- ANDERSON , J.R. 1983 . The Architecture of Cognition , Cambridge, MA : Harvard University Press .
- BEHR , M.J. , HAREL , G. , POST , T.R. and LESH , R. 1992 . “ Rational number, ratio, and proportion ” . In Handbook of Research on Mathematics Teaching and Learning , Edited by: GROUWS , D.A. 296 – 333 . New York : Macmillan .
- BEHR , M.J. , HAREL , G. , POST , T. and LESH , R. 1993 . “ Rational numbers: toward a sematic analysis-emphasis on the operator construct ” . In Rational Numbers: an integration of research , Edited by: CARPENTER , T.P. , FENNEMA , E. and ROMBERG , T.A. 13 – 47 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- BEHR , M.J. , LESH , R. , POST , T.R. and SILVER , E. 1983 . “ Rational number concepts ” . In Acquisition of Mathematical Concepts and Processes , Edited by: LESH , R. and LANDAU , M. 92 – 127 . New York : Academic Press .
- BENTLER , P.M. 1990 . Comparative fit indexes in structural models . Psychological Bulletin , 107 : 238 – 246 .
- BRIGHT , G.W. , BEHR , M.J. , POST , T.R. and WACHSMUTH , I. 1988 . Identifying fractions on number lines . Journal for Research in Mathematics Education , 19 : 215 – 232 .
- BYRNES , J.P. and WASIK , B.A. 1991 . Role of conceptual knowledge in mathematical procedural learning . Developmental Psychology , 27 : 777 – 786 .
- CORREA , J. 1995 . Young children's understanding of the division concept , University of Oxford . Ph.D. thesis
- DUFOUR-JANVIER , B. , BEDNARZ , N. and BELANGER , M. 1987 . “ Pedagogical considerations concerning the problem of representation ” . In Problems of Representation in the Teaching and Learning Mathematics , Edited by: JANVIER , C. 109 – 122 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- ENGLISH , L. and HALFORD , G.S. 1995 . Mathematics Education: models and processes , Mahwah, NJ : Lawrence Erlbaum Associates .
- FISKE , D.W. and CAMPBELL , D.T. 1992 . Citations do not solve problem . Psychological Bulletin , 12 : 393 – 395 .
- GENTNER , D. 1983 . Structure mapping: a theoretical framework for analogy . Cognitive Science , 7 : 155 – 170 .
- GUTSTEIN , E. and ROMBERT , T.A. 1995 . Teaching children to add and subtract . Journal of Mathematical Behavior , 14 : 283 – 324 .
- HECHT , S.A. 1998 . Toward an information-processing account of individual differences in fraction skills . Journal of Educational Psychology , 90 : 545 – 559 .
- HIEBERT , J. and LEFEVRE , P. 1986 . “ Conceptual and procedural knowledge: an introductory analysis ” . In Conceptual and Procedural Knowledge: the case of mathematics , Edited by: HIEBERT , J. 1 – 27 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- HIEBERT , J. , WEARNE , D. and TABER , S. 1991 . Fourth graders' gradual construction of decimal fractions during instruction using different physical representations . The Elementary School Journal , 91 : 321 – 341 .
- JANVIER , C. , ed. 1987 . Problems of Representation in the Teaching and Learning Mathematics , Hillsdale, NJ : Lawrence Erlbaum Associates .
- KERSLAKE , D. 1986 . Fractions: children's strategies and errors: a report of the strategies and error in secondary mathematics project , Windsor : NFER-Nelson .
- KIEREN , T.E. 1989 . “ Personal knowledge of rational numbers: its intuitive and formal development ” . In Number Concepts and Operations in the Middle Grades , Edited by: HIEBERT , J. and BEHR , M. 162 – 181 . Reston, VA : National Council of Teachers of Mathematics . Hillsdale, NJ, Lawrence Erlbaum Associates
- KIEREN , T.E. 1993 . “ Rational and fractional numbers: from quotient fields to recursive understanding ” . In Rational Numbers: an integration of research , Edited by: CARPENTER , T.P. , FENNEMA , E. and ROMBERG , T.A. 49 – 84 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- LARSON , C.N. 1979 . Locating proper fractions on number lines: effects of length and equivalence . School Science and Mathematics , 53 : 423 – 428 .
- LESH , R. , BEHR , M. and POST , T. 1987 . “ Rational number relations and proportions ” . In Problems of Representation in the Teaching and Learning Mathematics , Edited by: JANVIER , C. 41 – 58 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- MACK , N.K. 1993 . “ Learning rational numbers with understanding: the case of informal knowledge ” . In Rational Numbers: an integration of research , Edited by: CARPENTER , T.P. , FENNEMA , E. and ROMBERT , T.A. 85 – 106 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- MACK , N.K. 1995 . Confounding whole-number and fraction concepts when building on informal knowledge . Journal for Research in Mathematics Education , 26 : 422 – 441 .
- MESSICK , S. 1989 . “ Validity ” . In Educational Measurement , Edited by: LINN , R.L. 13 – 103 . American Council on Education/Macmillan Publishing .
- MIX , S.K. , LEVINE , S.C. and HUTTENLOCHER , J. 1999 . Early fraction calculation ability . Developmental Psychology , 35 : 164 – 174 .
- NI , Y.J. Graphical Representations of Semantically Different Constructs: assessing children's understanding of rational number . Paper presented at the annual meeting of American Education Research Association . San Diego, CA. April ,
- NIEMI , D. 1996 . “ Instructional Influence on Content Area Explanations and Representational Knowledge: evidence for the construct validity of measures of principled understanding ” . In CSE Technical Report 403 , National Center for Research on Evaluation, Standards, and Student Testing Los Angeles, CA : University of California .
- NOVILLIS , C.F. 1976 . An analysis of the fraction concept into a hierarchy of selected subconcepts and the testing of the hierarchical dependencies . Journal for Research in Mathematics Education , May : 131 – 144 .
- NUNES , T. and BRYANT , P. 1996 . Children Doing Mathematics , Oxford : Blackwell .
- STREEFLAND , L. 1991 . Fractions in Realistic Mathematics Education: a paradigm of developmental research , The Netherlands : Kluwer Academic .
Educational Psychology
An International Journal of Experimental Educational Psychology
Volume 20, 2000 - Issue 2