Applying psychological theory to helping students overcome learned difficulties in mathematics: An alternative approach to intervention

School Psychology International

Volumn 24, Issue 1, 2003, Pages 95-114

  Dole, Shelley ^a  

^a UNIVERSITY OF TASMANIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037332281     PISSN: 01430343     EISSN: None     Source Type: Journal    
DOI: 10.1177/0143034303024001582     Document Type: Article

References (60)

1. Adelman, H. S. and Taylor, L. (1986) An Introduction to Lerining Disabilities. Glenview, IL: Scott Foresman.
2. Anderson, J. R. (1985) Cognitive Psychology and its Implications. New York: W. H. Freeman and Company.
3. Ashlock, R. B. (1994) Error Patterns in Computation - A Semi-Programmed Approach (6th edn) New York: Macmillan.
4. Ashlock, R. B., Johnson, M. L., Wilson, J. W. and Jones, W. L. (1983) Guiding each Child's Learning of Mathematics: A Diagnostic Approach to Instruction. Columbus, OH: Charles E. Merrill.
5. Ausubel, D. (1968) Educational Psychology: A Cognitive View. New York: Holt, Rinehart and Winston.
6. Baddeley, A. (1990) Human Memory: Theory and Practice. Hillsdale, NJ: Lawrence Erlbaum.
7. Baxter, E. P. and Dole, S. (1990) 'Working with the Brain, not Against It: Correction of Systematic Errors in Subtraction', British Journal of Special Education 17(1): 19-22.
8. Bell, A. (1986-87) 'Diagnostic Teaching 1-3', Mathematics Teaching, Nos. 115, 116, 118.
9. Booker, G., Irons, C. and Jones, G. (1980) Fostering Arithmetic in the Primary School. Canberra: Curriculum Development Centre.
10. Borassi, R. (1994) 'Capitalising on Errors as "Springboards for Inquiry": A Teaching Experiment', Journal for Research in Mathematics Education 25(2): 166-208.
11. Bourke, S. F. (1980) Numeracy in School: An Integrated Approach to Community Expectation, Student Assessment, and Error Analysis. Unpublished master's thesis, Monash University, Melbourne.
12. Brown, J. S. and Van Lehn, K. (1982) 'Towards a Generative Theory of "Bugs'", in T. P. Carpenter, J. M. Moser and T. A. Romberg (eds), Addition and Subtraction - A Cognitive Perspective, pp. 117-35. Hillsdale, NJ: Lawrence Erlbaum Associates.
13. Brumfield, R. and Moore, B. (1985) 'Problems with the Basic Facts may not be the Problem', Arithmetic Teacher 33(3): 17-18.
14. Cole, P. and Chan, L. (1990) Methods and Strategies for Special Education. New York: Prentice Hall.
15. Confrey, J. (1990a) 'What Constructivism Implies for Teaching', in R. B. Davis, C. A. Maher and N. Noddings (eds) Constructivist Views on Teaching and Learning of Mathematics, pp. 107-22. Reston, VA: NCTM.
16. Confrey, J. (1990b) 'Inconsistencies and Cognitive Conflict: A Constructivist's View', Focus on Learning Problems in Mathematics 12(3 & 4): 99-109.
17. Connell, M. and Peck, D. (1993) 'Report of a Conceptual Change Intervention in Elementary Mathematics', Journal of Mathematical Behaviour 12: 329-50.
18. Cox, L. S. (1975) 'Diagnosing and Remediating Systematic Errors in Addition and Subtraction Computations', Arithmetic Teacher 22(4): 202-20.
19. Dole, S. (1999) Percent Knowledge: Effective Teaching for Learning, Relearning and Unlearning. Unpublished doctoral dissertation, Queensland University of Technology, Australia.
20. Dole, S. (1995) 'Gaining Access to Mathematical Literacy: Application of Old Way/New Way to Mathematics Instruction for Adult Learners', Proceedings of the 3rd Annual International Conference on Post-Compulsory Education and Training, Brisbane.
