From convergence to divergence: The development of mathematical problem solving in research, curriculum, and classroom practice in Singapore

ZDM - International Journal on Mathematics Education

Volumn 39, Issue 5-6, 2007, Pages 491-501

  Fan, Lianghuo ^a   Zhu, Yan ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77149177486     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-007-0044-1     Document Type: Article

References (48)

1. Chan, C. M. (2003). English language proficiency and the effects of rewording semantic structures on P5 pupils' mathematical word problem solving. Unpublished master's thesis, National Institute of Education, Singapore.
2. Chang, S. H. (2004). Sense-making in solving arithmetic word problems among Singapore primary school students. Unpublished master's thesis, National Institute of Education, Singapore.
3. Charles, R., & Lester, F. K., Jr. (1984). Teaching problem solving. London: Edward Arnold.
4. Chong, T. H., Khoo, P. S., Foong, P. Y., Kaur, B., & Lim-Teo, S. K. (1991). A status-of-the-art review on mathematics education in Singapore. Singapore: Southeast Asian Review and Advisory Group (SEARRAG).
5. Chow, Y. P. (2004). Impact of open-ended problem solving as an alternative assessment on Secondary One mathematics students. Unpublished master's thesis, National Institute of Education, Singapore.
6. Cockcroft, W. H. (1982). Mathematic counts. London: HMSO.
7. Education Queensland (2002). Productive pedagogies classroom reflection manual. Queensland, Aystralia: The State of Queensland (Department of Education).
8. Fan, L. (2007). Editorial: Some matters about The Mathematics Educator. The Mathematics Educator, 10(1), 1-2.
9. Fan, L., & Quek, K. S. (2005). Integrating new assessment strategies into mathematics classrooms: What have we learned from a CRPP mathematics assessment project? Proceedings of the international conference on education: Redesigning pedagogy: Research, policy, practice. Singapore: Centre for Research in Pedagogy and Practice, National Institute of Education.
10. Fan, L., & Zhu, Y. (2000). Problem solving in Singaporean secondary mathematics textbooks. The Mathematics Educator, 5(1/2), 117-141.
11. Fan, L., & Zhu Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics. The Netherlands (in press).
12. Foong, P. Y. (1990). A metacognitive-heuristic approach to mathematical problem solving. Unpublished doctoral dissertation, Monash University, Melbourne, Australia.
13. Foong, P. Y. (2007). Teacher as researcher-a review on mathematics education research of Singapore teachers. The Mathematics Educator, 10(1), 3-20.
14. Garelick, B. (2006). Miracle math: A successful program from Singapore tests the limits of school reform in the suburbs. Education Next, 4. Retrieved on 25 March, 2007 from http://www.hoover.org/publications/ednext/3853357.html.
15. Goh, C. T. (1997). Shaping our future: Thinking Schools, Learning Nation. Opening Speech at the 7th International Conference on Thinking, Singapore. Retrieved on 15 April, 2007 from http://www.moe.gov.sg/speeches/1997/020697.htm.
16. Ho, G. L. (1997). A Cooperative Mathematical Problem Solving (CMPS) programme to enhance mathematical problem solving performance among secondary three female students. Unpublished master's thesis, National Institute of Education, Singapore.
17. Kantowski, M. G. (1981). Problem solving. In: E. Fennema (Ed.), Mathematics education research: Implications for the 80's (pp. 111-126). Reston, VA: National Council of Teachers of Mathematics.
18. Kho, T. H. (1987). Mathematical models for solving arithmetic problems. Proceedings of the Fourth Southeast Asian Conference on Mathematics Education (ICMI-SEAMS) (pp. 345-351). Singapore: Institute of Education.
19. Kho, T. H. (1989). Teaching thinking in mathematics. In: M. H. Kuok & N. P. Das (Eds.), Trends in science education (pp. 54-59). Singapore: Singapore National Academy of Science.
20. LeBlanc, J. F. (1982). Teaching textbook story problems. Arithmetic Teacher, 29(6), 52-54.
21. Lee, P. Y., & Fan, L. (2004). The development of Singapore mathematics curriculum-understanding the changes in syllabus, textbooks and approaches. In: P. Y. Lee, D. Zhang, & N. Song (Eds.), Proceedings of the ICM 2002 Satellite Conference on the Reform of Mathematics Curriculum and its Education in the 21st Century (pp. 31-36). Chongqing, China: Chongqing Publishing House.
22. Lee, P. Y., & Fan, L (Eds.), (2007a). New express mathematics 1. Singapore: Multimedia Communications.
23. Lee, P. Y., & Fan, L (Eds.), (2007b). New express mathematics 3. Singapore: Multimedia Communications.
24. Lester, F. K. Jr. (1980). Research on problem solving. In: R. J. Shumway (Ed.), Research in mathematics education (pp. 286-323). Reston, VA: National Council of Teachers of Mathematics.
25. Lester, F. K. Jr. (1982). Issues in teaching mathematics problem solving in the elementary grades. School Science and Mathematics, 82(2), 93-98.
26. Lester, F., & Kroll, D. (1990). Assessing student growth in mathematical problem solving. In: G. Kulm (Ed.), Assessing higher order thinking in mathematics (pp. 53-70). Washington, DC: American Association for the Advancement of Science.
27. Liu, Y. M. (2003). Primary school students' academic mathematics achievement and problem solving abilities. Unpublished master's thesis, National Institute of Education, Singapore.
28. Loo, C. F. (1996). Gender differences in mathematical problem solving among secondary four students. Unpublished master's thesis, National Institute of Education, Singapore.
29. Ministry of Education. (1971). Revised syllabus for Primary 1 and 2: Mathematics. Singapore: Ministry of Education.
30. Ministry of Education. (1980). Mathematics syllabus for the new education system. Singapore: Ministry of Education.
31. Ministry of Education. (1990). Mathematics syllabus (Lower Secondary). Singapore: Curriculum Planning Division.
32. Ministry of Education. (2000). Mathematics syllabus (Lower Secondary). Singapore: Curriculum Planning Division.
33. Ministry of Education. (2007a). Primary mathematics syllabus. Singapore: Curriculum Planning and Development Division.
34. Ministry of Education. (2007b). Secondary mathematics syllabus. Singapore: Curriculum Planning and Development Division.
35. National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics in the 1980s. Reston, VA: National Council of Teachers of Mathematics.
36. Ng, L. E. (2002). Representation of problem solving in Singaporean primary mathematics textbooks with respect to types, Polya's model and heuristics. Unpublished master's thesis, National Institute of Education, Singapore.
37. Pólya, G. (1980). On solving mathematical problems in high school. In: S. Krulik & R. E. Reys (Eds.), Problem solving in school mathematics, 1980 Yearbook (pp. 1-2). Reston, VA: National Council of Teachers of Mathematics.
38. Seto, C. (2002). Oral presentation as alternative assessment in primary mathematics in Singapore classroom. In: D. Edge & B. H. Yeap (Eds.), Mathematics education for a knowledge-based era (Proceedings of EARCOME-2) (Vol. 2) (pp. 33-39). Singapore: Association of Mathematics Educators.
39. Soeh, B. H. (2002). An open-ended approach to enhance critical thinking skill in mathematics among secondary five normal (academic) pupils. Unpublished master's thesis, National Institute of Education, Singapore.
40. Stiff, L. V. (1988). Problem solving by example. School Science and Mathematics, 88(8), 666-675.
41. Wong, P. S. K. (1989). The effects of academic settings on students' metacognition in mathematical problem solving. Paper presented at the Australian Association for Research in Education Annual Conference, Australia.
42. Wong, S. O. (2002). Effect of heuristics instruction on pupils' achievement in solving non-routine problems. Unpublished master's thesis, National Institute of Education, Singapore.
43. Yazilah, B. A., & Fan, L. (2002). Exploring how to implement journal writing effectively in primary mathematics in Singapore. In: D. Edge, & B. H. Yap (Eds.), Mathematics education for a knowledge-based era (Proceedings of EARCOME-2) (Vol. 2) (pp. 56-62). Singapore: Association of Mathematics Educators.
44. Yeap, B. H. (2004). Relationship between children's mathematical word problem posing and grade level, problem-solving ability and task type. Unpublished doctoral dissertation, National Institute of Education, Singapore.
45. Yeo, J. K. K. (2004). An exploratory study of secondary two students' mathematics anxiety and mathematical problem solving. Unpublished doctoral dissertation, National Institute of Education, Singapore.
46. Yeo, S. M., & Zhu, Y. (2005). Higher-order thinking in Singapore mathematics classrooms. Proceedings of the international conference on education: Redesigning pedagogy: Research, policy, practice. Singapore: Centre for Research in Pedagogy and Practice, National Institute of Education.
47. Ying, Y. J. (2005). Lower secondary school students' competency in solving algebra word problems. Unpublished master's thesis, National Institute of Education, Singapore.
48. Zhu, Y. (2003). Problem solving in China, Singapore and US mathematics textbooks: A comparative study. Unpublished doctoral dissertation, National Institute of Education, Singapore.