臺灣博碩士論文加值系統

本研究旨在探討國小現職教師的數常識表現，及其對數常識的觀點。研究者參考文獻設計數常識問題及數常識觀點訪談問題作為研究工具，並以此工具對六位國小現職教師進行半結構式訪談。研究結果發現：
在數常識的表現上，雖受訪教師雖呈現了較弱的數字關係洞察力與不理想的數常識解題比例(44.2%)，但受訪教師使用傳統算則的比例卻低於使用數常識的比例，這顯示受訪教師相對之下較不受算則束縛。此外，在比較數理相關科系與非數理相關科系教師的數常識表現上，非數理相關科系教師呈現出較高的數常識解題次數，數理相關科系教師則呈現出較高的數常識解題效率，但無法就此斷定何組教師的數常識發展較高。
而在數常識的觀點上，所有受訪教師都一致認同數常識對數學學習的正向影響，而且在瞭解數常識對學生有所幫助的前提下，有五位受訪教師表達願意進行數常識教學的意願，但若進行數常識教學時，缺乏教材內容及是否有多餘時間進行教學，是受訪教師較為擔心的問題。另外，在訪談中也發現數常識的推廣，可能顯露出不夠普及與可能不受重視的隱憂。

The purposes of this study were to examine six elementary school teachers’ number sense performance when solving number sense related problems and their perceptions about number sense. The researcher designed the number sense tasks and related perception questions as the instruments via the semi-structured interview to collect data. The interview results indicated that:
The results of teachers’ number sense performance showed that the participants have poor insight on numerical relations and do not perform well on the use of number sense methods. Moreover, the proportion on the use of rule-based methods was lower than the number sense methods. This demonstrated that participants were not limited by the rule-based methods comparatively. In addition, the number sense performance showed that participants who are not majored in mathematics have higher frequency on using number sense methods than participants majored in mathematics. However, the participants majored in mathematics showed that they have higher efficiency on using number sense methods to solve problems.
The results of teachers’ perceptions about number sense showed that all the participants showed the positive influence on number sense to the mathematics learning. Furthermore, based on the understanding of the positive effects on number sense, five out of six of the participants expressed willingness to teach number sense in mathematics classes. However, referring to the number sense teaching, the participants concerned about the content of teaching materials and time limits of teaching hours. In addition, the results of interviews also indicated that there is a concern that the number sense was lacking publicity and therefore it is not emphasized by the educators in here.

中文摘要 ……………………………………………. i
英文摘要 ….……………………………………...…. ii
目次 ………………………………………………….. iv
表次 ………………………………………………….. vi
圖次 ………………………………………………….. viii
第一章 緒論
第一節 研究動機 ……………………………………... 1
第二節 研究目的與問題 ……………………………... 2
第三節 名詞釋義 …………………….……………….. 3
第四節 研究範圍與限制 ………….………………….. 3
第二章 文獻探討
第一節 數常識的內涵 ………………………………… 5
第二節 數常識的組成架構 …………………………… 10
第三節 教師與數常識教學之相關研究 ……………... 19
第三章 研究方法與步驟
第一節 研究方法 ……………………………………… 24
第二節 研究對象與研究情境 ………………………... 24
第三節 研究工具 ……………………………………… 25
第四節 資料的蒐集與分析 …………………………... 27
第五節 研究步驟 ……………………………………… 35
第六節 試驗性研究結果 ……………………………... 37
第四章 研究結果與討論
第一節 教師在「瞭解數字的基本意義」問題之解題表現 47
第二節 教師在「運算對數字的意義和影響」問題解題表現 65
第三節 教師在「比較數字大小」問題之解題表現 ….. 92
第四節 教師在「參考點的運用」問題之解題表現 .. 112
第五節 教師在「靈活使用數字與運算並判斷答案的合理性」
問題之解題表現 …………………………….… 129
第六節 教師對數常識的觀點 ……………….………… 154
第五章 結論與建議
第一節 結論 …………………………………………… 205
第二節 建議 ………………………...……………….… 210
參考文獻
中文部分 ……………………………………………..… 214
外文部分 ……………………………………………….. 215
附錄
附錄一 教師數常識及數常識觀點訪談問題初編 … 220
附錄二 教師數常識及數常識觀點訪談正式問題 … 225

