Coordination in visual working memory

Psychol Res (1996) 58:294-306 © Springer-Vertag 1996

Herbert Hagendorf • Birgit S~i

Coordination in visual working memory

Received: 28 March 1995/Accepted: 24 July 1995

Abstract Coordination of mental procedures is considered in terms of control processes (Baddeley, 1989) in visual working memory and appears to be a separable aspect of the demand imposed by cascaded serial processes (Carlson & Lundy, 1992). The main task required subjects to indicate whether symbolically suggested rotations and reflections correctly describe the difference between matrix patterns of filled-in squares within a 3 x 3 grid or between line drawings. Experi- ments were carried out to show that coordination is a separable component in this transformation task. A marker for coordination is the difference between the time taken to execute two transformations as a whole and the sum of the component transformations in isolation. The separate coordination demand was found in an experiment with matrix patterns mentioned, in an experiment with letter-like line drawings, and also in an experiment that forced subjects to maintain whole- pattern representations. A last experiment checked whether coordination is carried out by an autonomous control unit. There was a self-paced control of serial presentation of transformation symbols instead of a simultaneous presentation of those symbols. This additional external triggering resulted in a substantial de- crease in the demand for coordination. Coordination of mental procedures and temporary representations is a fundamental constraint on the use of working- memory processes.

Introduction

The working-memory system is especially important in tasks in which individuals have to maintain a variety of

H. Hagendorf ( ~ ) • B. S~ Humboldt University, Department of Psychology, Oranienburger Strasse 18, D-10178 Berlin, Germany

temporary information about goals, intermediate results, and strategies. The regulation and the monitoring of successful performance in complex tasks require de- cisions as to which processes to engage in and in which order (Allport, 1992). Therefore working memory is seen as a centre for mental activity involving interactions among various mechanisms in such important tasks as reading, problem solving, reasoning, and skill acquisition (Kyllonen & Christal, 1990; Just & Carpen- ter, 1992; Woltz, 1988). The acceptance of the distinction of processing types and information types in multi- modal theories of memory (Engelkamp, 1990) and/or making a distinction between various cognitive procedures within a framework of controlled processing (Klix, 1992) makes it necessary to consider the functions of working memory in the fulfilment of task demands and to ask what are the constraints in the use of working- memory resources. According to Baddeley (1993a), its global function can be seen in the coordination of information from a number of sources and in projec- tions to the future.

Current models of working memory may be divided into two categories: (a) those that define a flexible single work space (Anderson, 1987; Cowan, 1988), and (b) those in which working-memory resources are distrib- uted over a variety of subcomponents (Baddeley, 1989; Schneider & Detweiler, 1987). Several lines of evidence suggest that working memory is best understood as a multicomponent model (Logie, 1993; Engelkamp & Zimmer, 1994). This model consists of at least three components: articulatory loop, visual-spatial scratch pad, and the central executive. In particular, aspects of the unexplored function of the central executive as a separate attentional control system can be studied in tasks in which a subject has to accomplish two or more things.

Several authors (Logie, 1991, 1993; Morris & Jones, 1990; Carlson et al., 1993) have suggested tasks that require moment-to-moment monitoring (Carlson & Lundy, 1992; Mayr & Kliegl, 1993) and need the

coordination and/or interaction of component processes and representations. In a general sense coordination can be thought of as an additional demand on working memory when a person has to coordinate a procedure with what is available in the representation. In mental imagery, such procedures can be mental transformations such as size scaling, rotations, or reflections working on mental representations of visual patterns.

Coordination and working-memory components

We are especially interested in the restricted coordination function in connection with the encoding and mental manipulation of visually presented information. There is a sense in which basic mental procedures such as rotation or scanning (Kosslyn, 1990) can be put together to simulate complex activities in the prediction of future events. It can be assumed that these predictive manipulative capacities of the cognitive system (Klix, 1992) rely heavily on the visual working- memory system component and the central executive component, which appears to have the characteristic of a system for allocating attention (Baddeley, 1993b; Logic, 1993) to different task components such as maintaining representation of information, processing of information, or intake of information from external sources. It can be assumed that a key role for this general-purpose executive resources in the visual-spatial domain is the generation and manipulation of mental images.

In a review of several lines of evidence Logic (1993) argued that some form of a general attentional resource is required in some of the operations attributed to the component responsible for buildir~g up and retaining structured visual representations. In an investigation undertaken by Morris (1987) secondary tasks that placed load on the central executive produced performance decrements during encoding. According to Logic and Salway (1990), the mental rotation of abstract shapes requires resources of the central executive. We want to assess the effectiveness of the hypothesized central attentional control system independently of performance in constituent procedures in a task in which subjects have to coordinate the execution of at least two mental procedures. Such a task is the serial execution of two mental transformations on a visual image. Trans- formations of interest are mental construction (Helstrup & Anderson, 1991), mental subtraction (Brandimonte et al., 1992), or procedures such as shrinking, expanding, rotating, or scanning part or all of an image (Novick & Tversky, 1987; Hanley et al., 1991; Bundesen et al., 1981). Control processes in such a task with two transformation procedures are needed to implement the en- gagement in a particular procedure, to protect ongoing activity from interruptions, and to refresh intermittently fading temporary representations.

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Different aspects of coordination have already been studied from various perspectives (Baddeley, 1993 a, b). Yee et al. (1991) have considered the use of various information sources. They have shown that the ability to process either visual-spatial information or verbal information is unrelated to the ability to perform visual-spatial and verbal information concurrently. So there is a general overall cost in performance efficiency in addition to the load on individual modality-related resources.

