or Level 3, as defined by Halford and Wilson (1980). An interaction was found between difficulty of the algebra problem and concurrent memory load, but the.
Does a Concurrent Memory Load Interfere with Reasoning? GRAEME S. HALFORD, JOHN D. BAIN, and MURRAY T. MAYBERY
University of Queensland, Australia
Adult participants were required to solve algebraic problems involving identification of unknown operations while they held a concurrent load in short-term memory. The load was varied in relation to participants' previously measured spans for the same materials. The algebra problems were at two levels of difficulty, Level 2 or Level 3, as defined by Halford and Wilson (1980). An interaction was found between difficulty of the algebra problem and concurrent memory load, but the point at which interference occurred was at or above span. These results support the contentions of Baddeley and Hitch (1974) and refute those of Evans and Brooks (1981). Several findings from the literature on concurrent memory and reasoning tasks are considered, and it is argued that competition between reasoning and memory occurs only when the memory task entails some form of active processing (such as encoding or rehearsal) that occurs simultaneously with reasoning. Simple storage of a concurrent memory load, or rehearsal that can be alternated with reasoning, does not interfere. It is also suggested that future studies of this problem should take care to adjust memory loads in relation to spans and to analyze the basis of the task difficulty manipulation they employ.
The concept of working m e m o r y as it has been developed by Baddeley (1981), Baddeley and Hitch (1974) and Hitch (1980), implies that cognitive performances such as reasoning, reading, mathematical computation, and language comprehension and production use working memory as a kind of workspace. Baddeley and Hitch postulate a working m e m o r y system that consists o f a general-purpose central executive and a number o f peripheral, or " s l a v e , " systems, including a visuo-spatial scratchpad and an articulatory loop. On the other hand, Allport (1980) and Crowder (1982) have challenged the notion that there is a general-purpose working memory, and have proposed instead a model in which there are a number of structurally distinct systems. The main evidence in favor o f the working m e m o r y concept comes from a paradigm in which a concurrent m e m o r y load has been found to interfere with a variety o f intellectual tasks such as sentence verification and prose comprehension (Baddeley & Hitch, 1974, Hitch & Baddeley 1976). For example, Baddeley and Hitch (1974) presented sentences such as "A precedes B , " followed by a letter sequence such as AB, and participants were required to respond " t r u e " or " f a l s e . " Problem difficulty was manipulated by varying sentence complexity, so that the example above would be an easy problem, whereas the sentence "A does not precede B " would be a difficult problem, requiring the processing of a passive and a negative. A concurrent short-term m e m o r y load, consisting of a string o f unrelated letters or digits, interfered with sentence verification. This interference took the form of in-
Halford, Bain, and Maybery
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creased verification latencies, and the increase was proportionately greater for the harder problems, thus demonstrating an interaction between problem difficulty and concurrent load. The logic of this type of study rests on the idea that if both tasks compete for a common resource, then performance on the concurrent task deprives the primary task of resources, with consequent reduced performance. The performance deficit is greater for a more difficult primary task, because its resource needs are greater. Thus, there is an interaction between primary-task difficulty and concurrent-task difficulty. Baddeley and Hitch did find this interaction, but it occurred only if the concurrent memory load was continuously rehearsed, and only if it was large (six items). Evans and Brooks (1981), on the other hand, found no interaction between difficulty of a conditional reasoning task and concurrent memory load, even though they used the same-size concurrent memory load as Baddeley and Hitch did (six items). Failure to find an interaction in any specific study does not necessarily mean that it does not exist, because it might simply reflect insufficient statistical power or some other problem of design. On the other hand, Evans and Brooks did interpret their data as damaging to Baddeley and Hitch' s hypothesis, and there is therefore a conflict in the literature that needs to be resolved. There are two factors that might explain the apparent conflict. First, neither Baddeley and Hitch nor Evans and Brooks provide any data concerning the short-term memory spans of their participants. They both used the same absolute number of items for their concurrent memory loads, but if, say, the spans of Evans and Brooks' participants had been higher, the load imposed would have been less burdensome to them, and this might explain the failure to find the interaction. A more precise approach would be to ipsitize the concurrent memory loads to participants' spans. This would help to establish comparability across different samples and, more importantly, it might answer the question whether only span-sized loads interfere with reasoning. One purpose of the