一、中文部份
支毅君(1995)。分數概念教學的省思-由個案談起。國教之聲,28期(4),頁1-7。方吉正(1995)。教師如何幫助學生建立數學概念。國教天地,108期,頁48-51。
呂玉琴(1991a)。國小學生的分數概念:1/2V.S.2/4。國民教育,31期(11,12),頁10-15。呂玉琴(1991b)。分數概念:文獻探討。台北師院學報,4,頁575-603。
呂玉琴(1996)。國小教師的分數知識。臺北師院學報,9,頁427-460。呂玉琴(1997)。數與計算教材設計對分數概念的處理。國民小學數學科新課程概說(中年級)(頁137-150)。台北縣。臺灣省國民學校教師研習會。
林碧珍(1987)。數學教師應有的認識,國教世紀,新竹師專,第33期,頁45-63。林碧珍(1990)。從圖形表徵與符號表徵之間的轉換探討國小學生的分數概念。新竹師院學報第4期,頁295-347。林福來、黃敏晃(1993)。分數啟蒙課程的分析、批判與辯證。科學教育學刊,第1卷,第1期,頁1-27。李端明(1997)。分數詞之解題活動類型:一個四年級兒童之個案研究。國立嘉義師範學院初 等教育研究所碩士論文未出版。周筱亭(1986)。75年度師專數學科教授座談會實錄,板橋教師研習會。
周筱亭(1995)。數學新課程的趨勢。國民小學新課程標準的精神與特色,頁107-135。臺北: 臺灣省國民學校教師研習會。
吳國銘、洪碧霞、邱上真(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。
孫扶志(1995)。認知解題策略對國小數學低成就學童文字題解題能力之實驗研究。 測驗統計年刊,4,71-124。Richard R. Skemp林義雄、陳澤民合譯(1988)。數學學習心理學。台北市:九章出版社。
黃世傑(1998)。建構與教學中部地區科學教育簡訊,第三期,頁47-58。
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。陳忠志(1991)。學生錯誤概念對教學之啟示。物理教育,第二卷第六期,66-69頁。陳靜姿(1997)。國小四年級兒童等值分數瞭解之初探。國立台中師範學院初等教育研究所碩士論文。陳淑敏(1995)。Vygotsky「最近發展區」概念內涵的探討。屏東師院學報,第8卷,頁503-526。楊壬孝(1988)。國中小學生分數概念的發展。行政院國家科學委員會專題研究計畫成果報告(編號。NSC.77-0111J。S-003-09A)。執行單位。國立台灣師範大學。
楊瑞智(2000)。探究師院生之分數基本概念及分數概念的課室教學。台北市師範學院學報,31期,357─382頁
張鳳燕(1991)。從概念學習談國小數學教育。師友天地,80,頁24-29。
蔣治邦(1994)。由表徵觀點探討新教材數與計算活動的設計。國民小學數學科新課程概說,台北:臺灣省國民學校教師研習會。
蔣治邦(1997)。由表徵的觀點,闡述國民小學低年級數學科實驗課程數與計算。國民小學數學科新課程概說(低年級)(頁60-77),臺灣省國民學校教師研習會:
羅鴻翔(1980)。分數的數之發展。國教之友,第四五五期,頁37-41。
劉德明(1992)。科學學習理論和建構主義之研究。花師數理教育學報,第1期,頁109-138。歐瑞賢(1997)。國小學生比例推理能力動態評量之效益分析。國立台南師範學院國民教育研究所碩士論文。羅素貞(1996)。問題表徵與問題解決。屏東師院學報,第九期,頁149-176。游麗卿(1998)。從實作表現診斷學生乘除法的錯誤概念。測驗與輔導,149卷.8 ,頁3094-3098甯自強(1993)。分數的啟蒙~量的子分割活動的引入。教師之友,34(3),頁45-51.
二、英文部份
Anderson, J. R.& Bower, G. H (1975).Human associative memory.Washington:V.H.Winston.
Bergeron,.J.C. & Herscovics,H.(1987).Unit Fraction of a Continuous Whole .
The 11th International Conference Study for the Psychooogy of Matjematics Education.
Brumby,M.N(1984)Misconceptions about the concept of natural selection by medical biology students,Science Education,68(4),493-503
Behr. M. J., Harel.G., Post,T. Lesh.R.(1992). Rationa lnumber, ratio, and proportion.Handbook of research on mathematics teaching and learning,296-333.New York :Macmillan Publishing Company.
Behr. M. J.,, Post,T.& Lesh.R.(1983).Representions in mathematics learning and problem solving. In C.Janvier(Ed)Problems of represention in the teaching and learning of mathmatics,41-58.
Bell,M.(1979).What most people need from mathmatics ;teaching mathmatics so as to be useful,unpublished paper.
Booth, L .R.(1984),Algebra:Children’s Strategies and Errors,N.F.E.R-Nelson.
Bruke, M.,Hiber, N. & Rouberg T. A.(1977).The teaching of initial fraction concepts;Madison;Wisonsin research and development center for cognitive learning.
Buddoff, M.(1974).Learning potential and educability among the deucable mentally retarded .Final Report Project No.312312. Cambridge. MA Research Institute for Educational Problem Cambridge Mental Health Association.
.
