. Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17–36.Google Scholar
  37. Kinach, B.M. (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18, 51–71.CrossRefGoogle Scholar
  38. Klein, R., & Tirosh, D. (1997). Teachers’ pedagogical content knowledge of multiplication and division of rational numbers. In H. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 3, 144–152.Google Scholar
  39. Labaree, D. F. (2008). An uneasy relationship: The history of teacher education in the university. In M. Cochran-Smith, S. Feiman-Nemser, & J. McIntyre (Eds.), Handbook of research on teacher education (3rd ed., pp. 290–306). New York: Routledge.Google Scholar
  40. Lagemann, E. C. (2000). An elusive science: The troubling history of education research . Chicago: University of Chicago Press.Google Scholar
  41. Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. New York: Routledge.Google Scholar
  42. Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41, 3–11.CrossRefGoogle Scholar
  43. McEwan, H., & Bull, B. (1991). The pedagogic nature of subject matter knowledge. American Educational Research Journal, 28, 316–334.CrossRefGoogle Scholar
  44. McKnight, C. C., Crosswhite, F. J., Dossey, J. A., Kifer, E., Swafford, J. O., Travers, K. J., & Cooney, T. J. (1987). The underachieving curriculum: Assessing U.S. school mathematics from an international perspective . Champaign: Stipes.Google Scholar
  45. McNamara, D. (1991) Subject knowledge and its application: Problems and possibilities for teacher educators. Journal of Education for Teaching, 17, 113–128.CrossRefGoogle Scholar
  46. Meredith, A. (1993) Knowledge for teaching mathematics: Some student teachers’ views. Journal of Education for Teaching, 19, 325–338.CrossRefGoogle Scholar
  47. Meredith, A. (1995) Terry’s learning: Some limitations of Shulman’s pedagogical content knowledge. Cambridge Journal of Education, 25, 175–187.CrossRefGoogle Scholar
  48. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge. Teacher College Record, 108, 1017–1054.CrossRefGoogle Scholar
  49. Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematics Thinking and Learning, 4, 189–212.CrossRefGoogle Scholar
  50. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston: Author.Google Scholar
  51. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: Author.Google Scholar
  52. Needels, M. C. (1988). A new design for process-product research on the quality of discourse in teaching. American Educational Research Journal, 25, 503–526.CrossRefGoogle Scholar
  53. Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21, 509–523.CrossRefGoogle Scholar
  54. Park, K. (2010). Mathematics teacher education in Korea. In Koon, F., Leung, S., & Li, Y. (Eds.), Reforms and issues in school mathematics in East Asia: Sharing and understanding mathematics education policies and practices (pp. 181–196). Chesapeake: AACE.Google Scholar
  55. Parker, J & Heywood, D. (2000). Exploring the relationship between subject knowledge and pedagogic content knowledge in primary teachers’ learning about forces. International Journal of Science Education, 22, 89–111.CrossRefGoogle Scholar
  56. Polly, D., McGee, J. R., & Martin, C. S. (2010). Employing technology-rich mathematical task in professional development to develop teachers’ technological, pedagogical, and content knowledge (TPACK). JI. Of Computers in Mathematics and Science Teaching, 29, 455–472.Google Scholar
  57. Ponde, J. P. D., & Chapman, O. (2006). Mathematics Teachers’ Knowledge and Practice. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present, and future (pp. 461–494). The Netherlands: Sense.Google Scholar
  58. Porter, A., McMaken, J., Hwang, J., & Yang, R. (2012). Common core standards: The new U.S. intended curriculum. Educational Researcher, 40, 103–116.CrossRefGoogle Scholar
  59. Rahman, F. A., Scaife, J., Yahya, N. A., & Jalil, H. A. (2010). Knowledge of diverse learners: Implications for the practice of teaching. International Journal of Instruction, 3, 83–96.Google Scholar
  60. Richards, J., & T. Farrell (2005). Professional development for language teachers: Strategies for teacher learning . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  61. Rivers, J. C., & Sanders, W. L. (2002). Teacher quality and equity in education opportunity: Findings and policy implications. In L. T. Izumi & M. E. Williamson (Eds.), Teacher quality (pp. 13–23). Stanford: Hoover.Google Scholar
