Short-term memory processes in counting

COGNITIVE

PSYCHOLOGY

17, 417-444 (1985)

Short-Term

Memory

Processes

in Counting

ALICE F. HEALY University

of Colorado,

Boulder

AND

JAMES S. NAIRNE University

of Texas, Arlington

Four experiments examined the memory processes used to maintain location in a counting sequence. In Experiment 1, subjects who rapidly counted forward omitted many repeated-digit numbers (e.g., 77), as found previously with backward counting. Subjects in Experiment 2 counted backward with normal auditory feedback or with headphones through which white noise was channeled. In both cases, repeated-digit errors predominated, suggesting that the contents of shortterm memory, rather than auditory sensory memory, are checked during counting. In Experiment 3, subjects silently wrote counting responses, and the omission errors resembled those in vocal counting. Repetition errors were also found and attributed to phonological recoding failures. Articulatory suppression in Experiment 4 greatly increased the number of repetition errors in the written counting task. A model of the counting process was proposed according to which subjects keep track of their location in the counting sequence by monitoring phonologically coded short-term memory representations of the numbers. 0 1985 Academic Press. Inc.

It is common for psychologists to emphasize the role that phonological factors can play in short-term mnemonic performance. An experimental subject, for example, is likely to confuse items in a memory list when they sound alike, even if those items have been presented visually (e.g., Conrad, 1964). It is assumed that these performance difficulties arise The order of authorship was determined alphabetically. This research was supported in part by National Science Foundation Grant BNS80-25020 to the Institute of Cognitive Science at the University of Colorado and a grant from the Organized Research Fund of the University of Texas at Arlington. Thanks are due to Geof Orr, Constance Pusen, and Elizabeth Gaas for help in the conduct and analysis of Experiments 1 and 2. We are indebted to Carry Ells for help with the conduct of Experiment 3 and the data tabulation of Experiments 3 and 4, to Bill Oliver for help with the conduct of Experiment 3, to Ike Chen for help with the conduct of Experiment 4, and to R. Frick and G. Loftus for helpful comments concerning an earlier version of this manuscript. Requests for reprints should be sent to Alice F. Healy, Department of Psychology, University of Colorado, Campus Box 345, Boulder, CO 80309. 417 OOlO-028Y8.5$7.50 Copyright 0 1985 by Academx Precc, Inc All rights of reproduction in any form reserved.

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because retrieval is often mediated by memory traces that possess speechlike features or attributes, regardless of the modality of input. In fact, speech-based coding and, as a consequence, occasional breakdowns under conditions of high phonological similarity, are often considered to be necessary characteristics of a short-term memory system that has evolved to comprehend and produce spoken langauge (see Crowder, 1976, for a review). To the researcher, however, such error patterns are significant because they reveal the structure and function of a number of cognitive activities related to mental functioning (e.g., Norman, 1981). The present article is concerned with a recent demonstration of ours (Nairne & Healy, 1983), which illustrates the role that speech-based coding and short-term memory processes play in simple counting tasks. In this earlier work, subjects were asked to count backward aloud from 100 down to 1, as quickly as possible. In the error data, 78% of all omissions (passing a number in sequence) occurred on either (1) numbers in which the first and second digits were the same (repeated digits; 99, 88, 77,66,55,44, 33,22, 11) or (2) numbers that were multiples of 10 (decade numbers: 90, 80, 70,60, 50,40, 30, 20, 10). In counting aloud, one salient property of repeated digits is that the decade prefix (ninety-, eighty-, seventy-, . . .) and the second digit (nine, eight, seven, . . .) often sound similar. Likewise, in counting backward, decade numbers sound just like the immediately preceding number’s decade prefix. Therefore, in counting, the sound of a number is an important predictor for the likelihood of its omission, which indicates that the locus of the performance breakdown may lie in a speech-based, short-term memory system. The link between counting errors and short-term memory is important because it suggests a specific way to model how temporary memory systems might be used when people count. Subjects may maintain location in a counting sequence by automatically updating a counter (decreasing it by one for the counting backward task), but before emitting the generated number, they may check the active contents of short-term memory to determine whether that number has already been emitted. We argued (Nairne & Healy, 1983) that subjects are likely to monitor a number’s second digit to maintain location (ninety-nine, ninety-eight, ninety-seven, . . .), since the first digit, or decade pretix, is redundant for the majority of its given interval. However, in those cases in which the decade prefix and the next second digit sound similar (i.e., repeated digits), subjects may conclude mistakenly that the next second digit has already been said because the similar sounding decade prefix is currently active in shortterm memory. In effect, subjects may act as if they have already said the repeated digit and continue in the counting sequence. A similar analysis applies to omission of the decade numbers, in which case the number to be reported is the decade prefix alone. Subjects may conclude that the

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decade number has been said because the decade prefix is already represented in short-term memory. We provided some support for these ideas by showing that the percentage of repeated-digit errors increased (from 42% of all errors to 66%) and the percentage of decade-number errors decreased (from 36% to 9%) when subjects said only the digits comprising a given number as they counted backwards (e.g., three-four instead of thirty-four). We reasoned that the repeated-digit errors would increase, on the average, in this new task (digit) because the first and second digits for the repeated-digit numbers would always sound exactly the same (five-five, three-three, twotwo, one-one); in standard counting, the decade prefix and repeated second digit can sound quite different (fifty-five, thirty-three, twenty-two, eleven). In addition, we expected relatively few decade-number errors because counting backward in the digit task required a second digit (zero) to be reported for the decade numbers (nine-zero, eight-zero, sevenzero). As a further test, for each task we computed the percentage of repeated-digit omissions that occurred on the numbers 11, 22, 33, and 55 (those numbers for which the decade prefix and second digit are least similar in normal counting). This percentage was much higher in the digit condition (58%) than in the standard condition (20%), suggesting, again, that the sound of a number is important in predicting omission errors. Whereas this earlier work increased our confidence that repeated-digit counting errors occur as a by-product of conventional “short-term memory” coding operations, there is an alternative interpretation of the data: Rather than sampling the contents of short-term memory, it is possible that subjects check at a more sensory stage in information processing to decide what has already been said (e.g., Morton, Marcus, & Ottley, 1981). Thus, omission errors may arise due to the operation of an auditory sensory memory system like precategorical acoustic storage (Crowder & Morton, 1969). This idea suggests that repeated-digit omission errors do not result from the mechanism that is responsible for general phonological confusion effects (perhaps the articulatory storage loop described by Baddeley & Hitch, 1974); rather, these errors may result from a storage mechanism that is active only when subjects count aloudwhen feedback from the counting sequence is processed directly through the auditory system. One major purpose of the present experiments was to discriminate between a short-term store and sensory store locus of the counting errors. In addition, we were interested in investigating a finding reported by Crovitz (1980) that when subjects write counting responses, repetition errors (when subjects emit the same number twice in a row) are as common as omission errors. In our earlier work with vocal counting backward (Nairne & Healy, 1983) repetition errors were rare. However, we reasoned that such errors might be more frequent in a