present study will be to test this hypothesis. A second possible reason for the conflict between Baddeley ahd Hitch and Evans and Brooks is that neither pair of researchers has considered how its primary tasks vary in difficulty. As mentioned earlier, Baddeley and Hitch manipulated primarytask difficulty by varying sentence complexity, so that harder tasks involved sentences that contained passive or negative constructions, or both (A is not preceded by B). Although there is evidence that passives and negatives increase the processing load (e.g., Razel, 1978; Sternberg, 1980) such a load might be imposed on only a very restricted, specialized system, such as a system used for decoding speech. Since auditory short-term memory is heavily dependent on rehearsal (Baddeley, Thomson, & Buchanan, 1975) it is possible that interference occurred only because both tasks loaded the same, highly specialized, language-processing system. It is also possible that Evans and Brooks may have failed to find an interaction between primary- and secondary-task difficulty because the main-task difficulty manipulation they used did not produce variations in the information-processing
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load. They varied problem difficulty by using four rule types and four inference forms, but these factors can produce problems that differ in difficulty for reasons other than processing load. There is evidence, for example, that some rule types are misinterpreted, which would mean that they could be associated with a high error rate without any corresponding increase in processing load. For example, the conditional rule (ifp then q) causes errors in the denial of the antecedent case because the conditional tends to be interpreted as a biconditional (ifp then q and if q then p). Given the premises "p implies q " and " n o t p , " this bias causes people to infer "not q " erroneously. Additionally, there is the bias mentioned by Evans and Brooks towards negative conclusions. These biases undoubtedly raise error rates, but they do not necessarily imply more difficult processing operations, and this might explain why this dimension of primary-task difficulty did not interact with concurrent memory load. A second purpose of the present study therefore will be to manipulate primatrytask difficulty in a way different from the somewhat specialized manipulation used by Baddeley and Hitch and in a way definitely known to produce variations in processing load. For this purpose we have adopted a mathematical reasoning task in which participants are required to find unknown operations in mathematical equations involving compound expressions. These tasks, which have already been shown to vary appropriately in difficulty (Halford, 1978), have the advantage that complexity can be varied with other factors held constant. Typical examples are as follows: (7[ ]3)/4= 1 (Level 2) (7[ ]3) [ ]4= 1 (Level 3) There is one task at Level 2 and one at Level 3, as shown. These levels are defined formally elsewhere (Halford, 1982, Halford & Wilson, 1980), but in essence they vary the amount of information that must be integrated in a single decision. This can be illustrated with the present examples in the following way. Notice that in the Level 2 task there is one unknown operation, whereas in the Level 3 task there are two. At Level 2 the problem is solved when it is realized that the missing operation is subtraction. In the Level 3 task one must discover that the missing operations are subtraction and division. Not only are there two operations to be found at Level 3, but both must be found before a decision can be made about either of them. One cannot test a hypothesis about the first unknown operation without testing hypotheses about the second unknown operation as well. The Level 3 task therefore requires more information to be considered before any decision is made and, according to Halford and Wilson's calculations, imposes a higher peak load on working memory. The two tasks are quite closely matched, however, in other respects: The format is identical, as are the arithmetic values and the stimuli that must be read. These tasks, therefore, meet our criteria for a main task that is not specifically linguistic and in which problem difficulty derives from processing load. Concurrent memory load was also manipulated more precisely than in previous studies by first measuring participant's spans, and ipsitizing concurrent memory
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loads to the spans. The loads used corresponded to span minus three items, span minus two, span minus one, span, and span plus one item. METHOD
Participants The participants were 18 first-year Psychology students at the University of Queensland who participated as a course requirement.
Problems and Design In the format shown in the introduction, 40 test problems were constructed by use of the 10 combinations of two operations four times each. For all problems the operands and all intermediate results were less than 20. The same set of problems was used for Level 2 and Level 3, but in Level 2 one operation (selected at random) was specified in the problem presentation (as shown in the introduction). Half of the participants were allocated to Level 2 problems and half to Level 3 at random. The five levels of concurrent memory load (span - 3 , span - 2 , span - 1, span, and span + 1) were each allocated to eight problems at random.
