Learning about teaching for understanding through the study of tutoring

Journal of Mathematical Behavior

Volumn 17, Issue 4, 1998, Pages 441-465

  Gutstein, Eric ^a   MacK, Nancy K ^b  

^a DEPAUL UNIVERSITY   (United States)

^b NATIONAL LOUIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040685568     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0732-3123(99)00005-x     Document Type: Article

References (41)

1. Anderson John R. The architecture of cognition. 1983;Harvard University Press, Cambridge, MA.
2. Ball Deborah L. Halves, pieces, and twoths: Construction and using representational contexts in teaching fractions. Carpenter T.P., Fennema E., Romberg T.A. Rational numbers: An integration of research. 1993;157-195 Lawrence Erlbaum Associates, Hillsdale, NJ.
3. Borko Harriet, Eisenhart Margaret, Brown Catherine, Underhill R., Jones D., Agard P. Learning to teach hard mathematics: Do novices and their instructors give up too easily? Journal for Research in Mathematics Education. 23:1992;194-222.
4. Brown Catherine A. A critical analysis of teaching rational number. Carpenter T.P., Fennema E., Romberg T.A. Rational numbers: An integration of research. 1993;197-218 Erlbaum Associates, Hillsdale, NJ.
5. Buchanan B., Shortliffe E. Rule-based expert systems: The MYCIN experiments of the Stanford Heuristic Programming Project. 1984;Addison-Wesley, Reading, MA.
6. Carpenter Thomas P. Teaching as problem solving. Charles R.I., Silver E.S. The teaching and assessing of mathematical problem solving. 1988;187-202 Erlbaum Associates and National Council of Teachers of Mathematics, Reston, VA.
7. Clark C.M., Peterson Penelope L. Teachers' thought processes. Wittrock M.C. Handbook of research on teaching. 3rd edn. 1986;255-296 Macmillan, New York.
8. Cobb Paul Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher. 23(7):1994;13-20.
9. Davis Robert B. A theory of teaching mathematics. The Journal of Mathematical Behavior. 11:1992;337-360.
10. Fennema Elizabeth, Franke Megan L. Teachers' knowledge and its impact. Grouws D. Handbook of research on mathematics teaching and learning. 1992;147-164 Macmillan, New York.
11. Fennema Elizabeth, Franke Megan L., Carpenter Thomas P., Carey Deborah A. Using children's mathematical knowledge in instruction. American Educational Research Journal. 30:1993;555-583.
12. Ginsburg Herbert P. Cocking R.R., Mestre J.P. Linguistic and cultural influences on learning mathematics. 1988;xi-xii Erlbaum Associates, Hillsdale, NJ.
13. Gutstein, Eric. (1991). A computer model of learning by human tutors. Unpublished manuscript, University of Wisconsin-Madison, Computer Sciences Department.
14. Gutstein, Eric. (1993). SIFT: A self-improving fractions tutor. Unpublished doctoral dissertation, University of Wisconsin-Madison.
15. Gutstein Eric, Lipman Pauline, Hernandez Patricia, de los Reyes Rebeca Culturally relevant teaching in a Mexican American context. Journal for Research in Mathematics Education. 28:1997;709-737.
16. Hiebert, James. (1986). The relation between drill-and-practice and understanding in mathematics. Paper prepared at the request of a Task Force of the Mathematical Sciences Education Board of the National Research Council.
17. Hiebert James A. Benefits and costs of research that links teaching and learning mathematics. Carpenter T.P., Fennema E., Romberg T.A. Rational numbers: An integration of research. 1993;219-238 Erlbaum Associates, Hillsdale, NJ.
18. Hiebert James, Carpenter Thomas P. Learning and teaching with understanding. Grouws D.A. Handbook of research on mathematics teaching and learning. 1992;65-97 Macmillan, New York.
19. Hiebert James, Carpenter Thomas P., Fennema Elizabeth, Fuson Karen C., Wearne Diana, Murray Hanlie, Olivier Alwyn, Human Piet Making sense: Teaching and learning mathematics with understanding. 1997;Heinemann, Portsmouth, NH.
20. Klahr David, Langley Patrick, Neches Robert Production system models of learning and development. 1987;MIT Press, Cambridge, MA.
21. Koehler Mary, Grouws Douglas A. Mathematics teaching practices and their effects. Grouws D.A. Handbook of research on mathematics teaching and learning. 1992;115-126 Macmillan, New York.
22. Ladson-Billings Gloria Dreamkeepers: Successful teachers of African American students. 1994;Jossey Bass, San Francisco.
23. Lampert Magadeline Knowing, doing, and teaching multiplication. Cognition and Instruction. 3:1986;305-342.
24. Lampert Magadeline When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal. 27:1990;29-63.
25. Lave Jean Cognition in practice: Mind, mathematics, and culture in everyday life. 1988;Cambridge University Press, Cambridge.
26. Leinhardt Gaea Getting to know: Tracing student's mathematical knowledge from intuition to competence. Educational Psychologist. 23(2):1988;119-144.
27. Lesh Richard, Kelly Anthony E. Teachers' evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment. Journal for Research in Mathematics Education. 28:1997;398-430.
28. Lewis Matthew W., McArthur David, Stasz Cathy, Zmuidzinas M. Discovery-based tutoring in mathematics. Working notes, American Association for Artificial Intelligence Spring Symposium on Knowledge-Based Environments for Learning and Teaching. 1990;21-28 Stanford University, Palo Alto, CA.
29. Mack, Nancy K. (1987). Learning fractions with understanding. Unpublished doctoral dissertation, University of Wisconsin-Madison.
30. Mack Nancy K. Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education. 21:1990;16-32.
31. Mack Nancy K. Confounding whole number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education. 26:1995;422-441.
32. McCarthy Cameron The problems with origins: Race and the contrapuntal nature of the educational experience. Sleeter C.E., McLaren P.L. Multicultural education, critical pedagogy, and the politics of difference. 1995;245-268 SUNY Press, Albany, NY.
33. Michalski Ryzgard S., Carbonell Jamie G., Mitchell Thomas M. Machine learning: An artificial intelligence approach. 1983;Morgan Kaufmann, Palo Alto, CA.
34. Newell Allen, Simon Herbert A. Human problem solving. 1972;Prentice Hall, Englewood Cliffs, NJ.
35. Pirie Susan, Kieren Thomas Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics. 26:1994;165-190.
36. Romberg Thomas A., Carpenter Thomas P. Research on teaching and learning mathematics: Two disciplines of scientific inquiry. Wittrock M.C. Handbook of research on teaching. 3rd edn. 1986;297-314 Macmillan, New York.
37. Saxe Geoff B. Culture and cognitive development: Studies in mathematical understanding. 1991;Erlbaum Associates, Hillsdale, NJ.
38. Schoenfeld Alan H., Gamoran M., Kessel C., Leonard M., Or-Bach R., Arcavi A. Toward a comprehensive model of human tutoring in complex subject matter domains. The Journal of Mathematical Behavior. 11:1992;293-319.
39. Secada Walter G. Diversity, equity, and cognitivist research. Fennema E., Carpenter T.P., Lamon S.J. Integrating research on teaching and learning mathematics. 1991;17-54 State University of New York Press, Albany, NY.
40. Shulman Lee S. Paradigms and research programs in the study of teaching: A contemporary perspective. Wittrock M.C. Handbook of research on teaching. 3rd edn. 1986;3-36 Macmillan, New York.
41. Waterman D.A. A guide to expert systems. 1986;Addison-Wesley, Reading, MA.