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written counting task if the errors result from failures of phonological recoding in short-term memory; i.e., the phonological code for the emitted number fails to be represented successfully in short-term memory. Such recoding may proceed with relative ease when the responses are vocal but may be considerably more difficult when the responses are written. According to this reasoning, repetition errors should be particularly sensitive to conditions like articulatory suppression that retard phonological short-term memory coding (Estes, 1973). Prior to investigating these specific hypotheses, however, we sought to increase the generality of the Nairne and Healy (1983) results by examining counting errors during a more ecologically valid task: counting forward. EXPERIMENT

1

Although it is certainly true that people count on a regular basis, it could be argued that counting backward is somewhat artificial. Counting backward may involve unique processes that do not operate when subjects count forward. It is important, therefore, to determine what kinds of errors are made when people count forward. In Experiment 1, subjects were recorded counting forward in two related tasks: First, subjects counted in the standard fashion (e.g., thirty-two, thirty-three, thirty-four); second, subjects were recorded counting via the digit method (three-two, three-three, three-four). The most obvious question raised by this experiment is whether subjects will tend to omit the repeated digits. According to the reasoning of Nairne and Healy (1983), subjects should pass by the repeated digits while counting forward for the same reason that these digits are omitted while counting backward. When a subject reaches a repeated digit (e.g., 77) in the counting sequence, a similar sounding decade prefix (e.g., seventy-) should already be represented in memory from the preceding number. Repeated digits should then be missed because of a possible confusion about what has already been said. Similarly, the percentage of repeateddigit errors should increase in the digit method of counting since the first and second digits sound exactly the same in this task (e.g., five-five instead of fifty-five). The important prediction, however, concerns the decade numbers. In counting forward, decade numbers are not preceded by a decade prefix that sounds similar (as they are in counting backward). Thus, subjects should not omit decade numbers while counting forward in either the standard or digit method of counting. Method Subjects and uppararus. The subjects were 50 undergraduates from the University of Texas who participated for course credit. All counting responses were recorded on a Teat stereo cassette recorder. Procedure. Each subject participated in two counting tasks. In the standard task, he or

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TABLE 1 Frequencies and Proportions of Omission and Repetition Errors in Experiment 1 as a Function of Number Type (Total, Repeated Digit, Decade, and Remainder) and Forward Counting Task (Digit and Standard) (IV = 50) Number type Task

Total

Repeated digit

Decade

Remainder

Error frequencies Digit Omission Repetition Standard Omission Repetition

58 19

51 4

0 3

I 12

5 4

4 1

0 0

1 3

Error proportions Digit Omission Repetition Standard Omission Repetition

.012 ,004

,113 ,009

.ooo ,007

,002 .003

.OOl ,001

.009 .002

,000 ,000

,000 .OOl

she was told simply to count from 1 to 100 as quickly as possible. Speed was emphasized in that each subject was told not to be overcautious about making errors at the expense of reducing counting speed. However, the subjects were told to count clearly; that is, each was warned not to slur the numbers together. In the digit task, similar instructions were given except that the subjects were told to say only the digits of a number as they counted. For the numbers 1 through 9, subjects were instructed to place a zero in front of each digit (e.g., O-5, O-6, O-7). Task order was counterbalanced across subjects. Error criteria. Following Naime and Healy (1983). an error was defined as an omission of a number in its proper sequence (e.g., 75, 76, 78). If the subjects omitted a number in sequence, but then returned to correct themselves (e.g., 75,76,78,77,79), only the omitted number was counted as an error; in other words, the subjects had to pass a number in sequence in order for an omission error to occur. In addition, sometimes immediate repetitions of numbers were recorded (e.g., 75, 76, 77, 77, 78); this mistake was scored as a repetition error. (Errors in which repetitions did not occur immediately after the original number were not included in this classification scheme.) Each counting sequence was scored by two independent raters.

Results and Discussion Subject required a mean of 41.3 s (SD = 7.5 s) to complete the standard counting sequence and a mean of 60.2 s (SD = 9.2 s) to complete counting in the digit fashion. Each of the 50 subjects required more time to count in the less familiar digit task, even though there are fewer syllables to be pronounced in the digit method of counting. The data of principal interest are shown in Table 1. Omission and repetition errors are reported for both the standard and digit methods of