Carlson et al. (1993) extended this research on the coordination of information from perception and working memory in a list-recall task. Their interest was based on results from Carlson et al. (1990) on the acquisition of a procedural skill for solving diagnostic problems with digital electronic circuits. In this research the integration of information retained in working memory with displayed information was analysed by a secondary task technique. The authors concluded that the coordination and integration of representations is a separable component of a complex skill. So they emphasized that it is necessary to specify the characteristics of this component. There are other results from skill acquisition in the domain of mental arithmetic (Elio, 1986; Frensch & Geary, 1991; Char- hess & Campbell, 1988) that show that composed knowledge is built up during skill acquisition. This knowledge is related to the control of the procedures and is dissociated from the computational procedures at the lower level. In the sense of the homogeneity assumption in the consideration of control (Neumann, 1992) the question is whether constraints in all these tasks can be understood as the reflection of an autonomous control system in working memory.

There is also a research line looking at the problem from the point of view of interaction between the visual working-memory component and the central executive (Logic, 1993; Quinn, 1994). Morris and Jones (1990) considered memory updating to be a task in which the coupling of the central executive and the visual working memory can be studied in the context of integrating past experience with the present. Lohman (1988) claim- ed that individual differences in the speed of solving simple problems in the visual-spatial domain are gener- ally a poor predictor of how complex problems are solved. The reason may be that complex problems require control operations independently of the procedures used in solving the simple tasks. Bundesen et al. (1981) also found in a recognition experiment with two transformations (size scaling, rotation) that reports of people speak against the hypothesis of a single two- stage serial organization by which one of the transformations is initiated when the other one is completed. Nevertheless these authors found additivity of tem- poral effects of disparities of size and angular orientation between patterns.

We are especially interested in the coordination of the visual working-memory component as a function of

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the attention-control system in manipulative tasks with structured visual representations. If control processes are those activities that draw on some kind of limited resource, the setting up and monitoring of the transmis- sion of information between cognitive procedures ac- tivated from memory should require cognitive demand. So we have tried to show that coordination is an additional demand on working memory when a person needs to accomplish two cognitive procedures on visual images. This requires the assessment of the effectiveness of the central controller independently of performance in the constituent controlled procedures.

General approach and questions

Coordination in the assumed central attentional- control system can be studied in tasks that differ in their demands of coordination of information exchange between processing steps. Mayr and Kliegl (1993) found different slowing rates for tasks with coordination complexity and tasks with sequential complexity. They argued that coordinative complexity results from demands on working memory. We therefore developed a serial mental transformation task (Bethell-Fox & Shepard, 1988; Cohen & Kubovy, 1993) which fulfils two requirements (Hagendorf & Sfi 1995). (1) The basis is the processing of visually presented patterns and figures and their images. (2) The task requires the coordination of cognitive procedures (mental rotations and reflections) and intermediate representations in working memory.

Subjects had to indicate whether symbolically suggested transformation rules correctly described the differences between two patterns. A trial (see Figure 1) consisted of three phases. Subjects pressed buttons to control the serial presentation of (1) a reference figure for encoding; (2) cues indicating the mental execution of 0, 1, or 2 transformations (rotations and/or reflections); and then (3) a comparison figure, which might or might

Encoding Transformation Comparison

"YES"

"NO"

Press Button Press Button Press Button (Inspection (Transformation (Comparison Time) Time Time)

Fig. 1 General serial mental transformation procedure: Subjects have to indicate whether symbolically suggested transformation rules (example: rotation 180 ° and horizontal reflection in this order) correctly describe the difference between reference pattern (on the left) and comparison pattern (on the right)

not be the reference figure transformed according to the transformation cues.

Subjects were instructed to examine the reference figure in the first phase so that they had a clear image and could imagine it without actually seeing it. The time they took before terminating this phase by pressing a key was the inspection time. After a key had been pressed, the reference figure was replaced either by one small square for indicating 0 or 1 transformation, or by two small squares for indicating 2 transformations. In the case of the 0-transformation condition the square was empty otherwise it contained a symbol that specified the desired transformation of the pattern. Subjects had to imagine the transformed pattern as quickly as possible. In Figure 1 the transformation symbols for a 180 ° rotation and a horizontal reflection are given for a 2-transformation trial. The transformations had to be executed in a prescribed order - that is, first the transformation presented above and then the other one presented below. Subjects finished this phase by pressing a key. The time it took them to complete this transformation phase was the transformation time. Then the symbols were replaced by a comparison pattern. The time to make a yes/no judgement was the comparison time. On the "yes" trials the comparison pattern was the reference pattern transformed according to the transformations indicated by the symbols in the preceding phase of a trial. On "no" trails the comparison pattern was also the reference pattern, but changed by the application of some transformations not indicated by the symbols in the preceding phase of the trial. On Figure 1 the "no" pattern is generated from the reference pattern by a 90 ° rotation.

In this task it is necessary to coordinate intermediate results and cognitive procedures to maintain and transform structured representations. Computation competes with maintenance for a common, flexibly deployable pool of resources for control operations. The first central question in this context is, therefore, whether coordination is a separable control component in this serial-transformation task. This can be checked by comparison of the performance level (transformation time and errors) in trials requiring coordination and execution of two transformations with the performance level in trials requiring only the execution of one transformation. In the case of the execution of two transformations sequentially without separate coordination cost, the transformation time predicted should be the sum of the time costs of the individual transformations. So the difference between the actual time taken to execute two transformations as a whole and this prediction, which is derived from the component transformations in isolation, is an estimate of coordination cost. It is assumed that this cost includes the cost for maintaining the goal, the intermediate products, and the time taken to switch to the next transformation episode. We shall consider these costs in relation to task fulfilment. The time taken to execute one