21. Dole, S. (1993) 'Error Patterns and Subtraction Knowledge Development - A Comparison of Methods', in J. Novak (ed.) Proceedings of the Third International Seminar on Misconceptions and Educational Strategies in Science and Mathematics. Ithaca, NY: Correll University. (Electronic publishing of seminar proceedings)
22. Cole, S. and Cooper, T. (1995) 'Errors as Springboards for Remediation of Year 7 Students' Subtraction Knowledge', in B. Atweh and S. Flavell (eds) Eighteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), pp. 235-40, Northern Territory University.
23. Dyer, F. (1973) 'The Stroop Phenomenon and its Use in the Study of Percentual, Congitive and Response Processes', Memory and Cognition 1(2): 106-20.
24. Erlwanger, S. H. (1975) 'Case Studies of Children's Conceptions of Mathematics', Journal of Mathematical Behaviour 1(3): 157-283.
25. Fernald, G. M. (1971) Remedial Techniques and Basic School Subjects (Edited by Lorna Idol) Austin, TX: ProEd.
26. Fischbein, E. (1987) Intuition in Science and Mathematics: An Educational Approach. AH Dordrecht, Holland: D. Reidel.
27. Fuson, K. and Briars, D. J. (1990) 'Using a Base-Ten Blocks Learning/Teaching Approach for First and Second Grade Place Value and Multidigit Addition and Subtraction', Journal for Research in Mathematics Education 21(3): 180-206.
28. Gable, R. A., Enright, B. E. and Hendrickson, J. M. (1991) 'A Practical Model for Curriculum-Based Assessment and Instruction in Arithmetic', Teaching Exceptional Children 24(1): 6-9.
29. Gagne, R. (1983) 'Some Issues in the Psychology of Mathematics Instruction', Journal for Research in Mathematics Education 14(1): 7-18.
30. Ginsburg, H. (1977) Children's Arithmetic: The Learning Process. New York: Van Nostrond.
31. Graeber, A. and Baker, K. M. (1991) 'Curriculum Materials and Misconceptions Concerning Multiplication and Division', Focus on Learning Problems in Mathematics 13(3): 25-38.
32. HMSO (1975) A Language for Life. Report of the Committee of Enquiry Appointed by the Secretary of State for Education and Science under the Chairmanship of Sir Alan Bullock.
33. Houston, J. P. (1991) Fundamentals of Learning and Memory, 4th edn. Orlando, FL: Harcourt Brace Jovanovich.
34. James, W. (1890) Principles of Psychology. New York: Holt, Rinehart and Winston.
35. Kephart, N. C. (1960) The Slow Learner in the Classroom. Columbus, OH: Charles E. Merrill.
36. Lampert, M. (1986) 'Knowing, Doing and Teaching Multiplication', Cognition and Instruction 3(4): 305-42.
37. Leinhardt, G. (1988) 'Getting to Know: Tracing Student's Mathematical Knowledge from Intuition to Competence', Educational Psychologist 23(2):119-44.
38. Lyndon, H. (1995) 'Conceptual Mediation - A New Approach to an Old Problem', Voice - A Journal for Educators 3(2):00-00.
39. Lyndon, H. (1989) 'I Did it My Way! An Introduction to the Old Way/New Way Methodology', Australasian Journal of Special Education 3(1): 32-37.
40. Lyndon, E. H. and Dawson, C. J. (1995) The Conceptual Mediation Program: A Practical Outcome from a Novel Perspective on Conceptual Change, paper presented at the Australian Association of Science Education Annual Conference, Adelaide, July 1995.
41. Mansfield, H. and Happs, J. (1992) 'Using Grade-Eight Students Existing Knowledge to Teach about Parallel Lines', School Science and Mathematics 92(8): 450-54.