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NAIRNE

counting. In addition to the total errors, the data are broken down into repeated-digit, decade, and remainder (or other) errors. Along with the error frequencies, error proportions are provided. These proportions were computed simply by dividing the frequency for each number type by the total number of opportunities for that type (50 subjects x 9 numbers = 450 opportunities for the repeated-digit and decade numbers, 50 subjects x 81 numbers = 4050 opportunities for the remainder numbers, and 50 subjects x 99 numbers = 4950 opportunities in total). These proportions provide an index of error rate on a given number type that is independent of the error rate on the other number types. Standard task. As might have been expected, when adult subjects were asked to count forward from 1 to 100, very few errors were made. Despite our emphasis upon speed, counting forward is a well-practiced task which our subjects had very little difficulty performing. Out of 50 subjects, only 5 omission errors were recorded. Still, despite the small number of errors, the data were consistent with the expected pattern. Four of the five omission errors occurred on repeated digits. One subject omitted the numbers 66 and 99, while a second subject omitted the numbers 77 and 88 (see Appendix A for the distribution of omission errors in the standard task). In each case, a similar sounding decade prefix is likely to have been represented in memory from the preceding number in the sequence. It is possible that this representation created confusion about whether the repeated digit had been reported and, consequently, played a role in the repeated-digit omission. In addition, as predicted, no omission errors occurred for the decade numbers. According to our reasoning, errors of this type were unlikely while counting forward because decade numbers were not preceded by a decade prefix which sounded similar. However, it is difficult to draw any firm conclusions because of the low error rate. Examination of the repetition errors, though, provides indirect support for the above conclusions. Out of four recorded repetition errors (produced by four different subjects), only one occurred on a repeated digit (99) (see Appendix B for the distribution of repetition errors in the Standard task). This pattern is different from that of the omission errors in which the largest percentage was found for the repeated digits. This result suggests that the process responsible for a repetition error (which we postulate to be a failure to enter a phonological code for the number into short-term memory) may be different from the one producing an omission error (a confusion of one short-term memory representation with another). The data described below and in the subsequent experiments further support this claim. Digit task. Performance on the digit task provided a much clearer pattern for analysis. Out of 58 total omission errors, 51 occurred on repeateddigit numbers. Appendix C shows a breakdown of these omission errors.

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423

These data provide a striking replication of the basic pattern described by Nairne and Healy (1983), except that the present subjects counted forward rather than backward. In fact, the data actually revealed a somewhat more systematic pattern of errors than that found when subjects counted backward. In our previous study of counting backward with the digit method, 66% of the omission errors occurred on repeated digits. In the present experiment, 88% of all errors occurred on repeated digits. While it is difficult to compare across experiments, it is clear that repeated-digit errors are not confined to the task of counting backward. Moreover, importantly, counting forward in the digit task did not result in any decade-number omissions. This result was expected, since decade numbers in this task were not preceded by a similar sounding decade prefix and since the second digit (zero) had not just been said. Examination of Appendix C reveals one puzzling finding: All the omission errors except the ones on the main diagonal (the repeated-digit errors) fall near the main diagonal (so the decade prefix and second digit are similar but not identical; e.g., 45). This regular pattern cannot easily be explained in terms of the memory processes we have proposed, because it seems to implicate a process that does not rely uniquely on phonological coding. However, it may be premature to interpret this finding because such a small number of errors off the main diagonal were involved (7) and this pattern was not consistently obtained in other counting conditions (see Tables 1 and 2 in the report by Nairne & Healy, 1983, and Appendices A, E, F, G, I, K, and M in the present report).’ Appendix D shows the distribution of repetition errors in the digit counting task. Out of 19 repetition errors, 4 occurred on repeated digits, 3 on decade numbers, and 12 errors were recorded on the remaining number types. The important point to note about these data is that the distribution of errors differs from the systematic pattern underlying the t In order to obtain some estimate of the magnitude and reliability of this pattern, for each of the two conditions in the study by Nairne and Healy (1983) and each of the eight conditions in the present set of four experiments, we examined all omission errors off the main diagonal excluding the ones occurring on the decade numbers and the ones occurring on the single-digit numbers. We divided these errors into those that occurred on the 36 numbers (4 from each decade) that are closest to the diagonal and those that occurred on the 36 numbers (again 4 from each decade) that are more distant from the diagonal. In total, there were 138 omission errors occurring near the diagonal and 105 far from the diagonal. For 7 of the 10 conditions, more omissions occurred near than far from the diagonal, whereas the opposite pattern occurred for the remaining 3 conditions. With conditions as a random variable, the mean numbers of omission errors of the two types did not differ significantly, r(9) = 2.03, p > .05, but the pattern is suggestive. It is possible that because of the process underlying repeated-digit omission errors, there is a general disruption in counting for numbers surrounding repeated-digit numbers, thereby increasing the likelihood of errors near the diagonal.

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omission error distribution. There appears to be no particular type of number that is susceptible to a repetition. This result again suggests that the process responsible for these errors may differ from the process underlying omission errors. Overall, the data of Experiment 1 enhance the generality of the basic error pattern reported by Nairne and Healy (1983). When omission errors occur while counting forward, they are likely to fall on numbers in which the decade prefix and second digit sound similar (i.e., repeated digits). As a result, it seems likely that analysis of these errors will help promote the development of more complete theories of counting rather than simply provide information about the unusual task of counting backward. In addition, the results conform to the predictions of the particular model of counting we suggested earlier (Nairne & Healy, 1983). According to these ideas, repeated-digit errors can be linked to a comparison stage which occurs during counting; specifically, these errors occur when subjects check the current contents of short-term memory to determine whether the number just generated has already been emitted. Since information about position comes primarily from the second digit of a number, subjects may become confused when the next second digit to be reported sounds similar to the decade prefix. Because the first and second digits of a number can sound exactly the same in the digit form of counting, repeated-digit errors should be especially likely in this task; Experiment 1 confirms this prediction. EXPERIMENT

2

The purpose of Experiment 2 was to examine the locus of counting errors in the information-processing system; specifically, we wanted to determine whether the errors resulted from short-term or sensory memory operations. One can distinguish between these two systems empirically in a relatively simple fashion: If subjects check the current contents of an auditory sensory memory system (such as precategorical acoustic storage), rather than a more central short-term memory system (e.g., Lee & Estes, 1981), then the occurrence of repeated-digit errors (and, if counting backward in the standard fashion, decade-number errors) ought to depend importantly upon whether subjects can hear their own voices when they count. According to most formulations (e.g., Crowder & Morton, 1969), there is no way for stimulus information to enter an auditory sensory memory system unless that information is processed directly through the auditory system (see Nairne & Pusen, 1984). One way to prevent auditory feedback is to ask the subject to wear headphones through which white noise is channeled during counting; this kind of procedure has been used before in simple serial recall tasks (e.g., Murray, 1965). When subjects are prevented from hearing their own

