Inverse reference in subtraction performance: An analysis from arithmetic word problems

REFERENCES

• Ashcraft , M. H. 1992 . Cognitive arithmetic: A review of data and theory . Cognition , 44 : 75 – 106 .
   PubMed Web of Science ®Google Scholar
• Ashcraft , M. H. 1995 . Cognitive psychology and simple arithmetic: A review and summary of new directions . Mathematical Cognition , 1 : 3 – 34 .
   Google Scholar
• Barrouillet , P. , Mignon , M. and Thevenot , C. 2008 . Strategies in subtraction problem solving in children . Journal of Experimental Child Psychology , 99 : 233 – 251 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. 1995 . Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation . Mathematical Cognition , 1 : 121 – 164 .
   Google Scholar
• Campbell , J. I. D. 1999a . Division by multiplication . Memory & Cognition , 27 : 791 – 802 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. 1999b . The surface form×problem size interaction in cognitive arithmetic: Evidence against an encoding locus . Cognition , 70 : 25 – 33 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. 2008 . Subtraction by addition . Memory & Cognition , 36 : 1094 – 1102 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. and Alberts , N. M. 2010 . Inverse reference in adults-elementary arithmetic . Canadian Journal of Experimental Psychology , 64 : 77 – 85 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. and Clark , J. M. 1992 . “ Cognitive number processing: An encoding complex perspective ” . In The nature and origins of mathematical skills , Edited by: Campbell , J. I. D. 457 – 492 . Amsterdam : Elsevier .
   Google Scholar
• Campbell , J. I. D. and Xue , Q. 2001 . Cognitive arithmetic across cultures . Journal of Experimental Psychology: General , 130 : 299 – 315 .
   PubMed Web of Science ®Google Scholar
• Devidal , M. , Fayol , M. and Barrouillet , P. 1997 . Stratégies de lecture et resolution de problèmes arithmétiques [Reading strategies and resolution of mathematical word problems] . L'Année Psychologique , 97 : 9 – 31 .
   Web of Science ®Google Scholar
• Geary , D. C. , Frensch , P. A. and Wiley , J. G. 1993 . Simple and complex mental subtraction: Strategy choice and speed-of-processing differences in younger and older adults . Psychology & Aging , 8 : 242 – 256 .
   PubMed Web of Science ®Google Scholar
• Hecht , S. A. 1999 . Individual solution processes while solving addition and multiplication math facts in adults . Memory & Cognition , 27 : 1097 – 1107 .
   PubMed Web of Science ®Google Scholar
• Hecht , S. A. 2006 . Group differences in adult simple arithmetic: Good retrievers, not-so-good retrievers, and perfectionists . Memory & Cognition , 34 : 207 – 216 .
   PubMed Web of Science ®Google Scholar
• Hegarty , M. , Mayer , R. E. and Monk , C. A. 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
• Jackson , N. and Coney , J. 2007 . Simple arithmetic processing: Surface form effects in a priming task . Acta Psychologica , 125 : 1 – 19 .
   PubMed Web of Science ®Google Scholar
• Klein , E. , Moeller , K. , Dressel , K. , Domahs , F. , Wood , G. Willmes , K. 2010 . To carry or not to carry—Is this the question? Disentangling the carry effect in multi-digit addition . Acta Psychologica , 135 : 67 – 76 .
   PubMed Web of Science ®Google Scholar
• Klein , E. , Nuerk , H.-C. , Wood , G. , Knops , A. and Willmes , K. 2009 . The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition . Brain and Cognition , 2 : 369 – 381 .
   Web of Science ®Google Scholar
• LeFevre , J. , DeStefano , D. , Penner-Wilger , M. and Daley , K. E. 2006 . Selection of procedures in mental subtraction . Canadian Journal of Experimental Psychology , 60 : 209 – 220 .
   PubMed Web of Science ®Google Scholar
• LeFevre , J.-A. , Sadesky , G. S. and Bisanz , J. 1996 . Selection of procedures in mental addition: Reassessing the problem size effect in adults . Journal of Experimental Psychology: Learning, Memory & Cognition , 22 : 216 – 230 .
   Web of Science ®Google Scholar
• Mauro , D. G. , LeFevre , J. and Morris , J. 2003 . Effects of problem format on division and multiplication performance: Division facts are mediated via multiplication-based representations . Journal of Experimental Psychology: Learning, Memory & Cognition , 29 : 163 – 170 .
   PubMed Web of Science ®Google Scholar
• Orrantia , J. , Rodriguez , L. and Vicente , S. 2010 . Automatic activation of addition facts in arithmetic word problems . The Quarterly Journal of Experimental Psychology , 63 : 310 – 319 .
   Web of Science ®Google Scholar
• Peters , G. , De Smedt , B. , Torbeyns , J. , Ghesquière , P. and Verschaffel , L. 2010 . Using addition to solve large subtractions in the number domain up to 20 . Acta Psychologica , 133 : 163 – 169 .
   PubMed Web of Science ®Google Scholar
• Riley , N. S. , Greeno , J. and Heller , J. I. 1983 . “ Development of children's problem solving ability in arithmetic ” . In The development of mathematical thinking , Edited by: Ginsburg , H. P. 153 – 196 . New York , NY : Academic Press .
   Google Scholar
• Seyler , D. J. , Kirk , E. P. and Ashcraft , M. H. 2003 . Elementary subtraction . Journal of Experimental Psychology: Learning, Memory & Cognition , 29 : 1339 – 1352 .
   PubMed Web of Science ®Google Scholar
• Thevenot , C. , Devidal , M. , Barrouillet , P. and Fayol , M. 2007 . Why does placing the question before an arithmetic word problem improve performance? A situation model account . The Quarterly Journal of Experimental Psychology , 60 : 43 – 56 .
   PubMed Web of Science ®Google Scholar
• Thevenot , C. , Fanget , M. and Fayol , M. 2007 . Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm . Memory & Cognition , 35 : 1344 – 1352 .
   PubMed Web of Science ®Google Scholar
• Verschafell , 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
• Widaman , K. F. and Little , T. D. 1992 . “ The development of skill in mental arithmetic: An individual differences perspective ” . In The nature and origins of mathematical skills , Edited by: Campbell , J. I. D. 189 – 253 . Amsterdam , , The Netherlands : North-Holland .
   Google Scholar
• Zbrodoff , N. J. and Logan , G. D. 2005 . “ What everyone finds: The problem size effect ” . In Handbook of mathematical cognition , Edited by: Campbell , J. I. D. 331 – 345 . New York , NY : Psychology Press .
   Google Scholar