3,026
Views
39
CrossRef citations to date
0
Altmetric
Original Articles

A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness

, , , , &
Pages 381-395 | Published online: 17 Oct 2011

REFERENCES

  • Bednarz , N. and Janvier , B. 1996 . “ Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic ” . In Approaches to algebra: Perspectives for research and teaching , Edited by: Bednarz , N. , Kieran , C. and Lee , L. 115 – 136 . Dordrecht, , The Netherlands : Kluwer Academic .
  • Brenner , M. E. , Mayer , R. E. , Moseley , B. , Brar , T. , Duran , R. , Smith Reed , B. and Webb , D. 1997 . Learning by understanding: The role of multiple representations in learning algebra . American Educational Research Journal , 34 : 663 – 689 .
  • Cai , J. and Knuth , E. J. 2005 . The development of students’ algebraic thinking in earlier grades from curricular, instructional, and learning perspectives . Zentralblatt fuer Didaktik der Mathematik , 37 ( 1 ) : 1 – 4 .
  • Cai , J. , Lew , H. C. , Morris , A. , Moyer , J. C. , Ng , S. F. and Schmittau , J. 2004 . The development of students’ algebraic thinking in earlier grades: A cross-cultural comparative perspective April Paper presented at the American Educational Research Association Annual Meeting, San Diego, CA
  • Carpenter , T. P. , Levi , L. , Franke , M. L. and Zeringue , J. K. 2005 . Algebra in elementary school: Developing relational thinking . Zentralblatt fuer Didaktik der Mathematik , 37 ( 1 ) : 53 – 59 .
  • Carraher , D. W. , Schliemann , A. D. , Brizuela , B. and Earnest , D. 2006 . Arithmetic and algebra in early mathematics education . Journal for Research in Mathematics Education , 37 : 87 – 115 .
  • Cawley , J. and Parmar , R. S. 2003 . Mathematics assessment for students with mild disabilities, frameworks and practices . Learning Disabilities: A Contemporary Journal , 1 : 20 – 26 .
  • Charbonneau , L. 1996 . “ From Euclid to Descartes: Algebra and its relation to geometry ” . In Approaches to algebra: Perspectives for research and teaching , Edited by: Bednarz , N. , Kieran , C. and Lee , L. 15 – 37 . Dordrecht, , The Netherlands : Kluwer Academic .
  • Chen , Z. 1999 . Schema induction in children's analogical problem solving . Journal of Educational Psychology , 91 : 703 – 715. .
  • Connolly , A. J. 1998 . Keymath revised/normative update , Circle Pines, MN : American Guidance Service .
  • Curcio , F. and Schwartz , S. L. 1997 . What does algebraic thinking look like and sound like with preprimary children? . Teaching Children Mathematics , 3 : 296 – 300 .
  • Friendly , M. 2000 . Power analysis for ANOVA designs Retrieved from http://davidmlane.com/hyperstat/power.html
  • Fuchs , L. S. , Fuchs , D. , Finelli , R. , Courey , S. J. and Hamlett , C. L. 2004 . Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems . American Educational Research Journal , 41 : 419 – 445 .
  • Fuchs , L. S. , Fuchs , D. , Prentice , K. , Burch , M. , Hamlett , C. L. , Owen , R. and Jancek , D. 2003 . Explicitly teaching for transfer: Effects on third-grade students’ mathematical problem solving . Journal of Educational Psychology , 95 : 293 – 305 .
  • Fuchs , L. S. , Seethaler , P. M. , Powell , S. R. , Fuchs , D. , Hamlett , C. and Fletcher , J. M. 2008 . Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties . Exceptional Children , 74 : 155 – 173 .
  • Gick , M. and Holyoak , K. H. 1983 . Schema induction and analogical transfer . Cognitive Psychology , 15 : 1 – 38 .
  • Goldin , G. A. 1982 . “ The measure of problem-solving outcomes ” . In Mathematical problem solving: Issues in research , Edited by: Lester , F. K. and Garofalo , J. 87 – 101 . Philadelphia, PA : The Franklin Institute Press .
  • Greer , B. 1992 . “ Multiplication and division as models of situations ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. 276 – 295 . New York, NY : Macmillan .
  • Hamson , M. 2003 . “ The place of mathematical modeling in mathematics education ” . In Mathematical modeling: A way of life , Edited by: Lamon , S. J. , Parker , W. A. and Houston , K. 215 – 255 . Chichester, , UK : Horwood .
  • Harel , G. and Confrey , J. 1994 . The development of multiplicative reasoning in the learning of mathematics , Albany : State University of New York Press .
