近年來數學素養儼然已成為數學教育的一項重要的指標，而九年一貫課程數學領域綱要中亦以數學素養作為其標的，鑑於國內尚無相關研究，因此本研究即以數學素養為研究方向，擬定研究目的三項：（1）探討數學素養的意涵；（2）建構數學素養能力指標；（3）初步探討與效化國小學生數學素養評量工具。在研究過程中即依據三項研究目的，分為三個子研究分別針對不同的研究問題予以探討。

一、研究一：何謂數學素養
研究一主要透過內容分析法與文獻資料的蒐集與分析，逐步形成對於研究主題的認識與觀點，並界定數學素養的意涵應當是「在社會文化的脈絡中，能用數學的眼光看世界，能認識及轉換多樣化的資訊成數學的形式，使用數學解決來自生活上的問題，以作為判斷和做決定的依據，並且能透過說明與溝通，讓別人瞭解據以決定的過程與結果。」

二、研究二：數學素養能力指標的建構
研究二則是以數學素養重要的組成要素為依據發展數學素養能力指標，並且認為解決問題的能力、推理思維的能力、溝通說明的能力、評斷做決定的能力、資訊取則與表徵的能力以及使用數學的意向是數學素養能力指標中六個重要的向度。

三、研究三：數學素養評量工具的開發與效化
本研究國小學生數學素養評量工具主要是以數學內容（數與計算、圖形空間與實測、資料處理）、數學素養能力指標（依數學素養重要的組成要素發展）以及情境類型（居家上課購物、健康衛生飲食、休閒娛樂交通）三個向度結構。在試題的部分，則以題組的方式呈現，包含一般的單選題及二階段評量試題，並於預試之後形成三份題本。評量工具的效化則是以「瞭解評量工具是否與數學素養的意涵對齊」、「試題的項目分析」以及「測驗的信效度分析」等作為評量工具效化的三個主軸。從訪談過程中歸納出三項教師與學生對於評量工具的觀感，分別是思考與使用數學解題、與生活經驗的連結以及訊息的多樣與閱讀，這些特質皆符合本研究中對於數學素養意涵的界定。而在試題的項目分析與測驗的信效度分析中，結果發現三份題本重測信度分別是0.91、0.80及0.92。透過進一步的分析亦發現，學校數學與數學素養評量的表現呈現中度相關，且相同情境類型中不同數學內容向度間的表現大多數呈現中度相關，而相同數學內容中不同情境類型向度間的表現亦多數呈現中度相關。

Mathematical literacy has held a special attraction for the community of mathematics education. The Curriculum Guidelines of Mathematics for grade 1-9 also recognizes the importance of mathematical literacy or numeracy. But there have been no related theses in internal research. In view of this, the purpose of this study is to: (1) investigate what mathematical literacy is; (2) construct attainment indicator of mathematical literacy; and (3) validate the rudimentary instrument and explore students’ performance. The study is then divided into three sub-studies according to each purpose.

A. Study 1: What is Mathematical Literacy?
Study 1 aims at developing ideas about mathematical literacy through content analysis and literature review. Mathematical literacy in this study is an individual’s capability to see the world with the eyes of mathematics, to recognize and transform varieties of information into mathematical forms, to use mathematics solving real life problems in social and cultural contexts. Mathematically literate individuals should communicate and evaluate the process and product of making decisions.

B. Study 2: Construction of Attainment Indicator
Study 2 aims at attainment indicators in accordance with the definition and key elements of mathematical literacy in the study. There are six dimensions of attainment indicator as follows: problem solving, thinking and reasoning, communicating, evaluating and decision making, information selecting and representing, and disposition to use mathematics.

C. Study 3: Instrument Design and Validation
The instrument in this study is organized by three dimensions: mathematical content, context, and attainment indicators. There are three booklets which are displayed by testnets or superitems including multiple choice and two-tail assessment items. Study 3 aims at validating the rudimentary instrument through interviews with teachers and students, item analysis, and analysis of validity and reliability of instrument. Three characteristics of the instrument from the interviews－are thinking and using mathematics, connecting with mathematics, and reading and varieties of information－will be summarized. The test-retest reliabilities of the three booklets are 0.91, 0.80, and 0.92 respectively. According to progressive analysis, the correlation coefficient indicates a moderate or low positive relationship between different mathematical content dimensions in the same context, and different context dimensions in the same mathematical content.

一、中文文獻
三民書局大辭典編纂委員會（1985）。大辭典。台北：三民。
王子興（2002）。論數學素養。數學通報，1，6-8。
孔企平（2000）。小學兒童如何學數學。上海：華東師範大學出版社。
孔企平（2002）。小學數學教學的理論與方法。上海：華東師範大學出版社。
尹建中、李英明、張一蕃、瞿海源、羅曉南、謝瀛春等（1997）。資訊科技對人文,社會的衝擊與影響：期末研究報告（計畫編號:(86)023-602）。台北：行政院經濟建設委員會。
王琪（2002）。淺談數學素養與數學素質教育。教育導刊，11月號上半月，32-33。
朱德全（2002）。數學素養組成要素探析。中國教育學刊，5，49-51。
朱德江（2004）。小學生數學素樣構成要速予培養策略。學科教育，7，27-31。
李樹臣（2002）。數學教師的素質教育觀。2003年9月27日，取自http://www.pep.com.cn/200212/ca6391.htm
何豔平、李邦榮（1999）。數學素質初論。湖北師範學院學報（自然科學版），19（2），87-89.
林樹聲（1999）。科學素養的省思。科學教育月刊，222，16-25。
侯發高（2002）。關於我國使用“科學素質”與“科學素養” 兩詞的調查與分析。論文發表於中國科協科普部、主辦之中國科普研究所第十屆全國科普理論研討會，北京。
唐海燕（2001）。提高學生數學素養的探討。2003年9月27日，取自http://www.edu.cn/20011122/3011270.shtml
教育部（2001）。國民中小學九年一貫課程暫行綱要－數學學習領域。台北：作者。
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：作者。
陳恒安（2003）。科學素養與民主社會。科學月刊，34（4），309-312。
章建躍（1999）。論科學素質及其培養。中國教育學刊，3，35-38。
張鈿富（2001）。OECD國際性學生評量之探討。教育研究月刊，83，28-43，
郭生玉（1999）。心理與教育測驗。台北：精華書局。
郭慧玲（2003）。探討量化素養的意涵與評量中學生量化素養工具之開發。國立台灣師範大學科學教育研究所碩士論文，未出版，台北。
黃秦安（2001）。數學文化觀念下的數學素質教育。數學教育學報，10（3），12-17。
靳知勤（2002）。「有素養」或「無素養」－解讀非科學主修大學生對三項全球性環境問題之敘述表徵。科學教育學刊，10（1），59-86。
董寶良（1994）。由應試教育轉向素質教育是教育改革和發展的戰略決策－學習《中國教育改革和發展綱要》的體會。湖北大學學報（哲學社會科學版），3，8-12。
閻育蘇（譯）（1991）。Polya, George著。怎樣解題。台北：九章。
戴紅兵（2000）。論數學素質教育。思茅師範高等專科學校學報，16（3），32-35。
顧沛（2000）。十種數學能力和五種數學素養。高等數學研究，4（1），5。