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transformation requires the interpretation of the symbol, the activation of the transformation procedure, and the generation of the transformed image sequentially. The end of this procedure is indicated by the pressure of a key. We now consider a trial with two transformations. Even if subjects work in a strong serial process, there should be control operations because subjects have to disengage from the first transformation procedure and allocate attentional resources to the next imperative stimuli for activating the second transformation procedure. AdditionaEy, coordination demand results from switching between the maintenance of the mental representation generated by the first transformation and executing the second transformation. Whatever the process is, it involves switching between refreshing and transforming the mental representation. So it cannot be excluded that subjects reexecute a transformational episode in the case of the quick fading of this representation. Because there is a strategic element in the task, subjects can also start with the interpretation of the two symbols in a 2- transformation trial. They then have also to hold in memory two goals. It is known that maintaining goals or preparing for action prolongs the execution of mental procedures (Umilta et al., 1992; Scheidereiter et al., 1983). All these componential processes may force subjects to do extra computations and should result at a molar level in coordination cost. So the first question is whether coordination is indicated by this difference between the prediction for 2-transformation trials and the actual transformation time for 2-transformation trials. This coordination should be the responsibility of the central executive.

According to Just and Carpenter (1985), it is assumed that mental transformations are piecemeal procedures that operate upon analysed and structured pattern representations. These procedures are assumed to be largely resource-limited mechanisms that transform the individual pieces of the representation sequentially. The efficiency of these procedures is a function (1) of practice; (2) of attended properties of mental representations of patterns and (3) of the nature of the comparison task. So the second question is whether we can prove the existence of coordination costs in experiments with variations on these critical task dimensions. Learning is dependent on the subprocesses that are recruited and organized to accomplish a task. If coordination is a separable control component we should expect that there should be a separable coordination cost at all stages of learning. But if subjects learn the outcomes of pattern-transformation trials, there should be no coordination costs at all. We expect coordination cost at all levels of practice because of low consistency over trials, which is necessary for outcome learning. The encoding of the reference pattern is some sort of structured visual representation. Those mental representations are not invariant. Efficient performance in different tasks may require subjects to form different

mental representations (Klix, 1983; Van der Meer, 1985; Cohen & Kubovy, 1993). So it could be that the complexity of patterns in mental-rotation tasks has no effect on speeded tasks such as mental rotation (Yuille & Steiger, 1982). There is much room for variability in the structuring and parsing of patterns (Klix, 1983; Schwarz, 1986) and thus considerable variability in the subsequent transformation and matching process (Kyl- lonen et al., 1984). Independently of the representations used, there should be a coordination cost. So we compare serial-transformation tasks with different types of patterns. A change in the comparison task would also force subjects to generate other representations. Al- though this should influence the transformation episode, it should not influence the coordination demand on working memory.

The third question is related to the interpretation of coordination costs. If coordination costs result from those activities that draw on some kind of limited resources of the central executive (Baddeley, 1993a), then these control processes should be autonomous and should not depend on external triggering of control operations. We therefore check whether the control demand is related to the self-paced procedure in the sense that the active disengagement from executing one procedure and allocating resources to the next transformation requires control demand. This switching is dependent on the stability of the intermediate representation generated. One possibility is to compare the simultaneous presentation of transformation symbols in 2-trial transformations with the sequential presentation of these symbols. If control operations are inter- nally triggered, we should expect no difference in coordination cost between these conditions. If, on the other hand, coordination cost is reduced in the sequential condition, this would be critical for the assumption of an autonomous control system.

We shall describe four experiments to answer these three questions. Experiments were carried out to show the additional demand for coordination. The separate coordination demand was assessed in an experiment with the patterns mentioned, in experiments with letter- like line drawings, and also in an experiment with a changed comparison stage, which forced subjects to maintain whole-pattern representations. A final experiment used a different procedure. In comparison to the general procedure, there was also self-paced control of serial presentation of transformation symbols to check whether the maintenance of goals and the readiness for executing a second transformation procedure are one important source for coordination cost.

Experiment 1

Evidence in favour of coordination

Our general hypothesis concerning coordination cost is based on the analysis of the times taken to execute the

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t r a n s f o r m a t i o n s ( t r a n s f o r m a t i o n time). W e expec t a difference b e t w e e n the e s t i m a t i o n for t r ia ls wi th two t r ans - f o r m a t i o n s a n d the a c t u a l score. In gene ra l the d a t a in this t a s k s h o u l d mee t the fo l lowing cond i t i ons . T h e subjec ts ' c o m p a r i s o n t ime m u s t be i n d e p e n d e n t of the v a r i a t i o n in the n u m b e r of t r a n s f o r m a t i o n s . A t least , d e p e n d e n c y of c o m p a r i s o n t ime on the n u m b e r of t r a n s f o r m a t i o n s execu ted m u s t be w e a k e r t h a n the de- p e n d e n c y of the t r a n s f o r m a t i o n t ime on the n u m b e r of t r a n s f o r m a t i o n s . Th is c o n d i t i o n m u s t be fulfi l led for an i n t e r p r e t a t i o n of the t r a n s f o r m a t i o n t imes. A n inc rease in c o m p a r i s o n t ime wi th the n u m b e r o f t r a n s f o r m a - t ions is a h in t on p o s t t r a n s f o r m a t i o n a l p rocesses in the c o m p a r i s o n s tage ( C o h e n & K u b o v y , 1993). E r r o r pa t - te rns s h o u l d show d e p e n d e n c i e s in the same d i r ec t i on as t r a n s f o r m a t i o n t imes. W e can then exc lude t i m e - a c - c u r a c y t rade-offs .