42. Melton, A. and Von Lockum, W. (1941) 'Retroactive and Proactive Inhibition in Retention: Evidence for a Two-Factor Theory of Retroactive Inhibition', American Journal of Psychology 54: 157-73.
43. Posner, G., Strike, K., Hewson, P. and Gertzog, W. (1982) 'Accommodation of a Scientific Computation: Toward a Theory of Conceptual Change', Science Education 66: 211-27.
44. Postman, L. and Underwood, B. (1973) 'Critical Issues in Interference Issues', Memory and Cognition 1: 19-40.
45. Putnam, R. T., Lampert, M. and Peterson, P. C. (1990) 'Alternative Perspectives on Knowing Mathematics in Elementary Schools', Review of Research in Education 16: 57-149.
46. Rauff, J. V. (1994) 'Constructivism, Factoring and Beliefs', School Science and Mathematics 94(8): 421-26.
47. Read, G. (1987) 'Following the Progress of Children who have Received "Remedial" Tuition', Support for Learning 2(1): 52-9.
48. Resnick, L. B. (1992) 'From Protoquantities to Operators: Building Mathematical Competence on a Foundation of Everyday Knowledge', in G. Leinhardt, R. Putnam and R. A. Hattrup (eds) Analysis of Arithmetic for Mathematics Teaching, pp. 373-429. Hillsdale, NJ: Lawrence Erlbaum.
49. Resnick, L. B. (1982) 'Syntax and Semantics in Learning to Subtract', in T. P. Carpenter, J. M. Moser and T. A. Romberg (eds) Addition and Subtraction - A Cognitive Perspective, pp. 136-55. Hillsdale, NJ: Lawrence Erlbaum Associates.
50. Resnick, L., Nesher, P., Leonard, F., Magone, M., Omanson, S. and Peled, R. (1989) 'Conceptual Bases of Arithmetic Errors: The Case of Decimal Fractions', Journal for Research in Mathematics Education 20(1): 8-27.
51. Rowell, J. A., Dawson, C. J. and Lyndon, E. H. (1990) 'Changing Misconceptions: A Challenge to Science Education', International Journal of Science Education 12(2): 167-75.
52. Stroop, J. R. (1935) 'Studies of Interference in Serial Verbal Reactives', Journal of Experimental Psychology 18: 643-62.
53. Swedosh, P. (1990) 'Reducing the Incidence of Mathematical Misconceptions in "Middle Band" Students', in J. Truran and K. Truran (eds) Making the Difference: Proceedings of the Twenty-Second Annual Conference of the Mathematics Education Research Group of Australasia. Adelaide: MERGA.
54. Swedosh, P. and Clark, J. (1998) 'Mathematical Misconceptions - We Have an Effective Method for Reducing their Incidence but will the Improvement Persist?', in C. Kanes, M. Goos. E. Warren (eds) Teaching Mathematics in New Times: Proceedings of the Twenty-First Annual Conference of the Mathematics Education Research Group of Australasia (2), pp. 588-95. Broadbeach: MERGA.
55. Tirosh, D. (1990) 'Inconsistencies in Students' Mathematical Constructs', Focus on Learning Problems in Mathematics 12 (3 & 4): 111-29.
56. Underwood, B. J. and Postman, L. (1969) 'Extra-Experimental Sources of Interference in Forgetting', Psychological Review 67(2): 73-95.
57. Underwood, B. J. (1966) Experimental Psychology, 2nd edn. New York: Appleton-Century Crofts.
58. Underwood, B. J. (1957) 'Interference and Forgetting', Psychological Review 64(1): 49-60.
59. Underwood, B. J. (1948) 'Retroactive and Proactive Inhibition after Five and Forty-Eight Hours', Journal of Experimental Psychology 38: 29-38.
60. Vinner, S. (1990) 'Inconsistencies: Their Causes and Function in Learning Mathematics', Focus on Learning Problems in Mathematics 2(3 & 4): 85-99.