Apparatus All problems were presented on an ADM3A visual display controlled by an M6800 Microcomputer, which was loaded from a PDPI i computer. Four keys of the teletype were labeled + , - , x , and/, and participants indicated their answers to the mathematical problems by pressing one key in the Level 2 or two in the Level 3 condition. Latencies and correct/incorrect responses were computed by the microcomputer. Rehearsal of the concurrent memory load items was recorded on an audiotape recorder through a microphone placed near the participant. Markers created by the microcomputer were also recorded on the tape to indicate the phases of the task.
Procedure Participants were tested individually in two sessions of approximately one hour each. The first session was devoted to the memory span task, which consisted of 18 blocks of six trials each. The first trial in a block consisted of five items, the next of six, and progressively to 10 items. The items were consonants selected so that no two alphabetically adjacent letters were temporally adjacent. Each trial was initiated by the participant's pressing a button. Two seconds later an asterisk appeared on the screen, followed by the first letter. Each letter remained visible for 800 msec and was separated from the next item by 200 msec of blank screen. All the items appeared in the same spatial location. Following the last item the screen remained
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blank for an interval equal to 500 msec for each item presented, to permit encoding. Then a prompt, consisting of a question mark, appeared on the screen as a cue to recall in the order of presentation. The items were recalled vocally and were recorded by the experimenter. The last 15 blocks were scored, and the span was defined as the longest sequence correct (position respecting) in a block, averaged over 15 blocks. The second session was devoted to the combined mathematical and concurrent memory load tasks, and consisted of 15 practice problems followed by 40 experimental problems. In the first five practice problems only the memory load was presented; in the second five only the mathematical task was presented; and in the last five both tasks were attempted concurrently. The 10 practice arithmetic problems involved one example of each of the combinations of operations. The sequence of events in the combined task was as follows: The participant pressed a button labeled " G o " ; 2 seconds later an asterisk appeared followed by sequential presentation of the concurrent memory load consonants. Each letter was visible for 800 msec and was separated from the next letter by 200 msec of blank screen. An interval equal to 500 msec for each item presented followed the last letter. A prompt consisting of a question mark then appeared, and the participant began rehearsing the consonants aloud, without pauses. After an interval equal to 1.5 seconds for each letter that had been presented, the arithmetic problem appeared. The participant indicated his or her answer by pressing keys labeled with the four operators as described previously, continuing rehearsal meanwhile. Feedback in the form "correct/incorrect" was given on the screen. Rehearsal was continued until a terminating prompt appeared on the screen after a further interval equal to 1.5 seconds for each memory load item. The interproblem interval was determined by the participant who pressed " G o " again for the next problem. Instructions stressed maintaining continuous rehearsal, but accuracy and speed on the arithmetic problem were also encouraged. In the single-task practice problems the procedure was the same except that the stimuli relating to the other task were omitted. The selection of the memory load items and their presentation procedure were the same as for the memory span test. RESULTS Errors and latencies were recorded for the mathematical task, and the number of items correctly rehearsed (position respecting) was scored for the intervals preceding and following each mathematical task. The latency used for the Level 3 task was for the first of the two key presses. The percentage of items lost from the preproblem rehearsal to the postproblem rehearsal was subjected to analysis of variance, which yielded a significant effect of load, F(4,64)=8.47, p < . 0 0 1 . The main effect of level was nonsignificant. The interaction between level of mathematical task and load was partitioned into four orthogonal components as follows: Level times span + 1 versus lower loads (span, span - 1 , span - 2 , span - 3 ) ; level times span versus lower loads (span - 1 , span - 2 , span - 3 ) ; level times span - 1 versus lower loads (span - 2 , span - 3 ) ; and
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FIGURE 1
Percentage of Preproblem to Postproblem Reduction in Memory Load Items Correctly Rehearsed
13Level 3
1211 109-
f
8tD 0 _J
7-
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