Supporting Algebraic Reasoning through Personalized Story Scenarios: How Situational Understanding Mediates Performance

REFERENCES

• Ainley , M. , Hidi , S. and Berndorff , D. 2002 . Interest, learning, and the psychological processes that mediate their relationship . Journal of Educational Psychology , 94 ( 3 ) : 545 – 561 .
   Web of Science ®Google Scholar
• Anand , P. and Ross , S. 1987 . Using computer-assisted instruction to personalize arithmetic materials for elementary school children . Journal of Educational Psychology , 79 ( 1 ) : 72 – 78 .
   Web of Science ®Google Scholar
• Baker , R. S. J. D. , Corbett , A. T. and Koedinger , K. R. 2007 . The difficulty factors approach to the design of lessons in intelligent tutor curricula . International Journal of Artificial Intelligence in Education , 17 ( 4 ) : 341 – 369 .
   Google Scholar
• Barab , S. , Zuiker , S. , Warren , S. , Hickey , D. , Ingram-Goble , A. , Kwon , E. , Kouper , I. and Herring , S. 2008 . Situationally embodied curriculum: Relating formalisms and contexts . Science Education , 91 ( 5 ) : 750 – 782 . &
   Web of Science ®Google Scholar
• Baranes , R. , Perry , M. and Stigler , J. 1989 . Activation of real-world knowledge in the solution of word problems . Cognition and Instruction , 6 ( 4 ) : 287 – 318 . &
   Web of Science ®Google Scholar
• Bardini , C. , Pierce , R. and Stacey , K. 2004 . Teaching linear functions in context with graphics calculators: students' responses and the impact of the approach on their use of algebraic symbols . International Journal of Science and Mathematics Education , 2 : 353 – 376 .
   Google Scholar
• Bates, D., & Maechler, M.2010lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-35 http://CRAN.R-project.org/package=lme4 (http://http://CRAN.R-project.org/package=lme4)
   Google Scholar
• Bates , E. and Wiest , L. 2004 . The impact of personalization of mathematical word problems on student performance . The Mathematics Educator , 14 ( 2 ) : 17 – 26 .
   Google Scholar
• Boaler , J. 1994 . When do girls prefer football to fashion? An analysis of female underachievement in relation to ‘realistic' mathematics contexts . British Education Research Journal , 20 ( 5 ) : 551 – 564 .
   Google Scholar
• Cakir , O. and Simsek , N. 2010 . A comparative analysis of computer and paper-based personalization on student achievement . Computers & Education , 55 ( 4 ) : 1524 – 1531 .
   Web of Science ®Google Scholar
• Carnegie Learning.2008Cognitive Tutor Algebra I. Retrieved August 2008 from http://www.carnegielearning.com/secondary-curricula/algebra1/ (http://http://www.carnegielearning.com/secondary-curricula/algebra1/)
   Google Scholar
• Carnegie Learning.2011Carnegie Learning Math Series: Carnegie Learning MATHia Software. Retrieved May 24, 2011 from http://mathseries.carnegielearning.com/product-info/software (http://http://mathseries.carnegielearning.com/product-info/software)
   Google Scholar
• Carpenter , T. , Fennema , E. and Franke , M. 1996 . Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction . The Elementary School Journal , 97 ( 1 ) : 3 – 20 .
   Web of Science ®Google Scholar
• Carraher , T. , Carraher , D. and Schliemann , A. 1987 . Written and oral mathematics . Journal for Research in Mathematics Education , 18 ( 2 ) : 83 – 97 .
   Web of Science ®Google Scholar
• Carraher , D. , Schliemann , A. , Brizuela , B. and Earnest , D. 2006 . Arithmetic and algebra in early mathematics education . Journal for Research in Mathematics Education , 37 ( 2 ) : 87 – 115 .
   Web of Science ®Google Scholar
• Chazan , D. 2000 . Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom , New York : Teachers College Press .
   Google Scholar
• Cogan , L. , Schmidt , W. and Wiley , D. 2001 . Who takes what math and in which track? Using TIMSS to characterize U.S. students' eighth-grade mathematics learning opportunities . Educational Evaluation and Policy Analysis , 23 ( 4 ) : 323 – 341 .
   Web of Science ®Google Scholar
• 1997 . Cognition and Technology Group at VanderbiltThe Jasper Project: Lessons in Curriculum, Instruction, Assessment, and Professional Development , Mahwah , NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Collins , A. and Halverson , R. 2009 . Rethinking Education in the Age of Technology: The Digital Revolution and Schooling in America , New York : Teachers College Press .