Carlson, S., & Wiedle, K. H.(1978).Use of testing —the limits procedure in the assessment of intellectual capability in children with learning difficulity.American Journal of Deficiency,82,pp559-564.
Campione, J.C & Brown,A.L.(1985).Dynamic assessment :One approach and some initial
data.Teachnical report No.361. Nation Institute of Child Health and Human Development , Washington,DC(ERIC Document Reproduction Service No.ED 26973)
Clements, M.A & Lean, G. A.(1987) Discrete fraction concepts and cognitive structure , P.M.E.XII,pp.215-232.
Driver ,R.and Oldham ,V(1985)A constructivist approach to curriculum design in science .Studies in Science Education ,13,105-122.
Embretson, S. E.(1987)Toward development of a psychometric approach In C.S.Lidz(Ed),Dynamic assessment :An Interactional approach to evaluation learning potential ,147-170.New York: Guiford Press.
Feuerstein, R(1979).The dymamic assessmentof retarded performers:The learning potential assssment device .theory,instrument,and techniques.Baltimore,MP :Universits Park .
Figueras, O.,Filloy, E.& Volderuoros, M(1985).The Develo[ment of Spatial Imagination Ability and Contextualisation Strategies:Model Based on the Teaching of Fractions;The 9th International Conference for the psychology of Mathmatics Education.
Figueras , O., Filloy, E.& Volderuoros, M,( 1987 ).Some difficulties which obscure the Appropriation of the Fraction concept.The 11th International Conference for the psychology of Mathmatics Education.
Figueras , O.(1989).Two different Views of fractions:Fractionating and Operating. .The 13th International Conference for the psychology of Mathmatics Education.
Gilbert, J. K,Osborne,R.J & Fensham,P.J.(1982)children’s science and it’s consequence
For teaching .Science Education,66(4),pp623-633
Hart , K. M.(1981).Children’s Understanding of Mathmatics,11-16.John Murray Ltd.London.
Hart, K. M.(1984). Ratio:Children’s Strategies and Error,N.F.E.R-Nelson.
Hart, K. M.(1987).What are Equivalent Fractions?Mathmatics in School,September,pp.5-7.
Haywood, H. C.,Brown, A, L.,& Wingenfeld, S(1990).Dynamic approach to psycheducational assessment.School Psychology Review,19(4), pp411-422
Hiebert, J.& Tonnessen. L. H(1978).Development of the Fraction Concept in Two Psysival Contexts:An Exploratory Inverstigation.Journal for Research in Mathematics Education ,vol.9,pp374-378.
Hunting, R. P.(1986).Rachel’s Schemes for Constructing Fraction Knowledge .Educational Studies in Mathematics,17,49-66.
Janvier,C(1978).The interpretation of complex Cartesian graph representing situations-studied and teachiments.Doctorial dissertation .University of Nottingham.
Jecks P. (1981) : Conceptual issues in the teaching and learning of fractions,Jurnal research of mathmatics education 1981,pp.339-348
Kerslake, D.(1986).Fractions:Children’s Strategies and Error. N.F.E.R
Kerslake,D.(1986).Children’s Perception of Fractions;The 10th International Conference for the Psychology of Mathmatics Education .
Kaput, J.(1987).Representation Systems and Mathmatics. In C.Janvier(Ed)Problems of represention in the teaching and learning of mathmatics ,147-158.
Larry, W. E.,& Joseph, N. P.(1987).A teaching sequence from initial fraction concepts through the addition of unlike fraction .In M. Suydam(Ed.),Development computational skills. The 1978 Yearbook of N.C.T.M.(pp.129-147).Reston VA:N.C.T.M.
Larson, C. N.(1980).Locating Proper Fractions on Number Lines:Effect of Length and Equivalence.School Science and Mathematics,423-428.
Lesh, R.,Post, T. & Behr, M.(1987):Representations and Translations among
Representations in Mathematics Learning and Problem Solving. In C.Janvier(Ed)Problems of represention in the teaching and learning of mathmatics,33-40.
Ning,T.C.(1992).Children’s meanings of fractional number words.Unpublished doctoral dissertation.The University of Georgia,Athens,GA.
Palmer, S. E. (1977). Fundational aspects of cognitive representation. In E. Rosch & B. B. Loyd (Eds). Cognition and categorization. Hillsdale, NJ: Lawrence Erlbaum Association
Peter, P. C(1992).Even honors students have conceptual difficulties with physics,50(6),501-508
Piaget, J. ,Inhelder, B.& Szeminska(1960)A:The child’s conception of geomethmy New York: Basic books.
Pope,M and Gilbert, J (1983).Personal experience and the construction of knowledge in science .Science Education ,67,193-203.
Skemp,R.R.(1971).The psychology of learning mathmatics(1 st ed.)Harmondsworth:Penguin.
Van Hiele,P.M(1984).A Child”s thought and Grometry .In D.Fuys,D.Geddes,& R.Tischier,
Selected Writings of Dina Van Hiele-Geldof and Pierre M.van Hiele .237-241.
Columbus,OH:ERIC information Analysis Center for Science ,Mathematics,and Environment Education .(ERIC Document Reproduction Service No.ED287697)
Vygotsky, L. S.(1978)Mind in society:The Development of Higer Psychological Processes.Cambridge ,MA:Harvard University Press.