Mental planning and the Tower of London task
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THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 200x, 5?A (?), 000–000 Mental planning and the Tower of London task L. H. Phillips University of Aberdeen, Aberdeen, Scotland, UK V. E. Wynn Oxford Brookes University, Oxford, UK S. McPherson University of Aberdeen, Aberdeen, Scotland, UK K. J. Gilhooly Brunel University, Uxbridge, UK The Tower of London (TOL) task has been used extensively as a test of planning ability in neuro- psychological patients and normal populations. Participants are asked to preplan mentally a sequence of moves to match a start set of discs to a goal, and then to execute the moves one by one. The mental preplanning stage has been identified as critical to efficient performance. The current experiments examined whether manipulations of mental preplanning influence performance on the TOL. In Experiment 1, the effect of different planning instructions was examined. Those told to make full mental plans spent considerably longer in planning than participants given no specific planning instructions, yet there was no effect of instruction condition on the efficiency of executing plans. Experiment 2 investigated whether people were able to plan mentally, by looking at their ability to identify intermediate states of an optimum mental plan. Results indicated that most individuals could make accurate preplans up to two subgoals ahead, but not three. However, making an efficient preplan did not result in better subsequent execution of moves to solve the TOL trial. It is concluded that people can make effective mental plans for a limited number of moves. However, on the TOL task, mental preplanning does not offer benefits in terms of quicker performance, or more accurate solution. The nature of planning in the TOL task is therefore questioned. Requests for reprints should be sent to Louise H. Phillips, Department of Psychology, William Guild Building, University of Aberdeen, Aberdeen, AB24 2UB, Scotland, UK. Email: email@example.com We thank Jim Urquhart for creating all the computer programs discussed here, Sharin Garden for assistance with data input and the analysis of Experiment 2, and Geoff Ward and an anonymous reviewer for their comments on the paper. 200x The Experimental Psychology Society http://www.tandf.co.uk/journals/pp/02724987.html DOI:10.1080/02724980042000237
2 PHILLIPS ET AL. Being able to plan efficiently is important in many of the complex behaviours of life such as organizing work schedules, making travel plans, or preparing meals (Cohen, 1996; Owen, 1997). The frontal lobes of the brain have long been associated with the ability to plan (e.g., Harlow, 1868; Luria, 1973). Patients with injuries to the frontal lobes of the brain often per- form well on conventional neuropsychological tests of memory and intelligence, but cannot cope with formulating and executing plans in the complex environment outside of the hospital (Cockburn, 1995; Shallice & Burgess, 1991). In order to study deficits in planning, Shallice (1982) developed the Tower of London (TOL) paradigm, based upon the Tower of Hanoi problem. In the TOL (see Figure 1), col- oured discs must be moved one by one from an initial state to match a goal state. Instructions are given to plan the whole sequence of moves that must be carried out mentally, before exe- cuting the sequence. Measures can be taken of preplanning time (time between seeing the discs and making the first move), average move time (time spent on executing the plan), num- ber of trials solved to meet a particular criterion (e.g., trials solves in the minimum moves pos- sible or within a specified time limit), and excess moves (number of moves in excess of the minimum necessary to complete the task). Poor performance on the TOL is usually inter- preted as inability to plan efficiently (see, e.g., Morice & Delahunty, 1996; Owen, 1997; Shallice, 1982; Temple, Carney, & Mullarkey, 1996). It has been argued that TOL perfor- mance is dependent on efficient mental preplanning of a sequence of moves: “It is necessary for the participant to anticipate and plan ahead in order to accomplish the task correctly” (Temple et al., 1996, p. 346); “The Tower of London clearly requires ‘forward thinking’ or planning” (Owen, 1997, p. 432). However, a number of authors have highlighted our relative lack of knowledge of the cognitive components of planning (Cohen, 1996; Kafer & Hunter, 1997; Owen, 1997; Phillips, Wynn, Gilhooly, Della Sala, & Logie, 1999; Ward & Allport, 1997). Figure 1. Example of a Tower of London trial.
