University students’ self-reports indicate that they often solve basic subtraction problems (13−6=?) by reference to the corresponding addition problem (6+7=13; therefore, 13−6=7). In this case, solution latency should be faster with subtraction problems presented in addition format (6+_=13) than in standard subtraction format (13+6=_). In Experiment 1, the addition format resembled the standard layout for addition with the sum on the right (6+_=13), whereas in Experiment 2, the addition format resembled subtraction with the minuend on the left (13=6+_). Both experiments demonstrated a latency advantage for large problems (minuend > 10) in the addition format as compared with the subtraction format (13+6=_), although the effect was larger in Experiment 1 (254 msec) than in Experiment 2 (125 msec). Small subtractions (minuend ≤ 10) in Experiment 1 were solved equally quickly in the subtraction or addition format, but in Experiment 2, performance on small problems was faster in the standard format (5−3=_) than in the addition format (5=3+_). The results indicate that educated adults often use addition reference to solve large simple subtraction problems, but that they rely on direct memory retrieval for small subtractions.
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Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75–106.
Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition, 1, 3–34.
Barrouillet, P., Mignon, M., & Thevenot, C. (2008). Strategies in subtraction problem solving in children. Journal of Experimental Child Psychology, 99, 233–251.
Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121–164.
Campbell, J. I. D. (1997). Reading-based interference in cognitive arithmetic. Canadian Journal of Experimental Psychology, 51, 74–81.
Campbell, J. I. D. (1999). Division by multiplication. Memory & Cognition, 27, 791–802.
Campbell, J. I. D. (Ed.) (2005). Handbook of mathematical cognition. New York: Psychology Press.
Campbell, J. I. D., Fuchs-Lacelle, S., & Phenix, T. L. (2006). Identical elements model of arithmetic memory: Extension to addition and subtraction. Memory & Cognition, 34, 633–647.
Campbell, J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology, 39, 338–366.
Campbell, J. I. D., & Gunter, R. (2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71–96.
Campbell, J. I. D., & Robert, N. D. (2008). Bidirectional associations in multiplication memory: Conditions of negative and positive transfer. Journal of Experiment Psychology: Learning, Memory, & Cognition, 34, 546–555.
Campbell, J. I. D., & Timm, J. C. (2000). Adults’ strategy choices for simple addition: Effects of retrieval interference. Psychonomic Bulletin & Review, 7, 692–699.
Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299–315.
Geary, D. C., Frensch, P. A., & 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.
Geary, D. C., & Wiley, J. G. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in young and elderly adults. Psychology & Aging, 6, 474–483.
Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory & Cognition, 27, 1097–1107.
LeFevre, J., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S. L., & Sadesky, G. S. (1996). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284–306.
LeFevre, J., DeStefano, D., Penner-Wilger, M., & Daley, K. E. (2006). Selection of procedures in mental subtraction. Canadian Journal of Experimental Psychology, 60, 209–220.
LeFevre, J., & Morris, J. (1999). More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication. Memory & Cognition, 27, 803–812.
LeFevre, J., Sadesky, G. S., & 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.
Mauro, D. G., LeFevre, J., & 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.
Rickard, T. C. (2005). A revised identical elements model of arithmetic fact representation. Journal of Experimental Psychology: Learning, Memory, & Cognition, 31, 250–257.
Robinson, K. M. (2001). The validity of verbal reports in children’s subtraction. Journal of Educational Psychology, 93, 211–222.
Rusconi, E., Galfano, G., Rebonato, E., & Umiltà, C. (2006). Bidirectional links in the network of multiplication factst. Psychological Research, 70, 32–42.
Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of Experimental Psychology: Learning, Memory, & Cognition, 29, 1339–1352.
Siegler, R. S., & Shrager, J. (1984). A model of strategy choice. In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
Zbrodoff, N. J., & Logan, G. D. (2005). What everyone finds: The problem size effect. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 331–346). New York: Psychology Press.
This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.