Learning Mathematics via a Problem-Centered Approach: A Two-Year Study

REFERENCES

• Adams , L. M. 2000 . Middle School Mathematics Comparisons for Singapore Mathematics, Connected Mathematics Program and Mathematics in Context , Washington D.C : National Science Foundation .
   Google Scholar
• Balacheff , N. 1986 . Cognitive versus situational analysis of problem-solving behavior . For the Learning of Mathematics , 6 ( 3 ) : 10 – 12 .
   Google Scholar
• Baxter , J. A. , Woodward , J. and Olson , D. 2005 . Writing in mathematics: An alternative form of communication for academically low-achieving students . Learning Disabilities Research and Practice , 20 ( 2 ) : 119 – 135 .
   Google Scholar
• Boaler , J. 1996 . Learning to lose in the mathematics classroom: A critique of traditional schooling practices in the UK . International Journal of Qualitative Studies in Education , 9 ( 1 ) : 17 – 33 .
   Google Scholar
• Boaler , J. 1997 . Setting, social class and survival of the quickest . British Educational Research Journal , 23 ( 5 ) : 575 – 595 .
   Google Scholar
• Boaler , J. 2002 . Learning from teaching: Exploring the relationship between reform curriculum and equity . Journal for Research in Mathematics Education , 33 ( 4 ) : 239 – 258 .
   Web of Science ®Google Scholar
• Bower , B. 2001 . Math fears subtract from memory, learning . Science News , 159 ( 26 ) : 405
   Google Scholar
• Buschman , L. 2003 . Children who enjoy problem solving . Teaching Children Mathematics , 4 May : 539 – 544 .
   Google Scholar
• Byrd , S. and Finnan , C. 2003 . Expanding expectations for students through accelerated schools . Journal of Staff Development , 24 ( 4 ) : 48 – 52 .
   Google Scholar
• Clark , J. V. " Minorities in Science and Math ." Columbus, Ohio; ERIC Clearinghouse for Science, Math, and Environmental Education, 1999 , ERIC Document No. ED433216 . 1999
   Google Scholar
• Cobb , P. and Bauersfeld , H. 1995 . The emergence of mathematical meaning: Interaction in classroom cultures , Hillsdale, N.J : Lawrence Erlbaum .
   Google Scholar
• Cobb , P. , Wood , T. and Yackel , E. 1991a . “ A constructivist approach to second grade mathematics ” . In Radical constructivism in mathematics education , Edited by: von Glasersfeld , E. 157 – 176 . Dordrecht : Kluwer .
   Google Scholar
• Cobb , P. , Wood , T. , Yackel , E. , Nicholls , J. , Wheatley , G. Trigatti , B. 1991b . Assessment of a problem centered second grade mathematics project . Journal for Research in Mathematics Education , 22 ( 2 ) : 3 – 29 .
   Google Scholar
• Covington Clarkson , L. M , Fawcett , G. , Shannon-Smith , E. and Goldman , N. T. 2007 . Attitude adjustments . Educational Leadership , 65 ( 3 ) : 72 – 76 .
   Google Scholar
• Dickens , A. 1996 . Revisiting Brown v. Board of Education: How tracking has resegregated America's public schools . Columbia Journal of Law & Social Problems , 29 ( 4 ) : 469 – 506 .
   Google Scholar
• Fullan , M. G. 2000 . The three stories of education reform . Phi Delta Kappan , 82 : 581 – 584 .
   Google Scholar
• Good , T. L. and Brophy , J. E. 2000 . Looking in Classrooms , 8th , New York : Longman .
   Google Scholar
• Gonzales , P. , Williams , T. , Jocelyn , L. , Roey , S. , Kastberg , D. and Brenwald , S. 2008 . Highlights from TIMSS 2007: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in and International Context , Washington D.C : U.S. Department of Education National Center for Education Statistics, NCES 2009-001 .
   Google Scholar
• Hankes , J. 1996 . An alternative to basic-skills remediation . Teaching Children Mathematics , 2 : 452 – 458 .
   Google Scholar
• Hanushek , E. A. 1986 . The economics of schooling: Production and efficiency in the public schools . Journal of Economic Literature , 24 ( 3 ) : 1141 – 1178 .
   Web of Science ®Google Scholar
• Helwig , R. , Anderson , L. and Tindal , G. 2002 . Using a concept-grounded, curriculum-based measure in mathematics to predict statewide test scores for middle school students with LD . The Journal of Special Education , 36 ( 2 ) : 102 – 112 .
   Web of Science ®Google Scholar
• Herbel-Eisenmann , B. A. , Lubienski , S. T. and Id-Deen , L. 2006 . Reconsidering the study of mathematics instructional practices: The importance of curricular context in understanding local and global teacher change . Journal of Mathematics Teacher Education , 9 : 313 – 345 .