MENTAL PLANNING 3 Owen (1997) argues that successful performance on the TOL typically involves a number of stages, and outlines the following sequence of cognitive processes; (1) The overall situation is assessed by comparing initial and goal states; (2) a series of subgoals is defined; (3) a sequence of moves is mentally generated to attain the subgoals; (4) the sequence is revised in line with mental rehearsal; and (5) the correct sequence is executed. Although this sequence seems very plausible for the easiest 3-move TOL trials used in neuropsychological studies, it is question- able whether such an extensive sequence of processes can be retained and manipulated mentally in memory during 6-move or 10-move trials as used to assess planning ability in non- clinical populations (Kafer & Hunter, 1997; Phillips et al., 1999; Ward & Allport, 1997). One of the questions addressed in the current paper is whether efficient mental preplanning is pos- sible for sequences with a large number of subgoals. Ward and Allport (1997) carried out a series of experiments to examine the nature of subgoals in planning on the TOL task. They concluded that a subgoal consists of a “chunk of indirect moves”—that is, a series of moves that do not put a disk in its final goal position, but are essential for solution. Trials with indirect moves engender conflict between the overall goal (move discs to their final positions) and the subgoal (move disc away from its final posi- tion). Such goal–subgoal conflicts cause particular difficulties for frontal lobe patients (Goel & Grafman, 1995; Morris, Feigenbaum, Bullock, & Polkey, 1997; Shallice, 1982), and increase time spent planning on the TOL (Ward & Allport, 1997). Goel and Grafman (1995) differentiate between the construction of a plan and its subse- quent execution. In particular, they define planning in terms of mentally looking ahead and distinguish this from subsequently following the plan. Ward and Allport (1997) differentiate between mental preplanning on TOL trials, and on-line planning (during the execution phase). In one manipulation of the TOL, they restricted to 2.5 s the time available to make each indi- vidual move on the TOL task, and they forced participants to solve the trials in the minimum number of moves possible. Ward and Allport argue that these conditions ensure that all of the planning in the TOL consists of mental preplanning. This fits with the model of TOL perfor- mance proposed by Owen (1997), where all the subgoals of the task are preplanned prior to execution. However, often task instructions on the TOL do not restrict time per move, or number of moves made. It is not clear whether, under these conditions, people carry out full mental preplanning. Also, in some versions of the task participants are instructed to make full mental plans before beginning to execute movements (e.g., Morris et al., 1997), whereas in other versions there is no explicit requirement to preplan (e.g., Temple et al., 1996). Owen, Sahakian, Semple, Polkey, and Robbins (1995) discuss a variant of the TOL task in which participants were asked to plan a minimum move sequence on a TOL trial, then report how many moves were needed for solution. This manipulation resulted in considerably longer planning times in the TOL trials than did the usual methodology. However, Kafer and Hunter (1997) carried out a similar manipulation in a much larger population, and found no difference in planning time between a TOL condition in which participants had to specify the minimum number of moves to solution, and a condition without this requirement. Questions have been raised about the validity of TOL as a task of planning (Kafer & Hunter, 1997; Phillips et al., 1999). Kafer and Hunter (1997) used structural equation model- ling to assess the validity of the TOL and concluded that the TOL does not measure planning. However, this analysis is dependent on the assumption that other tests used in their study (the Six Elements Test, the 20 Questions Test, and the Complex Figures Test) are valid and
4 PHILLIPS ET AL. sensitive measures of planning. There are also indications from protocol analysis that preplan- ning may not play as important a role in he TOL as is often assumed (Gilhooly, Phillips, Wynn, Logie, & Della Sala, 1999). Concurrent verbal reports of planning during the TOL indicated that there were relatively frequent mismatches between the plan that people articu- late and the actual moves that they subsequently execute. Older adults’ mental plans had less depth and more errors than younger adults’ plans, but there were no age differences in the accuracy of the actual moves executed. Gilhooly et al. conclude that people do sometimes attempt to make a full mental preplan; however, rather than storing the resulting plan for use in the execution phase of the trial, participants seem to start on-line planning from scratch with the advantage of stimulus support. Performing secondary tasks concurrently