Storage and retrieval of addition facts: The role of number comparison

References

• Ashcraft , M. H. 1992 . Cognitive arithmetic: A review of data and theory . Cognition , 44 : 75 – 106 .
   Google Scholar
• Ashcraft , M. H. and Battaglia , J. 1978 . Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition . Journal of Experimental Psychology: Human Memory anil Learning , 4 : 527 – 538 .
   Google Scholar
• Ashcraft , M. H. and Christy , K. S. 1995 . The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1–6 . Journal for Research in Mathematics Education , 26 ( 5 ) : 396 – 421 .
   Google Scholar
• Ashcraft , M. H. and Stazyk , E. H. 1981 . Mental addition: A test of three verification models . Memory & Cognition , 9 : 185 – 196 .
   Google Scholar
• Baroody , A. J. 1983 . The development of procedural knowledge: An alternative explanation for Chronometrie trends of mental arithmetic . Developmental Psychology , 3 : 225 – 230 .
   Google Scholar
• Baroody , A. J. 1984 . A reexamination of mental arithmetic models and data: A reply to Ashcraft . Developmental Review , 4 : 148 – 156 .
   Google Scholar
• Baroody , A. J. 1995 . The role of the Number-After rule in the invention of computational shortcuts . Cognition and Instruction , 13 ( 2 ) : 189 – 219 .
   Google Scholar
• Baroody , A. J. and Cannon , K. E. 1984 . The development of the commutativity principle and economical addition strategies . Cognition and Instruction , 1 ( 3 ) : 321 – 339 .
   Google Scholar
• Baroody , A. J. and Ginsburg , H. P. 1986 . “ The relationship between initial meaningful and mechanical knowledge of arithmetic ” . In Conceptual and procedural knowledge: The case of mathematics , Edited by: Hiebert , J. Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Butterworth , B. 1999 . The mathematical brain , London : Macmillan .
   Google Scholar
• Campbell , J. I. D. 1994 . Architectures for numerical cognition . Cognition , 53 : 1 – 44 .
   Google Scholar
• Campbell , J. I. D. 1995 . Mechanisms of number-fact retrieval: A modified network-interference theory and simulation . Mathematical Cognition , 1 : 121 – 164 .
   Google Scholar
• Campbell , J. I. D. and Tarling , B. 1996 . Production, verification and error priming in cognitive arithmetic . Memory and Cognition , 24 ( 2 ) : 156 – 172 .
   Google Scholar
• Dehaene , S. , Bossini , S. and Ciraux , P. 1993 . The mental representation of parity and numerical magnitude . Journal of Experimental Psychology: General , 122 : 371 – 396 .
   Google Scholar
• Dehaene , S. and Cohen , L. 1995 . Towards an anatomical and functional model of number processing . Mathematical Cognition , 1 : 83 – 120 .
   Google Scholar
• Dehaene , S. and Mehler , J. 1992 . Cross-linguistic regularities in the frequency of number words . Cognition , 43 : 1 – 29 .
   Google Scholar
• Delazer , M. and Butterworth , B. 1997 . A dissociation of number meanings . Cognitive Neuropsychology , 14 : 613 – 636 .
   Google Scholar
• Duncan , E. M. and McFarland , C. E. 1980 . Isolating the effects of symbolic distance and semantic congruity in comparative judgments: An additive-factors analysis . Memory and Cognition , 8 : 612 – 622 .
   Google Scholar
• Foltz , G. S. , Poltrock , S. E. and Potts , G. R. 1984 . Mental comparison of size and magnitude: Size congruity effects . Journal of Experimental Psychology: Learning, Memory and Cognition , 10 : 442 – 453 .
   Google Scholar
• Fuson , K. 1988 . Children's counting and concepts of number , New York : Springer-Verlag .
   Google Scholar
• Gelman , R. and Gallistel , C. R. 1978 . The child's understanding of number , Cambridge, MA : Harvard University Press .
   Google Scholar
• Giaquinto , M. 1995 . Concepts and calculation . Mathematical Cognition , 1 : 61 – 81 .
   Google Scholar
• Groen , G. J. and Parkman , J. M. 1972 . A Chronometrie analysis of simple arithmetic . Psychological Review , 79 : 329 – 343 .
   Google Scholar
• Groen , G. J. and Resnick , L. B. 1977 . Can preschool children invent addition algorithms . Journal of Educational Psychology , 69 : 645 – 652 .
   Google Scholar
• Gum , T. and Bub , D. 1988 . Psychlab v. 0.85 software
   Google Scholar
• Hamann , M. S. and Ashcraft , M. H. 1986 . Textbook presentations of basic arithmetic facts . Cognition & Instruction , 3 : 173 – 192 .
