摘 要
本研究旨在探討幼兒一對一對應、計數能力與基數概念在不同年齡的發展表現。本研究採立意取樣之方式，以台北市三所公立托兒所161名幼兒為對象，採研究者自編之幼兒一對一對應、計數能力與基數概念等相關能力作業二十三項遊戲題為個別施測之評量工具。研究結果顯示：一、三至五歲幼兒的一對一對應能力的發展層次依序為：相同物的對應發展、異質互補物的靜態對應發展、相同圖形的對應發展、異質互補物的動態對應發展。二、幼兒在數物活動中計數原則的發展狀況依序為固定順序原則發展在先，一對一原則發展其次，基數原則發展第三，抽象原則發展第四，最後是發展順序無關原則。三、三至五歲幼兒分別在三種不同問法中的基數概念表現不同。幼兒對於「這裡有幾隻○○？」的問法表現最好，其次為「這裡有○隻○○嗎？」的問法，最後是「請給我○隻○○？」的問法。而幼兒對「請給我○隻○○？」和「這裡有○隻○○嗎？」的問法，表現相差非常些微，幾乎是一樣好。本研究也綜合研究的發現，提供指導幼兒進行數概念活動之教師做教學之參考。

壹、中文部分
西斐德Carol Seefeldt（民88），桂冠編譯室。幼教課程－當代研
究的回顧。台北市：桂冠。
伯魯迪ArthurJ.Baroody（民89），桂冠前瞻教育叢書編譯組。兒童
的數學思考。台北市：桂冠。
Constance Kamii（民86），幸曼玲譯。皮亞傑的理論、行為主義和教
育中的其他理論。建構主義在國小低年級和幼稚園數學教學的應
用學術研討會論文集。台北市立師範學院。
Juanita V. Copley（民92），何雪芳、陳彥文譯。幼兒數學教材教法
The Young Child Mathematics。台北市：禾楓。
吳新華（民81）。數與計算的啟蒙。台北市：五南。
吳惠芬（民89）。發展遲緩幼兒學習數與金錢之探討：自閉症幼兒之
個案研究。國立台灣師範大學家政教育系碩士論文，未出版，台
北市。
林怡君（民90）。建構教學對輕度智能障礙學生數概念應用成效之研
究。國立高雄師範大學特殊教育學系碩士論文，未出版，台北市。
林亮宜（民72）。學前兒童的數概念：數數字與比較數字。國立台灣
大學心理學研究所碩士論文，未出版，台北市。
林嘉綏、李丹玲（民88）。幼兒數學教材教法。台北市：五南。
周淑惠（民88）。幼兒數學新論－教材教法。台北市：心理。
姜忠信（民79）。學前兒童的數量概念。國立台灣大學心理學研究所
碩士論文，未出版，台北市。
翁麗芳（民87）。幼兒數學概念學習研討會論文集。國立台北師範學
院。
許惠欣（民81）。幼兒「該」如何學習數概念？－統合模式。台南市：
光華女中。
許惠欣（民84）。我國傳統與蒙特梭利教育之幼兒數學能力比較研究。
台南師院學報，28，533-568。
許惠欣（民86）。我國幼稚園幼兒算數策略之研究。台南師院學報，
30，339-372。
陳李綢（民81）。認知發展與輔導。台北市：心理。
張建妤（民74）。學前兒童的數能力。國立台灣大學心理學研究所碩
士論文，未出版，台北市。
張玉成（民82）。思考技巧與教學。台北市：心理。
張春興、林清山（民77）。教育心理學。台北市：東華書局。
蔡亞倫（民90）。學前與國小一年級兒童數字符號表徵能力與數能力的關係。國立中正大學心理學研究所碩士論文，未出版，嘉義縣。
簡楚瑛（民82）。幼兒數學知識結構及其發展趨勢之文獻探討。新竹
師院學報，第七期，17-57。
貳、西文部份
Alibali, M. W. & Dirusso, A. A. (1999). The function of gesture in learing
to count: More than keeping track, Cognitive Development, 14,
37-56.
Aneell, S., & Keating, D. P.(1983). Perception of numerical invariance in neonates. Child Development, 54, 695-701.
Baroody, A. J., Berent, R., & Packman, D. (1982). The use of mathematical structure by inner city children. Focus on Learning Problems in Mathematics, 4(2), 5-13.
