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Articles

A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries

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Pages 117-151 | Published online: 25 Mar 2010

REFERENCES

  • Ball , D. L. 1993 . “ Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions ” . In Rational numbers: An integration of research , Edited by: Carpenter , T. P. , Fennema , E. and Romberg , T. A. 157 – 195 . Hillsdale, NJ : Lawrence Erlbaum .
  • Barry , K. , Manning , P. , O'Neill , S. and Roche , T. 2003 . Mathemagic 5 , Dublin, , Ireland : C.J. Fallon .
  • Baturo , A. R. . Empowering Andrea to help year-5 students construct fraction understanding . Proceedings of the 28th Conference for the Psychology of Mathematics Education . Bergen. Edited by: Hoines , M. J. and Fuglestad , A. B. Vol. 2 , pp. 95 – 102 . University College .
  • Beck , I. , McKeown , M. G. and Gromoll , E. W. 1989 . Learning from social studies texts . Cognition and Instruction , 6 : 99 – 158 .
  • Behr , M. J. , Harel , G. , Post , T. and Lesh , R. 1993 . “ Rational numbers: Toward a semantic analysis ” . In Rational numbers: An integration of research , Edited by: Carpenter , T. P. , Fennema , E. and Romberg , T. A. 13 – 47 . Hillsdale, NJ : Lawrence Erlbaum .
  • Behr , M. , Lesh , R. , Post , T. and Silver , E. 1983 . “ Rational number concepts ” . In Acquisition of mathematics concepts and processes , Edited by: Lesh , R. and Landau , M. 91 – 125 . New York : Academic .
  • Boulet , G. 1998 . Didactical implications of children's difficulties in learning the fraction concept . Focus on Learning Problems in Mathematics , 20 ( 4 ) : 19 – 34 .
  • Brousseau , G. 1997 . Theory and didactical situations in mathematics: Didactique des mathematiques 1970–1990 , Edited by: Balacheff , N. , Cooper , M. , Sutherland , R. and Warfield , V. Dordrecht, , The Netherlands : Kluwer .
  • Carpenter , T. P. , Coburn , T. G. , Reys , R. E. and Wilson , J. W. 1976 . Notes from national assessment: Addition and multiplication with fractions . Arithmetic Teacher , 23 : 137 – 141 .
  • Carpenter , T. P. , Fennema , E. and Romberg , T.A. 1993 . “ Toward a unified discipline of scientific inquiry ” . In Rational numbers: An integration of research , Edited by: Carpenter , T. P. , Fennema , E. and Romberg , T.A. 1 – 11 . Hillsdale, NJ : Lawrence Erlbaum .
  • Charalambous , C. Y. , Delaney , S. , Hsu , H. and Mesa , V. . Opportunities to learn fractions in fourth-grade elementary classes: Insights from an analysis of textbooks used in Cyprus, Ireland, and Taiwan . Poster presented at the Annual Meeting of the American Educational Research Association . Chicago, Illinois.
  • Charalambous , C. Y. and Pitta-Pantazi , D. 2007 . Drawing on a theoretical model to study students' understanding of fractions . Educational Studies in Mathematics , 64 : 293 – 316 .
  • Courtney , D. 2002 . Action maths: 5th class , Dublin, , Ireland : Folens .
  • Davis , J. D. 2007 . Real-world contexts, multiple representations, student-invented terminology, and y-intercept . Mathematical Thinking and Learning , 9 : 387 – 418 .
  • Delaney , S. , Charalambous , Y. C. , Hsu , H.-Y. and Mesa , V. . The treatment of addition and subtraction of fractions in Cypriot, Irish, and Taiwanese textbooks . Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education . Seoul. Edited by: Woo , J. H. , Lew , H. C. , Park , K. S. and Seo , D. Y. Vol. 2 , pp. 193 – 200 . The Korea Society of Educational Studies in Mathematics .
  • Dewey , J. 1906 . The child and the curriculum , Chicago : The University of Chicago Press .
  • Freeman , D. J. and Porter , A. C. 1989 . Do textbooks dictate the content of mathematics instruction in elementary schools? . American Educational Research Journal , 26 : 403 – 421 .
  • Fuson , K. C. 1992 . “ Research on whole number addition and subtraction ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. A. 243 – 275 . New York : MacMillan .
  • Fuson , K. C. , Stigler , J. W. and Bartsch , K. 1988 . Grade placement of addition and subtraction topics in Japan, mainland China, the Soviet Union, Taiwan, and the United States . Journal for Research in Mathematics Education , 19 : 449 – 456 .
  • Government of Ireland . 1999 . Primary school curriculum: Mathematics , Dublin, , Ireland : The Stationery Office .
  • Haggarty , L. and Pepin , B. 2002 . An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? . British Educational Research Journal , 28 : 567 – 590 .
  • Herbel-Eisenmann , B. A. 2007 . From intended curriculum to written curriculum: Examining the “voice” of a mathematics textbook . Journal for Research in Mathematics Education , 38 : 344 – 369 .
  • Herbst , P. 1995 . The construction of the real number system in textbooks: A contribution to the analysis of discursive practices in mathematics , Athens : Unpublished master's thesis. University of Georgia .