   Google Scholar
• Common Core State Standards Initiative.2010Common Core State Standards (Mathematics Standards). Retrieved July 6, 2010 from http://www.corestandards.org/the-standards/mathematics (http://http://www.corestandards.org/the-standards/mathematics)
   Google Scholar
• Cooper , B. and Dunne , M. 1998 . Anyone for tennis? Social class differences in children's responses to national curriculum mathematics testing . Sociological Review , 46 ( 1 ) : 117 – 148 .
   Web of Science ®Google Scholar
• Cooper , B. and Harries , T. 2005 . Making sense of realistic word problems: Portraying working class “failure” on a division with remainder problem . International Journal of Research & Method in Education , 28 ( 2 ) : 147 – 169 .
   Google Scholar
• Cooper , B. and Harries , T. 2009 . “ Realistic contexts, mathematics assessment, and social class ” . In Word and Worlds: Modelling Verbal Descriptions of Situations , Edited by: Greer , B. , Verschaffel , L. , Van Dooren , W. and Mukhopadhyay , S. Rotterdam , The Netherlands : Sense . InEds.
   Google Scholar
• Cordova , D. and Lepper , M. 1996 . Intrinsic motivation and the process of learning: Beneficial effects of contextualization, personalization, and choice . Journal of Educational Psychology , 88 ( 4 ) : 715 – 730 .
   Web of Science ®Google Scholar
• Davis-Dorsey , J. , Ross , S. and Morrison , G. 1991 . The role of rewording and context personalization in the solving of mathematical word problems . Journal of Educational Psychology , 83 ( 1 ) : 61 – 68 .
   Web of Science ®Google Scholar
• Dewey , J. 1916 . Democracy and Education , New York : Free Press .
   Google Scholar
• Durik , A. and Harackiewicz , J. 2007 . Different strokes for different folks: How individual interest moderates effects of situational factors on task interest . Journal of Educational Psychology , 99 ( 3 ) : 597 – 610 .
   Web of Science ®Google Scholar
• Ericsson , K. and Simon , H. 1998 . How to study thinking in everyday life: Contrasting think-aloud protocols with descriptions and explanations of thinking . Mind, Culture, and Activity , 5 ( 3 ) : 178 – 186 .
   Google Scholar
• Filloy , E. and Rojano , T. 1989 . Solving equations: The transition from arithmetic to algebra . For the Learning of Mathematics , 9 ( 2 ) : 19 – 25 .
   Google Scholar
• Fives , H. and Manning , D. 2005 . Teachers' strategies for student engagement: Comparing research to demonstrated knowledge , Washington DC : American Psychological Association . Paper presented at 2005 Annual Meeting of
   Google Scholar
• Flowerday , T. , Schraw , G. and Stevens , J. 2004 . The role of reader choice and interest in reader engagement . Journal of Experimental Education , 72 ( 2 ) : 93 – 114 .
   Web of Science ®Google Scholar
• Gravemeijer , K. and Doorman , M. 1999 . Context problems in realistic mathematics education: A calculus course as an example . Educational Studies in Mathematics , 39 : 111 – 129 .
   Google Scholar
• Greer , B. 1997 . Modelling reality in mathematics classrooms: The case of word problems . Learning and Instruction , 7 ( 4 ) : 293 – 307 .
   Web of Science ®Google Scholar
• Hall , R. , Kibler , D. , Wenger , E. and Truxaw , C. 1989 . Exploring the episodic structure of algebra story problem solving . Cognition and Instruction , 6 ( 3 ) : 223 – 283 .
   Web of Science ®Google Scholar
• Hattikudur , S. , Prather , R. W. , Asquith , P. S. , Alibali , M. W. , Knuth , E. J. and Nathan , M. 2012 . Constructing graphical representations: Exploring middle schoolers' intuitions and developing knowledge about slope and intercept . School Science and Mathematics , 112 ( 4 ) : 230 – 240 .
   Google Scholar
• Heffernan , N. and Koedinger , K. R. 1998 . “ A developmental model for algebra symbolization: The results of a difficulty factors assessment ” . In Proceedings of the Twentieth Annual Conference of the Cognitive Science Society , Edited by: Gernsbacher , M. A. and Derry , S. J. 484 – 489 . Mahwah , NJ : Erlbaum . InEds.pp
   Google Scholar
• Heilman , M. , Collins , K. , Eskenazi , M. , Juffs , A. and Wilson , L. 2010 . Personalization of reading passages improves vocabulary acquisition . International Journal of Artificial Intelligence in Education , 20 ( 1 ) : 73 – 98 .