  • Hedges , L. and Olkin , I. 1985 . Statistical methods for meta-analysis , Orlando, FL : Academic Press .
  • Jitendra , A. K. , Griffin , C. C. , Deatline-Buchman , A. and Sczesniak , E. 2007 . Mathematical word problem solving in third-grade classroom . The Journal of Educational Research , 100 : 283 – 302 .
  • Jitendra , A. K. , Griffin , C. C. , McGoey , K. , Gardill , M. C. , Bhat , P. and Riley , T. 1998 . Effects of mathematical word problem solving by students at risk or with mild disabilities . The Journal of Educational Research , 91 : 345 – 355 .
  • Jonassen , D. H. 2003 . Designing research-based instruction for story problems . Educational Psychology Review , 15 : 267 – 296 .
  • Kazdin , A. E. 1982 . Single-case research designs: Methods for clinical and applied settings , New York, NY : Oxford University Press .
  • Kilpatrick , J. , Swafford , J. and Findell , B. 2001 . Adding it up: Helping children learn mathematics , Washington, DC : National Academy Press .
  • Maccini , P. , McNaughton , D. and Ruhl , K. L. 1999 . Algebra instruction for students with learning disabilities: Implications from a research review . Learning Disability Quarterly , 22 : 13 – 126 .
  • Maletsky , E. M. 2004 . Harcourt math , Indiana ed. , Chicago, IL : Harcourt .
  • Mevarech , Z. R. and Kramarski , B. 2004 . Mathematical modeling and meta-cognitive instruction Unpublished manuscript. Retrieved from http://www.icme-organisers.dk/tsg18/S32MevarechKramarski.pdf
  • Moses , B. 1997 . Algebra for a new century . Teaching Children Mathematics , 3 : 264 – 265 .
  • Moyer , J. C. , Moyer , M. B. , Sowder , L. and Threadgill-Sowder , J. 1984 . Story problem formats: Verbal versus telegraphic . Journal for Research in Mathematics Education , 15 ( 1 ) : 64 – 68 .
  • National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston, VA : Author . [Electronic version]
  • National Mathematics Advisory Panel . 2008 . Foundation for success: The final report of the National Mathematics Advisory Panel , Washington, DC : U.S. Department of Education .
  • Sherin , B. 2001 . How students understand physics equations . Cognition and Instruction , 19 : 479 – 541 .
  • Sowder , L. 1988 . Children's solutions of story problems . Journal of Mathematical Behavior , 7 : 227 – 238 .
  • Van de Walle , J. A. 2004 . Elementary and middle school mathematics: Teaching developmentally , 5th ed. , Boston, MA : Allyn and Bacon .
  • Verschaffel , L. , Greer , B. and De Corte , E. 2000 . Making sense of word problems , Lisse, , The Netherlands : Swets & Zeitlinger BV .
  • Vygotsky , L. S. 1978 . Mind and society: The development of higher psychological processes , Cambridge, MA : Harvard University Press .
  • Wechsler , D. 2003 . Wechsler Intelligence Scale for Children , 4th ed. , San Antonio, TX : Harcourt Assessment .
  • Woodcock , R. W. , McGrew , K. S. and Mather , N. 2001 . Woodcock-Johnson III , Itasca, IL : Riverside .
  • Xin , Y. P. 2008 . The effect of schema-based instruction in solving word problems: An emphasis on prealgebraic conceptualization of multiplicative relations . Journal for Research in Mathematics Education , 39 : 526 – 551 .
  • Xin , Y. P. and Jitendra , A. K. 1999 . The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis . The Journal of Special Education , 32 : 207 – 225 .
  • Xin , Y. P. , Jitendra , A. and Deatline-Buchman , A. 2005 . Effects of mathematical word problem-solving instruction on middle school students with learning problems . The Journal of Special Education , 39 : 181 – 192 .
  • Xin , Y. P. , Tzur , R. and Si , L. 2008 . “ [Nurturing multiplicative reasoning in students with learning disabilities in a computerized conceptual-modeling environment] (National Science Foundation, No. DRL-0822296) ” . Unpublished raw data
  • Xin , Y. P. , Wiles , B. and Lin , Y. 2008 . Teaching conceptual model-based word-problem story grammar to enhance mathematics problem solving . The Journal of Special Education , 42 : 163 – 178 .
  • Xin , Y. P. and Zhang , D. 2009 . Exploring a conceptual model-based approach to teaching situated word problems . The Journal of Educational Research , 102 : 427 – 441 .

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.