中文部分
幼獅數學大辭典編輯小組(1983)。幼獅數學大辭典(下卷)。臺北:幼獅文化事業公司。
朱建正(1997)。國小數學課程的數學理論基礎。國科會成果報告。未出版。
呂玉琴 ( 1991 ) 。分數概念:文獻探討。國立臺北師範學院學報,第4期,753-606。呂玉琴(1996)。國小教師的分數知識。臺北師院學報,9,427-460。呂玉琴(1998)。分數的四則運算與等值分數的設計。國立嘉義師範學院86 學年度數學教育研討會論文之10,165- 181
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分數概念。新竹師院學報,4,295-347。許天維(1995)。數學試題分析法-以「八十一學年度國民教育階段國小數科學生基本學習成就評量」的分析為例。高雄:大漢唐有限公司。
教育部(2003):國民中小學九年一貫課程綱要--數學學習領域。教育部。
楊壬孝(1988)。國中小學分數概念的發展。行政院國家科學委員會專題研究計畫成果報告(編號:NSC-77-0111-S-003-09A)。執行單位:國立臺灣師範大學數學系。
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。臺北市立師範學院學報,31,357-382。
鄭昭明(1993)。認知心理學-理論與實踐。臺北: 桂冠。
劉秋木(1996)。國小數學科教學研究。臺北: 五南圖書出版公司。
劉祥通、周立勳(2001)。發展國小教師數學教學之佈題能力:以分數乘除法教學為例。科學教育學刊,第九卷第一期,15- 34。
簡茂發、劉湘川、許天維、林原宏(1995):試題關聯結構分析法在國小高年級學生乘除文字題列式之分析研究。測驗年刊,42,113-156。英文部分
Airasian, P. W. & Bart, W. M.(1973). Ordering theory: A new and useful measurementmodel. Journal of Educational Technology, Vol.5,pp.56-60.
Aksu , M. (1997). Student performance in dealing with fractions. The Journal of
educational research 90(6), 375-380 .
Ashlock, R. D. (1990). Error patterns in computation. New York:Macmillan.
Barash, A., & Klein, R. (1996). Seventh grades students’ algorithmic intuitive and
formal knowledge of multiplication and division of non negative rational
numbers. In L. Puig& A. Gutierrez.(Eds.), Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education(Vol. 2.
pp.35-42). Valencia. Spain:University of Valencia.
Behr,M.J.& Post,T.R.(1988).Teaching rational number and decimal concepts. In T. R.Post (Eds.),Teaching mathematics in grades K-8,190-229. Boston, MA: Allyn and Bacon.
Behr, M.J., Harel, G., Post, T., & Lesh, R.(1992). Rational number, ratio, and proportion. In D.A. Grouws(ED), Handbook of Research on Mathematics Teaching and Learning, 296-333.
Brueckner,L.J.& Melby,E.O.(1931). Diagnostic and Remedial Teaching, Boston: Houghton Miffin Co.
Corwin,R.B.,Russell,S.J.,& Tierney,C.C.(1990).Seeing Fractions: A unit for the upper elementary grades. Developed by TERC (Technical Education Research Centers,Inc.) for the California Department of Education.
Cummins, D. D.(1991). Children’s Interpretations of Arithmetic Word Problems.
Cognition and Instruction, 8(3), 261-289.
Dickson, L., Brown, M., & Gibson, O. (1984). Child Learning Mathematics: A
Teacher’s Guide to Recent Research (pp.274-298).Oxford, Great Britain,
England: Schools Council Publications.
Fendel, D. M. (1987). Understanding the structure of elementary school mathematics.
Newton, MA: Allyn & Bacon.
Fischbein, E., Deri, M., Nello, M., & Marino, M. (1985). The role of implicit
models in solving verbal problems in multiplication and division. Journal for
research in Mathematics Education, 16, 3-17.
Greer, B. (1992). Multiplication and division as models of situations.In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning, 276 – 295. MacmillanPublishing Company.
Hart, K. M. (Ed.). (1981). Children’s understanding of Mathematics, 11-16. London:
John Murray.
Hopkins, K. D. (1998). Educational and psychological measurement and evaluation (8th ed.). MA: Allyn & Bacon
Kieren,T.E.(ed).(1980).The Rational Number Cunstruct-its Elements and Mechanisms,7-15.
Lankford,L.k.(1972).Final report:Some computational Strategies of seventh grade pupils ,Charlottesville,VA:University of Virginia.(ERIC Document Reproduction Service No.Ed 069 496).
Painter,R.R.(1989).A comparsion of the procedural error patterns,scores,and other variables,of select ed groups of university and eight-grade studentd in Mississippi on a test involving arithmetic operation on fractions.( Doctoraldissertation,University of Southern Mississppi,1988)
Payne, J. N. (1976). Review of research on fraction. In R. Lesh(Ed.).Number and
measurement(pp.145-187). Athens: University of Georgia.
Sinicrope, R., Mick, H. W., &Kolb, J. R. (2002). Interpretations of Fraction Division.
InB. Litwiller & G. Bright (Ed.), Making Sense of Fractions, Ratios, and
Proportions(pp.153-161). Reston,VA: NCTM.
Van Hiele, P. M.(1986). Structure and insight: A theory of mathematics education.Orlando, FL:Academic Press.
Vergnaud, G (1983). Multiplicative Structures. In R. Lesh & M. Landau (Eds.). Acquisition of mathematics concepts and procedures (pp. 127-174). New York : Academic Press.