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voices while counting, the frequency of repeated-digit errors should be reduced given that a sensory, rather than a short-term, memory system is checked to maintain position in the sequence. Method Subjects and apparatus. The subjects were 30 undergraduates from the University of Texas who participated for course credit. Counting responses were recorded using the equipment from the previous experiment. Procedure and error criteria. All subjects counted backward using the digit method of counting. The digit, rather than standard, method was employed simply to guarantee a high number of repeated-digit errors. Each subject counted backward twice, with and without hearing his or her voice while counting. On noise trials, each subject wore headphones through which approximately 85-90 dB of white noise was channeled. The exact level was determined separately for each subject; the criteria was that the subject could no longer hear his or her spoken voice, but without discomfort. For aloud trials, no headphones were worn. Task order was counterbalanced across subjects. The general instructions were the same as in the previous experiment (with the exception that subjects were asked to count backward rather than forward). Speed with clarity was emphasized; subjects were told not to be overcautious about making errors. As in Experiment 1, an error was defined as an omission of a number in its proper sequence; repetition errors were not scored in the present experiment.

Results and Discussion The major question of interest in this experiment is whether the occurrence of repeated-digit errors depends upon the subject hearing his or her own voice while counting. Table 2 reports the frequencies and proportions of omission errors for the noise and aloud tasks, broken down into total, repeated-digit, decade, and remainder errors. (See Appendices E and F for the distributions of the omission errors in the aloud and noise tasks, respectively.) Examination of the error pattern for the aloud task reveals the expected pattern reported by Nairne and Healy (1983). Out of 89 total errors, 58% TABLE 2 Frequencies and Proportions of Omission Errors in Experiment 2 as a Function of Number Type (Total, Repeated Digit, Decade, and Remainder) and Backward Counting Task (Aloud and Noise) (N = 30) Number type Task

Total

Repeated digit

Decade

Remainder

Error frequencies Aloud Noise

89 89

52 58

5 3

32 28

Error proportions Aloud Noise

.030 ,030

.193 .21.5

,019

,011

.013 ,012

426

HEALY

AND

NAIRNE

occurred on repeated-digit numbers. In addition, as we found in our earlier work, relatively few decade-number errors were recorded when subjects counted backward using the digit method. Presumably, decade numbers were not omitted in this task because there is a second digit (zero) to be reported instead of just the decade prefix alone. Since zero does not sound similar to the decade prefix, there is little reason for subjects to become confused about whether the decade number had already been reported. Thus, with the digit method, decade numbers are similar functionally to the “remainder” numbers and are not systematically omitted. This claim is further substantiated by the similar error proportions for the decade and remainder numbers. The results of most interest are those from the noise task. As the data clearly indicate, masking auditory feedback while counting backward had no effect upon the total number of omission errors or the relative likelihood that omissions would occur on the repeated-digit numbers. Repeated-digit errors accounted for 65% of the total omission errors in this task. From a theoretical standpoint, these results effectively eliminate the possibility that subjects were checking an auditory sensory memory system like precategorical acoustic storage to maintain position in the counting sequence. If such a system had been operating, then it should have been necessary for the raw, acoustic information itself to have been represented for repeated-digit omission errors to occur. Rather, it seems necessary to assign the performance breakdown to a more central locus; namely, repeated-digit omission errors are likely to be caused by the operation of conventional short-term memory coding operations (e.g., Lee & Estes, 1981). In terms of generality, this shortterm memory locus increases the chances that repeated-digit errors will be found in a variety of counting preparations, since counting is often internally driven via the “inner voice” instead of aloud, as illustrated in the following experiments. EXPERIMENT

3

The results of Experiment 2 implicated short-term memory, rather than auditory sensory memory, as the locus of counting errors. If auditory sensory memory is not responsible for counting errors, then such errors should remain even during a counting task in which no auditory stimulation is present. This hypothesis was tested again in Experiment 3 by examining the errors in a counting task which involved written, rather than vocal, responses by the subject. Specifically, subjects were required to write down numbers on a moving roll of paper tape. Just as in the case of the vocal counting task, temporary memory was required for keeping track in the written counting task, because subjects were not allowed to look down at their written responses while counting. Not only should

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this experiment provide coverging evidence for short-term memory as the locus of counting errors, but it should also reveal the nature of the shortterm memory representations. If the numbers are coded as they are norrather than as they are actually mally spoken (e.g., “thirty-three”), written (e.g., as the digit pair “33”), then the pattern of errors in the written counting task should more closely resemble that obtained during the standard rather than digit vocal counting procedure. For counting backward, in other words, if the numbers are coded as they are normally spoken, then decade-number omission errors should be prevalent as well as omission errors on repeated-digit numbers. This experiment should also allow us to understand the process responsible for repetition errors. If such errors are due to the subjects’ failures to store phonological codes successfully in short-term memory, as suggested in the introduction, then there should be an increase in the percentage of repetition errors in the present experiment relative to that found in the previous experiments involving vocal counting tasks. In other words, it may be more difficult to translate written counting responses into phonological form for storage in short-term memory, whereas the counting responses should be closer to the form required for short-term memory storage in the case of vocal counting responses. Further, if the repetition errors are due to memory coding failures whereas the omission errors are due to memory confusions, then the pattern of repetition errors would not be expected to resemble the pattern of omission errors, as verified in the vocal forward counting tasks of Experiment 1. The flowchart shown in Fig. 1 should clarify the operation of the model we have proposed for the counting task. The model consists of four distinct processes: (1) The subject begins by updating the current counter, which is achieved by adding 1 to the counter when counting forward or by subtracting 1 from the counter when counting backward. (2) The subject then checks the contents of short-term memory to see whether it contains the current counter value. A negative outcome of this check is expected, but under some circumstances (with probability p), a positive outcome occurs. For example, a positive outcome would be likely for a repeated-digit number if the subject monitors the second digit of the number stored in short-term memory, and there is a perturbation of the memory representations which causes the first and second digits to be transposed, in accord with Estes’ perturbation model (Estes, 1972; Lee & Estes, 1981). In the event of a positive outcome, the subject would repeat the updating process before emitting any number, thus causing a number to be omitted. In the event of a negative outcome, the subject would proceed to the following process: (3) The subject emits the current counter, saying it aloud in the vocal counting task or writing it in the