In genera l , m e n t a l t r a n s f o r m a t i o n p r o c e d u r e s a re a func t ion of l ea rn ing . L e a r n i n g can be o b s e r v e d wi th respec t to severa l p roces s c o m p o n e n t s . P r a c t i c e can inf luence the level of e n c o d i n g of the pa t t e rns , the efficiency of t r a n s f o r m a t i o n ep i sodes , a n d the a s s u m e d c o o r d i n a t i o n c o m p o n e n t . So the ove ra l l benef i t in 2- t r a n s f o r m a t i o n t r ia ls can be a t t r i b u t e d to severa l t a s k c o m p o n e n t s . W e have the re fo re to c o n t r o l the inf luence of p rac t i ce on c o o r d i n a t i o n cost . W e check espec ia l ly w h e t h e r p r ac t i ce d imin i shes c o o r d i n a t i o n cost . I f subjec ts l e a r n the co r rec t o u t c o m e for p a t t e r n - t r a n s f o r - m a t i o n pai rs , t hen there s h o u l d be d e c r e m e n t s of c o o r d i n a t i o n cos t d u r i n g learn ing .

M e t h o d

Subjects. Subjects were 20 students (mean age 23;7 years) from Humboldt University participating for course requirement or credit.

Material and procedure. We used three matrix patterns (see Figure 2a) from the set of Bethell-Fox and Shepard (1988) in the experiment and an additional pattern during the practice phase.

According to the general procedure (see Figure 1), a trial started with the presentation of an asterisk located at the centre of the computer screen for 1,500 ms. The reference pattern was presented at a location in the left part of the screen. After a key had been pressed, the transformation symbols were presented in the centre. At the end of the transformation episode the symbols were replaced by the comparison pattern at a location in the right part of the screen. So individuals had to use a location-independent mental representation of the patterns.

In the 0-transformation trials a blank small square was presented. In the 1-transformation trials a small square with a transformation symbol was shown. The most complex condition contained two squares with a symbol in each of them. The arrangement of the squares was as illustrated in Figure 1. This arrangement of two symbols signalled the order of execution. Four transformations (rotations by 90 ° and 180 ° , horizontal and vertical reflection) were applied singly or in pairs for the patterns. Each subject had to work on control trials without any transformations, trials with single transformations, and trials with four of the eight possible pairs of transformations (altogether nine transformation conditions).

Subjects were assigned randomly to one of two experimental groups (see Table 1). One group was tested with four of the eight

Fig. 2 (a)Matrix patterns of Experiment 1 (from Bethell-Fox & Shepard, 1988). The left pattern was used in the practice phase. The other three patterns were used in the experimental phase. (b) Line drawings of Experiment 2 (from Tarr & Pinker, 1989). The left-hand drawing was used in the practice phase, the other three drawings in the experimental phase

Table 1 Experimental conditions

Experimental Group 1 Experimental Group 2

Control: No Transformation 90 ° Rotation 180 ° Rotation Horizontal Reflection Vertical Reflection Horizontal/90 ° Vertical/90 ° 180 ° Horizontal 180 ° Vertical

Control: No Transformation 90 ° Rotation 180 ° Rotation Horizontal Reflection Vertical Reflection Horizontal/t80 ° Vertical/180 ° 90 ° Horizontal 90 ° Vertical

combinations of rotations and reflections, while the other one was tested with the other four pairs of transformations.

To familiarize subjects with the task, a block of 18 trials was conducted. The practice trials consisted of the nine transformation types combined with a practice pattern similar to those used later in the experiment proper (see left patterns in Figure 2a) and one correct and one incorrect trial. During practice, false responses were cor- rected and reexecuted with cards. Practice was provided sufficiently only for the subjects to understand what to do. Then subjects had to perform a sequence of 216 items consisting of four blocks of 54 trials (three patterns, nine transformation types, same number of correct and incorrect trials) each. The order of the trials in one block was randomized before the testing, with the condition that two success- ive trials never contained the same pattern or the same transformation type. The trials were presented in the same fixed order in each block. Subjects received accuracy feedback only in the practice trials. They participated in individual sessions lasting approximately 90 minutes.

Resu l t s a n d d i scuss ion

T h e effects of the n u m b e r of t r a n s f o r m a t i o n s were c he c ke d on the bas i s of i n d i v i d u a l m e d i a n r e a c t i o n t imes for i n s p e c t i o n t ime, t r a n s f o r m a t i o n t ime, a n d c o m p a r i s o n t ime, wi th on ly co r rec t dec i s ions in each c ond i t i on . I n d i v i d u a l e r r o r p e r c e n t a g e s were c o m p u t e d for each c ond i t i on . The typ i ca l g r o u p d a t a were con- s t ruc t ed b y m e a n s of these med ians . S e p a r a t e o n e - w a y ana lyses of v a r i a n c e ( M a n o v a ) wi th n u m b e r of t r ans - f o r m a t i o n s as f ac to r were c o n d u c t e d on the i n d i v i d u a l m e d i a n s for i n spe c t i on t ime, t r a n s f o r m a t i o n t ime,

Response Time (s) 6

rm0 Transformation

D1 Transformation

~N2 Transformations

5

4 Coordination

3

2

Inspection Time Transformation Time Comparison Time

Response Time Categodes

Fig. 3 Inspection time, transformation time, and comparison time as a function of the number of transformations for trials with matrix patterns

comparison time, and error percentages. The main group results on inspection time, transformation time, and comparison time are represented in Figure 3. There was no dependence of inspection time on number of transformations (F < 1). A dependence of transformation time F(2, 38) = 123.4, p < .01, and of comparison time F(2, 38)= 15.64, p < .001 on number of transformations was found in separate analyses. The comparison time for control trials (0 transformation) was significantly lower than for the other two trial types (Tukey, CD = 78.1, p < .05).