  • Hiebert , J. , Gallimore , R. , Garnier , H. , Givvin , K. B. , Hollingsworth , H. Jacobs , J. K. 2003 . Teaching mathematics in seven countries: Results from the TIMSS 1999 video study, (NCES 2003-013 Revised) , Washington, DC : U.S. Department of Education, National Center for Education Statistics .
  • Howson , G. 1995 . Mathematics textbooks: A comparative study of grade-8 texts , Vancouver, , Canada : Pacific Education Press .
  • Huang , R. and Li , Y. 2009 . Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China: A case study . ZDM—The International Journal on Mathematics Education , 41 : 297 – 309 .
  • Kaur , B. 2009 . Characteristics of good mathematics teaching in Singapore grade-8 classrooms: A juxtaposition of teachers' practice and student perception . ZDM—The International Journal on Mathematics Education , 41 : 333 – 347 .
  • Keijzer , R. and Terwel , J. 2001 . Audrey's acquisition of fractions: A case study into the learning of formal mathematics . Educational Studies in Mathematics , 47 : 53 – 73 .
  • Kieren , T. E. 1976 . “ On the mathematical, cognitive, and instructional foundations of rational numbers ” . In Number and measurement: Papers from a research workshop , Edited by: Lesh , R. 101 – 144 . Columbus, OH : ERIC/SMEAC .
  • Lamon , S. J. 1999 . Teaching fractions and ratios for understanding , Mahwah, NJ : Erlbaum .
  • Lamon , S. L. 2001 . “ Presenting and representing: From fractions to rational numbers ” . In The roles of representations in school mathematics , Edited by: Cuoco , A. and Curcio , F. 146 – 165 . Reston, VA : National Council of Teachers of Mathematics .
  • Landis , J. R. and Koch , G. G. 1977 . The measurement of observer agreement for categorical data . Biometrics , 33 : 159 – 174 .
  • Leinhardt , G. 2001 . “ Instructional explanations: A commonplace for teaching and location for contrast ” . In Handbook for research on teaching , 4th , Edited by: Richardson , V. 333 – 357 . Washington, DC : American Educational Research Association .
  • Li , K. 2004 . Mathematics 4 (vol. 1) , Taipei, , Taiwan : Han Lin .
  • Li , K. 2005 . Mathematics 4 (vol. 2) , Taipei, , Taiwan : Han Lin .
  • Li , Y. 2000 . A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks . Journal for Research in Mathematics Education , 31 : 234 – 241 .
  • Lin , P.-J. and Li , Y. 2009 . Searching for good mathematics instruction at primary school level valued in Taiwan . ZDM—The International Journal on Mathematics Education , 41 : 363 – 378 .
  • Mack , N. K. 2001 . Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions . Journal for Research in Mathematics Education , 32 : 267 – 295 .
  • Marshall , S. P. 1995 . Schemas in problem solving , New York : Cambridge University Press .
  • Mayer , R. E. , Sims , V. and Tajika , H. 1995 . A comparison of how textbooks teach mathematical problem solving in Japan and the United States . American Educational Research Journal , 32 : 443 – 460 .
  • McDonnell , L. M. 1995 . Opportunity to learn as a research concept and a policy instrument . Educational Evaluation and Policy Analysis , 17 : 305 – 322 .
  • Mesa , V. 2004 . Characterizing practices associated with functions in middle school textbooks: An empirical approach . Educational Studies in Mathematics , 56 : 255 – 286 .
  • Mesa , V. . Instructors and textbooks . Paper presented at the 10th Conference of the SIG/MAA Research in Undergraduate Mathematics Education . San Diego, CA. February ,
  • Mesa , V. 2010 . Strategies for controlling the work in mathematics textbooks for introductory calculus . Research in Collegiate Mathematics Education , 16 : 235 – 265 .
  • Ministry of Education . 2000 . Grades 1–9 curriculum temporary guidelines , Taipei, , Taiwan : Author .
  • Ministry of Education and Culture . 1998 . Mathematics for fourth grade (Vol. 1–4) , Nicosia, Cyprus : Author .
  • Moss , J. and Case , R. 1999 . Developing children's understanding of the rational numbers: A new model and an experimental curriculum . Journal for Research in Mathematics Education , 30 : 122 – 147 .
  • Mou , L. and Yang , J. 2004 . Mathematics 4 (vol. 1) , Taipei, , Taiwan : Kang Hsuan .
  • Mou , L. and Yang , J. 2005 . Mathematics 4 (vol. 2) , Taipei, , Taiwan : Kang Hsuan .
  • Mullis , I. , Martin , M. O. , Gonzalez , E. J. and Chrostowski , S. J. 2004 . TIMSS 2003 International mathematics report , Chestnut Hill, MA : Lynch School of Education & Boston College .
  • National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : Author .
  • Newton , D. P. and Newton , L. D. 2006 . Could elementary mathematics textbooks help give attention to reasons in the classroom? . Educational Studies in Mathematics , 64 : 69 – 84 .