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-

UPDATE CURRENT COUNTER

FIG. 1. Flowchart of counting processes according to the model. STM stands for shortterm memory.

written counting task. (4) The final process involves phonological recoding. Specifically, the subject attempts to enter the current counter into short-term memory. If this attempt fails (with probability s), then the subject reverts to the immediately preceding process and emits once more the current counter, thereby making a repetition error. On the other hand, if the attempt is successful, the subject moves to the beginning of the process series and updates once more the current counter. Consider a specific example in which a subject is performing the written counting backward task. Assume the subject has just written the number 78 and successfully stored it in short-term memory. At that point the subject updates the current counter so that it contains the number 77. The subject then checks short-term memory to see if the second digit 7 is stored there. Since the last number stored in memory was 78, not 77, a negative outcome of the check is expected. However, a perturbation in memory may lead to a transposition of the two digits comprising 78, so 7 may be found in the second position, thereby yielding a positive outcome of the check. Given a positive outcome, the subject repeats the updating process, so that the current counter now contains the number 76. Again short-term memory is checked. Since there is no 6 in memory, the check yields a negative outcome, so the subject proceeds to write the current counter 76. Note that in this example the number 77 was never written, so that an omission error was made. The subject at this point

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attempts to translate the written response to a phonological code for storage in short-term memory. If phonological coding is unsuccessful, the subject once again writes the current counter 76. In this event, a repetition error has been made. If phonological coding does then succeed, the subject returns to the updating process, generating the current counter 75, and so on. Method Subjects and apparatus. Fifty-five undergraduates from the University of Colorado participated as subjects in order to obtain course credit. Two additional subjects from the same pool were tested, but the data from those subjects were not included in the analyses because many of the written responses made by one of these subjects were illegible, and the other subject failed to complete the task. The subjects wrote their responses on a roll of paper tape 7.6 cm wide which was advanced underneath a board at the rate of approximately 1.7 cm per s. The board had an opening 9.7 x 2.5 cm through which the paper was exposed. The subject placed his or her hand on the board so that he or she could write through the opening onto the paper without having to move his or her hand or look down at the paper. Procedure. Subjects were tested individually in a session that also included other cognitive tasks. Each subject participated in two counting tasks, one involving forward and the other backward counting. In the forward task, subjects were instructed to write the numbers counting forward from 0 to 100 as quickly as possible onto the moving roll of paper. The subjects were told that it was very important for them to write rapidly and that they should not be overcautious about making errors at the expense of reducing their speed. The subjects were further instructed that they should look straight ahead at the wall in front of them and they should never look down at their hand or the paper while writing. They were also told not to say anything aloud while they were writing. The instructions given in the backward task were identical except that the subjects were told to write the numbers counting backward from 100 to 0, instead of forward. As practice, the subjects were told to write down their names on the moving roll as rapidly as they could while they were looking straight ahead. The experimenter remained beside the subjects throughout the counting tasks in order to make sure that they looked straight ahead and remained silent while performing the tasks. The order of the two counting tasks was counterbalanced across subjects; 28 subjects performed the forward task first, and 27 performed the backward task first. Error criteria. Two types of errors were scored, as in Experiment 1: omissions (including substitutions) of numbers and immediate repetitions of numbers. Omissions or repetitions of the numbers 100 and 0 were not treated as errors.

Results and Discussion

The results are summarized in Table 3 in terms of frequencies and proportions of omission and repetition errors for the forward and backward counting tasks, broken down into total, repeated-digit, decade, and remainder errors. Omission errors. Just as with the vocal counting conditions of Experiment 1, fewer omission errors were made in the forward counting task (20) than in the backward task (84). In both tasks, as expected, the repeated digits accounted for disproportionately many of the omission errors, 8 of the 20 omissions in the forward task, and 26 of the 84 omissions

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TABLE 3 Frequencies and Proportions of Omission and Repetition Errors in Experiment 3 as a Function of Number Type (Total, Repeated Digit, Decade, and Remainder) and Counting Task (Forward and Backward) (N = 55) Number type Task

Total

Repeated digit

Decade

Remainder

Error frequencies Forward Omission Repetition Backward Omission Repetition

20 21

8 0

3 3

9 18

84 24

26 2

17 2

41 20

Error proportions Forward Omission Repetition Backward Omission Repetition

.004 .004

.016 .ooo

.006 .006

SW2 .004

.01.5 .004

,053 .004

.034 .004

,009 .004

in the backward task. In addition, importantly, the decade-number omissions were clearly apparent and were more numerous in the backward task. The decade-number omissions accounted for 40% of the critical number omissions (excluding the remainder numbers) compared with only 27% in the forward task. This last result was expected since the decade numbers were preceded in the backward task but not in the forward task by a similar sounding decade prefix. Appendices G and I show the distributions of omission errors in the forward and backward tasks, respectively. The pattern of errors in the backward condition is very similar to that reported in the standard condition of the vocal counting task of the study by Nairne and Healy (1983). Repetition errors. Repetition errors were more frequent in this study than in the previous vocal-counting conditions, at least in the forward task. For example, repetition errors accounted for 51% of the total errors scored in the present forward task, whereas repetitions accounted for only 25% of the total errors in the vocal digit condition of Experiment 1. In fact, in the present forward task, slightly more repetition errors occurred (21) than omission errors (20). It is particularly important to note, however, that the pattern of repetition errors differed markedly from that of omission errors (see Appendices H and J for the distributions of repetition errors in the forward and backward tasks, respectively). Only 14% of the repetition errors in the forward task and 17% in the backward task

