1,100
Views
54
CrossRef citations to date
0
Altmetric
Articles

Mathematics Teaching and Learning as a Mediating Process: The Case of Tape Diagrams

Pages 374-406 | Published online: 21 Oct 2008

REFERENCES

  • Andersen , M. 2007 . Introduction of a new construct: The conceptual tool “Flexibility.” . The Montana Mathematics Enthusiast , 4 ( 2 ) : 230 – 250 .
  • Beckman , S. 2004 . Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4–6 texts used in Singapore . The Mathematics Educator , 14 ( 1 ) : 42 – 46 .
  • Boaler , J. 1994a . When do girls prefer football to fashion? An analysis of female underachievement in relation to “realistic” mathematics contexts . British Educational Research Journal , 20 ( 5 ) : 551 – 564 .
  • Boaler , J. 1994b . The role of contexts in the mathematics classroom: Do they make mathematics more “real”? . For the Learning of Mathematics , 13 ( 2 ) : 12 – 17 .
  • Boaler, J., Cleare, N., Dieckmann, J. Fiori, N., Segunpta-Irving, T., & Shahan, E. (2008). Making mathematics “colorful & bright”—how students became more engaged and successful during five weeks of mathematics class. (Manuscript under preparation).
  • Brown , J. , Collins , A. and Duguid , P. 1989 . Situated cognition and the culture of learning . Educational Researcher , 18 ( 1 ) : 32 – 42 .
  • Carpenter , T. , Fennema , E. , Franke , M. L. , Levi , L. and Empson , S. B. 1999 . Children's mathematics: Cognitively guided instruction , Portsmouth, NH : Heinemann .
  • Charles , R. I. , Crown , W. , Fennell , F. , Caldwell , J. H. , Cavanagh , M. , Chancellor , D. , Ramirez , A. B. , Ramos , J. F. , Sammons , K. , Schielack , J. F. , Tate , W. , Thompson , M. and Van de Walle , J. A. 2004 . Scott Foresman–Addition Wesley mathematics , Glenview, IL : Pearson Education .
  • Cooper , B. and Dunne , M. 1998 . Anyone for tennis? Social class differences in children's responses to national curriculum mathematics testing . The Sociological Review , 46 ( 1 ) : 115 – 148 .
  • Forman , E. A. , Mccormick , D. E. and Donato , R. 1997 . Learning what counts as a mathematical explanation . Linguistics and Education , 9 ( 4 ) : 313 – 339 .
  • Fosnot , C. T. and Dolk , M. 2001 . Young mathematicians at work: Constructing the number system, addition and subtraction , Portsmouth, NH : Heinemann .
  • Freudenthal , H. F. 1973 . Mathematics as an educational task , Dordrecht : Reidel .
  • Freudenthal , H. F. 1978 . Weeding and sowing. Preface to a science of mathematical education , Dordrecht : Reidel .
  • Freudenthal , H. F. 1991 . Revisiting mathematics education. China lectures , Dordrecht : Kluwer .
  • Fuson , K. C. 2003 . “ Developing mathematical power in whole number operations ” . In A research companion to Principles and Standards for school mathematics , Edited by: Kilpatrick , J. , Martin , W. G. and Shifter , D. 68 – 94 . Reston, VA : National Council of Teachers of Mathematics .
  • Fuson , K. C. and Murata , A. 2007 . Integrating the NRC principles and the NCTM process standards: Cognitively guided teaching to individualize instruction within whole-class activities and move all students within their learning path . National Council of Supervisors of Mathematics Journal , 10 ( 1 ) : 72 – 91 .
  • Gakkotosho Publication . 2005 . Study with your friends: Mathematics for elementary school , Tokyo : Author .
  • Gallimore , R. and Tharp , R. G. 1990 . “ Teaching mind in society: Teaching, schooling, and literate discourse ” . In Vygotsky and education: Instructional implications and applications of sociohistorical psychology , Edited by: Moll , L. NY : Cambridge University Press .
  • Gal'perin , P. 1969 . “ Stages in the development of mental acts ” . In A handbook of contemporary soviet psychology , Edited by: Cole , M. and Maltzman , I. NY : Basic Books .
  • Guin , D. , Ruthven , K. and Trouche , L. , eds. 2006 . The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument , Netherlands : Springer .
  • Horizon Research. (2002). 2000 National survey of science and mathematics education: Status of elementary school mathematics teaching. www.horizon-research.com (Accessed: 9 December 2006 ).
  • Hufferd-Ackles , K. , Fuson , K. and Sherin , M. 2004 . Describing levels and components of a math-talk learning community . Journal for Research in Mathematics Education , 35 ( 2 ) : 81 – 116 .
  • Japanese Ministry of Education, Culture, Sports, Science, and Technology. (2006). General description of textbook system. http://www.mext.go.jp/a_menu/shotou/kyoukasho/gaiyou/04060901.htm (Accessed: 15 December 2006 ).
  • Lave , J. 1988 . Cognition in practice: Mind, mathematics, and culture in everyday life (learning in doing) , NY : Cambridge University Press .
  • Lerman , S. 1996 . Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm . Journal for Research in Mathematics Education , 27 ( 2 ) : 133 – 150 .