   Google Scholar
• Hoyt , C. J. 1941 . Test reliability estimated by analysis of variance . Psychometrika , 6 : 153 – 160 .
   Google Scholar
• Institution of Education Sciences . 2004a . Connected Mathematics Project: What Works Clearinghouse Intervention Report , Washington D.C : U.S. Department of Education .
   Google Scholar
• Institution of Education Sciences . 2004b . Saxon Math: What Works Clearinghouse Intervention Report , Washington D.C : U.S. Department of Education .
   Google Scholar
• Johnson, D., Johnson, R., & Stanne, M. (2000). Cooperative learning methods: A meta analysis. Minneapolis, Minn.: University of Minnesota. July 2005 http://www.clcrc.com/pages/cl-methods.html.2000
   Google Scholar
• Knapp , M. S. , Shields , P. M. and Turnbull , B. J. 1995 . Academic challenge in high poverty classrooms . Phi Delta Kappan , 76 : 770 – 776 .
   Web of Science ®Google Scholar
• Lubienski , S. T. 2000 . Problem solving as a means towards “mathematics for all”. An exploratory look through a class lens . Journal for Research in Mathematics Education , 31 ( 4 ) : 454 – 482 .
   Web of Science ®Google Scholar
• Lubienski , S. T. . Are the new NCTM Standards reaching all students? An examination of race, class, and instructional practices . Annual Meeting of the American Educational Research Association . 2001 , Seattle. Paper presented and the ,
   Google Scholar
• Lubienski , S. T. 2002 . Research, reform, and equity in U.S. mathematics education . Mathematical Thinking and Learning , 4 ( 2&3 ) : 103 – 125 .
   Google Scholar
• Lubienski , S. T. 2004 . Traditional or standards-based mathematics? The choices of students and parents in one district . Journal of Curriculum and Supervision , 19 ( 4 ) : 338 – 365 .
   Google Scholar
• Lubienski, S. T. (2006). Examining instruction, achievement, and equity with NAEP mathematics data. Education Policy Analysis Archives, 14(14) http://epaa.asu.edu/epaa/v14n14
   Google Scholar
• Lubienski , S. T. 2007 . What we can do about achievement disparities . Educational Leadership, November , : 54 – 59 .
   Google Scholar
• Lubienski , S. T. and Crockett , M. 2007 . “ NAEP mathematics achievement and race/ethnicity ” . In Results from the Ninth Mathematics Assessment of NAEP , Edited by: Kloosterman , P. and Lester , E. 227 – 260 . Reston, VA : National Council of Teachers of Mathematics .
   Google Scholar
• MacIver , M. A. and MacIver , D. J. 2009 . Urban middle-grade student mathematics achievement growth under comprehensive school reform . Journal of Educational Research , 102 ( 3 ) : 223 – 236 .
   Google Scholar
• Mack , N. K. 1990 . Learning fractions with understanding: Building on informal knowledge . Journal for Research in Mathematics Education , 21 ( 1 ) : 16 – 32 .
   Web of Science ®Google Scholar
• Marks , G. N. 2006 . Influences on, and the consequences of, low achievement . The Australian Educational Researcher , 33 ( 1 ) : 95 – 115 .
   Google Scholar
• Marshall , J. 2003 . Math wars: Taking Sides . Phi Delta Kappan , 85 : 193 – 200 .
   Web of Science ®Google Scholar
• McCrone , S. S. 2005 . The development of mathematical discussions: An investigation in a fifth-grade classroom . Mathematical Thinking and Learning, An International Journal , 7 ( 2 ) : 111 – 133 .
   Google Scholar
• Merriam , S. 1988 . Case Study Research in Education: A qualitative approach , San Francisco, CA : Jossey-Bass .
   Google Scholar
• National Assessment of Educational Progress (NAEP) (2006, January) www.NCES.ed.gov/nationsreportcard/NAEPdata
   Google Scholar
• National Council of Teachers of Mathematics . 1991 . Professional Standards for Teaching Mathematics , Reston, VA : Author .
   Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and Standards for School Mathematics , Reston, VA : Author .
   Google Scholar
• Newmann , F. M. and Wehlage , G. G. 1995 . Successful school restructuring: A report to the public and educators , Washington, D.C : Office of Educational Research and Improvement .
   Google Scholar
• Patton , M. Q. 2002 . Qualitative Research & Evaluation Methods , Thousand Oaks, CA : Sage Publications .
   Google Scholar
• Pesek , D. and Kirshner , D. 2000 . Interference of instrumental instruction in subsequent relational leaning . Journal for Research in Mathematics Education , 31 ( 5 ) : 524 – 540 .
   Google Scholar
• Pogrow , S. 1996 . On scripting in the classroom . Education Week , 16 ( 4 ) : 38 – 46 .
   Google Scholar
• Pogrow , S. 2004 . Supermath: An alternative approach to improving math performance in grades 4 through 9 . Phi Delta Kappan , 86 : 297 – 303 .