It was shown that there was a difference between the transformation time for trials with two transformations and the prediction derived from trials with component transformations in isolation, t(19)= 11.71, p < .001. The predicted time was calculated from control trials and trials with one transformation (predicted = control + 2* (1 transformation - control)) and is

indicated in Figure 3. We found that errors depended (1.9%, 5.0%, and

10.2%) on the number of transformations, F(2, 38) = 19.01, p < .001. Subjects committed more errors in de- cisions when they had to make two transformations (Tukey, CD = 3.32, p < .05).

In Figure 4 the transformation time is presented as a function of the level of coordination demand of the task (0, 1, or 2 transformations) and the level of practice (block number). A two-way Manova on data from blocks 1-4 with block number and number of transformations as factors was performed to investigate the influence of practice on mental transformations. The estimation derived from a linear additive model for performance of the two transformation task is also shown. The result is consistent with the expectation that additional processing requirements emerge when two transformations need to be used, F(2,38) = 125.95, p < .01. Figure 4 shows a general practice

effect. The Manova revealed a significant effect of block number, F(3, 57) = 23.6, p < .01, as well as an interaction between block number and number of transformations, F(6, 114) = 7.76, p < .01. Even after four blocks of practice, coordination demand is a mere quarter of

Transformation Time (s)

299

~-0 Transformation 7 ~.. 1 Transformation

6 ~ ' ~ ~ +2 Transformations 5 ~ m a t e

4

3 m •

2

1 ~ . D a

0 I I I I Block 1 Block 2 Block 3 Nock 4

Block Number

Fig. 4 Transformation time for trials with 0, 1, or 2 transformations and estimate for 2-transformation trials as a function of the number of blocks

the resources necessary for successful performance in 2-transformation trials.

To summarize the results: first, transformation time for all trial types decreased with practice; second, coordination cost was reduced with practice too, but was not eliminated; third, transformation time for the 2- transformation trials cannot be predicted from the transformation time of the other types of trial. In general, at all stages of practice, coordination was about one-third of the transformation time. Although there was an absolute difference in the coordination cost between the first and last blocks (1,106 ms), the relative proportion of coordination had not changed. In a similar design with 18 blocks of trials, Hagendorf and S/t (1994) showed that coordination cost was not consider- ably diminished. The learning of outcomes to pattern- transformation pairs can be excluded on the basis of these results.

Unexpectedly, comparison time depended on the number of transformations. This result shows that posttransformational processes were executed, but to the same small extent in both 1- and 2-transformation trials. This small effect does not influence our interpretation because comparison times in general were much lower than was transformation time. This can be learned from Figure 3. Because of these encouraging results, we decided to pursue this approach and to check the stability of this result in experiments with variations in patterns and in the comparison task.

Experiment 2

Variation of patterns

To show that our results are independent of the specific mental representations of the patterns used, we carried out a new experiment with line drawings from the investigation of Tarr and Pinker (1989) on orientation- specific representations in mental rotation. Unlike the matrix patterns, these letter-like line drawings have strong intrinsic vertical axes. The effect of non-additiv-

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ity should be replicated with patterns with different features which can be assumed also to have a different mental representations. Four figures from the set of Tarr and Pinker (1989) were selected (see Figure 2b).

Method

Subjects. Subjects were 20 students (mean age 22;1 years) from the Humboldt University, who participated for course requirement or credit.

Material alTd procedure. We used three figures from the set used by Tart and Pinker (1989) in the experimental phase and another in the practice phase (see Figure 2b). The procedure was conducted in the same manner as in Experiment 1, except that the four matrix patterns were replaced by four line drawings. The reference pattern was always presented in an upright orientation.

Response Time (s) 5

inspection Time

C30 Transformation ~ 1 Transformation

C o o r a m a u o n ~ ' " " ^ ' " []2Transformations

Transformation Time Comparison Time

Response Time Categories

Fig. 5 Inspection time, transformation time, and comparison time as a function of the number of transformations for trials with line drawings

Results and discussion

The analyses were the same as in Experiment 1. Figure 5 displays inspection time, transformation time, and comparison time as a function of trial type (0, 1, or 2 transformations).

We obtained almost identical results to those in experiment with matrix patterns (Experiment 1). The number of transformations had a significant effect on the transformation time, F(2, 38) = 75.2, p < .01. The estimation for trials with two transformations differed significantly from the empirical transformation time for those trials, t(19) = 10.35, p < .001. The coordination cost is marked in Figure 5.

Unexpectedly, the inspection time decreased with the number of transformations, F(2, 38) = 9.03, p < .01. It was higher in trials with no transformations (Tukey, CD = 155.1, p < .05). Comparison time increased with the number of transformations, F(2, 38) = 19.3, p < .05. In particular, comparison time was lower in trials with no transformations of drawings than in the other two trial types (Tukey, CD = 119.5, p < .05). Error percentages (0.8%, 5.0%, and 10.84%) also increased with the number of transformations, F(2, 38) = 21.46, p < .001, and were at the same level as in the experiment with matrix patterns.

The main outcome of this experiment with line drawings was similar to the result of the experiment with matrix patterns. Coordination cost was about one-third of the transformation time in this type of experiment. Variation of the patterns did not influence the coordination cost. This can be concluded from the results. Both experiments gave converging results. Co- ordination is a separable component in these mental manipulation tasks.

We did not expect to see any effect of the number of transformations on inspection time or comparison time. There was an effect, but it was very small in comparison with the most interesting effects on transformation time. It seems that there were at least some posttransformational processes (Hertzog & Rypma,

1991). This small effect does not influence the coordination cost. Transformation time of 727 ms for one transformation is much higher than the posttransformational component of 163 ms of the comparison time (difference between comparison time for 0-transformation trials and 2-transformation trials).

