Psychological Research *2001) 65: 24±27 Ó Springer-Verlag 2001 ORIGINAL ARTICLE Michael A. Stadler á David C. Geary á Mary E. Hogan Negative priming from activation of counting and addition knowledge Received: 15 February 2000 / Accepted: 8 June 2000 Abstract In two experiments, subjects were presented counting are not explicit features of the task *LeFevre, with digit pairs *e.g., 32) and asked to respond to the Bisanz, & Mrkonjic, 1988; LeFevre & Kulak, 1994; rightmost number. Negative priming, that is, slowed Zbrodo & Logan, 1986). LeFevre and her colleagues, processing, was evident when the rightmost number was for instance, reported that the presentation of digit pairs, a counting-string *e.g., 43 following 12) or addition-sum such as 34, oftenresulted inthe obligatory activationof *e.g., 65 following 32) associate of the number pair from the associated sum, 7 *LeFevre et al., 1988). Young the preceding trial. The studies are the ®rst to demon- children often retrieve familiar counting-string associ- strate negative priming with counting and arithmetical ates, such as retrieving 3 when presented with 1, 2, in memory representations and suggest the obligatory sequence, even when the task does not involve counting activation of these representations with the presentation *Siegler & Shrager, 1984). of number pairs. The results are also consistent with the If counting-string and addition knowledge do in fact view that negative priming often occurs at the semantic show obligatory activationwhenrelated numbers are level. presented, then negative-priming eects should be evident when the activated information is to be ignored on one trial and processed on the next *Driver & Tipper, Introduction 1989; Fox, 1995; May, Kane, & Hasher, 1995; Stadler & Hogan, 1996). In the current studies, subjects were pre- The fast and accurate solving of simple addition prob- sented with pairs of digits, such as 32, and were asked to lems *e.g., 4+5 ?) and skill at reciting number series press a key corresponding to the rightmost digit, 2 in this *e.g., 1, 2, 3, 4) appear to be dependent on the formation case. If the presentation of these pairs results in obliga- of associations between the presented and related num- tory activationof associated numbers, thenreactiontime bers *Ashcraft & Battaglia, 1978; Campbell, 1995; *RT) should be slowed when the next trial involves re- LeFevre & Bisanz, 1986; Siegler & Shrager, 1984). For sponding to this associate. So, responding to the 5 in the instance, problems such as 5 + 4 can be solved by re- pair 15 should be slower whenit is preceded by the pair trieving the answer, 9, from long-term memory, with the 32 thanwhenit is preceded by the pair 62, for example. retrieval process apparently dependent on the formation Although the mechanisms associated with such neg- of an association between the presented problem and the ative priming are not fully understood, one possibility is answer *Siegler, 1986; see also Shrager & Siegler, 1998). that the to-be-ignored information *i.e., information not Similarly, performance on counting series appears to be directly relevant to the immediate goal) is inhibited so in¯uenced by the strength of associations among the that it will not interfere with the on-line processing of digits in often repeated number strings, such that the the goal-related information *Campbell & Clark, 1989; sequence 1, 2, 3 often leads to the retrieval of 4 *LeFevre Fox, 1995; May et al., 1995). Inthis view, when5 is & Bisanz, 1986; Siegler & Shrager, 1984). automatically activated with the presentation of the 32 Moreover, anobligatory activationof these associa- pair, it is inhibited during the processing of the 2 and tions is found under some conditions where addition or apparently for several seconds thereafter *May et al.). If this is true, then negative priming should be found when target digits are counting-string associates *e.g., 3, fol- M. A. Stadler *&) á D. C. Geary á M. E. Hogan lowing the 12 pair) or the sum *e.g., 6 following the 42 Department of Psychology, University of Missouri-Columbia, 210 McAlester Hall, Columbia, MO 65211, USA pair) of the digit-pair of the preceding trial. Tel.: +1-573-8823009; Fax: +1-573-8827710 Analternativetheory that attributes negativepriming e-mail: [email protected] to episodic retrieval appears to make a similar prediction 25 *e.g., Neill, 1997). With this theory, negative priming Results results from retrieval of a preceding trial based on sim- ilarity betweenit andthe currenttrial. The retrieved Data from three subjects were discarded because they episode, however, includes information activating an failed to follow instructions about responding accurately incorrect response, and this response con¯ict leads to and made errors on more than 10% of the trials; another negative priming. Following up on the example above, if subject's data were discarded because