   Google Scholar
• Herscovics , N. and Linchevski , L. 1994 . A cognitive gap between arithmetic and algebra . Educational Studies in Mathematics , 27 : 59 – 78 .
   Google Scholar
• Hidi , S. 1990 . Interest and its contribution as a mental resource for learning . Review of Educational Research , 60 ( 4 ) : 549 – 571 .
   Web of Science ®Google Scholar
• Hidi , S. 1995 . A reexamination of the role of attention in learning from text . Educational Psychology Review , 7 ( 4 ) : 323 – 350 .
   Web of Science ®Google Scholar
• Hidi , S. and Renninger , K. 2006 . The four-phase model of interest development . Educational Psychologist , 41 ( 2 ) : 111 – 127 .
   Web of Science ®Google Scholar
• Hulleman , C. , Godes , O. , Hendricks , B. and Harackiewicz , J. 2010 . Enhancing interest and performance with a utility value intervention . Journal of Educational Psychology , 102 ( 4 ) : 880 – 895 .
   Web of Science ®Google Scholar
• Inoue , N. 2005 . The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving . Learning and Instruction , 15 ( 1 ) : 69 – 83 .
   Web of Science ®Google Scholar
• Johanning , D. 2004 . Supporting the development of algebraic thinking in middle school: A closer look at students' informal strategies . Journal of Mathematical Behavior , 23 ( 4 ) : 371 – 388 .
   Google Scholar
• Jonassen , D. 2003 . Designing research-based instruction for story problems . Educational Psychology Review , 15 ( 3 ) : 267 – 296 .
   Web of Science ®Google Scholar
• Kaput , J. J. 2000 . Teaching and Learning a New Algebra With Understanding , Dartmouth, MA: National Center for Improving Student Learning and Achievement .
   Google Scholar
• Kazemi , E. 2002 . Exploring test performance in mathematics: The questions children's answers raise . Journal of Mathematical Behavior , 21 ( 2 ) : 203 – 224 .
   Google Scholar
• Kieran , C. 1988 . “ Two different approaches among algebra learners ” . In The Ideas of Algebra, K-12. 1988 Yearbook of the National Council of Teachers of Mathematics , Edited by: Coxford , A. F. 91 – 96 . Reston , VA : National Council of Teachers of Mathematics . InEd.pp
   Google Scholar
• Kintsch , W. 1986 . Learning from text . Cognition and Instruction , 3 ( 2 ) : 87 – 108 .
   Google Scholar
• Kintsch , W. and Greeno , J. 1985 . Understanding and solving arithmetic word problems . Psychological Review , 92 ( 1 ) : 109 – 129 .
   PubMed Web of Science ®Google Scholar
• Koedinger , K. , Alibali , M. and Nathan , M. 2008 . Trade-offs between grounded and abstract representations: Evidence from algebra problem solving . Cognitive Science , 32 ( 2 ) : 366 – 397 .
   PubMed Web of Science ®Google Scholar
• Koedinger , K. and McLaughlin , E. 2010 . “ Seeing language learning inside the math: Cognitive analysis yields transfer ” . In Proceedings of the 32nd Annual Conference of the Cognitive Science Society , Edited by: Ohlsson , S. and Catrambone , R. 471 – 476 . Austin , TX : Cognitive Science Society . InEds.pp
   Google Scholar
• Koedinger , K. and Nathan , M. 2004 . The real story behind story problems: Effects of representations on quantitative reasoning . Journal of the Learning Sciences , 13 ( 2 ) : 129 – 164 .
   Web of Science ®Google Scholar
• Ladsen-Billings , G. 1995 . “ New directions for equity in mathematics education ” . In For Equity in Mathematics Education , Edited by: Secada , W. 126 – 145 . New York: Cambridge : University Press . InEd.pp
   Google Scholar
• Lampert , M. 2001 . Teaching Problems and the Problems of Teaching , New Haven , CT : Yale University Press .
   Google Scholar
• Lave , J. and Wenger , E. 1991 . Situated Learning: Legitimate Peripheral Participation , New York : Cambridge University Press .