   Google Scholar
• LeFevre , J.-A. , Bisartz , J. and Mrkonjic , L. 1988 . Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts . Memory & Cognition , 16 : 45 – 53 .
   Google Scholar
• LeFevre , J.-A , Sadesky , G. S. and Bisartz , J. 1996 . Selection of procedures in mental addition: Reassessing the problem-size effect in adults . Journal of Experimental Psychology: Learning, Memory and Cognition , 22 ( 1 ) : 216 – 230 .
   Google Scholar
• Lemaire , P. and Fayol , M. 1995 . When plausibility judgements supersede fact retrieval: The example of the oddeven effect on product verification . Memory and Cognition , 23 ( 1 ) : 34 – 48 .
   Google Scholar
• Logan , G. D. and Klapp , S. T. 1991 . Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity . Journal of Experimental Psychology: Learning, Memory and Cognition , 17 : 179 – 195 .
   Google Scholar
• McClelland , J. L. and Rumelhart , D. E. 1981 . An interactive activation model of context effects in letter perception: Part 1. An account of basic findings . Psychological Review , 88 : 375 – 407 .
   Google Scholar
• McCloskey , M. 1992 . Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia . Cognition , 44 : 107 – 157 .
   Google Scholar
• McCloskey , M. , Caramazza , A. and Basili , A. 1985 . Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia . Brain and Cognition , 4 : 171 – 196 .
   Google Scholar
• Miller , K. , Perlmutter , M. and Keating , D. 1984 . Cognitive arithmetic: Comparison of operations . Journal of Experimental Psychology: Learning, Memory and Cognition , 10 : 46 – 60 .
   Google Scholar
• Moyer , R. S. and Landauer , T. K. 1967 . Time required for judgments of numerical inequality . Nature , 215 : 1519 – 1520 .
   Google Scholar
• Parkman , J. M. 1971 . Temporal aspects of digit and letter inequality judgments . Journal of Experimental Psychology , 91 ( 2 ) : 191 – 205 .
   Google Scholar
• Pavese , A. and Umiltà , C. 1998 . Symbolic distance between numerosity and identity modulates Stroop interference . Journal of Experimental Psychology: Human Perception and Performance , 24 : 1535 – 1545 .
   Google Scholar
• Posner , M. H. 1979 . Chronometric explorations of mind , New York : Oxford University Press .
   Google Scholar
• Resnick , L. B. and Ford , W. W. 1981 . The psychology of mathematics for instruction , Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Secada , W. G. , Fuson , K. C. and Hall , J. 1983 . The transition from counting-all to counting-on in addition . Journal for Research in Mathematics Education , 14 : 47 – 57 .
   Google Scholar
• Siegler , R. S. 1987 . The perils of averaging over strategies: An example from children's addition . Journal of Experimental Psychology: General , 116 : 250 – 264 .
   Google Scholar
• Siegler , R. S. and Jenkins , E. 1989 . How children discover new strategies , Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Siegler , R. S. and Shrager , J. 1984 . “ Strategy choices in addition and subtraction: How do children know what to do? ” . In Origins of cognitive skills , Edited by: Sophian , C. 229 – 293 . Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Sokol , S. M. , McCloskey , M. , Cohen , N. J. and Aliminosa , D. 1991 . Cognitive representations and processes in arithmetic: Inferences from the performance of brain-damaged subjects . Journal of Experimental Psychology: Learning, Memory and Cognition , 17 ( 3 ) : 355 – 376 .
   Google Scholar
• Treiman , R. , Mullennix , J. , Bjeljac-Babic , R. and Richmond-Welty , E. D. 1995 . The special role of rimes in the description, use, and acquisition of English orthography . Journal of Experimental Psychology: General , 124 ( 2 ) : 107 – 136 .
   Google Scholar
• Widaman , K. F. , Geary , D. C. , Cormier , P. and Little , T. D. 1989 . A componential model for mental addition . Journal of Experimental Psychology: Learning, Memory and Cognition , 15 : 898 – 919 .
   Google Scholar
• Zbrodoff , N. J. 1995 . Why is 9+7 harder than 2+3? Strength and interference as explanations of the problem size effect . Memory & Cognition , 23 : 689 – 700 .
   Google Scholar
• Zbrodoff , N. J. and Logan , G. D. 1990 . On the relation between production and verification tasks in the psychology of simple arithmetic . Journal of Experimental Psychology: Learning, Memory, and Cognition , 16 : 83 – 97 .
   Google Scholar
• Zorzi , M. and Butterworth , B. On the representation of number concepts . Proceedings of the Nineteenth Annual Meeting of the Cognitive Science Society . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Zorzi , M. and Butterworth , B. A computational model of number comparison . Proceedings of the Twenty-First Annual Meeting of the Cognitive Science Society . Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar