The strategic use of alternative representations in arithmetic word problem solving

References

• Abedi , J and Lord , C . (2001) . The language factor in mathematics tests . Applied Measurement in Education , 14 : 219 – 234 .
   Web of Science ®Google Scholar
• Carpenter TP Moser JM (1982) The development of addition and subtraction problem-solving skills In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective Hillsdale Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Coquin-Viennot , D . (2000) . Lecture d'énoncés de problèmes arithmétiques: Effet d'une introduction thématique sur la construction de la représentation . Archives de Psychologie , 68 : 41 – 58 .
   Google Scholar
• Coquin-Viennot , D and Moreau , S . (2003) . Highlighting the role of the episodic situation model in the solving of arithmetical problems . European Journal of Psychology of Education , 3 : 267 – 279 .
   Web of Science ®Google Scholar
• Crutcher , RJ . (1994) . Telling what we know: The use of verbal report methodologies in psychological research . Psychological Science , 5 : 241 – 244 .
   Web of Science ®Google Scholar
• Cummins , D , Kintsch , W , Reusser , K and Weimer , R . (1988) . The role of understanding in solving word problems . Cognitive Psychology , 20 : 405 – 438 .
   Web of Science ®Google Scholar
• De Corte , E and Verschaffel , L . (1981) . Children's solution processes in elementary arithmetic problems: Analysis and improvement . Journal of Educational Psychology , 73 : 765 – 779 .
   Web of Science ®Google Scholar
• De Corte E Verschaffel L (1991) Some factors influencing the solution of addition and subtraction word problems In K. Durkin & B. Shire (Eds.), Language and mathematical education Milton Keynes UK Open University Press
   Google Scholar
• De Corte , E , Verschaffel , L and Pauwels , A . (1990) . Influence of the semantic structure of word problems on second graders' eye movements . Journal of Educational Psychology , 82 : 359 – 365 .
   Web of Science ®Google Scholar
• Devidal , M , Fayol , M and Barrouillet , P . (1997) . Stratégies de lecture et résolution de problèmes arithmétiques . L'Année Psychologique , 97 : 9 – 31 .
   Web of Science ®Google Scholar
• Ericsson , KA and Simon , HA . (1980) . Verbal reports as data . Psychological Review , 87 : 215 – 251 .
   Web of Science ®Google Scholar
• Ericsson KA Simon HA (1993) Protocol analysis: Verbal reports as data (Rev. ed.). Cambridge MA Bradford/MIT Press
   Google Scholar
• Evans JSt. BT (2000) What could and could not be a strategy in reasoning In W. Schaeken, G. De Vooght, A.Vandierendonck, & G. d'Ydewalle (Eds.), Deductive reasoning and strategies Mahwah NJ Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Evans , JSt. BT , Handley , SJ , Harper , CNJ and Johnson-Laird , PN . (1999) . Reasoning about necessity and possibility: A test of the mental model theory of deduction . Journal of Experimental Psychology: Learning, Memory, and Cognition , 25 : 1495 – 1513 .
   Web of Science ®Google Scholar
• Fayol , M , Abdi , H and Gombert , JE . (1987) . Arithmetic problem formulation and working memory load . Cognition and Instruction , 4 : 183 – 202 .
   Google Scholar
• Fayol M Barrouillet P Camos V (1997) Early mathematics learning: What can research tell us Report for the DG 22 of the European Community, Brussels, Belgium.
   Google Scholar
• Gernsbacher MA (1990) Language comprehension as structure building Hillsdale NJ Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Hegarty , M , Mayer , RE and Green , CE . (1992) . Comprehension of arithmetic word problems: Evidence from students' eye fixations . Journal of Educational Psychology , 84 : 76 – 84 .
   Web of Science ®Google Scholar
• Hegarty , M , Mayer , RE and Monk , CA . (1995) . Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers . Journal of Educational Psychology , 87 : 18 – 32 .
   Web of Science ®Google Scholar
• Hinsley DA Hayes JR Simon HA (1977) From words to equations: Meaning and representation in algebra word problems In M. Just & P. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89–106) Hillsdale NJ Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Hudson , T . (1983) . Correspondences and numerical differences between disjoint set . Child Development , 54 : 84 – 90 .
   Web of Science ®Google Scholar
• Just MA Carpenter PA (1987) The psychology of reading and language comprehension Pittsburgh PA Carnegie Mellon University
   Google Scholar
• Kintsch , W . (1986) . Learning from text . Cognition and Instruction , 3 : 87 – 108 .
   Google Scholar
• Kintsch , W and Greeno , JG . (1985) . Understanding and solving word arithmetic problems . Psychological Review , 92 : 109 – 129 .
   PubMed Web of Science ®Google Scholar
• Kirk , EP and Ashcraft , MK . (2001) . Telling stories: The perils and promise of using verbal reports to study math strategies . Journal of Experimental Psychology: Learning, Memory, and Cognition , 27 : 157 – 175 .