二、英文文獻
Allen, R.E. (Ed.). (1990). The Concise Oxford dictionary of current English(8th ed.). New York : Oxford University Press.
American Association for the Advancement of Science (1989). Science for All Americans: A Project 2061 Report on Literacy Goals in Science, Mathematics, and Technology. Washington, D.C.: Author.
American Association for the Advancement of Science (1993). Benchmarks for science literacy. NY: Oxford University Press.
Amit, M. & Fried, M. N. (2002). High-stakes Assessment as a Tool for Promoting Mathematical Literacy and the Democratization of Mathematics Education. Journal of Mathematical Behavior, 21, 499-514.
Australian Association of Mathematics Teachers (1997). Numeracy = Everyone’s Business. The Report of the Numeracy Strategy Development Conference, Perth, April, Australian Association of Mathematics Teachers, Adelaide.
Australian Association of Mathematics Teachers (1998). Policy on Numeracy Education in Schools. Retrieved November 20, 2003, from AAMT Web site: http://www.aamt.edu.au/about/policy/numpol.pdf
Bishop, A. J. (2000, July 31-Au gust 6). Overcoming obstacles to the democratisation of mathematics education. Regular lecture presented at the Ninth International Congress on Mathematics Education, Makuhari, Japan.
Bonotto, C. (2001). How to Connect School Mathematics with Students’ Out-of-School Knowledge. International Reviews on Mathematical Education, 33(3), 75-84.
Brown, M., Millett A., Bibby T. & Johnson, D. C. (2000). Turning Our Attention from the What to the How: the National Numeracy Strategy. British Educational Research Journal, 26(4), 458-471.
Bybee, R. W. (1995). Achieving Scientific Literacy. The Science Teacher, 62(7), 28-33.
Bybee, R. W. (1997). Achieving scientific literacy : from purposes to practices. Portsmouth, NH : Heinemann.
Ciancone, T. (1988). Adult numeracy: Taking mathematics from the real world into the classroom and back. Toronto: Toronto Board of Education. (Report to the Adult Basic Education Unit)
Ciancone, T. (1996). Numeracy in the Adult ESL Classroom. ERIC Digest (ED392316). Retrieved November 6, 2002, from http://www.ericfacility.net/databases/ERIC_Digests/ed392316.html
Collis, K. T. (1973). Key Words in Education. London : Longman.
Collis, K. F., Romberg, T. A. & Jurdak, M. E. (1986). A Technique for Assessing Mathematical Problem-Solving Ability. Journal for Research in Mathematics Education, 17(3), 206-221.
Cooper, D. A. (1999). Navigating the thorny path: A colloquial definition of mathematical literacy with connections to various school mathematics standards. In Kathy Comfort(Ed.), Advancing Standards for Science and Mathematics Education: Views From the Field(chat4). Washington, DC: American Association for the Advancement of Science.
Cox, P. (2001). What is “Math Literacy”?. Retrieved September 11, 2003, from
http://members.cox.net/mathmistakes/literacy.htm.
Cremin, L. A. (1988). American Education, The Metropolitan Experience. New York : Harper & Row.
Curry, D., Schimitt, M. J., & Waldron, S. (1996). A Framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adults Need to Be Eqipped for the Future. Boston, MA: The Adult Numeracy Practitioners Network.