   Google Scholar
• Pogrow , S. 2005 . HOTS revisited: A thinking development approach to reducing the learning gap after grade 3 . Phi Delta Kappan , 87 : 64 – 75 .
   Web of Science ®Google Scholar
• Pogrow , S. 2006 . The Bermuda Triangle of American education: Pure traditionalism, pure progressivism, and good intention . Phi Delta Kappan , 88 : 142 – 150 .
   Google Scholar
• Pogrow , S. 2009 . Accelerate the learning of 4th and 5th graders born into poverty . Education Digest , 74 ( 9 ) : 28 – 33 .
   Google Scholar
• Program for International Student Assessment (PISA) (2004).Washington, D.C.: U.S. Department of Education National Center for Education Statistics. October 2005 http://nces.ed.gov/pisa
   Google Scholar
• Remillard , J. T. and Bryans , M. B. 2004 . Teachers' orientations toward mathematics curriculum materials: Implication for teacher learning . Journal for Research in Mathematics Education , 35 ( 5 ) : 352 – 388 .
   Web of Science ®Google Scholar
• Ridlon , C. 2004 . The effect of a problem centered approach to mathematics on low achieving 6th-graders . Focus on Learning Problems in Mathematics , 26 ( 2 ) : 18 – 48 .
   Google Scholar
• Rosales , J. , Orrantia , J. , Vincente , S. and Chamoso , J. M. 2008 . Studying mathematics problem-solving classrooms. A comparison between the discourse of in-service teachers and student teachers . European Journal of Psychology of Education , 23 ( 3 ) : 275 – 294 .
   Web of Science ®Google Scholar
• Rothenberg , D. 1997 . Supporting girls in early adolescence , Washington, D.C : Office of Educational Research and Improvement .
   Google Scholar
• Sfard , A. 2000 . Steering (dis)course between metaphors and rigor: Using focal analysis to investigate an emergence of mathematical objects . Journal for Research in Mathematics Education , 31 ( 3 ) : 296 – 327 .
   Web of Science ®Google Scholar
• Shellard , E. G. 2004 . Helping students struggling with math . Principal , 84 ( 2 ) : 40 – 43 .
   Google Scholar
• Silver , E. A. and Lane , S. 1995 . Can instructional reform in urban middle schools help students narrow the mathematics performance gap? Some evidence from the QUASAR Project . Research in Middle Level Education Quarterly , 18 ( 2 ) : 49 – 70 .
   Google Scholar
• Smith , J. P. I II . 1996 . Efficacy and teaching mathematics by telling: A challenge for reform . Journal for Research in Mathematics Education , 27 ( 4 ) : 387 – 402 .
   Web of Science ®Google Scholar
• Stein , M. K. 2001 . Mathematical argumentation: putting umph into classroom discussions . Mathematics Teaching in the Middle School , 7 ( 2 ) : 110 – 112 .
   Google Scholar
• Stigler , J. W. and Hiebert , J. 1999 . The Teaching Gap , New York, N.Y : Free Press .
   Google Scholar
• Tarr , J. E. , Reys , R. E. , Reys , B. J. , Chavez , O. , Shih , J. and Osterlind , S. J. 2008 . The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement . Journal for Research in Mathematics Education , 39 ( 3 ) : 247 – 280 .
   Web of Science ®Google Scholar
• Wang , J. and Goldschmidt , P. 2003 . Importance of middle school mathematics on high school students' mathematics achievement . Journal of Educational Research , 97 ( 1 ) : 3 – 19 .
   Web of Science ®Google Scholar
• Wayne , A. J. and Youngs , P. 2003 . Teacher characteristics and student achievement gains: A review . Review of Educational Research , 73 ( 1 ) : 89 – 122 .
   Web of Science ®Google Scholar
• Webb , N. , Nemer , K. M. , Kersting , N. , Ing , M. and Forrest , J. The Effects of Teacher Discourse on Student Behavior and Learning in Peer-Directed Groups . CSE Report 627. Washington D.C.: U.S. Department of Education . 2004 .
   Google Scholar
• Wiest , L. R. 2008 . Problem-solving support for English language learners . Teaching Children Mathematics , 14 ( 8 ) : 479 – 484 .
   Google Scholar
• Wheatley , G. 1996 . Quick Draw , Tallahassee, FL : Mathematics Learning, Inc .
   Google Scholar
• Wheatley , G. 1999 . “ Negotiating effective learning environments for promising students ” . In Developing Mathematically Promising Students , Edited by: Sheffield , L. 58 – 67 . Reston, VA : National Council of Teachers of Mathematics .
   Google Scholar
• Wood , T. and Sellars , P. 1996 . Assessment of a problem centered mathematics program: Third grade . Journal for Research in Mathematics Education , 27 ( 3 ) : 337 – 353 .
   Google Scholar