The development of fifth-grade children's problem-posing abilities

Educational Studies in Mathematics

Volumn 34, Issue 3, 1997, Pages 183-217

  English, Lyn D ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012061634     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1002963618035     Document Type: Article

References (66)

1. Baroody, A. J.: 1993, Problem Solving, Reasoning, and Communicating (K-8): Helping Children Think Mathematically, Macmillan Publishing Company, New York.
2. Bergeron, J. C. and Herscovics, N.: 1990, 'Psychological aspects of learning early arithmetic', in P. Nesher and J. Kilpatrick (eds.), Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education, Cambridge University Press, Cambridge, pp. 31-52.
3. Borasi, R.: 1993, 'The invisible hand operating in mathematics instruction: Students' conceptions and expectations'. In S. I. Brown and M. I. Walter, M. I. (eds.), Problem posing: Reflections and applications, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 83-91.
4. Brown, S. I. and Walter, M. I.: 1983, The Art of Problem Posing, Franklin Institute Press, Philadelphia.
5. Brown, S. I. and Walter, M. I. (eds.): 1993, Problem Posing: Reflections and Applications, Lawrence Erlbaum Associates, Hillsdale, New Jersey.
6. Carpenter, T. P. and Moser, J. M.: 1984, 'The acquisition of addition and subtraction concepts in grades one through three', Journal for Research in Mathematics Education, 15, 179-202.
7. Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E. and Weisbeck, L.: 1993, 'Models of Problem Solving: A Study of Kindergarten Children's Problem-solving Processes', Journal for Research in Mathematics Education, 24(5), 428-441.
8. Charles, R. I. and Lester, F. K.: 1982, Teaching Problem Solving: What, Why and How. Dale Seymour Publications, Palo Alto, CA.
9. Cobb, P., Yackel, E. and Wood, T.: 1992, 'A constructivist alternative to the representational view of mind in mathematics education', Journal for Research in Mathematics Education, 23(1), 2-33.
10. DeLange, J.: 1993, 'Between end and beginning,' Educational Studies in Mathematics, 25, 137-160.
11. Ellerton, N. F.: 1986, 'Children's made-up mathematics problems: A new perspective on talented mathematicians', Educational Studies in Mathematics, 17, 261-271.
12. English, L. D.: in press a, 'Promoting a Problem-posing Classroom', Teaching Children Mathematics.
13. English, L. D.: in press b, 'Children's problem posing within formal and informal contexts', Journal for Research in Mathematics Education.
14. English, L. D.: in press c, 'Children's reasoning processes in classifying and solving computational word problems', in L. D. English (ed.), Mathematical Reasoning: Analogies, Metaphors, and Images. Mahwah, New Jersey: Lawrence Erlbaum Associates.
15. English, L. D.: 1993, 'Evidence for deductive reasoning: Implicit versus explicit recognition of syllogistic structure', British Journal of Developmental Psychology, 11, 391-409.
16. English, L. D.: 1996, 'Children's problem posing and problem-solving preferences', in J. Mulligan and M. Mitchelmore (eds.), Research in Early Number Learning. Australian Association of Mathematics Teachers.
17. English, L. D.: 1997, 'Development of seventh-grade students' problem posing'. Paper submitted for the annual conference of the International Group for the Psychology of Mathematics Education, Finland, July.
18. English, L. D., Cudmore, and Tilley, D.: under review, 'Problem posing and critiquing: How it can happen in your classroom: Manuscript submitted for publication.
19. English, L. D. and Halford, G. S.: 1995, Mathematics Education: Models and Processes, Lawrence Erlbaum Associates, Hillsdale, New Jersey.
20. Fischbein, E., Deri, M., Nello, M. S. and Marino, M. S.: 1985, 'The role of implicit models in solving verbal problems in multiplication and division'. Journal for Research in Mathematics Education, 16, (1) 3-17.
21. Freudenthal, H.: 1991, Revisiting Mathematics Education, Kluwer Academic Publishers, Dordrecht, The Netherlands.
22. Fuson, K. C.: 1992, 'Research on whole number addition and subtraction', inD. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan Publishing Company, New York; National Council of Teachers of Mathematics, Reston, Virginia, pp. 243-275.