To define and characterize the nature of the intermediate representations of matrix patterns formed by the visual system alone or in connection with visual knowledge is rather difficult (Van der Meer, 1985). So we decided to influence the internal representation by changing the comparison task (adapted from Emmorey, Bellugi, & Kosslyn, 1993). This change generated a pressing need for the storage of the whole pattern so that the position of each filled cell in the matrix pattern can be reconstructed.

Experiment 3

Variation of the demand in the comparison phase

We know from experiments that have patterns similar to our stimuli (Schwarz, 1986; Van der Meer, 1985) that during practice subjects reduce the complexity of the mental representation (see also Haider & Frensch, 1994). A change in the comparison task may require subjects to form a different mental representation for efficient performance. Without question, the set of features to which people attend is chosen in dependence on the comparison task. In Experiments 1 and 2 the comparison task of the subject was to decide whether or not the reference pattern was transformed correctly. The negative test item was always the original pattern, but transformed incorrectly. Subjects could extract cer- tain units of the mental representation for an efficient solution of a task. Efficient means that they extract only the units that allow the discrimination of the result of various transformations. We looked for a way to in- duce subjects to perform complete mental transformations with fully detailed images. So we decided to force

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them to maintain more structura] information in the transformed image by changing the comparison task. Subjects received only two cells in the comparison phase with the instruction to decide whether these filled cells are on the transformed mental representation of the pattern. This should also increase the cost for single transformations. But from the point of view of converging operations, we also expected coordination costs resulting from control operations that set up and moni- tor the transmision of information between transformation episodes.

Method

Subjects. Again in this study the subjects were 20 students (mean age 23;0 years) from the Humboldt University participating for course requirement or credit.

Material and procedure. These were the same as in Experiment 1, except that in the comparison phase the subject saw only two of the four filled squares of the matrix. On "yes" trials these two filled squares were located on the transformed pattern. They were chosen by a random process. On "no" trials one of them was located outside of the transformed pattern. It was placed next to a correct location.


The mean inspection time, the comparison time, and the transformation time are presented in Figure 6. First, separate one-way Manovas with number of transformations as factor were conducted for inspection time, transformation time, comparison time, and error percentages.

Transformation time increased with the number of transformations, F(2, 38) = 44.09, p < .001. The estimation derived from trials with component transformations in isolation differed significantly from the transformation time for trials with two transformations, t(19) = 4.2, p < .001. The coordination cost is marked in Figure 6. Comparison times did not depend on the number of transformations, F(2, 38) = 2.24, p > .1,

Response Time (s) 7

Inspection Time Transformation T i m e Comparison Time

Response Time Categories

Fig. 6 Inspection time, transformation time, and comparison time as a function of the number of transformations for trials with matrix patterns and changed comparison task

although inspection time decreased with the number of transformations, F(2, 38) = 10.13, p < .001. Inspection time was higher in trials with no transformations (Tukey, CD = 143.4, p < .05). More errors occurred (4.8%, 10.4%, and 16.2%) as the number of transformations increased, F(2, 38) = 20.1, p < .001.

Additionally, separate two-way Manovas on inspection time, transformation time, comparison time, and error percentages from Experiments 1 and 3 with experimental condition as a between-subjects factor and number of transformations as a within-subjects factor were performed to investigate the influence of the demand in the comparison phase on dependent variables. In general, comparison time, F(1, 38)= 14.23, p <.01, was higher in this study than in the Ex- periment 1. The error rate was also higher than in the Experiment 1 F(1, 38) = 7.62, p < .01. The number of transformations had a significant effect on all dependent variables (inspection time: F(2, 76)= 6.36, p < .01; transformation time: F(2, 76) = 116.26, p < .001; comparison time: F(2, 76) = 3.36, p < .05, and error rate: F(2, 76)= 38.34, p < .001). We found a significant interaction between experimental condition and number of transformation for inspection time, F(2, 76)= 4.33, p < .05. There were no further significant main effects or interactions.

In Experiment 3 we had changed the difficulty of the comparison task. Although there was no statistical effect from this change on the transformation times, the comparison times were higher (Figure 6) than in Ex- periment 1 (Figure 3). This is in accordance with a piecemeal transformation process. The more complex the representations and the longer the transformation process, the greater the likelihood of the degraded quality of the mental representations, or perhaps even of complete loss of information from the visual working memory. In general, this should result in more coordination cost, because subjects have to maintain and transform more complex representations (more units) and may have to reexecute transformation episodes (Lohman, 1988). As was expected, there was a substantial coordination cost. Thus, the results cannot be ex- plained by item-specific recoding mechanisms.

The fact that subjects generated more complex representations (containing more units) can also be derived from the prolonged comparison time in comparison to that in Experiment 1. But we must be careful with this conclusion, because comparison times also vary with the quality of representations and the confidence level of the subjects (Luce, 1986). Neither was controlled in our experiments. In summary, all three experiments gave evidence for a coordination cost in this serial mental transformation task. By studying this task, we may arrive at a first specification of one function of the central executive. But this now requires a change in the approach. Until now we have only asked whether there is coordination cost. The question we raise now is: What factors determine the cost of coordination.

302

Experiment 4

Serial presentation of transformation symbols

In each complex cognitive task subjects have to organ- ize mental processes in a strategy intended to achieve an established goal. This strategy can be seen as a com- promise resulting from constraints imposed by the task structure, the structure of cognitive abilities, and the structure of the goal. Our assumption was that coordination costs in the self-paced procedure with random presentation of trial types are related to the allocation of resources to transformations and to establishing the goal to execute two transformations. If coordination cost is the result of the demand on a central autonomous control unit, we would expect that transformation costs should be the same if time allocation for the generation of stable representations is triggered by external cues. But if there is a reduction in coordination cost in the case of external triggering for disengagement from the first transformation episode and for the allocation of resources to the activation of the next transformation procedure in a 2-transformation trial, then this is evidence against this assumption of an autonomous unit. In a pilot study Hagendorf and S~ (1995) therefore decided to replicate Experiment 1 with the followir~g exceptions: (1) in trials with two desired mental transformations subjects controlled the sequential presentation of transformation symbols; (2) subjects worked only on trials with one or two transformations; (3) patterns (four filled cells in a 3 x 3 matrix) were generated by a random process and used instead of the four patterns in the original experiment. The question was how a clear external structure in the allocation of resources to the desired transformations influenced the coordination cost. According to Hagendorf and S/t (1995), there was no coordination cost at all in this sequential condition of the presentation of transformation symbols.

This result is some of our first indirect evidence for the assertion of Neumann (1992) that the attentional controller is not an autonomous unit. But we have to confirm the outcome of this exploratory study because there were also unsolved problems in this investigation. The low coordination cost might be caused by the high variability of the patterns (random generation procedure) when compared with Experiment 1. Nor was the control condition (0 transformations) included in the design of Hagendorf and Sfi (1995). Because of the importance of the main result with the sequential procedure of the transformation task, we decided to carry out an experiment in which we solved these problems and made a within-subjects comparison of the sequential and simultaneous conditions.

Because subjects in the sequential condition with external triggering can build up and exercise a control structure that guides the transformation process in the

simultaneous condition, we check also for transfer between the conditions.

Method

Subjects. The subjects were 30 students (mean age 22;8 years) from Humboldt University who were participating for course requirement or credit.

Material and procedure. The material was the same as in Experi- ment 2. The experiment consisted of two main parts. One part was a replication of the procedure in Experiment 2. This procedure was characterized by the simultaneous presentation of the transformation symbols in 2-transformation trials. This part of the experiment is called the simultaneous condition. The other part was a replication of the first part, with the exception that in 2-transformation trials subjects also controlled the sequential presentation of the two transformation symbols, as in Hagendorf and Sfi (1995). So subjects did not know before finishing the execution of the first transformation whether or not a further transformation had to be executed. This part of the experiment is called the sequential condition of transformation symbol presentation. All subjects had to work on two blocks of trials with the simultaneous, and on two blocks of trials with the sequential, condition.

Subjects were randomly assigned to one of two experimental subgroups. One subgroup started with the simultaneous condition in Block 1. From Block 3 on they had to work with the sequential condition. The other subgroup worked on the reversed order of both conditions.

Before solving the experimental trials subjects solved 18 practice trials. One block of 9 trials was presented in the simultaneous condition, another block of 9 trials in the sequential condition. The order of practice blocks corresponded to the experimental phase.


Group means of inspection time, transformation time, and comparison time are presented in Table 2 as a function of presentation condition and number of transformations.

We conducted separate two-way Manovas with the factors Condition of symbol presentation (sequential and simultaneous) and Number of transformations on inspection time, transformation time, comparison time, and error percentages. Condition of symbol presentation had no effect on inspection time (F < 1) and comparison time (F < 1), but both were dependent on the number of transformations (inspection time: F(2, 58) = 7.6, p < .001; comparison time: F(2, 58) -- 55.96, p < .001). The interactions between the presentation condition and the number of transformations for both inspection time (F < 1) and comparison time, F(2, 58) = 1.13, p > .1, were nonsignificant.

The number of transformations had a significant influence on the transformation time F(2,58) = 122.88, p < .001, but there was no influence of the symbol-presentation condition (F < 1) and no interaction between the presentation condition and the number of transformations (F < 1). Transformation time in the sequential condition did not differ from the transformation time in the simultaneous condition.

303

Table 2, Group Means (in ms) of inspection time, transformation time, and comparison time as a function of presentation condition (simultaneous versus sequential) and number of transformations (0, I, or 2)

Simultaneous Presentation Sequential Presentation

0 1 2 0 1

Inspection Time 2658 2392 2333 2405 2172 2195 Transformation Time 1132 2275 5112 1190 2285 5019 Comparison Time 832 1077 1023 858 1149 1054

2,5

2

1,5

1

0,5

0

Coordination Cost (s) Coordination Cost ( % )

Number of Block ~ l C3 Block 1 (ms)

~Block 2 (ms} r~Block 1 (%) NaB ock 2 (%)

Sequential Simultaneous N

Simultaneous Sequential

Presentation of Transformation Symbols

40

35

30

25

20

15

10

5

0

Fig. 7 Absolute (ms) and relative (%) coordination cost as a function of the presentation condition of transformation symbols and block number of each symbol presentation condition

Next, coordination cost in the simultaneous condition was calculated according to ~,he procedure in Ex- periment 1. The calculation was changed in the sequential condition because in two transformation trials the algorithm contained the planning and execution of two motor responses in comparison to only one such response in the sequential condition (predicted = 2* control + 2* (1 t rans format ion- control)). We consider absolute and relative (coordination cost in relation to actual transformation time in 2-transformation trials) coordination cost in dependence on block number (see Figure 7).

We conducted a two-way Manova with Block number as between-subjects factor and Condition of symbol presentation (sequential vs. simultaneous) as within- subjects factor on the relative coordination cost. A consideration of the relative coordination cost showed that there was no influence from the order of the two presentation conditions (F < 1). Relative coordination cost was lower in the sequential condition, F(1, 28)=85.31, p< .01 . The interaction between Block number and presentation Condition was nonsignificant (F < 1). This result demonstrates that there was no effect of the presentation condition in block 1 on the presentation condition in block 2. So we can compare the simultaneous condition with the sequential condition without considering the effect of order or block number. The estimation of the absolute coordination cost was much higher in the simultaneous condition (1,695ms) than in the sequential condition (449 ms), t(29) = 6.71, p < .001. So the main outcome of this experiment was a substantial reduction in coord-

ination cost from the simultaneous to the sequential condition. Error percentages (1.8%, 7.76%, 13.83%), also increased with the number of transformations, F(2, 58)=26.21, p< .001 . The effect of symbol- presentation condition was nonsignificant, F(2, 58) = 1.29, p > 1. The interaction was also nonsignificant (F < 1).