   Google Scholar
• Lesh , R. , Cramer , K. , Doerr , H. , Post , T. and Zawojewksi , J. 2003 . “ Model development sequences ” . In Beyond Constructivism: A Models and Modeling Perspective on Mathematics Problem Solving, Learning and Teaching , Edited by: Lesh , R. and Doerr , H. M. Hillsdale , NJ : Lawrence Erlbaum . InEds.
   Google Scholar
• Lesh , R. and Harel , G. 2003 . Problem solving, modeling, and local conceptual development . Mathematical Thinking and Learning: An International Journal , 5 ( 2–3 ) : 157 – 190 .
   Google Scholar
• Lesh , R. and Zawojewski , J. 2007 . “ Problem solving and modeling ” . In Second Handbook of Research on Mathematics Teaching and Learning , Edited by: Lester , F. 763 – 800 . Greenwich , CT : Information Age Publishing . InEd.pp
   Google Scholar
• Lopez , C. and Sullivan , H. 1992 . Effects of personalization of instructional context on the achievement and attitudes of Hispanic students . Educational Technology Research and Development , 40 ( 4 ) : 5 – 13 .
   Web of Science ®Google Scholar
• Loveless, T, Fennel, F., Williams, V., Ball, D.Banfield, M.2008Chapter 9: Report of the Subcommittee on the National Survey of Algebra I Teachers. In Foundations for Success: Report of the National Mathematics Advisory PanelOctober 14, 2010 from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/nsat.pdf (http://http://www2.ed.gov/about/bdscomm/list/mathpanel/report/nsat.pdf)
   Google Scholar
• Maas , C. and Hox , J. 2005 . Sufficient sample sizes for multilevel modeling . Methodology , 1 ( 3 ) : 86 – 92 .
   Google Scholar
• Masingila , J. , Davidenko , S. and Prus-Wisniowska , E. 1996 . Mathematics learning and practice in and out of school: A framework for connecting these experiences . Educational Studies in Mathematics , 31 : 175n200
   Google Scholar
• McDaniel , M. , Waddill , P. , Finstad , K. and Bourg , T. 2000 . The effects of text-based interest on attention and recall . Journal of Educational Psychology , 92 ( 3 ) : 492 – 502 .
   Web of Science ®Google Scholar
• Mitchell , M. 1993 . Situational interest: Its multifaceted structure in the secondary school mathematics classroom . Journal of Educational Psychology , 85 ( 3 ) : 424 – 436 .
   Web of Science ®Google Scholar
• Moses , R. and Cobb , C. 2001 . Radical Equations: Math Literacy and Civil Rights , Boston : Beacon Press .
   Google Scholar
• Nathan , M. , Kintsch , W. and Young , E. 1992 . A theory of algebra-word-problem comprehension and its implications for the design of learning environments . Cognition and Instruction , 9 ( 4 ) : 329 – 389 .
   Web of Science ®Google Scholar
• Nathan , M. and Koedinger , K. 2000a . Teacher and researchers' beliefs about the development of algebraic understanding . Journal for Research in Mathematics Education , 31 ( 2 ) : 168 – 190 .
   Web of Science ®Google Scholar
• Nathan , M. J. and Koedinger , K. R. 2000b . Moving beyond teachers' intuitive beliefs about algebra learning . Mathematics Teacher , 93 : 218 – 223 .
   Google Scholar
• Nathan , M. J. , Stephens , A. C. , Masarik , D. K. , Alibali , M. W. and Koedinger , K. R. 2002 . Representational fluency in middle school: A classroom based study . In Proceedings of PME-NA XXXIII, The North American chapter of the International Group for the Psychology of Mathematics Education ,
   Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and Standards for School Mathematics , Reston , VA : Author .
   Google Scholar
• National Council of Teachers of Mathematics. 2006 . Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics: A Quest for Coherence , Reston , VA : Author .
   Google Scholar
• National Council of Teachers of Mathematics . 2009 . Executive Summary: Focus in High School Mathematics: Reasoning and Sense-making , Reston , VA : Author .
   Google Scholar
• Palm , T. 2008 . Impact of authenticity on sense making in word problem solving . Educational Studies in Mathematics , 67 : 37 – 58 .
   Google Scholar
• Palm , T. 2009 . “ Theory of authentic task situations ” . In Word and Worlds: Modelling Verbal Descriptions of Situations , Edited by: Greer , B. , Verschaffel , L. , Van Dooren , W. and Mukhopadhyay , S. Rotterdam , the Netherlands : Sense . InEds.
