本研究進行為期 2 個月的數感動態評量，雖然結果顯示在質與量兩方面均有顯著 效果，但數感強調的是數學思考與知識內化的能力，要在短期教學與評量中明顯提升 學生的數感能力，似乎不容易。本研究中學生數感能力之所以進步如此顯著，研究者 認為可能因為：作為前、後測的「四年級數感能力測驗」與動態評量過程中的教學與 評量，為強化並檢測學生的數感能力，均以數感六向度來設計，因此實驗結果有可能 是教學效益所致，推論上難免有其限制。若能長期融入數學教學，也許更能客觀分析 其對學生的影響，真正改進教學與評量上的缺失。
Ёăඕኢᄃޙᛉ
˘ăඕኢ
（一）數感動態評量的效益
1.實驗組的後測成績明顯高於前測成績。
2.實驗組後測成績明顯優於控制組後測成績。
3.實驗組兩次數學月考成績明顯優於控制組兩次月考成績。
（二）學生在數感動態評量過程中數感能力的改變 1.量的分析方面，每單元個人學習單成績有明顯進步。
2.質的分析方面，學生的概念愈加強化，思考愈加多元，策略愈加靈活。
（三）行動研究中的教師專業成長
1.活動的預估時間必須彈性計畫，才不致影響整個活動流程。
2.學習單量化的標準要依賴專業素養，盡量求得客觀。
3.提高學生討論的動機在活動中很重要，甚至影響教學的進行。
4.當討論呈現冷清或停滯時，教師要適時引導學生；當學生討論得欲罷不能時，老 師要保持討論的熱烈氣氛。
6.任何活動的設計與進行，均以學生最佳學習利益為主。
7.教學活動的設計老師必須先動手操作。
（四）數感動態評量融入數學科教學的限制
「四年級數感能力測驗」與動態評量均依據數感六向度來設計，可能導致教學效 益，有推論上的限制。
˟ăޙᛉ
（一）教學方面的建議：
1.生活中許多活動或資訊都可作為訓練學生數感能力的材料與教學活動。
2.老師在設計教學活動時，要多提供學生小組討論的機會。
3.對於低、中程度的學生，老師應常給予具體物操作的機會，讓學生能從中建構並 內化概念，讓學生在生活情境中，不知不覺培養數感能力。
4.老師在課堂上不應只要求標準答案，要多讓學生有多元思考，並常要求學生在生 活中與課堂上使用估計策略作合理判斷。
5.老師應尋求支援，不應單打獨鬥，多和同事或朋友討論，才能集思廣益，找到最 適合的教學策略。
（二）對評量方面的建議：
1.數學的評量不再侷限於靜態的紙筆評量。
2.在評量中，要多提供學生動手操作的機會，並重視學習過程而非學習結果，這樣 學生的基本數學能力才會逐漸養成。
3.老師應嘗試多元評量，多從操作中、討論中觀察學生的思考與解題，並在評量中 隨時修正教學內容與方法，以適合學生的能力及需要。
（三）對教材方面的建議：
1.老師設計數感教學教材時，一定要多方考慮數感的六個向度。
2.教學內容除了取材於課本，老師自行設計的活動更能符合數感教學的需求。
3.數感教材的設計，時間可長可短，重質亦可重量，須根據老師上課的需求與學生 的參與情形作調整、修正。
（四）對未來研究的建議：
1.可針對不同程度學生作學習潛能之分析。
2.可進行較長時間的實驗處理。
3.數感能力測驗可再修改得更完善。
4.行動研究過程中多方詢問意見及多元思考。
ણ҂͛ᚥ
支毅君（1997）：我國國小三年級數感教學研究。台東師院學報，8，83-116。
吳國銘、洪碧霞、邱上貞（1995）：國小學童在動態評量中數學解題學習歷程與遷移 效益之探討。測驗年刊，42，61-84。
林素微（1996）：國小六年級學童數學解題彈性思考動態測量之研究。國立台南師範 學院國民教育研究所碩士論文。
莊麗娟（1996）：國小六年級浮力概念動態評量的效益分析。國立高雄師範大學教育 學系碩士論文。
莊麗娟（2000）：系統化多元評量模式之發展研究。國立高雄師範大學教育學系博士 論文。
陳進福（1997）：國小輕度智障學童數學解題動態測量之研究。國立嘉義師範學院國 民教育研究所碩士論文。
楊德清（1998）：筆算能力與數字常識表現之差異性的探討。科學教育月刊，212，
3-10。
Australian Education Council (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.