D’Ambrosio, U. (1998). Literacy, Matheracy.and Technoracy – The New Trivium for the Era of Technology. Paper presented at the meeting The First Mathematics Education and Society Conference, Nottingham, UK.
D’Ambrosio, U. (1999a). Literacy, Matheracy, and Techonoracy: A New Trivium for Today. Mathematical Thinking and Learning, 1(2), 131-153.
D’Ambrosio, U. (1999b). In Focus…Mathematics, History, Ethnomathematics and Education: A Comprehension Program. The Mathematics Educator, 9(2), 34-36.
Department of Education and the Arts (1995). Numerate Students – Numerate Adults: A Booklet for Teachers. Hobart, Australia: Author.
Department of Education, Training and Youth Affairs (2000) Numeracy, A Priority for All: Challenges for Australian Schools. Canberra, New South Wales: Author.
Doig, B., McCrae, B. &, Rowe, K. (2003). A Good Start to Numeracy: Effective Numeracy Strategies from Research and Practice in Early Childhood. Commonwealth: Commonwealth Department of Education.
Educational Testing Service (1999). Adult Literacy and Lifeskills Survey: Numeracy. Princeton, NJ: Author.
Gal, I. (1995). Big Picture: What Does “Numeracy” Mean?. GED Items, 12(4/5). http://forum.swarthmore.edu/teachers/adult.ed/articles/gal.html.
Gal, I. (2002). Systematic Needs in Adult Numeracy Education. Adult Basic Education, 12(1), 20-33.
Gellert, U., Jablonka, E. & Keitel, C. (2001). Mathematical Literacy and Common Sense in Mathematics. In Atweh, B., Forgasz, H. & Nebres, B. (Eds.). Sociocultural Research on Mathematics Education. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Good, C. V. (1973). Dictionary of Education. New York: McGraw-Hill.
Guralnik, D. B. (Ed.). (1972). Webster's new world dictionary. N.Y.: World Pub. Co.
Hoogland, K. (2003). Mathematical Literacy and Numeracy. Retrieved November 20, 2003, from Web site: http://www.gecijferdheid.nl/pdf/HooglandJablonka_UK.PDF
Hyman, B.（2003）. Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician's Perspective. Teaching Children Mathematics, 9（6）, 322-327.
Jablonka, , Eva (2003). Mathematical Literacy. In A.J. Bishop, M.A.Clements, C. Keitel, J. Kilpatrick, F.K.S. Leung (Eds.). Second International Handbook of Mathematics Education (pp. 75-102). The Netherlands, Dordrecht: Kluwer Academic Publishers.
Kemp, M. & Hogan, J. (2000). Planning for An Emphasis on Numeracy in the Curriculum. Commonwealth: Commonwealth Department of Education.
Kerka, S. (1995). Not just a number: Critical numeracy for adults. Eric Digest No.163. Retrieved September 11, 2003, from
http://www.ericfacility.net/ericdigests/ed385780.html.
Kilpatrick, J. (2001). Understanding Mathematics Literacy: The Contribution of Research. Educational Studies in Mathematics, 47, 101-116.
Kilpatrick, J., Swafford, J. & Findell, B. (Eds.) (2001). Adding It Up: Helping Children Learn Mathematics. Washington, D.C.: National Academy Press.
Lake, D. (1999). Helping Students to Go SOLO: Teaching Critical Numeracy in the Biological Sciences. Journal of Biological Education, 33(4), 191-198.
Mathematics Council of The Alberta Teachers’ Association (2001). Mathematical Literacy…an idea to talk about. Retrieved September 11, 2003, from
http://www.mathteachers.ab.ca/MCATA%20referent%20paper.pdf
National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston Va: Author.
National Council of Teachers of Mathematics (1991). Professional Standards for Teaching Mathematics. Reston Va: Author.
National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston Va: Author.
National Research Council (1989). Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington, D. C.: National Academy Press.
Neil, W. A. (2001). The Essentials of Numeracy. Paper presented at the New Zealand Association for Research in Education (NZARE) conference, Christchurch.
Nohara, D. (2001). A Comparison of the National Assessment of Educational Progress (NAEP), the Third International Mathematics and Science Study Repeat (TIMSS-R), and the Programme for International Student Assessment (PISA). Washington, DC: U.S. Department of Education – Office of Educational Research and Improvement.
Organization for Economic Co-operation and Development. (1999). Measuring student knowledge and skills - A new framework for assessment. Paris: Author.
Organization for Economic Co-operation and Development. (2003). The PISA 2003 Assessment Framework – Mathematics, Reading, Science and Problem Solving Knowledge and Skills. Paris: Author.
Pearsall, J. & Hanks, P. (Eds.). (1998). The new Oxford dictionary of English. Oxford: Clarendon Press.
Pugalee, D. K. (1999a). Constructing a model of mathematical literacy. The Cleaning House, 73(1), 19-22.
Pugalee, D. K. (1999b). Mathematical and technological literacy: Developing an integrated 21st century model. Paper presented at the Annual Meeting of the Mathematics Teacher Educators, Chicago, IL.
Pugalee, D. K. (2001). Using Communication to Develop Students’ Mathematical Literacy. Teaching Children Mathematics, 6(5), 296-299.
Paulos, J. A. (1988). Innumeracy: Mathematical Illiteracy and Its Consequences. NY: Hill & Wang.
RAND Mathematics Study Panel（2002）. Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education. Santa Monica：Science & Technology Policy Institute.
Romberg, T. A. (2001a). Mathematical Literacy: What does It Mean for School Mathematics?. Wisconsin School News, 56(6), 5-31.
Romberg, T. A. (2001b). Mathematics goals and achievement in the United States. Paper presented at the Proceedings of the 25th conference of the international group for the Psychology of Mathematics Education, Netherlands, Utrecht.
Skovsmose, O. (1998). Linking Mathematics Education and Democracy: Citizenship, Mathematical Archaeology, Matheracy and Deliberative Interaction. International Reviews on Mathematical Education, 30(6). Retrieved November 20, 2003, from Web site: http://www.fiz-karlsruhe.de/fiz/publications/zdm/zdm986a5.pdf
Steen, L. A. (1990). Numeracy. Daedalus, 119 (2), 211-231.
Steen, L. A. (1999). Numeracy: The New Literacy for a Data-Drenched Society. Educational Leadership, 57(2), 8-13.
Steen, L. A. (1999b). Mathematical Reasoning. In Lee Stiff (Ed.). Developing Mathematical Reasoning in Grades K-12 (pp. 270-285). Reston Va: National Council of Teachers of Mathematics.
Steen, L. A. (2001). Mathematics and Numeracy: Two Literacies, One Language. Retrieved September 11, 2003, from
http://www.stolaf.edu/people/steen/Papers/twolits.htm.
Stoessiger, R. (2003). An introduction to critical numeracy. Australian Mathematics Teacher, 58(4), 17-20.
Wilson, L. D. & Chavarria, S. (1993). Superitem Tests as a Classroom Assessment Tool. In Webb, N. L. & Coxford, A. F. (Eds.). Assessment in the Mathematics Classroom (pp. 135-142). Reston Va: National Council of Teachers of Mathematics.