Baroody, A. J., & Ginsburg, H. P. (1984). TMR and EMR children’s ability
to learn counting skills and principles. Paper presented at the annual
meeting of the American Educational Reserch Association, New
Orleans.
Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical Knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics. Hills-dale, N. J.: Lawrence Erlbaum.
Baroody, A. J., (1987). Children’s mathematical thinking: a developmental framework for preschool, primary, and special education teacher. New York: Teachers College .
Baroody, A. J., (1992). The Development of preschooler’s counting skill and principles. In J. Bideaud,C. Meljac, & J. P. Fisch (Eds.), Pathways to number: Children’s development numerical abilities. Hillsdale, N. J.: Lawrence Erlbaum.
Barron, L. (1979). Mathematic experiences for the early childhood years.
Columbus, OH: Charles E. Merrill Publishing Company, A Bell &
Howell Company.
Bassler, O. C., Kolb, J. R., Craighead, M. S., & Gray, W. L. (1981). Succeeding in mathematics(K) (Teacher’s ed) (rev. ed). Austin, TX: Steck-Vaughn Company.
Becker, J. (1989). Preschooler’s use of number words to denote one-to- one correspondence. Child development, 60, 1147-1157.
Bideaud, C. Meliac, & J. P. Fischer (Eds.), Pathways to number: Children’s development numerical abilities. Hillsdale, N.J.: Lawrence Erlbaum.
Bolster, L. C., Crown, W., Hamndn, R., Hasen, V., Lindquist, M. M.,
MeNereny, C., Nibbelink, W., Prigge, G., Rahlfs, Robitaille, D.,
Schultz, J., Sharron, S., Swafford, J., Vanc e, I., Williams, D.E.,
Wilson, J., & Wisner, R. (1987). Invitation to mathematics (k)
(Teacher’s ed). Glenview, IL: Scott, Foresman & Company.
Briars, D., & Siegler, R. S. (1984). A featural analysis of preschoolers
counting knowledge. Developmental Psychology, 20 (4), 607-618.
Carpenter, T., P. (1985). Learning to add and subtract: an exercise in problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: multiple research perspectives. Hillsdale, N. J.: Lawrence Erlbaum.
Carpenter, T., P., Carey, D., & Kouba, V. (1990). Aproblem-solving
approach to the operations. In J. N. Payne (Ed.), Mathematics for the young child. Reston, VA: The National Council of Teachers of Mathematics.
Chi, N. T. H., & Klahr, D, (1975). Span and rate of apprehension in children and adults. Journal of Experimental. Child Psychology, 19, 434-439.
Company, A Bell & Howell Company. Bassler, O, C., Kolb, J. R.,
Craighead, M, S., & Gray, W. L. (1981) Successding in mathematics
(K) (Teachers ed) (rev.ed) Austin, TX: Steck-Vaughn Company.
Cruikshank, D., Fitzgerald, D., & Jensen, L. R. (1980) Young children
learningMathematics. Boston, MA: Alyn & Bacon, Inc.
Cruikshank , D., Fitzgerald, D., &Jensen, L. R. (1980) Young children learning mathematics. Boston, MA:Allyn & Bacon, Inc.
Dawes, C. G (1977). Early maths. New York: Longman.
Ducan, E. R., Cappa, L. R., Dolicani, M.P., Quast, W. G., & Zweng, M. J.
(1972). Modern school mathematics:Structure and use (K )(Teacher’s
annotated ed.) (rev. ed.). Boston, MA: Houghton Mifflin Company.
Eicholz, R. E., O’Daffer, P. G., & Fleenor, C. R. (1987). Addison-Wesley
mathematics (K) (Teacher’s ed.). Menlo Park, CA: Addison-Wesley Publishing Company.
Elkind, D. (1964). Discrimination seriation and numeration of size and
dimen-Sional difference in young children：Piagetian replication
study VI . Jourrnal of Cenetic Psycholopy, 104, 275-296.
Flavell, J. H. (1985). Cognitive Development. (2nd ed.). Englewood
Cliffs, N. J.: Prentice-Hall.
Frye, D., Braisby, N., Lowe, J., Maroudas, C., & Nicholls, J., (1989)
Young children’s understanding of counting and cardinality. Child
Development, 60, 1158-1171.
Fuson. K. C., & Mierkiewicz, D. B. (1980). A detailed analysis of the act counting. Paper presented at the annual meeting of the American Educational Research Association ,Boston .