In this experiment, the reduction of coordination cost is considered to be the most interesting result which confirms the result of our first exploratory study (Hagendorf & S/t, 1995). The following conclusions can be drawn from the consideration of the differences between the two procedures. The first difference between the simultaneous condition (see General Proced- ure and Experiment 2 in this paper) and this new sequential condition of transformation-symbol presentation is that in the simultaneous condition subjects have both transformation symbols available. They have to establish a strategy for interpreting and executing the transformation symbols and for allocating resources to the transformation episodes. In the sequential condition there is an external triggering of this process that reduces the control costs in this self-paced procedure. There is a second difference between the two procedural conditions. Subjects switch goals between trials in the simultaneous condition. In some trials they have the goal "execute one transformation", a signaled by the presentation of one transformation symbol. In other trials two transformation symbols are presented simultaneously, signaling the goal "execute two transformations." It is known that goal switching between trials costs extra time (Umiltfi etal., 1992; Logan et al., 1983). With sequential control of the presentation of transformation symbols subjects did not execute this goal switching. A third difference is that of the interpretation of the symbols. In the simultaneous condition there was uncertainty about separating the interpretation process from the transformation process.

To sum up, the external triggering of resource allocation in trials with two transformations and the reduc- ing of costs for establishing goals reduced coordination costs. So we conclude that those factors are sources for what we called coordination.

General discussion

Across variations in stimulus materials and demand in the decision stage transformation times for trials with

304

two transformations were substantially longer than es- timates derived from the sum of component transformations in isolation. The difference is spent on the coordination of two component tasks. In a first step the subject has to transform the image of the reference pattern according to the first transformation symbol. A stable, clear representation of the result of this step has to be created in the visual working memory in order to for the second transformation to be executed. This is possible only if the subject is able to secure the availability of resources of the working memory and to focus his or her attention on the relevant units in the mental representation in every moment. Coordination cost results from cost for maintaining goals, maintaining the intermediate representation, and the time to switch to the next transformation episode. If the subject is not able to do so efficiently, he or she has to repeat transformation episodes, which leads to increasing coordination cost. There is evidence for this dynamic interpretation from developmental psychological research (Mayr & Kliegl, 1993). So coordination is related to the allocation of appropriate resources to the transformations episodes and to the monitoring or progress in the transformation of units or representations.

However, a simple alternative interpretation of coordination cost has to be considered. It may be that coordination cost results from differences in the time taken to interpret one symbol in 1-transformation trials and two symbols in 2-transformation trials. On the basis of new results (Fischer, Hagendorf, & Sfi, submitted), this explanation can be excluded. These authors report an experiment in which subjects in all trials had to interpret two symbols, but did not always have to execute two transformations. The main outcome was that coordination cost was still substantial.

The question is whether there are hints in the litera- ture on coordination components in other task domains. Because we assume that coordination is related to the function of the central executive, it should not be bound to tasks in which visual-spatial representations are manipulated in cognitive procedures. Eysenck (1985) reported some evidence for coordination in mental computation. He used letter-transformation tasks that involved transforming between one or four letters by the movement of a given distance (2 or 4) through the alphabet. All the letters had to be transformed before the answer was given. His data showed that the demand on working memory grew nonadditively with the number of letters to be transformed. So there was an overall similar nonlinearity effect in the data, show- ing that intermediate representations and their maintenance, as well as the processing of units, require attentional resources of the central executive that deter- mines this effect. In analogy to letters in this transformation experiment we can see the units in mental representations of patterns in the serial mental-transformation task. In both cases we have a piecemeal

transformation process. This similarity should be tested in future research.

Different authors working in the field of mental arithmetic (Elio, 1986; Frensch, 1991) have presented evidence for a component that is independent of the efficiency of the mental procedures that have to be coordinated in the tested algorithms. Charness and Campbell (1988) found that different components of their complex computational procedure were different- ly influenced by practice. Most interestingly, the gain in the control component was smaller than the gain in the efficiency of the basic arithmetical procedural components. So after extended practice, about 70% of the gain in the execution of the complex procedure was related to control. Similarly, we also found that after practice the relative proportion of coordination cost was as high as at the beginning of the experiment. Hagendorf and S/t (1994) recently presented the results of an experiment with 18 blocks of practice in comparison to 6 blocks. In this study, with extended practice relative coordination cost was even greater at the end of the practice phase than at the beginning.

In Experiment 4 it was shown that the external triggering of the next transformation procedure in 2- transformation trials resulted in a substantial decre- ment in coordination cost. This result is evidence against the assumption of an autonomous control unit. Control operations should be studied for different representation domains.

Thus there is much evidence that coordination appears to be a separable component of the working- memory system. This component seems to be related to the characteristics of the function of the central executive (Baddeley, 1993a). The ability to coordinate cognitive activities appears to make a separable contribution to task demand and may be a separable contribution to individual differences (Gopher, 1992; Oberauer, 1993). It is a constraint on the use of working memory in the realization of mental procedures. The question is whether coordination is a homogeneous component in coordinating mental procedures or whether there are different control operations that depend on these procedures and representations.

Acknowledgements This research was supported by Grant Ha 1999/2-1 from the German Research Foundation (DFG). We thank C. Riecke for carrying out Experiments 3 and 4; and two anonymous reviewers for their comments and criticisms of an earlier version of this article.

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