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involved the two critical number types (repeated-digit and decade numbers), whereas 55% of the omission errors in the forward task and 51% in the backward task involved those numbers. These results are consistent with our proposed flowchart model (see Fig. l), according to which repetition errors are caused by a different process from that responsible for omission errors. By the model, the repetition errors are caused by failures of phonological recoding in short-term memory, unlike the omission errors which are due to confusions of one short-term memory code for another. The similarity between the pattern of omission errors in this experiment and those in the vocal counting conditions of previous studies is consistent with the hypothesis that short-term memory, rather than auditory sensory memory, is the memory store which allows subjects to keep track of their position in sequence when counting, since no auditory information was available in the present writing tasks. The relatively high percentage of decade-number omissions among the critical number omissions (40% in the backward task) also suggests that the numbers were represented in memory as they are normally spoken, rather than in terms of the digits that comprise them, since this pattern is similar to that found by Nairne and Healy (1983) in the standard vocal counting task. EXPERIMENT

4

On the basis of the results of Experiments 2 and 3, it was concluded that short-term memory was employed by subjects to keep track of their counting responses, and the memory representations were tentatively identified to be the names of the numbers as they are normally spoken. Experiment 4 was designed to examine further the locus of repetition errors in the counting task. According to our model (see Fig. I), a phonological recoding process is the source of these counting errors. Presumably subjects will repeat a number whenever they fail to store the phonological code for that number in short-term memory, and the probability for such failures is represented by parameter s in our model. In terms of the model, disruption of the phonological recoding process should raise the value of parameter s and thereby increase the frequency of repetition errors. In order to test this prediction of the model, phonological recoding was disturbed in Experiment 4 by requiring subjects to vocalize an irrelevant word (“the”) while they were performing the written counting task. Such articulatory suppression has been found to disrupt phonological coding in previous studies of short-term memory and specifically reduce the proportion of phonological confusion errors (see, e.g., Estes, 1973; Healy, 1975; Levy, 1971; Murray, 1967; Tell, 1971). If phonological recoding failures are responsible for the repetition errors, such errors should increase under the articulatory suppression condition

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relative to the standard written counting condition. Since errors in the previous writing study were most frequent in the backward counting task, Experiment 4 was limited to that situation. Method Subjects and apparatus. Thirty-two undergraduates from the University of Colorado participated for course credit; none of these subjects had participated in Experiment 3. One additional subject was tested, but the data from that subject were not included in the analyses, because of many illegible responses. The same apparatus was employed as in Experiment 3. Procedure and error criteria. The procedure was the same as in Experiment 3 except that only the backward counting task was employed and there were two versions of that task. The “silent” version was equivalent to that used in Experiment 3. The procedure in the “suppression” version was the same as that in the silent version except that subjects were told to say aloud the word “the” repeatedly and continuously while they were writing. Each subject participated in the two versions of the backward counting task, in a counterbalanced order. The error criteria used for scoring were the same as those used in Experiment 3.

Results and Discussion

The results are summarized in Table 4 in terms of frequencies and proportions of omission and repetition errors for the silent and suppression versions of the backward counting task, broken down into total, repeated-digit, decade, and remainder errors. TABLE 4 Frequencies and Proportions of Omission and Repetition Errors in Experiment 4 as a Function of Number Type (Total, Repeated Digit, Decade, and Remainder) and Backward Counting Task Version (Silent and Suppression) (N = 32) Number type Version

Total

Repeated digit

Decade

Remainder

Error frequencies Silent Omission Repetition Suppression Omission Repetition

50 10

12 1

5 2

33 7

68 82

10 7

6 7

52 68

Error proportions Silent Omission Repetition Suppression Omission Repetition

.016 .003

.042 ,003

.017 ,007

.013 .003

.021 .026

.035 .024

.021 .024

.020 .026

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Omission errors. The frequency of repeated-digit errors was somewhat lower than in previous experiments involving the backward counting task but still disproportionately large in the silent version of the task; specifically, 24% of the omission errors occurred on these numbers in the silent counting backward task (see Appendices K and M for the distributions of omission errors in the silent and suppression conditions, respectively). The frequency of errors of this type was no larger in the suppression condition (10) than in the silent condition (12), but the errors on other numbers increased substantially in the suppression condition (58) relative to the silent condition (38), so that only 15% of omission errors occurred on the repeated digits in the suppression condition. Although the percentage of repeated-digit errors was lower under suppression, articulatory suppression did not eliminate them. This finding suggests that articulatory suppression may not affect the process responsible for repeated-digit errors in the written counting task but, instead, has its influence on another process associated with the counting task. Further, because articulatory suppression is known to reduce sharply phonological confusion effects (e.g., Levy, 1971), these data reduce the likelihood that the same mechanism is responsible for repeated-digit omission errors and the short-term memory phonological confusion effects reported by Conrad (1964). As an example, it might prove difficult to explain repeated-digit omission errors by appealing to the operation of Baddeley and Hitch’s (1974) articulatory storage loop: Articulatory suppression should have cut out operation of such a loop, thereby eliminating repeated-digit omission errors. The percentages of decade-number omissions among the critical number omissions were not as high in this experiment (29% in the silent version and 38% in the suppression version) as in the backward counting task of Experiment 3 (40%), which is inconsistent with the hypothesis proposed earlier that the numbers may be represented in short-term memory as they are normally spoken rather than in terms of the digits comprising them. The intermediate values of the percentages in this experiment relative to those found in the vocal counting backward task of Nairne and Healy (46% in the standard condition and 13% in the digit condition) make it difficult to establish how these numbers were actually represented in short-term memory. One possibility is that the numbers were sometimes represented in terms of the digits comprising them rather than in the standard form as suggested from the data of Experiment 3. Repetition errors. Articulatory suppression had its most dramatic effect on the repetition errors. Whereas only 10 errors of this type occurred in the silent condition, there were 82 repetition errors in the suppression condition. These repetition errors, like those observed in Experiments 1 and 3, were not dominated by the two critical number types (see Ap-

434

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pendices L and N for the distributions of the repetition errors in the silent and suppression conditions, respectively). Only 30% of the repetition errors in the silent condition and 17% in the suppression condition involved the repeated-digit and decade numbers. The large frequency of repetition errors in the suppression condition is consistent with the assumption of our model that these errors result from failures of phonological recoding. GENERAL