   Google Scholar
• Papert , S. 1980 . Mindstorms: Children, Computers and Powerful Ideas , New York : Basic Books .
   Google Scholar
• Papert , S. 1993 . The Children's Machine , New York : Harper Collins .
   Google Scholar
• Paterson , L. and Goldstein , H. 1991 . New statistical methods for analyzing social structures: An introduction to multilevel models . British Educational Research Journal , 17 ( 4 ) : 387 – 393 .
   Google Scholar
• Reber , R. , Hetland , H. , Chen , W. , Norman , E. and Kobbeltvedt , T. 2009 . Effects of example choice on interest, control, and learning . Journal of the Learning Sciences , 18 : 509 – 548 .
   Web of Science ®Google Scholar
• Renninger , K. , Ewen , L. and Lasher , A. 2002 . Individual interest as context is expository text and mathematical word problems . Learning and Instruction , 12 ( 4 ) : 467 – 491 .
   Web of Science ®Google Scholar
• Renninger , K. and Wozinak , R. 1985 . Effect of interest on attentional shift, recognition, and recall in young children . Developmental Psychology , 21 ( 4 ) : 624 – 632 .
   Web of Science ®Google Scholar
• Reusser , K. and Stebler , R. 1997 . Every word problem has a solution: The social rationality of mathematical modeling in schools . Learning and Instruction , 7 ( 4 ) : 309 – 327 .
   Web of Science ®Google Scholar
• Rittle-Johnson , B. and Koedinger , K. 2005 . Designing knowledge scaffolds to support mathematical problem solving . Cognition and Instruction , 23 ( 3 ) : 313 – 349 .
   Web of Science ®Google Scholar
• Roschelle , J. , Kaput , J. and Stroup , W. 2000 . “ SimCalc: Accelerating students' engagement with the mathematics of change ” . In Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning , Edited by: Jacobson , M. J. and Kozma , R. B. 47 – 75 . Mahwah , NJ : Lawrence Erlbaum Associates . InEds.pp
   Google Scholar
• Roth , W. 1996 . Where is the context in contextual word problems: Mathematical practices and products in grade 8 students' answers to story problems . Cognition and Instruction , 14 ( 4 ) : 487 – 527 .
   Web of Science ®Google Scholar
• Saxe , G. 1988 . Candy selling and math learning . Educational Researcher , 17 ( 6 ) : 14 – 21 .
   Google Scholar
• Schiefele , U. 1999 . Interest and learning from text . Scientific Studies of Reading , 3 ( 3 ) : 257 – 279 .
   Google Scholar
• Schraw , G. and Lehman , S. 2001 . Situational interest: A review of the literature and directions for future research . Educational Psychology Review , 13 ( 1 ) : 23 – 52 .
   Web of Science ®Google Scholar
• Snijders , T. and Bosker , R. 1999 . Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling , Sage Publications .
   Google Scholar
• Stacey , K. and MacGregor , M. 1999 . Learning the algebraic method of solving problems . Journal of Mathematical Behavior , 18 ( 2 ) : 149 – 167 .
   Google Scholar
• Stein , M. K. , Kaufman , J. H. , Sherman , M. and Hillen , A. F. 2011 . Algebra: A challenge at the crossroads of policy and practice . Review of Educational Research , 81 ( 4 ) : 453 – 492 .
   Web of Science ®Google Scholar
• Walkington , C. in press . Using learned technologies to personalize instruction to student interests: The impact of relevant contexts of performance and learning outcomes . Journal of Educational Psychology ,
   Google Scholar
• Walkington , C. , Nathan , M. , Wolfgram , M. , Alibali , M. , Srisurichan , R. , Strobel , J. , Purzer , S. and Cardella , Monica . in press . “ Bridges and barriers to constructing conceptual cohesion across modalities and temporalities: Challenges of STEM integration in the precollege engineering classroom ” . In Engineering in PreCollege Settings: Research into Practice , Rotterdam , The Netherlands : Sense . InEds
   Google Scholar
• Xin , Z. 2009 . “ Realistic problem solving in China ” . In Word and Worlds: Modelling Verbal Descriptions of Situations , Edited by: Greer , B. , Verschaffel , L. , Van Dooren , W. and Mukhopadhyay , S. Rotterdam , the Netherlands : Sense . InEds.
   Google Scholar