  • Lerman , S. 2000 . A case of interpretations of ‘social’: A response to Steffe and Thompson . Journal for Research in Mathematics Education , 31 ( 2 ) : 210 – 227 .
  • Lewis , C. , Perry , R. and Murata , A. 2006 . What is the role of the research in an emerging innovation: The case of lesson study . Educational Researcher , 35 ( 3 ) : 3 – 14 .
  • Lubienski , S. T. 2000 . Problem solving as a means toward mathematics for all: An exploratory look through a class lens . Journal of Research in Mathematics Education , 31 ( 4 ) : 454 – 482 .
  • Luria , A. R. 1973 . The working brain , Harmondsworth, , UK : Penguin .
  • 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 ( 2 ) : 443 – 460 .
  • Moll , L. 1990 . Vygotsky and education: Instructional implications and applications of sociohistorical psychology , NY : Cambridge University Press .
  • Means , B. and Knapp , M. S. 1991 . Cognitive approaches to teaching advanced skills to educationally disadvantaged students . Phi Delta Kappan , 73 : 282 – 289 .
  • Murata , A. 2004 . Paths to learning ten-structured understanding of teen sums: Addition solution methods of Japanese grade 1 students . Cognition and Instruction , 22 ( 2 ) : 185 – 218 .
  • Murata, A. (2008). Assisting mental math methods through visual supports, problem sequencing, and learning of conceptual prerequisites. Manuscript in preparation.
  • Murata , A. and Fuson , K. C. 2006 . Teaching as assisting individual constructive paths within an interdependent class learning zone: Japanese first graders learning to add using ten . Journal for Research in Mathematics Education. , 37 ( 5 ) : 421 – 456 .
  • Murata , A. , Otani , N. , Hattori , N. and Fuson , K. C. 2004 . “ The NCTM Standards in a Japanese primary classroom: Valuing students' diverse ideas and learning paths ” . In National Council of Teachers of Mathematics 2004 Yearbook: Perspectives on the teaching of mathematics , Edited by: Rubenstein , R. 82 – 95 . Reston, VA : National Council of Teachers of Mathematics .
  • National Center for Education Statistics . 2003 . Teaching mathematics in seven countries: Results from the TIMSS 1999 video study , Washington, DC : Author .
  • National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : author .
  • Pape , S. and Tchshanov , M. A. 2001 . The role of representation(s) in developing mathematical understanding . Theory into Practice , 40 ( 2 ) : 118 – 127 .
  • Pirie , S. and Kieren , T. 1994 . Growth in mathematical understanding: How can we characterize it and how can we represent it? . Educational Studies in Mathematics , 26 : 61 – 86 .
  • Programme for International Student Assessment . 2003 . First results from PISA 2003 , Paris, , France : Author .
  • Remillard , J. T. 2005 . Examining key concepts in research on teachers' use of mathematics curricula . Review of Educational Research , 75 ( 2 ) : 211 – 246 .
  • Rogoff , B. 1990 . Apprenticeship in thinking: Cognitive development in social context , NY : Oxford University Press .
  • Saxe , G. 1991 . Culture and cognitive development: Studies in mathematical understanding , Hillsdale, NJ : Erlbaum .
  • Schmidt , W. H. , McKnight , C. C. and Raizens , S. A. 1997 . A splintered vision: An investigation of U.S. science and mathematics education , Boston : Kluwer .
  • Sfard , A. 2000 . On reform movement and the limits of mathematical discourse . Mathematical Thinking and Learning , 2 ( 3 ) : 157 – 189 .
  • Stevenson , H. W. and Bartsch , K. 1991 . “ An analysis of Japanese and American textbooks in mathematics ” . In Japanese educational productivity , Edited by: Leetsma , R. and Wallberg , H. Ann Arbor : Center for Japanese Studies .
  • Stigler , J. , Fuson , K. , Ham , K. and Kim , E. 1986 . An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks . Cognition and Instruction , 3 : 153 – 171 .
  • Tharp , R. G. and Gallimore , R. 1988 . Rousing minds to life: Teaching, learning, and schooling in social context , Cambridge, MA : Cambridge University Press .
  • van de Veer , R. and Valsiner , J. 1991 . Understanding Vygotski: A quest for synthesis , Cambridge, MA : Blackwell .
  • Verllion , P. and Rabardel , P. 1995 . Cognition and artifacts: A contribution of the study of thought in relation to instrument activity . European Journal of Psychology in Education , 9 ( 3 ) : 77 – 101 .
  • Vygotski , L. S. 1978 . Mind in society: The development of higher psychological processes , Cambridge, MA : Harvard University Press .
  • Vygotski , L. S. 1999 . Thought and language , Edited by: Kozulin , A. Cambridge, MA : The MIT Press . (A. Kozulin, trans.), (Original work published in 1986.).
  • Wertsch , J. V. 1991 . Voices of the mind: A sociocultural approach to mediated action , Cambridge, MA : Harvard University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.