DISCUSSION

Summary In an earlier report (Nairne & Healy, 1983), we described a systematic pattern of errors that occurs when subjects count backward aloud, and we postulated that these errors were due to short-term memory processes. More specifically, we proposed a model of counting in which subjects keep track of their location in sequence by monitoring their short-term memory store. Support for this model was provided by the different error patterns in two counting backward tasks, the standard task, in which subjects said the names of the numbers as they are normally spoken (e.g., “thirty-three”), and the digit task, in which subjects said the names of the digits comprising the numbers (e.g., “three-three”). Errors involving repeated-digit numbers (e.g., 77) increased, whereas those involving decade numbers (e.g., 70) decreased in the digit task relative to the standard task, as expected. In the present study, we extended the generality of these findings by examining performance in the more typical counting forward task; we found a very similar pattern of errors in that case. We were also able to confirm our speculation that short-term memory, rather than auditory sensory memory, was responsible for the counting errors, since the errors persisted when no auditory input was available because either white noise heard through earphones prevented the subjects from listening to their own voices or the subjects silently wrote the numbers instead of saying them aloud. The present experiments also helped us identify the representations of the numbers used in short-term memory. A high percentage of decadenumber omissions among the critical number omissions in the written version of the counting backward task (most notably in Experiment 3) suggested that the representations were the names of the numbers as they are normally spoken, since that percentage resembled the one found in the standard vocal version of the counting backward task studied by Nairne and Healy (1983). The percentages in Experiment 4 were intermediate in value, though, suggesting that both types of representations (the numbers as normally spoken or as pairs of digits) may be used. Errors in the written counting task were composed of number repetitions as well as omissions. These repetitions, which were no more

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common on the repeated-digit or decade numbers than on the remainder, were attributed by our model to breakdowns in the phonological recoding process necessary for storing the number representations in short-term memory. Support for this assumption of the model was found by comparing the silent version of the written counting task to a suppression version, in which phonological recoding was hampered by the requirement to say the word the repeatedly and continuously while counting. Repetition errors increased dramatically in the suppression version relative to the silent version, presumably because the frequency of phonological recoding failures increased. If a number was not successfully coded in short-term memory, it was repeated. Model

According to our model (see Fig. I), repetition and omission errors are caused by distinct processes. Omission errors occur when the second process (checking the contents of short-term memory) yields a positive outcome, which is assumed to occur with probability p, and repetition errors occur when the fourth process (storage in short-term memory through phonological recoding) fails, which is assumed to occur with probability s. Thus, the probabilities of the two types of errors (p and s) should be independent. Although we expect the value of s (phonological recoding failures) to increase with articulatory suppression, our expectations are less clear for the value of p (memory confusions). We acknowledge the possibility that articulatory suppression could produce fundamental changes in the way subjects code information in memory, thereby affecting p. For example, articulatory suppression may induce alternative forms of coding, e.g., visual, that lead to a different pattern of confusion errors. On the other hand, we have no reason to expect that the value of s would depend on the specific number being coded, but the value of p is expected to depend on whether the number being checked is a repeated-digit number, a decade number, or one of the remainder numbers. The results from Experiment 4 enable us to test these hypotheses. The proportions of omission and repetition errors provide estimates of the probabilities of p and s, respectively. The error proportions in Table 4 seem reasonably consistent with the hypothesis that the value of s (the probability of a repetition error) increases substantially with articulatory suppression (from approximately .003 to .026), whereas there is not as large or as consistent a difference in the value of p (the probability of an omission error) between the silent and suppression versions of the task. Further, the value of s does not seem to vary consistently as a function of number type, whereas the value of p seems to be largest for the repeated digit numbers (approximately .038), intermediate for the decade numbers (.019), and smallest for the remainder numbers (.016).

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Our flowchart model provides a framework in which to understand and predict counting errors and relate them to other breakdowns of shortterm memory processes. The counting task may thus provide a useful and ecologically valid diagnostic of short-term memory deficits. For example, we should find that individuals who have problems in phonological recoding would be especially likely to make repetition errors in the written counting task. Thus, children with reading disorders, who have been found to have deficits in phonological recoding (see, e.g., Katz, Healy, & Shankweiler, 1983; Shankweiler, Liberman, Mark, Fowler, & Fischer, 1979), may show an increased tendency to make repetition errors in the written counting task (the value of s may be elevated), although the number of omission errors they make in counting (as reflected in the value of p) should not be particularly great. Our future research will be aimed in part at testing such predictions.

APPENDIX A Omission Errors in the Standard Task of Experiment 1 (N = 50) Decade digit 9 8 7 6 5 4 3 2

Second digit 9

8

7

6

5

4

3

2

1

0

1 1 1 1

1

1 0 Note. Here and in the subsequent appendices, the entries in italics are for the repeateddigit numbers.

431

MEMORY PROCESSES IN COUNTING

APPENDIX B Repetition Errors in the Standard Task of Experiment 1 (N = 50) Decade digit 9 8

Second digit 9

8

7

6

5

4

3

2

1

0

1

1

7

1

6 5 4 3 2

1 0

APPENDIX C Omission Errors in the Digit Task of Experiment 1 (N = 50) Decade digit 9 8 7 6 5 4 3 2

1 0

Second digit 9

8

7

8

1 I 1

6

5

4

3

2

1

1

2

5 7

1

2

2

1

10 11 5

0

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APPENDIX D Repetition Errors in the Digit Task of Experiment 1 (N = 50) Decade digit

Second digit 9

8

7

2

1

6

5

4

2

3

1

9 8

0 1

7

I 1

6

5

I 1

4 3 2

1 1

3 1

2

1

1

1 0

1

APPENDIX E Omission Errors in the Aloud Task of Experiment 2 (N = 30) Decade digit 9 8 7 6 5 4 3 2

1 0

Second digit 9

8

7

6

2

1

1

1

1 1

13

1

1 1

2

1

1

3

1

2

3 7

1 1 1

2

5

4

3

1

3 5

1

1

11

1

1

3

2

1

1 8

1

0

1

2

1

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IN COUNTING

APPENDIX F Omission Errors in the Noise Task of Experiment 2 (N = 30) Decade digit 9 8 1 6 5 4 3 2 1 0

