Preservice elementary school teachers' conceptions of multidigit whole numbers

Journal for Research in Mathematics Education

Volumn 40, Issue 3, 2009, Pages 251-281

  Thanheiser, Eva ^a  

^a PORTLAND STATE UNIVERSITY   (United States)

Author keywords

Addition; Content knowledge; Preservice teacher education; Subtraction; Teacher education; Whole numbers

Indexed keywords

EID: 67649661898     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. (Doctoral dissertation, Michigan State University. 1988). Retrieved from http://www-personal.umich.edu/~dball/books/index.html
2. Ball, D. L., Hill, H. C, & Bass, H. (2005, Fall). Knowing mathematics for teaching: Who knows math- ematics well enough to teach third grade, and how can we decide? American Educator, 14, 16-17, 20-22,43-46.
3. Bransford, J., Brown, A., & Cocking, R. (1999). How people learn. Washington, DC: National Academy Press.
4. Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers. Washington, DC: Mathematical Association of America.
5. Fuson, K. C. (1990). Conceptual structures for multidigit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction, 7,343-403.
6. Fuson, K. C, & Kwon, Y. (1992). Korean children's understanding of multidigit addition and subtrac- tion. Child Development, 63, 491-506.
7. Fuson, K. C, Wearne, D., Hiebert, J. C, Murray, H. G., Human, P. G., Olivier, A. I., et al. (1997). Children's conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28, 130-162.
8. Geertz, C. (1973). Thick description: Toward an interpretive theory of culture. In C. Geertz (Ed.), The interpretation of cultures: Selected essays (pp. 3-30). New York: Basic Books.
9. Ginsburg, H. P. (1997). Entering the child's mind: The clinical interview in psychological research and practice. New York: Cambridge University Press.
10. Guba, E. G., & Lincoln, Y. S. (1989). Fourth generation evaluation. Newbury Park, CA: Sage.
11. Hill, H. C, Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
12. Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1,75-86.
13. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathe- matics. Washington, DC: National Academy Press.
14. Lundin, J., & Burton, S. (Eds.). (1998). Mathematics framework for California public schools: Kindergarten through grade twelve. Sacramento, CA: CDE Press.
15. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
16. Miles, M., & Huberman, M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Newbury Park, CA: Sage.
17. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
18. Philipp, R. A., Ambrose, R., Lamb, L. L. C, Sowder, J. T., Schappelle, B. P., Sowder, L., et al. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38,438-476.
19. Ross, S. H. (1990). Children's acquisition of place-value numeration concepts: The roles of cognitive development and instruction. Focus on Learning Problems in Mathematics, 12(1), 1-17.
20. Sowder, J. T., Philipp, R. A., Armstrong, B. E., & Schappelle, B. (1998). Middle-grade teachers' math- ematical knowledge and its relationship to instruction. Albany: State University of New York Press.
21. Stigler, J. W., & Hiebert, J. (1997). Understanding and improving classroom mathematics instruction: An overview of the TIMSS video study. Phi Delta Kappan, 79, 14-21.
22. Stigler, J. W., & Hiebert, J. (1999). The teaching gap. New York: The Free Press.
23. Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and tech- niques. Newbury Park, CA: Sage.
24. Thanheiser, E. (2005). Preservice teachers' conceptions of multidigit whole numbers. Unpublished doctoral dissertation, University of California, San Diego and San Diego State University, San Diego, CA.
25. Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and concep- tual orientations in teaching mathematics. In D. B. Aichele & A. F. Coxford (Eds.), Professional devel- opment for teachers of mathematics (pp. 79-92). Reston, VA: National Council of Teachers of Mathematics.
26. Valeras, M., & Becker, J. (1997). Children's developing understanding of place value: Semiotic aspects. Cognition and Instruction, 15,265-286.
27. Zazkis, R., & Khoury, H. A. (1993). Place value and rational number representations: Problem solving in the unfamiliar domain of non-decimals. Focus on Learning Problems in Mathematics, I5( 1), 38-51.