23. Gentner, D.: 1989, 'The mechanisms of analogical learning', in S. Vosniadou and A. Ortony (eds.), Similarity and Analogical Reasoning, Cambridge University Press, Cambridge, pp. 199-241.
24. Greer, B.: 1992, 'Multiplication and division as models of situations', in D. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, New York; National Council of Teachers of Mathematics, Reston, Virginia, pp. 276-295.
25. Haylock, D. W.: 1987, A framework for assessing mathematical creativity in school children', Educational Studies in Mathematics, 18, 59-74.
26. Holyoak, K. J. and Koh, K.: 1987, 'Surface and structural similarity in analogical transfer, Memory & Cognition, 15, 332-340.
27. Jones, G. A., Thornton, C. A. and Putt, I. A.: 1994, 'A model for nurturing and assessing multidigit number sense among first grade children', Educational Studies in Mathematics, 27, 117-143.
28. Kilpatrick, J.: 1987, 'Problem formulating: Where do good problems come from?' in A. H. Schoenfeld, (ed.), Cognitive Science and Mathematics Education, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 123-147.
29. Kouba, V. L.: 1989, 'Children's solution strategies for equivalent set multiplication and division word problems', Journal for Research in Mathematics Education, 20(2), 147-158.
30. Lester, F.: 1989, 'Reflections about mathematical problem-solving research', in R. I. Charles and E. A. Silver (eds.), The Teaching and Assessing of Mathematical Problem Solving, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 115-124.
31. Leung, S. S.: 1993, The Relation of Mathematical Knowledge and Creative Thinking to the Mathematical Problem Posing of Prospective Elementary School Teachers on Tasks Differing in Numerical Information Content. Unpublished doctoral dissertation, University of Pittsburgh.
32. Leung, S. S.: in press, 'Problem posing as assessments: Reflections and re-constructions', The Mathematics Educator.
33. McLeod, D.: 1992, 'Research on affect in mathematics education: A reconceptualization', in D. A. Grouws, (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan Publishing Company, New York, pp. 575-596.
34. Moses, B., Bjork, E. and Goldenberg, E. P.: 1990, 'Beyond problem solving: Problem posing', in T. J. Cooney and C. R. Hirsch (eds.), Teaching and Learning Mathematics in the 1990s, National Council of Teachers of Mathematics, Reston, Virginia, pp.82-91.
35. Nathan, M. J., Kintsch, W. and Young, E.: 1992, A theory of algebra word-problem comprehension and its implications for the design of learning environments', Cognition and Instruction 9(4), 329-391.
36. National Council of Teachers of Mathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, National Council of Teachers of Mathematics, Reston, Virginia.
37. National Council of Teachers of Mathematics: 1991, Professional Standards for Teaching Mathematics, National Council of Teachers of Mathematics, Reston, Virginia.
38. Nesher, P.: 1988, 'Multiplicative school word problems: Theoretical approaches and empirical findings', in J. Hiebert and M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Lawrence Erlbaum Associates, Hillsdale, New Jersey; National Council of Teachers of Mathematics, Reston, Virginia, pp. 19-40.
39. Nesher, P.: 1992, 'Solving multiplication word problems', in G. Leinhardt, R. T. Putnam, and R. Hattrup (eds.), Analysis of Arithmetic for Mathematics Teaching, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 189-220.
40. Novick, L. R.: 1988, Analogical transfer, problem similarity, and expertise', Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 510-520.
41. Novick, L. R.: 1992, 'The role of expertise in solving arithmetic and algebra word problems by analogy', in J. I. D. Campbell (ed.), The Nature and Origins of Mathematical Skills, Elsevier Science Publishers B.V., Amsterdam, pp. 155-188.
42. Payne, J. N. and Huinker: 1993, 'Early number and numeration', in R. J. Jensen (ed.), Research Ideas for the Classroom: Early Childhood Mathematics, National Council of Teachers of Mathematics Research Interpretation Project, Macmillan Publishing Company, New York, pp.43-71.
43. Resnick, L. B.: 1987, Education and Learning to Think, National Academy Press, Washington, DC.