Behr, M. (1989, August). Reflections on the conference. In J. T. Sowder & B. P.
Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 85-88). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Carpenter, T. P. (1989, August). Number sense and other nonsense. In J. T. Sowder & B. P.
Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 89-91). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Dehaene, S. (1997).The number sense: How the mind creates mathematics. New York:
Oxford University Press.
Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
Hope, J. (1989). Promoting number sense in school. Arithmetic Teacher, 36(6), 12-16.
Hopkins, L. (1995). Popping up number sense. Teaching Children Mathematics, 2(2), 82-86.
Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
Markovits, Z. & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4-29.
Markovits, Z. (1989, August). Reflections to the number sense conference. In J. T. Sowder
& B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 78-81). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Markovits, Z., Hershkowitz, R., & Bruckheimer, M. (1989). Research into practice.
Arithmetic Teacher, 36(6),53-55.
Marshall, S. P. (1989, August). Retrospective paper: Number sense conference. In J. T.
Sowder & B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 40-42). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
McIntosh,A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examing basic number sense. For the Learning of Mathematics, 12, 2-8.
Nation Research Council(1989). Everybody Counts: A report to the nation on the future of mathematics education. Washington, D.C.: National Academy Press.
National Council of Teachers of Mathematics(1989). Curriculum and evaluation standards
for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics(2000). The Principles and Standards for School Mathematics. Reston, VA: Author.
Resnick, L. B. (1989, August). Defining, assessing, and teaching 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. 35-39). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Reys, R. (1989, August). Some personal reflections on the conference on number sense, mental computation, and estimation. In J. T. Sowder & B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 65-66). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Reys, R.E. & Der-Ching Yang (1998). Relationship between computational performance and number sense among sixth- and eight-grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237.
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 Unit237.ed States. School Science and Mathematics, 99(2), 61-70.
Ritchhart, R. (1994).Making numbers make sense. Menlo Park, CA: Addison-Wesley.
Schoen, H. L. (1989, August). Reaction to 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. 67-69). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Silver, E. A. (1989, August). On making sense of 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. 92-96). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Sowder, J. T. (1988). Mental computation and number comparison: Their roles in the development of number sense and computational estimation. In J. Hiebert & M. Behr
(Eds.). Number Concepts and Operations in the Middle Grades (pp.182-197).
Hillsdale, NJ: Erlbaum & Reston, VA: NCTM.
Sowder, J. T. (1989, August). Introduction. In J. T. Sowder & B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp.1-50). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Sowder, J. T. (1992a). Estimation and number sense. In D.A. Grouws (Ed.). Handbook of research on mathematics teaching and learning. (pp.371-389). New York:
Macmillan.
Sowder, J. T. (1992b).Making sense of numbers in school mathematics. In G. Leinhardt, R.
Putnam, & R. A. Hattrup (Eds.). Analysis of Arithmetic for Mathematics Teaching (pp.1-51). Hillsdale, NJ: Erlbaum.
Stanger, C., Symington, L., Miller, H., & Johns, S. (2000). Teaching number sense concepts to all students. Teaching Exceptional Children, 33(1), 65-69.
Thompson, C. S. & Rathmell, E. C. (1989). By way of introduction. Arithmetic Teacher, 36(6), 2-3.
Thornton, C. A., & Tucker, S. C. (1989). Lesson Planning: The key to developing number sense. Arithmetic Teacher, 36(6), 18-21.
Trafton, P. (1989, August). Reflections on the number sense conference. In J. T. Sowder &
B. P. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 74-77). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Trafton, P. R., & Hartman, C. L. (1997). Developing number sense and computational strategies in problem-entered classrooms promising research, programs, and projects.
Teaching Children Mathematics, 4(4), 230-233.
Vacc, N. N. (1995). Gaining number sense through a restructured hundreds chart. Teaching Exceptional Children, 28(1), 50-55.