國小高年級學童數字常識評定量表編製之研究

The Design of "The Fifth and Sixth Grade Number Sense Rating Scale"

10.6173/CJSE.2001.0904.02

許清陽(Ching-Yang Hsu)；楊德清(Der-Ching Yang)；李茂能(Mao-Neng Li)

有意義的學習 ； 紙筆計算 ； 數字常識 ； 數字常識評定量表 ； Meaningful Learning ； Written Computation ； Number Sense ； Number Sense Rating Scale

科學教育學刊

9卷4期（2001 / 12 / 01）

351 - 374

繁體中文

在數學有意義的學習領域裏，數字常識已受到先進國家的重視，目前國內並無一套標準化的評量工具，欠缺評量工具將無法了解學生數字常識的發展情形；本研究之研究目的在編製一份適合國內國小學童數字常識的評定量表。本研究是以電腦網際網路線上測驗為研究工具，透過線上測驗進行資料蒐集，樣本為中南部地區國小高年級學童共800人。「國小高年級學童數字常識評定量表」共分為五個組成成份：1.瞭解數字的意義和關係的能力；2.辨認數字大小的能力；3.瞭解運算對數字的意義和影響的能力；4.發展計算策略與判斷答案合理性的能力；5.以多重方式表徵數字的能力。在信度考驗方面，建立了各分量表及總量表的內部一致性信度和重測信度；在效度考驗方面，本研究建立了內容效度、專家效度及建構效度。研究發現，「國小高年級學童數字常識評定量表」有不錯之信、效度。

The purpose of this study was to design a ”Number Sense Rating Scale” that can be used appropriately to evaluate students' number sense ability. This study utilized the internet as the instrument, through an on-line test to collect data. The sample of this study was from the middle and south parts of Taiwan, including 800 fifth and sixth grade students. The fifth and sixth grade ”Number Sense Rating Scale” includes 5 components: 1. Understanding the number meanings and relationships; 2. Recognizing the magnitude of numbers; 3. Understanding the relative effect of operations on numbers; 4. Developing computational strategies and being able to judge their reasonableness; 5. Ability to represent numbers in multiple ways. The reliability of the test was based on a coefficient of internal consistency and test-retest reliability. Content validity of the test was determined through the use of specialists and construct validity was also established. The result of this study revealed that the fifth and sixth grade ”Number Sense Rating Scale” has very good reliability and validity.

1. Australian Education Council(1991).,Melbourne:Curriculum Corporation.
2. Behr, M. J.(1989).Reflections on the conference.Establishing foundations for research on numbersense and related topics:Report of a conference,San Diego:
3. Cockcroft, W. H.(1982).Math Counts.London:Her Majesty.
4. Emanuelsson, G.,Johansson, B.(1996).,未出版
5. Enzmann. D.(1997).RanEigen: A program todetermine the parallel analysis criterion for thenumber of principal components.AppliedPsycholgical Measurement,21(3),232.
6. Grouws, D. A.(Ed.)(1992).Handbook ofresearch on mathematics teaching and learning.New York:Macmillan.
7. Hiebert, J.(1989).The struggle to link writtensymbols with understandings: An update.Arithmetic Teacher,36(7),38-44.
8. Japanese Ministry of Education(1989).Curriculum of Mathematics for the ElementarySchool.Tokyo:Printing Bureau.
9. Lautenschlager, G. J.(1989).A comparison of alternatives to conducting Monte Carlo analysesfor determining parallel analysis criteria.MultivariateBehaviora
10. Leihardt, G.(Ed.),Putnam, R.(Ed.),Hattrup, R.(Ed.)(1992).Analysis of Arithmetic forMathematics Teaching.Hillsdale, NJ:Erlbaum.
11. McIntosh, A.,Reys, B.J.,Reys, R. E.(1992).A proposed framework for examining basicnumber sense.For the Learning of Mathematics,12,2-8.
12. McIntosh, A.,Reys, B.J.,Reys, R. E.,Farrel, B.(1997).Number Sense in SchoolMathematics: Student Performance in FourCountries.MASTEC: Mathematics, Science ＆Technology Education Centre.
13. Nation Research Council(1989).EverybodyCounts.Washington, D. C.:National AcademyPress.
14. National Council of Teachers of Mathematics(1989).Curriculum and Evaluaion Standards forSchool Mathematics.Reston, VA:NCTM.
15. National Council of Teachers of Mathematics(2000).Principles and Standards for SchoolMathematics.Reston, VA:NCTM.
16. Reys, R. E.,Yang, D. C.(1998).Relationshipbetween Computational Performance andNumber Sense among Sixth- and Eighth-GradeStudents in Taiwan.Journal for Research inMathematics Education,29,225-237.
17. Sowder, J. T.(Ed.),Schappelle, B. P.(Ed.)(1989).Sowder, J. T., & Schappelle, B. P. (Eds.) (1989). Establishing foundations for research on numbersense and related topics: Report of a conference. San Diego, CA: San Diego State University, Center for Research in Mathematics and ScienceEducation..
18. Sowder, L.(1988).Children’s solution of storyproblems.Journal of Mathematical Behavior,7,227-238.
19. Thompson, C. S.,Rathmell, E. C.(1989).Byway of introduction.Arithmetic Teacher,36(6),2-3.
20. Yang, D. C.(1995).Columbia,University of Columbia.
21. 支毅君(1997)。我國國小學三年級數感教學研究。台東師院學報，8，83-116。
22. 支毅君(1996)。我國國小學生估算概念之研究。台東師院學報，7，1-51。
23. 李茂能(2001)。李茂能（2001）：四分相關係數計算程式。未出版軟體。
24. 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。
25. 楊德清(2000)。數字常識與筆算能力。教師之友，41(2)，12-18。
26. 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。