What Do Students Know? Facing Challenges of Distance, Context, and Desire in Trying to Hear Children

  • Deborah Loewenberg Ball
Part of the Springer International Handbooks of Education book series (SIHE, volume 3)


No task is more fundamental to teaching than figuring out what students are learning. Paradoxically, no endeavour is more difficult. In his well-known sociological analysis of teachers and teaching, Lortie (1975) found that questions about the assessment of student learning evoked significant emotional response from teachers. Although the teachers whom he interviewed believed that good teachers inform their practice by closely monitoring students, many despaired of really knowing about the effects of their teaching.


Pedagogical Content Knowledge Native Speaker Teacher College Curriculum Material Student Thinking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, J., Reder, L., & Simon, H. (1996). Situated learning and education. Educational Researcher, 25(4), 5–11.CrossRefGoogle Scholar
  2. Ball, D. L. (1991). Research on teaching mathematics: Making subject matter part of the equation. In J. Brophy (Ed.), Advances in research on teaching (Vol. 2, pp. 1–48). Greenwich, CT: JAI Press.Google Scholar
  3. Ball, D. L. (1993a). Moral and intellectual, personal and professional: Restitching practice. In M. Buchmann & R. E. Floden (Eds.), Detachment and concern: Topics in the philosophy of teaching and teacher education (pp. 193–204). New York: Teachers College Press.Google Scholar
  4. Ball, D. L. (1993b). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373–397.CrossRefGoogle Scholar
  5. Ball, D. L. (1995). Transforming pedagogy — Classrooms as mathematical communities: A response to Lensmire and Pryor. Harvard Educational Review, 65(4), 670–677.Google Scholar
  6. Ball, D. L. (in press). Working on the inside: Designing to use one’s own practice as a site for studying mathematics teaching and learning. In R. Lesh (Ed.), Designing research for reform: In mathematics and science education.Google Scholar
  7. Ball, D. & Wilson, S. (1996). Integrity in teaching: Recognizing the fusion of the moral and intellectual. American Educational Research Journal, 33(1), 155–192.CrossRefGoogle Scholar
  8. Barnett, C. (1991). Building a case-based curriculum to enhance the pedagogical content knowledge of mathematics teachers. Journal of Teacher Education, 42(4), 263–273.CrossRefGoogle Scholar
  9. Barnett, C. & Sather, S. (1992, April). Using case discussions to promote changes in beliefs among mathematics teachers. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.Google Scholar
  10. Bruner, J. (1960). The process of education. Cambridge, MA: Harvard University Press.Google Scholar
  11. Chazan, D. (1992). Implementing the ‘Professional Standards for Teaching Mathematics.’ Mathematics Teacher, 85(5), 371–375.Google Scholar
  12. Cohen, D. K. (in preparation). Teaching practice and its predicaments. Unpublished manuscript, University of Michigan, Ann Arbor.Google Scholar
  13. Cohen, D. (1995). Rewarding teachers for students’ performance. In S. Fuhrman & J. O’Day (Eds.), Rewards and reform (pp. 60–112). San Francisco: Jossey Bass.Google Scholar
  14. Darling-Hammond, L., Ancess, J., & Falk, B. (1995). Authentic assessment in action: Studies of schools and students at work. New York: Teachers College Press.Google Scholar
  15. Delpit, L. D. (1988). The silenced dialogue: Power and pedagogy in educating other people’s children. Harvard Educational Review, 58, 280–298.Google Scholar
  16. Dewey, J. (1902/1990). The child and the curriculum. Chicago: University of Chicago.Google Scholar
  17. Dewey, J. (1916/1944). The nature of method. In Democracy and education (pp. 164–179). New York: Macmillan.Google Scholar
  18. Duckworth, E. (1987). The having of wonderful ideas and other essays. New York: Teachers College Press.Google Scholar
  19. Edwards, D. (1993). What do children really think? Discourse analysis and conceptual content in children’s talk. Cognition and Instruction, 11, 207–225.CrossRefGoogle Scholar
  20. Edwards, D. & Mercer, N. (1989). Reconstructing context: The conventionalization of classroom knowledge. Discourse Processes, 12, 91–104.CrossRefGoogle Scholar
  21. Elbow, P. (1986). Embracing contraries: Explorations in learning and teaching. New York: Oxford University Press.Google Scholar
  22. Erlwanger, S. (1975). Benny’s conceptions of rules and answers in IPI mathematics. Journal of Children’s Mathematical Behavior, 1, 157–283.Google Scholar
  23. Hammer, D. (1995). Epistemological considerations in teaching introductory physics. Newton, MA: Center for the Development of Teaching, Education Development Center.Google Scholar
  24. Hawkins, D. (1974). Nature, man, and mathematics. In The informed vision: Essays on learning and human nature (pp. 109–131). New York: Agathon. (Original work published in 1972.).Google Scholar
  25. Heaton, R. (1994). Creating and studying a practice of teaching elementary mathematics for understanding. Unpublished doctoral dissertation, Michigan State University, East Lansing.Google Scholar
  26. Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21.CrossRefGoogle Scholar
  27. Jackson, P. (1968). Life in classrooms. New York: Holt, Rinehart, and Winston.Google Scholar
  28. Jackson, P. (1986). The practice of teaching. New York: Teachers College Press.Google Scholar