中文部分
支毅君（1997）。我國國小三年級數感教學研究。台東師院學報。86（8），83-166。
王菱玉（2003）。職前教師面對數字常識問題表現之研究。未出版之碩士論文，國立嘉義大學數學教育研究所，嘉義。
林怡靜（2005）。國小教師的數感相關知識與其教學觀點之探討。未出版之碩士論文，臺北市立教育大學數學資訊教育研究所，臺北。
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，21，51-67。
徐俊仁、楊德清（2004）。數字常識對九年一貫數學新課程的影響及啟示。教師之友，45（1），78-87。
許清陽（2001）。國小高年級學童數字常識發展之研究。未出版之碩士論文，國立嘉義大學國民教育研究所，嘉義。
許清陽（2005）。後設認知理論及其在國小學童數感發展上的應用。教育研究，13，139-148。
教育部（2003）。國民中小學九年一貫課程綱要數學學習領域。台北：教育部。
陳昇飛（2004）。理論與實務的對話:建構主義在數學教育上的再思。臺中師院學報，18(2)，71-87。
陳霈頡（2007）。數常識補教教學活動模組實施之研究～以國小三年級學生為例。未出版之碩士論文，國立嘉義大學數學教育研究所，嘉義。
黃瑞琴（2003）。質的教育研究方法（再版八刷）。台北：心理。
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。
楊德清（2002）。從教學活動中幫助國小六年級學生發展數字常識能力之研究，科學教育學刊，10(3)，233-259。
楊德清、黃明章（2003）。建構教學對實施數字常識教學活動之省思。國民教育研究學報，10，155-188。
葉俊谷（2007）。完成國小五年級數學課程之數常識電腦化診斷測驗系統之開發與應用。未出版之碩士論文，國立嘉義大學數學教育研究所，嘉義。
溫世展、呂玉琴（2004）。影響國小教師數學教學相關信念與教學是否一致之原因探討。國立台北師範學院學報，17（2），23-52。
潘慧玲（2003）。社會科學研究典範的流變。教育研究資訊，11（1），115-143。
蔡鳳秋（2005）。國小四年級學童在生活情境文字題使用數常識解題表現之研究。未出版之碩士論文，國立嘉義大學數學教育研究所，嘉義。
蔡美怡（2006）。國小六年級學童在不同情境問題中數常識策略運用之研究。未出版之碩士論文，國立嘉義大學數學教育研究所，嘉義。
外文部分
Australian Education Council. (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.
Alajmi, A. & Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65, 77-94.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. What makes it special ? Journal of Teacher Education, 59, 389-407.
Dooren, W. V., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact . In D. A. Grouws(Ed.), Handbook of research on mathematics teaching and learning(pp. 147-164). New York:Macmillan Publishing Company.
Gertsen, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for student with mathematical disabilities. The Journal of Special Education, 33, 18-28.
Griffin, S. (2004a). Teaching number sense. Educational Leadership, 61(5), p. 39-42.
Griffin, S. (2004b). Building number sense with number worlds: A mathematics program for young children. Early childhood research quarterly, 19, p. 173-180.
Gurganus, S. (2004).Promote number sense. Intervention in school and clinic, 40(1),55-58.
Hiebert, J. (1989). Reflections after the conference on number sense. In J. T. Sowder & B. P. Schappelle (Eds.). Establishing foundations for research on number sense and related topics: Report of a conference (pp.82-84). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Howden, H. (1989). Teaching number sense. The Arithmetic Teacher, 36(6), 6-11.
Hope, J. (1989). Prompting number sense in school. Arithmetic Teacher, 36 (6), 12-16.
Japanese Ministry of Education. (1989). Curriculum of mathematics for the elementary school. Tokyo: Printing Bureau.
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.
Markovits, Z & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathmatics Education, 25(1), 4-29.
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.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (2000). The Principles and Standards for School Mathematics. Reston, VA: NCTM.
Reys, R. E., Rybolt, J. F., Bestgen, B. J. & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183-201.
Resnick, L.B. (1989). Defining, assessing and teaching number sense. In Sowder & Schappelle (Eds.), 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.
Reys, B. J. (1994). Promoting number sense in middle grades. Teaching Mathematics in the Middle School, 1(2), 114-120.
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.
Sowder, J. T. (1990). Mental computation and number sense. Arithmetic Teacher, 37(7), 18-20.
Sowder, J. T. (1992). Making sense of numbers in school mathematics. In G. Leinhardt, R. & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1-51). Hillsdale, NJ: Erlbaum.
Sowder, J. T. & Kelin, J. (1993). Number sense and related topics. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 41-57). New York: Macmillan.
Yang, D. C., & Reys, R. E. (2001a) Developing Number Sense, Mathematics Teaching, 176, 39-41.
Yang, D. C., & Reys, R. E. (2001b). One Fraction Problem: Many Solution Paths, Mathematics Teaching in the Middle School, 7(3), 164-166.
Yang, D. C. (2002). Teaching and learning number sense: One successful process-oriented activity with six grade students in Taiwan. School Science and Mathematics, 102(4), 152-157.
Yang, D. C. & Reys, R. E. (2002). Fractional Number Sense Strategies Possessed by Sixth Grade Students in Taiwan. Hiroshima Journal of Mathematics Education, 10 (December), 53-70.
Yang, D. C. (2003) Teaching and learning number sense: An intervention study of fifth grade students activity with in Taiwan. International Journal of Science and Mathematics Education, 1(1), 115-134.
Yang, D. C., Hsu, C. J., & Huang, M. C. (2004). A study of teaching and learning number sense for six grade student in Taiwan. International Journal of Science and Mathematics Education, 2, 407-430.
Yang, D. C. (2005). Number Sense Strategies used by Sixth Grade Students in Taiwan, Educational Studies, 31(3), 317-334.
Yang, D. C. (2006). Developing number sense through real-life situations in school of Taiwan. Teaching Children Mathematics. 13(2), 104-110.
Yang, D. C. (2007). Investigating the strategies used by pre-service teachers in Taiwan when responding to number sense questions, School Science and Mathematics. 107(7), 293-301.
Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics.
Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education. 7, 383-403.