  62. Robinson, N., Even, R., & Tirosh, D. (1994). How teachers deal with their students’ conceptions of algebraic expressions as incomplete. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 4, 129–136.Google Scholar
  63. Rowland, T., P. Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 3, 255–281.CrossRefGoogle Scholar
  64. Schmidt, D. A., Baran, E., Thompson, A. D., Mishra, P., Koehler, M. J., & Shin, T. S. (2009). Technological pedagogical content knowledge (TPACK): The development and validation of an assessment instrument for preservice teachers. Journal of Research on Technology in Education, 42, 123–149.CrossRefGoogle Scholar
  65. Schwab, J. J. (1964). The structure of the disciplines: Meanings and significances. In: G. W. Ford and L. Pugno, (Eds.), The structure of knowledge and the curriculum (pp. 6–30), Chicago: Rand McNally.Google Scholar
  66. Segall, A. (2004) Revisiting pedagogical content knowledge: The pedagogy of content/the content of pedagogy. Teaching and Teacher Education, 20, 489–504.CrossRefGoogle Scholar
  67. Shulman, L. S. (1986). Paradigms and research programs in the study of teaching: A contemporary perspective. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 3–36). New York: Macmillan.Google Scholar
  68. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.Google Scholar
  69. Shulman, L. (1992). Ways of seeing, ways of knowing, ways of teaching, ways of learning about teaching. Journal of Curriculum Studies, 28, 393-396.Google Scholar
  70. Steele, D. F. (2001). Using sociocultural theory to teach mathematics: A Vygotskian perspective . School Science and Mathematics, 101, 404–416.CrossRefGoogle Scholar
  71. Stones, E. (1992). Quality teaching: A sample of cases . London: Routledge.CrossRefGoogle Scholar
  72. Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, 307–332.CrossRefGoogle Scholar
  73. Tanase, M. (June 15, 2011). Teaching place value concepts to first grade Romanian students: Teacher knowledge and its influence on student learning. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.plymouth.ac.uk/journal/ November 12, 2012.
  74. The Ministry of Education in South Korea. (2009). The educational history of South Korea Retrieved from http://www.mest.go.kr. March 28, 2013 http://www.mest.go.kr.
  75. The National Commission on Excellence in Education. (1983). A nation at risk: The imperative for education reform. http://datacenter.spps.org/uploads/SOTW_A_Nation_at_Risk_1983.pdf.
  76. The Seoul National University of Education. (2012). The Seoul National University of Education: College Bulletin. Seoul, South Korea: The Seoul National University of Education Press.Google Scholar
  77. Turnuklu, E., & Yesildere, S. (2007). The pedagogical content knowledge in mathematics: Pre-service primary mathematics teachers’ perspective in Turkey. IUMPST: The Journal, 1, 1–13.Google Scholar
  78. U.S. Department of Education, Office of Policy Planning, & Innovation. (2003) Meeting the highly qualified teachers challenge: The secretary’s second annual report on teacher quality. Washington, D.C.: Author.Google Scholar
  79. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  80. Vygotsky, L. S. (1981). The development of higher forms of attention in childhood. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 189–240). Armonk: Sharpe.Google Scholar
  81. Vygotsky, L. S. (1997). Genesis of higher mental functions. In R. W. Rieber (Ed.). The collected works of L. S. Vygotsky (Vol. 4, pp. 1–251). New York: Plenum (Original work published 1931).Google Scholar
  82. Wertsch, J. V. (1985a), Culture, communication and cognition: Vygotskian perspectives, Cambridge: Cambridge University Press.Google Scholar
  83. Wertsch, J. V. (1985b). V ygotsky and the social formation of mind . Cambridge: Harvard University Press.Google Scholar
  84. Wilson, S., Shulman, L., & Richert, A. (1987). 150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 104–123). Eastbourne: Cassell.Google Scholar
  85. Wiseman, D. L., Cooner, D. D., & Knight, S. L. (1999). Becoming a teacher in a field-based setting . New York: Wadsworth.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Seoul Mogun Elementary SchoolSeoulSouth Korea
  2. 2.Teacher EducationBoston College Lynch School of EducationChestnut HillUSA

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