   PubMed Web of Science ®Google Scholar
• Knoblich , G , Ohlsson , S and Raney , GE . (2001) . An eye movement study of insight problem solving . Memory and Cognition , 29 : 1000 – 1009 .
   PubMed Web of Science ®Google Scholar
• Lewis , A and Mayer , RE . (1987) . Students' miscomprehension of relational statements in arithmetic word problems . Journal of Educational Psychology , 79 : 363 – 371 .
   Web of Science ®Google Scholar
• Luchins AS Luchins EH (1959) Rigidity of behavior: A variational approach to the effect of Einstellung Eugene University of Oregon Press
   Google Scholar
• Moreau , S and Coquin-Viennot , D . (2003) . Comprehension of arithmetic word problem by fifth-grade pupils: Representation and selection of information . British Journal of Educational Psychology , 73 : 109 – 121 .
   PubMed Web of Science ®Google Scholar
• Nathan , MJ , Kintsch , W and Young , E . (1992) . A theory of algebra word problem comprehension and its implication for the design of learning environments . Cognition and Instruction , 4 : 329 – 390 .
   Web of Science ®Google Scholar
• Newstead , SE and Griggs , RA . (1999) . Premise misinterpretation and syllogistic reasoning . Quarterly Journal of Experimental Psychology , 52A : 1057 – 1075 .
   Google Scholar
• Newstead , SE , Handley , SJ and Buck , E . (1999) . Falsifying mental models: Testing the predictions of theories of syllogistic reasoning . Memory and Cognition , 27 : 344 – 354 .
   PubMed Web of Science ®Google Scholar
• Newstead , SE , Thompson , VA and Handley , SJ . (2002) . Generating alternatives: A key component in human reasoning? . Memory and Cognition , 30 : 129 – 137 .
   PubMed Web of Science ®Google Scholar
• Norris , DG . (1984) . A computer-based programmable tachistoscope for nonprogrammers . Behavior Research Methods, Instruments and Computers , 16 : 25 – 27 .
   Google Scholar
• Palladino , P , Cornoldi , C , De Beni , R and Pazzaglia , F . (2001) . Working memory and updating processes in reading comprehension . Memory and Cognition , 29 : 344 – 354 .
   PubMed Web of Science ®Google Scholar
• Payne , JW . (1994) . Thinking aloud: Insights into information processing . Psychological Science , 5 : 241 – 248 .
   Web of Science ®Google Scholar
• Polk , TA and Newell , A . (1995) . Deduction as verbal reasoning . Psychological Review , 102 : 533 – 566 .
   Web of Science ®Google Scholar
• Pynte , J . (1974) . Une expérience automatisée en psycholinguistique . Informatique et Sciences Humaines , 22 : 45 – 46 .
   Google Scholar
• Rayner , K and McConkie , GW . (1976) . What guides a reader's eye movements? . Vision Research , 16 : 829 – 837 .
   PubMed Web of Science ®Google Scholar
• Restle , F . (1970) . Speed of adding and comparing numbers . Journal of Experimental Psychology , 83 : 274 – 278 .
   Google Scholar
• Riley , MS and Greeno , JG . (1988) . Developmental analysis of understanding language about quantities and of solving problems . Cognition and Instruction , 5 : 49 – 101 .
   Web of Science ®Google Scholar
• Riley MS Greeno JG Heller JI (1983) Development of children's problem solving ability in arithmetic In H. P. Ginsburg (Ed.), The development of mathematical thinking New York Academic Press
   Google Scholar
• Shrager , J and Siegler , RS . (1998) . SCADS: A model of children's strategy choices and strategy discoveries . Psychological Science , 9 : 405 – 410 .
   Web of Science ®Google Scholar
• Siegler RS Shipley C (1995) Variation, selection, and cognitive change In T. J. Simon & G. S. Halford (Eds.), Developing cognitive competence: New approaches to process modeling Hillsdale NJ Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Stevenson HW Stigler JW (1992) The learning gap New York Summit Books
   Google Scholar
• Stigler JW Lee S-Y Stevenson HW (1990) Mathematical knowledge of Japanese, Chinese, and American elementary school children Reston VA National Council of Teachers in Mathematics
   Google Scholar
• Thevenot , C , Barrouillet , P and Fayol , M . (2001) . Algorithmic solution of arithmetic problems and operands-answer associations in LTM . Quarterly Journal of Experimental Psychology , 54A : 599 – 611 .
   Web of Science ®Google Scholar
• Thevenot , C , Barrouillet , P and Fayol , M . (2004) . Mental representation and procedures in arithmetic word problems: The effect of the position of the question . L'Année Psychologique , 104 : 683 – 699 .
   Web of Science ®Google Scholar
• Verschaffel , L , De Corte , E and Pauwels , A . (1992) . Solving compare problems: An eye movement test of Lewis and Mayer's consistency hypothesis . Journal of Educational Psychology , 84 : 85 – 94 .
   Web of Science ®Google Scholar
• Wilson , TD . (1994) . The proper protocol: Validity and completeness of verbal reports . Psychological Science , 5 : 249 – 252 .
   Web of Science ®Google Scholar