Second digit 9

8

1

1 6

1

7

12 1

6

5

4

1

3

1

1 4 1

1

1

3

2

1

0

1

1 1

1 7 2

1

1

3

1

8 1

1 12

2 5

1

1

1

1

1

1

APPENDIX G Omission Errors in the Forward Task of Experiment 3 (N = 55) Decade digit 9 8 7 6 5 4 3 2 1 0

Second digit 9

8

1

6

1 1

5

4

3

2

1

1

0 1 1

2 1

2

1 I

1 1 1

I I 1

1 1

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APPENDIX H Repetition Errors in the Forward Task of Experiment 3 (N = 55) Decade digit 9 8 I 6 5 4 3 2 1 0

Second digit 9

8

I

6

5

4

1

3

2

1

1

1

0

2

1

1 1

1

1

1

1 1

1

1

1

1 1 1

1

1

APPENDIX I Omission Errors in the Backward Task of Experiment 3 (N = 55) Second digit Decade digit 9 8 I 6 5 4 3 2 1 0

9

8

I

1

2 1

1 9 3 1 2 1 2

6

5

4

3

2

1

1

1 1

2

1 1 1

1 1

1

1 5 2

3 1

3 3 1 1

2 3

1

2

2 1 1 I

0 3 4 4 3 1 1 1

MEMORY PROCESSES IN COUNTING

441

APPENDIX J Repetition Errors in the Backward Task of Experiment 3 (N = 55) Decade digit 9 8 7 6 5 4 3 2 1 0

Second digit 9

8

1

1 1 1 1

7

6

5

4

3

2

1

0

1

1 1

1 1 1 1

1

1

1

2

1

1

2

1

APPENDIX K Omission Errors in the Silent Condition of Experiment 4 (N = 32) Decade digit 9 8 7 6 5 4 3 2

1 0

Second digit 9

8

2 2 2

2

7

6

5

4

3

2

1

0

2

1

1

1

2 2

1 1

I

1

1 1

1

1

1

1

1

1 1

2

1

4

1

1 1

1 I 2

1

1

1 1

2

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APPENDIX L Repetition Errors in the Silent Condition of Experiment 4 (N = 32) Decade digit

Second digit 9

9 8 7 6 5 4 3 2

8

7

I 1

6

5

4

3

2

1

0

1

1 1

1 1 1

1 0

1

1

APPENDIX M Omission Errors in the Suppression Condition of Experiment 4 (N = 32) Decade digit 9 8 7 6 5 4 3 2

1 0

Second digit 9

8

7

6

1 1

3

3

2

1

1 1

3 2

4

1

1 1

3

2

1

2

1

3 1

1

1

1

1

I

2 2

2

2

I

0 1 1 1 1

1 2 4

1 1

5

1

1 2 3

3

1

2

MEMORY PROCESSES 1N COUNTING

443

APPENDIX N Repetition Errors in the Suppression Condition of Experiment 4 (N = 32) Decade digit 9 8 7 6 5 4 3 2 1 0

Second digit 8

9

7

6

5

1

1 1

2

1 2 3 2

2

1 5 3

1 1

2

3

3 2

1 2 2

3

1 2

2

4

1

1 1 1

1 1 1

3 I 2

1

1

0 2 2 1

1 1 1

1

1

1 1 2

2

1 1

2

1 1

2

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55, 15-84.

Crovitz, H. F. (1980). A new forgetting paradigm. Paper presented at the 21st annual meeting of the psychonomic Society, St. Louis, MO. Crowder, R. G. (1976). Principles of/earning and memory. Hillsdale, NJ: Erlbaum. Crowder, R. G., & Morton, J. (1969). Precategorical acoustic storage (PAS). Perception & Psychophysics,

5, 365-373.

Estes, W. K. (1972). An associative basis for coding and organization in memory. In A. W. Melton & E. Martin (Eds.), Coding processes in human memory (pp. 161-190). Washington, DC: Winston. Estes, W. K. (1973). Phonemic coding and rehearsal in short-term memory for letter strings. Journal of Verbal Learning and Verbal Behavior, 12, 360-372. Healy, A. F. (1975). Coding of temporal-spatial patterns in short-term memory. Journal of Verbal Learning and Verbal Behavior, 14, 481-495. Katz, R. B., Healy, A. E, & Shankweiler, D. (1983). Phonetic coding and order memory in relation to reading proficiency: A comparison of short-term memory for temporal and spatial order information. Applied Psycholinguistics, 4, 229-250. Lee, C. L., L Estes, W. K. (1981). Item and order information in short-term memory: Evidence for multilevel perturbation processes. Journal of Experimenral Psychology: Human Learning and Memory, 7, 149-169. Levy, B. A. (1971). Role of articulation in auditory and visual short-term memory. Journal of Yerbal Learrzing and Yerbaf Behavior,

10, 123 - 132.

Morton, J., Marcus, S. M., & Ottley, P. (1981). The acoustic correlates of “speechlike”: A use of the sufiix effect. Journal of Experimental Psychology: General, 110, 568593.

Murray, D. J. (1965). The effect of white noise upon the recall of vocalized lists. Canadian Journal of Psychology, 10, 333-345.

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Murray, D. J. (1967). The role of speech responses in short-term memory. Canadian Journal of Psychology,

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Nairne, J. S., & Healy, A. F. (1983). Counting backwards produces systematic errors. Journal of Experimental Psychology: General, 112, 37-40. Nairne, J. S., & Pusen, C. (1984). Serial recall of imagined voices. Journal of Verbal Learning and Verbal Behavior, 23, 331-342. Norman, D. A. (1981). Categorization of action slips. Psycho/ogica/ Review, 88, l-15. Shankweiler, D., Liberman, I. Y., Mark, L. S., Fowler, C. A., & Fischer, E W. (1979). The speech code and learning to read. Journal of Experimental Psychology: Human Learning and Memory, 5, 53 l-545. Tell, P. M. (1971). Influence of vocalization on short-term memory. Journal of Verbal Learning and Verbal Behavior, 10, 149- 156. (Accepted June 25, 1985)