  29. Kitcher, P. (1984). The nature of mathematical knowledge. New York: Oxford University Press.Google Scholar
  30. Kline, M. (1970). Logic versus pedagogy. American Mathematical Monthly, 77, 264–282.CrossRefGoogle Scholar
  31. Kuhn, T. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.Google Scholar
  32. Lampert, M. (1986). Knowing, doing, and teaching multiplication. Cognition and Instruction, 3(4), 305–342.CrossRefGoogle Scholar
  33. Lampert, M. (1990a). Connecting conventions with inventions. In L. Steffe & T. Wood (Eds.), Transforming children’s mathematics education (pp. 253–265). Hillsdale, NJ: Erlbaum.Google Scholar
  34. Lampert, M. (1990b). When the problem is not the question and the answer is not the solution: Mathematical knowing and teaching. American Educational Research Journal, 27, 29–64.CrossRefGoogle Scholar
  35. Lampert, M. (1992). Practices and problems in teaching authentic mathematics. In F. Oser, A. Dick, & J. L. Patry (Eds.), Effective and responsible teaching: The new synthesis (pp. 295–314). San Francisco: Jossey-Bass.Google Scholar
  36. Lampert, M. (in press). Studying teaching as a thinking practice. In J. Greeno & S. G. Goldman (Eds.), Thinking practices. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  37. Lampert, M. & Ball, D. L. (1995). Aligning teacher education with contemporary K-12 reform visions. Paper prepared for the National Commission on Teaching and America’s Future, Teachers College, New York.Google Scholar
  38. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (in press). Connected mathematics project. Palo Alto, CA: Dale Seymour Publications.Google Scholar
  39. Lensmire, T. (1993). Following the child, socioanalysis, and threats to community: Teacher response to student texts. Curriculum Inquiry, 23, 265–299.CrossRefGoogle Scholar
  40. Lensmire, T. (1994a). When children write: Critical revisions of the writing workshop. New York: Teachers College Press.Google Scholar
  41. Lensmire, T. (1994b). Writing workshop as carnival: Reflections on an alternative learning environment. Harvard Educational Review, 64(4), 371–391.Google Scholar
  42. Lord, B. (1994). Teachers’ professional development: Critical colleagueship and the role of professional communities. In N. Cobb (Ed.), The future of education: Perspectives on national standards in America (pp. 175–204). New York: The College Board.Google Scholar
  43. Lortie, D. C. (1975). Schoolteacher: A sociological study. Chicago: The University of Chicago Press.Google Scholar
  44. Osborne, M. (1993). Teaching with and without mirrors: Examining science teaching in elementary school from the perspective of a teacher and learner. Unpublished doctoral dissertation, Michigan State University, East Lansing.Google Scholar
  45. Paley, V. (1986). On listening to what the children say. Harvard Educational Review, 56(2), 122–131.Google Scholar
  46. Paley, V. (1995). Kwanzaa and me: A teacher’s story. Cambridge, MA: Harvard University Press.Google Scholar
  47. Peterson. P. L., Carpenter, T., & Fennema, E. (1989). Teachers’ knowledge of students’ knowledge in mathematics problem solving: Correlational and case analyses. Journal of Educational Psychology, 81, 558–569.CrossRefGoogle Scholar
  48. Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. New York: Routledge & Kegan Paul.Google Scholar
  49. Ramsey, P. (1991). Social dynamics of early childhood classrooms. In Making friends in school: Promoting peer relationships in early childhood (pp. 43–70). New York: Teachers College Press.Google Scholar
  50. Roth, K. (1992). The role of writing in creating a science learning community (Elementary Subjects Center Series No. 62). East Lansing: Michigan State University, Elementary Subjects Center.Google Scholar
  51. Russell, S. J. & Rubin, A. (1994). Landmarks in the hundreds. In Investigations in number, data, and space. Palo Alto, CA: Dale Seymour Publications.Google Scholar
  52. Scheffler, I. (1965). Conditions of knowledge: An introduction to epistemology and education. Chicago: University of Chicago Press.Google Scholar
  53. Schifter, D., Russell, S. J., & Bastable, V. (in press). Teaching to the big ideas. In M. Solomon (Ed.), Reinventing the classroom. New York: Teachers College Press.Google Scholar
  54. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15 2), 4–14.CrossRefGoogle Scholar
  55. Schwille, J., Porter, A., Floden, R., Freeman, D., Knapp, L., Kuhs, T., & Schmidt, W. (1983). Teachers as policy brokers in the content of elementary school mathematics. In L. Shulman & G. Sykes (Eds.), Handbook of teaching and policy (pp. 370–391). New York: Longman.Google Scholar
  56. Wilson, S. M. (1995). Not tension, but intention. A response to Wong’s analysis of the researcher-teacher. Educational Researcher, 24(1).Google Scholar
  57. Wilson, S. M. (in press). Mastodons, maps, and Michigan: Exploring uncharted territory while teaching elementary school social studies. Elementary School Journal.Google Scholar
  58. Wilson, S. M., Shulman, L. S., & Richert, A. (1987). ‘150 different ways of knowing’: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teacher thinking (pp. 104–124). Sussex: Holt, Rinehart, & Winston.Google Scholar
  59. Wong, D. (1995). Challenges confronting the researcher/teacher: Conflicts of purpose and conduct. Educational Researcher, 24(3), 22–28.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Deborah Loewenberg Ball
    • 1
  1. 1.University of MichiganUSA

Personalised recommendations