44. Riley, M. S., Greeno, J. G. and Heller, J. L: 1983, 'Development of children's problem-solving ability in arithmetic', in H. Ginsburg (ed.), The Development of Mathematical Thinking, Academic Press, New York, pp. 153-196.
45. Santos, M.: 1995 (October), Students' Recognition of Structural Features in Mathematical Problem Solving Instruction. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, Ohio.
46. Silver, E. A.: 1981, 'Recall of mathematical problem formulation: Solving related problems', Journal for Research in Mathematics Education, 12(1), 54-64.
47. Silver, E. A.: 1990, 'Contributions of research to practice: Applying findings, methods, and perspectives', in T. J. Cooney and C. R. Hirsch (eds.), Teaching and Learning Mathematics in the 1990s, National Council of Teachers of Mathematics, Reston, Virginia, pp 1-11.
48. Silver, E. A.: 1994, 'On mathematical problem posing', For the Learning of Mathematics, 14(1), 19-28.
49. Silver, E. A. and Burkett, M. L.: 1993, The Posing of Division Problems by Preservice Elementary School Teachers. Unpublished manuscript, Learning Research and Development Center, University of Pittsburgh.
50. Silver, E. A. and Cai, J.: 1993, Mathematical Problem Posing and Problem Solving by Middle School Students, Paper presented at the annual meeting of the American Educational Research Association, Atlanta, GA.
51. Silver, E. A. and Mamona, J.: 1989, 'Problem posing by middle school mathematics teachers', in C. A. Maher, G. A. Goldin, and R. B. Davis (eds.), Proceedings of the Eleventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, New Brunswick, New Jersey, pp. 263-269.
52. Simon, M. A.: 1993, 'Prospective elementary teachers' knowledge of division', Journal for Research in Mathematics Education, 24: 233-254.
53. Smith, M. S. and Silver, E. A.: 1995, 'Meeting the challenges of diversity and relevance', Mathematics Teaching in the Middle School, 1(6), 442-448.
54. Sowder, J. T.: 1988, 'Mental computation and number comparison: Their roles in the development of number sense and computational estimation', in J. Hiebert, and M. Behr (eds.), Number Concepts and Operations in the Middle Grades (vol.2), Lawrence Erlbaum Associates, Hillsdale, New Jersey; National Council of Teachers of Mathematics, Reston, Virginia, pp. 182-197.
55. Sowder, J. T.: 1992, 'Estimation and number sense', in D. A. Grouws, (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan Publishing Co., New York, pp. 371-389.
56. Stavy, R. and Tirosh, D.: 1993, 'When analogy is perceived as such', Journal of Research in Science Teaching, 30(10), 1229-1239.
57. Stern, E.: 1993, 'What makes certain arithmetic word problems involving the comparison of sets so difficult for children?' Journal of Educational Psychology, 85, (1), 7-23.
58. Stern, E.: 1995, August, Longitudinal Consequences of Early Understanding of Quantitative Comparison, Paper presented at the annual meeting of the European Association for Research on Learning and Instruction.
59. Stigler, J. W., Fuson, K. C., Ham, M. and Kim, M. S.: 1986, An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks', Cognition and Instruction, 3, 153-171.
60. Streefland, L.: 1993, 'The design of a mathematics course: A theoretical reflection', Educational Studies in Mathematics, 25, 109-135.
61. Treffers, A.: 1993, 'Wiskobas and Freudenthal: Realistic mathematics education', Educational Studies in Mathematics, 25, 89-108.
62. Van den Heuvel-Panhuizen, M., Middleton, J. A. & Streefland, L.: 1995, 'Student-generated problems: Easy and difficult problems on percentage', For the Learning of Mathematics, 15(3), 21-27.
63. Vergnaud, G.: 1988, 'Multiplicative structures', in J. Hiebert and M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Lawrence Erlbaum Associates, Hillsdale, New Jersey; National Council of Teachers of Mathematics, Reston, Virginia, pp. 141-161.
64. Vosniadou, S.: 1989, 'Analogical reasoning as a mechanism in knowledge acquisition: A developmental perspective', in S. Vosniadou and A. Ortony (eds.), Similarity and Analogical Reasoning, Cambridge University Press, Cambridge, pp. 413-437.
65. Vygotsky, L.: 1978, Mind in Society: The Development of Higher Psychological Processes, Harvard University Press, Cambridge, MA.
66. Wittmann, E.: 1995, 'Mathematics education as a design science,' Educational Studies in Mathematics, 29, 355-374.