  • Pang , J. S. 2009 . Good mathematics instruction in South Korea . ZDM—The International Journal on Mathematics Education , 41 : 349 – 362 .
  • Patton , M. Q. 2002 . Qualitative research and evaluation methods , 3rd , Thousand Oaks, CA : Sage .
  • Pepin , B. , Haggarty , L. and Keynes , M. 2001 . Mathematics textbooks and their use in English, French and German classrooms: A way to understand teaching and learning cultures . ZDM Mathematics Education , 33 : 158 – 174 .
  • Raths , L. E. 1932 . The grade-placement of addition and subtraction of fractions . Educational Research Bulletin , 11 ( 2 ) : 29 – 38 .
  • Remillard , J. T. 2005 . Examining key concepts in research on teachers' use of mathematics curricula . Review of Educational Research , 75 : 211 – 246 .
  • Remillard , J. T. 2009 . “ Part II-Commentary: Considering what we know about the relationship between teachers and curriculum materials ” . In Mathematics teachers at work: Connecting curriculum materials and classroom instruction , Edited by: Remillard , J. T. , Herbel-Eisenmann , B. A. and Lloyd , G. M. 85 – 92 . New York : Routledge .
  • Renkl , A. 2002 . Worked-out examples: Instructional explanations support learning by self-explanations . Learning and Instruction , 12 : 529 – 556 .
  • Resnick , L. B. , Nesher , P. , Leonard , F. , Magone , M. , Omanson , S. and Peled , I. 1989 . Conceptual bases of arithmetical errors: The case of decimal fractions . Journal for Research in Mathematics Education , 20 : 8 – 27 .
  • Rezat , S. . A model of textbook use . Proceedings of the 30th Conference of the international group of the Psychology of Mathematics Education . Prague. Edited by: Novotnå , J. , Moraovå , H. , Kråtkå , M. and Stehlíkovå , N. Vol. 4 , pp. 409 – 416 . Charles University .
  • Schmidt , W. H. , McKnight , C. C. , Valverde , G. , Houang , R. T. and Wiley , D. E. 1997 . Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics , Dordrecht, , The Netherlands : Kluwer .
  • Schoenfeld , A. H. 1999 . Looking toward the 21st Century: Challenges of educational theory and practice . Educational Researcher , 28 : 4 – 14 .
  • Sfard , A. 1991 . On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 : 1 – 36 .
  • Smith , J. P. 2002 . “ The development of students' knowledge of fractions and ratios ” . In Making sense of fractions, ratios, and proportions , Edited by: Litwiller , B. and Bright , G. 3 – 17 . Reston, VA : National Council of Teachers of Mathematics .
  • Stein , M. K. , Grover , B. W. and Henningsen , M. 1996 . Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms . American Educational Research Journal , 33 : 455 – 488 .
  • Stein , M. K. , Smith , M. S. , Henningsen , M. and Silver , E. A. 2000 . Implementing standards-based mathematics instruction , New York : Teachers College Press .
  • Stevenson , H. W. and Bartsch , K. 1992 . “ An analysis of Japanese and American textbooks in mathematics ” . In Japanese educational productivity , Edited by: Leetsma , R. and Walberg , H. 103 – 133 . Ann, Arbor : Center for Japanese Studies, University of Michigan .
  • Stigler , J. W. and Hiebert , J. 1999 . The teaching gap , New York : Free Press .
  • Strauss , A. and Corbin , J. 1998 . Basics of qualitative research: Techniques and procedures for developing grounded theory , Thousand Oaks, CA : Sage .
  • Tate , W. F. and Rousseau , C. 2006 . “ Engineering change in mathematics education ” . In Second handbook for research in mathematics teaching and learning , Edited by: Lester , F. K. 1209 – 1246 . Reston, VA : National Council of Teachers of Mathematics .
  • Thompson , P. W. and Saldanha , L. 2003 . “ Fractions and multiplicative reasoning ” . In A research companion to Principles and Standards of School Mathematics , Edited by: Kilpatrick , J. , Martin , W. G. and Schifter , D. 95 – 113 . Reston, VA : National Council of Teachers of Mathematics .
  • Valverde , G. A. , Bianchi , L. J. , Wolfe , R. G. , Schmidt , W. H. and Houang , R. T. 2002 . According to the book: Using TIMSS to investigate the translation of policy into practice in the world of textbooks , Dordrecht, , The Netherlands : Kluwer .
  • Verschaffel , G. , Greer , B. and Torbeyns , J. 2006 . “ Numerical thinking ” . In Handbook of research on the psychology of mathematics education: Past, present, and future , Edited by: Gutierrez , A. and Boero , P. 51 – 82 . Rotterdam, , The Netherlands : Sense Publishers .
  • Vinner , S. , Hershkowitz , R. and Bruckheimer , M. 1981 . Some cognitive factors as causes of mistakes in the addition of fractions . Journal for Research in Mathematics Education , 12 : 70 – 76 .
  • Watson , A. and Mason , J. 2005 . Mathematics as a constructive activity: Learners generating examples , Mahwah, NJ : Lawrence Erlbaum .

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