of extremely long the target digit is 3 after subjects respond to 12, then the RTs *nearly double the mean of other subjects; inclusion retrieved episode carries information that 2 is the correct of that subject's data also nearly doubled the standard response and that 3 is an incorrect response, in con¯ict deviation). Accuracy for the remaining subjects was high with the response to be made on the current trial, that is, *M 92%) and did not vary signi®cantly across con- 3. Presumably retrieval of 12 from the previous trial ditions. Mean RTs for correct responses from the re- would also automatically activate 3, which, of course, is maining subjects are presented in Table 1. Nominally, the correct response for the current trial. Nonetheless, both counting-string associates and addition sums pro- retrieval of 12 should still interfere with the response on duced negative priming. When the target on one trial the current trial and thus slow RTs *e.g. Conway & completed a counting string begun on the preceding Engle, 1994). Our studies were not designed to distin- trial, RTs averaged 21 ms slower thanoncontrol trials. guish betweenthese theories but rather to assess more Similarly, whenthe target ononetrial was the sum of general negative-priming eects with the processing of the target and ¯anker from the preceding trial, RTs numerical and addition stimuli. averaged 29 ms slower thanoncontroltrials. Although the former eect was not signi®cant, F*1, 11) 1.32, MSE 4,132, p > 0.10, the latter one was, F*1, 11) 5.23, MSE 1,937, p < 0.05; the two eects Experiment 1 did not dier from one another, F*1, 11) < 1. Method Subjects. The subjects were 16 University of Missouri-Columbia Experiment 2 students who participated as part of the requirements for Intro- ductory Psychology. One problem with the method of randomly generating trials, as was used in Experiment 1, is that many more Apparatus. Stimulus presentation and response recording were addition trials are produced than counting-string trials. controlled by IBM-compatible computers equipped with VGA This had a direct eect onthe reliability of the results of monitors. All timing was in milliseconds, and all stimulus presen- Experiment 1; the standard error for the counting-string tation was synchronized with the raster scan on the monitor. The trials was about twice that of the sum trials. Another stimuli were the digits 1 through 6, which were approximately weakness of Experiment 1 was the relatively small 4 mm high and 3 mm wide and were presented in white on a black background. Subjects responded to the digits by pressing the 1±6 number of subjects. Finally, because the trials were keys at the top of the keyboard, respectively. They responded with generated randomly, there was no control over numer- their left ring *1), left middle *2), left index *3), right index *4), right ous other factors *e.g., the frequency with which various middle *5), and right ring *6) ®ngers. digits appeared as targets) that may have varied across control and negative-priming conditions. Therefore, Procedure. Each trial consisted of the presentation of two digits Experiment 2 was designed to provide a more powerful side-by-side in adjacent columns in the center of the screen *e.g., 12). Subjects were instructed to press the key corresponding to the test of the eects of interest by increasing sample size right-hand digit as quickly as possible without making errors on and more systematically generating counting-string and more than5% of the trials. After the subject's response,the screen addition-sum trials. was blank for 500 ms, and then the next trial was presented. At the end of a block of trials, subjects were allowed to rest until they were ready to initiate the next block. Method For each subject, 10 blocks of 100 trials each were generated by randomly selecting a target digit and then randomly selecting one The method was the same as in Experiment 1, with the following of the remaining digits to serve as a ¯anker. On average, this exceptions. procedure produced a total of 14 `counting-string' trials per subject where the target was the next digit in a counting string begun by the Table 1 Mean RT in milliseconds *standard deviations in ¯anker and target in the preceding trial *e.g., 45 followed by 36), parentheses) and priming eects as a function of the relation and 61 `addition' trials per subject where the target was the sum of betweenprime andprobe trial stimuli * RT reactiontime) the ¯anker and target in the preceding trial *e.g., 42 followed by 36). Trials in which the target was 3 after the preceding ¯anker was Experimental trials Control trials Priming 1 and the preceding target was 2, which would be both counting string trials and addition trials, were rare and were not analyzed. Experiment 1 Out of the remaining trials, an average of 448 were used as con- Counting string 762 *101) 741 *76) )21 trols.