從教學活動中幫助國小六年級學生發展數字常識之研究

A Study of Sixth Grade Students' Development of Number Sense through Well-Designed Number Sense Activities

10.6173/CJSE.2002.1003.02

楊德清(Der-Ching Yang)

數字大小 ； 估算 ； 參考點 ； 數字常識教學 ； Number Magnitude ； Benchmark ； Estimation ； Teaching Number Sense

科學教育學刊

10卷3期（2002 / 09 / 01）

233 - 259

繁體中文

Two 6th grade classes from two public schools in south Taiwan participated in this experimental study. The Posttest and Retention test results revealed that students' number sense performance significantly improved (p＜0.01) after instruction. The results of Retention tests also indicated that these students' learning was meaningful. Interviews with 12 students revealed that many students did not have any ideas or tended to use standard written algorithms. Few number sense strategies were found before instruction. However, after instruction few rule-based methods were found and students' responses reflected number sense strategies, such as number magnitude, benchmarks, and estimation were observed..

Two 6th grade classes from two public schools in south Taiwan participated in this experimental study. The Posttest and Retention test results revealed that students' number sense performance significantly improved (p＜0.01) after instruction. The results of Retention tests also indicated that these students' learning was meaningful. Interviews with 12 students revealed that many students did not have any ideas or tended to use standard written algorithms. Few number sense strategies were found before instruction. However, after instruction few rule-based methods were found and students' responses reflected number sense strategies, such as number magnitude, benchmarks, and estimation were observed..

1. Alitzer-Tuning, C.(1984).One point of view: crisis in arithmetic teaching: The future is here.Arithmetic Teacher,32,2.
2. Australian Education Council(1991).A national statement on mathematics for Australian schools.Melbourne:Curriculum Corporation.
3. Behr, M. J.,Wachsmuth, I.,Post, T. R.,Lesh, R.(1984).Order and equivalence of rational numbers: A clinical teaching experiment.Journal for Research in Mathematics Education,15,323-341.
4. Bezuk, N.,Cramer, K.,P. R. Trafton,A. B. Shult (Eds.)(1989).New directions for elementary school mathematics.Reston, VA:NCTM.
5. Brownell, W. A.,Reeve (Ed.)(1935).The teaching of arithmetic.Reston, VA:NCTM.
6. Burns, M.(1994).Arithmetic: The Last holdout.Phi Delta Kappen,1,471-476.
7. Cai, Jinfa(2001).Improving mathematics learning: Lessons from cross-national studies of Chinese and U.S. students.Phi Delta Kappan,2,400-404.
8. Capenter, T. P.,Corbbit, M. K.,Kepner, H. S.,Lindquist, M. M.,Reys, R. E.,S. Hill (Ed.)(1982).Education in the 80`s: Mathematics.Washington, DC:National Education Association.
9. Cobb, P.,Wood, T.,Yackel, E.,Nicholls, J.,Wheatly, G.,Trigatti, B.,Perlwitz, M.(1991).Assessment of a problem-centered second-grade mathematics project.Journal for Research in Mathematics Education,22(1),3-29.
10. Cockcroft, W. H.(1982).Math Counts.London:Her Majesty`s Stationery office.
11. Emanuelsson, G.,Johansson, B.(1996).Kommentarer till kursplan I matematik, Lpo 94. (Nn-statutory guidance to the ne Swedish curriculum of mathematics).
12. Fraivillig, J.(2001).Strategies for advancing children`s mathematical thinking.Teaching Children Mathematics,454-459.
13. Highlights from TIMSS-R
14. Greeno, J. G.(1991).Number sense as situated knowing in a conceptual domain.Journal for Research in Mathematics Education,22,170-218.
15. Hibert, J.(1984).Children`s mathematics learning: The struggle to link form and Understanding.Elementary School Journal,84,496-513.
16. Hiebert, J.,J. T. Sowder,B. P. Schappelle (Eds.)(1989).Establishing foundations for research on number sense and related topics: Report of a conference.San Diego:San Diego University, Center for Research in Mathematics and Science Education.
17. Howden, H.(1989).Teaching number sense.Arithmetic Teacher,36,6-11.
18. Japanese Ministry of Education(1989).Curriculum of mathematics for the elementary school.Tokyo:Printing Bureau.
19. Jarvis, C. H.,Blank, B. B.(1989).Great starts mathematics approach 1987-88.
20. Kamii, C.(1989).Young children continue to reinvent arithmetic, second grades: Implications of Piaget`s theory.New York:Teachers College Press.
21. Kamii, C.(1994).Young children continue to reinvent arithmetic, Third grade.New York:Teachers College Press.
22. Kerslake, D.(1986).Fractions: Children`s strategies and errors: A report of the strategies and errors in secondary mathematics project.Windsor, England:NFER-Nelson.
23. Markovits, Z.,Sowder J. T.(1994).Developing number sense: An Intervention study in grade 7.Journal for Research in Mathematics Education,25(1),4-29.
24. McIntosh, A.,Reys, B. J.,Reys, R. E.(1992).A proposed framework for examining Basic number sense.For the Learning of Mathematics,12(3),2-8.
25. McIntosh, A.,Reys, B. J.,Reys, R. E.(1997).Number sense grades 6-8.Palo Alto:Dale Seymour.
26. McIntosh, A.,Reys, B. J.,Reys, R. E.,Bana, J.,Farrel, B.(1997).Number sense in school mathematics: Student performance in four countries.Mathematics, Science, & Technology Education Centre, Edith Cowan University.
27. National Council of Teachers of Mathematics(1989).Curriculum and Evaluation Standards for School Mathematics.Reston, VA:NCTM.
28. National Council of Teachers of Mathematics(2000).The Principles and Standards for School Mathematics.Reston, VA:NCTM.
29. National Research Council(1989).Everybody Counts. A report to the nation on the future of mathematics education.Washington, DC:National Academy Press.
30. Owens, D. T.(Ed.),Super, D. B.(1993).Research ideas for the classroom in middle grades mathematics.Reston, VA:NCTM.
31. Plunkett, S.(1979).Decomposition and all that rot.Mathematics in Schools,8,2-5.
32. Resnick, L. B.,Sowder,Schappelle (Eds.)(1989).Establishing foundations for research on number sense and related topics: Report of a conference.San Diego, CA:San Diego State University, Center for Research in Mathematics and Science Education.
33. Reys, B. J.(1994).Promoting number sense in middle grades.Teaching Mathematics in the Middle School,1(2),114-120.
34. Reys, B. J.,Barger, R.,Dougherty, B.,Hope, J.,Markovits, Z.,Parnas, A.,Reehm, S.,Sturdevant, R.,Weber, M.,Bruckheimer, M.(1991).Developing number sense in the middle grades.Reston, VA:NCTM.
35. Reys, R. E.,Reys, B. J.,McIntosh, A.,Emanuelsson G.,Johansson, B.,Yang, D. C.(1999).Assessing Number Sense of Students in Australia, Sweden, Taiwan and the United States.School Science and Mathematics,99(2),61-70.
36. Reys, R. E.,Reys, B. J.,Nohda, N.,Ishidda, J.,Yoshikawa, S.,Shimizu, K.(1991).Computational estimation performance and strategies used by fifth-and eighth-grade Japanese students.Journal for Research in Mathematics Education,22(1),39-58.
37. Reys, R. E.,Yang, D. C.(1998).Relationship between Computational Performance and Number Sense among Sixth-and Eighth-Grade Students in Taiwan.Journal for Research in Mathematics Education,29,225-237.
38. Sowder, J. T.,Schappelle, B. P. (Eds.)(1989).Establishing foundations for research on number sense and related topics: Report of a conference.San Diego, CA:San Diego State University, Center for Research in Mathematics and Science Education.
39. Sowder, J.,D. A. Grouws (Ed.)(1992).Handbook of research on mathematics teaching and learning.New York:Macmillan.
40. Sowder, J.,G. Leinhardt, R.,R. Hattrup (Eds.)(1992).Analysis of Arithmetic for Mathematics Teaching.Hillsdale, NJ:Erlbaum.
41. Stevenson, H. W.,Chen, C.,Lee, S. Y.(1993).Mathematical achievement of Chinese, Japanese, & American children: Ten years later.Science,259,53-58.
42. Stevenson, H. W.,Lee, S. Y.,Stigler, J. W.(1986).Mathematical achievement of Chinese, Japanese, and American children.Science,231,693-699.
43. Stigler, J. W.,Lee, S. Y.,Stevenson, H. W.(1991).Mathematical knowledge of Japanese, Chinese, and American elementary school children.Reston, VA:NCTM.
44. Threadgill-Sowder, J.(1984).Computational estimation procedures of school children.Journal of Educational Research,77,332-336.
45. Treffers, A.(1991).Meeting innumeracy at primary school.Educational Studies in Mathematics,26(1),333-352.
46. Warrington, M. A.,Kamii, C.(1998).Multiplication with Fractions: A Piagetian, Constructivist Approach.Mathematics Teaching in the Middle School,3(5),339-343.
47. Wright, R. J.(1994).A study of the numerical development of 5-year-olds and 6-year-olds.Educational Studies in Mathematics,26(1),25-44.
48. Yang, D. C.(2002).Teaching and Learning number sense: one successful process-oriented activity with six grade students in Taiwan.School Science and Mathematics Journal,102(4),152-157.
49. Yang, D. C.(1995).Columbia,University of Missouri.
50. Yang, D. C.,Reys, R. E.(2001).One Fraction Problem: Many Solution Paths.Mathematics Teaching in the Middle School,7(3),164-166.
51. Yang, D. C.,Reys, R. E.(2001).Developing Number Sense.Mathematics Teaching,176,39-41.
52. 徐俊仁、楊德清(2000)。從數字常識的觀點探討九年一貫數學學習領域「數與計算」的能力指標。科學教育研究與發展季刊，21，56-67。
53. 楊德清(1997)。數學教育中目前大眾所關切之一個主題－數字常識。科學教育月刊，200，12-18。
54. 楊德清(2000)。教育部科技顧問室89年度補助研究計畫之部分教育部科技顧問室89年度補助研究計畫之部分,未出版
55. 楊德清(2000)。數字常識與筆算能力。教師之友，41(2)，30-35。
56. 楊德清(2000)。國小六年級學生回答數字常識問題所使用之方法。科學教育學刊，8(4)，379-394。

1. 劉曼麗、侯淑芬(2006)。整數數感融入國小四年級數學科教學之研究。科學教育學刊，14(2)，121-147。
2. 龍姿蓁、張葶葶(2017)。從磁振造影研究探討數學學習障礙之認知神經機制。當代教育研究季刊，25(4)，173-206。
3. 楊德清、李茂能、余明杰(2016)。國小四年級學童數常識三階段診斷測驗工具的發展與應用之研究。科學教育學刊，24(1)，89-114。
4. 楊德清、吳宛儒(2007)。數常識情境教學活動融入國小三年級數學科教學之研究。科學教育學刊，15(6)，647-669。
5. (2004)。從數學有意義的學習談建構式教學與講述式教學二元對立的迷思。教育研究，12，83-90。
6. (2006)。從解題中探究數常識的重要性。國立編譯館館刊，34(2)，83-94。
7. (2024)。基礎數感測驗編製之研究。教育心理學報，55(3)，577-605。