Fuson, K, C, & Hall, J. W. (1983). The acquisition of early number word
meanings：A conceptual analysis and review. In H. P. Ginsburg (ed),
The development of mathematical thinking. NY: Academic Press.
Fuson, K. C., Secada, W. G., & Hall, J. W. (1983). Matching, counting, and conervation of numerical equivalence. Child Development, 54 (1), 91-97.
Fuson. K. C., Pergament, G. G., Lyons, B. G., & Hall, J. W. (1985). Children’s conformity to the cardinality rule as a function of set size and counting accuracy. Child Development, 56, 1429-1436.
Fuson, K. C. (1988). Children’s counting and concepts of number. New
York: Springer-Verlag.
Fuson, K. C. (1992). Relationships between counting and cardinality from age 2 to age 8. In J. Bideaud, C. Meljac & J. Fischer (Ed.), Pathways to number: children’s development numerical abilities. Hillsdale, N. J.: Lawrence Erlbaum.
Gallistel, C. R. (1989). Animal cognitive: The representation of space, time and number. Annual Review of Psychology, 40, 155-189.
Gelman, R. (1969) Conservation acquisition: A problem of learning to
attend to relevant attributes. Journal of Experimental Child
Psychology, 7, 167-187.
Gelman, R. (1972). Logical capacity of very young children: Number invariance rules. Child Development, 43, 75-90.
Gelman, R. (1972). The nature and development of early number concepts. In H. W. Reese (Ed.), Advances in child development and behavior, 7, 115-167. New York：Academic Press.
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of
number. Cambridge, MA: Harvard University Press.
Gelman, R., & Meck, E. (1983). Preschoolers’ counting: principles befoe skill. Cognitive, 13, 343-359.
Gelman, R., & Meck, E. (1986). The notion of principle: The case of
counting. In J. Hiebert (Ed.), Conceptual and procedural knowledge:
The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Gelman, R., Meck, E., & Merkin, S. (1986). Young childrens’ numerical competence. Cognitive Development, 1, 1-29.
Gelman, R. & Meck, B. (1992). Early principles aidinitial bnt not later
conceptions of number. In J. Gellman, R. & Gallistel, C. R. (1983).
The child’s understanding of number. In Donaldson, M. Griere, R & Pratt, C. (Ed.). Early Childhood Development and Education, 185-203. Oxford: Basil Blackwell.
Gelman, R., & Greeno, G. (1989). On the nature of competence: principles for understanding in a domain. In L. B. Resnick (Ed.), Knowing, learning and instruction: essays in honor of Robert Glaser. Hillsdale, N. J.: Lawrence Erlbaum.
Ginsburg, H. P. (1977). Children’s arithmetic: the learning process. New York: D. Van Nostrand.
Ginsburg, H. P. (1980). Children’s surprising knowledge of arithmetic. Arithmetic Teacher, 28 (1), 42-44.
Ginsburg, H. P. (1982). Children arithmetic. Austin, TX: Pro-Ed.
Ginsberg, H. P., & Baroody, A. J. (1983). Test of early mathematics abilty.
Austin, TX: Pro-Ed.
Ginsburg, H. P. (1989). Children’s arithmetic :How the learn it and how
you teach it (2 nd ed.). Austin, TX: PRO-ED.
Ginsburg, H. P. & Opper, S. (1988). Piaget’s theory of intellectual
development. Englewood cliffs, NewJersey: Prentice Hall.
Good, R (1979). Children’s abilities with the four basic arithmetic operations in grades k-2 School Science and Mathematics, 79 (2), 93-98.
Greeno, J. G., Riley, M. S., & Gelman, R. (1984) Conceptual competence and children’s counting. Cognitive Psychology, 16, 94-143.
Groen, G. J. & Resnick, L. B. (1977). Can preschool children invent addition algorithms? Juornal of Education Psychology, 69, 645-652.
Gross, T. F. (1985). Congnitive development. Moneerey, CA: Brooks
Cole. Cognitive Psychology, 16 (1). 94-143.
Haenish, S., & Hill, M. B. (1987) Riverside mathematics (K) (Teachers ed)
Chicago. IL: The Riverside Publishing.
Holmes, E, E. (1995). Children learning mathematics: A cognitive
approach to teaching. Englewood Cliffs, NJ: Prentice-Hall, Inc.
Hudson, T. (1983). Correspondences and numerical difference between disjoint sets. Child Development, 54, 84-90.
Hughes, M. (1981) Can perschool children add and subtract? Educational
Preschool, 1, 207-219.
Hughes, M. (1985). Children and Number: difficulties in learing
mathematics.
Jong, J., T. (1997) Parents and kindergartners: Money and number,
practice, concepts and skills. Ames Iowa.
Kemler, D. G. (1982). Classification in young and retarded children: The
primacy of overall similarity relations. Child Development, 53 (3),
768-779.
Kennedy, L. M. (1984). Guiding childrens learning of mathematics
(4thed.). Belmont, CA: Wadsworth Publishing Company, A Division
of Wadsworth, Inc.
Klahr, D., & Wallace, J. G. (1976). Cognitive Development: an
Information Processing View. Hillsdale, N. J.
Larsen, G. Y &Flavell, J. H. (1970) Verbal factors in compensation
performance and the relation between conservation and compensation. Child Development, 41, 956-977.
Lovell, K. (1971).The growth of understanding in mathematics:
Kindergarten through grade three. New York: Holt, Rinehart &
Winston, Inc.
Mckillip, W. D. (1981). Mathematics for mastery (K) (Teachers ed).
Glenview, IL: Silver Burdett Company.
Milliar, C., & Mackay, C. K. (1978). Conflict between cues in number conservation task. British Journal of Educational Psycholopy, 50, 188-191.
Piaget, J. (1965). The Child’s conception of number. New york: Norton.
Piaget, (1977). The role of action in the development of thinking. In W. F.
Overton & J. M. Gallagher (Eds), Knowledge and development , 1,
17-42. New York: Plenum.
Piaget, J. (1952). The child’s conception of number. New York: The Norton library. W. W. Norton & Company.
Potter, M. C. & Levy, E. I. (1968). Spatial enumeration without counting. Child Development, 39, 265-272.
Resnick, L. B., & Ford, W. W. (1981). The psychology of mathematics for instruction. Hillsdale, N. J.: Lawrence Erlbaum .
Rothenberg, B. B. (1969). Conservation of number among four and five-year-old children: Some methodological considerations. Child Development, 49, 383-406.
Saxe, G. B. (1977). A developmental analysis of notational counting. Child Development, 48 (4), 1512-1520.
Saxe, G. B. (1979). Developmental relations between notational counting and number conservation. Child Development, 50, 180-187.
Saxe, G. B. (1983). Culture, counting, and number conservation. International Journal of Psychology,18 (3-4), 313-318.
Schaeffer, B., Eggleston, V. H. & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6, 357-399.
Sophian, C. (1988a). Limitations preschool children’s Knowledge about
counting: Using counting To compare two set. Development
Psychology, 24, 634-640.
Sophian, C. (1988b). Early developments in children’s understanding of
number: inferences about numerosity and one-to-one corresponderce.
Child development, 59, 1397-1414.
Sophian, C. (1992). Lesrning about numbers: lessons for mathematics education from preschool number development. IN J. Bideaud., C. Meljac & J. Fischer (Ed.), Pathways to number: children’s developing numerical abilities. Hillsdale, N. J.: Lawrence Erlbaum.
Starkey, P., & Cooper, R. G., Jr. (1980). Perception of numbers by human infants. Science, 210, 1033-1035.
Strauss, M. S., & Curtis, L. E. (1981). Infant perception of numerosity.
Child Development, 52, 1146-1152.
Troutman, A. P., Bezdek, J. J., Bertoni, P. E., Chin, C., Smith, L. P., &
Wright, A. E. (1982). Laidlaw mathematics (Red Book) (Teacher’s ed.). IL: Laidlaw Brothers Publishers.
Von Glasersfeld, E. (1982). subitizing: The role of figural patterns in the
development of numerical concepts. Archives de Psychologie, 50,
191-218.
Wagner, S., & Walters, J. (1982). A longitudinal analysis of early number
concepts: From numbers to number. In G. Formam (Ed). Action and
thought, 137-161. New York: Academic Press.
Wang, M, C., Resnick, L. B., & Boozer, R. F. (1971). The sequence of
development of some early mathematics behaviors. Child
Development, 42, 1767-1778.
Wilkinson, A. C. (1984) Children’s partial knowledge of the cognitive skill of counting. CognitivePsychology, 16, 28-64.
Wynn, K. (1990). Children’s understanding of counting. Cognition. 36,
155-193.
Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology. 24, 220-251.
Zimiles, H. (1963). A note on Piagets concept of conservation. Child
Development, 34, 691-695.