with the TOL had unexpected effects on plan- ning (Phillips et al., 1999). Concurrent secondary tasks caused a dramatic decrease in time spent preplanning, but did not cause slower move times: For example, concurrent articulatory suppression caused a drop in preplanning times on the TOL from 14 to 5 s, yet also resulted in a decrease in time spent moving the discs. Further, concurrent articulatory suppression did not result in more moves being made to solve the TOL trials, despite huge decreases in time spent preplanning. In other words, dramatic decreases in preplanning time did not adversely affect TOL move times or number of excess moves made. Phillips et al. conclude that TOL performance is generally controlled by on-line planning rather than mental preplanning. The requirement to preplan a whole sequence of actions in advance is contrary to naturalistic plan- ning, in which people plan only the beginning of a sequence, and then intersperse execution and planning phases (the “opportunistic” model of planning, Hayes-Roth & Hayes-Roth, 1979). Such opportunistic planning places less load on memory than does full preplanning. Indeed, at some point it may become impossible to preplan all the required moves ahead, as the limits of memory are reached. The current paper investigates the role of preplanning in TOL performance and further specifies the cognitive components of planning. Three questions are addressed: 1. Does time invested in preplanning result in more efficient solution of TOL trials? 2. Can people make accurate mental plans? 3. Are there limitations on the length of mental plans? EXPERIMENT 1 The TOL task has been used widely in studies of neuropsychological patient deficits and nor- mal individual variation in executive function. However, a range of different instructions has been given to participants attempting the task. In some studies no instructions about preplan- ning are given, whereas in others participants are asked to make a full mental preplan before beginning to move the discs. Also, participants are sometimes told how many moves are the minimum in which to solve the task, whereas in other studies this information is not given. Experiment 1 addresses the question of whether these different instructions impact upon TOL performance. Further, the effect of spending time constructing a mental plan on subse- quent execution of a solution is addressed. Participants were assigned to one of three condi- tions that differed in the task instructions given:
MENTAL PLANNING 5 Plan condition: asked to construct mentally a full plan of a minimum move path before exe- cuting the solution, Inform condition: informed of the minimum moves in which to solve the task, and then asked to construct mentally a full plan before execution, or Control condition: no specific planning instructions given. First, it is of interest to ask whether giving no specific planning instructions (the control condition) will result in considerably shorter preplanning times. If so, and preplanning is criti- cal in efficient TOL performance, then the full preplan/informed conditions should result in quicker move times and fewer excess moves than the control condition. Further, if individuals are informed of the minimum number of moves to solution, efficient plan checking should result in longer plan times as individuals check the number of moves in the plan against the number given as the minimum. Method Participants A total of 94 unpaid participants, 37 male and 57 female university students, with ages ranging from 18 to 40 years, took part in the experiment, which lasted for approximately 20 min. Materials Twenty TOL problems were presented on a computer monitor, increasing in number of moves required from 1 to 10, and with a varying number of indirect or goal conflict moves (0 to 5) and subgoal chunks (0 to 4) as defined by Ward and Allport (1997) as a consecutive series of indirect moves that all transfer discs to and from the same pegs. Trials were always presented in the same order. The same trials were used in all three conditions, and the minimum moves required to solve all trials were 118. Partici- pants moved the discs using a mouse. It can be noted from Figure 1 that the version of the task used in the current study was based on that reported by Ward and Allport (1997), which differs from the usual neuropsychological version of the task in two respects: It involves five rather than three discs, and the three rods are the same size rather than differing. These features allow a wide range of difficulty levels of TOL trials to be created. Procedure Each participant was individually tested and randomly assigned to one of three conditions: control (n = 32), plan (n = 33), or inform (n = 29). The following instructions were given while the experimenter demonstrated the task by pointing. Five very simple example trials were given as practice to allow partic- ipants to get used to the interface. Control instructions: “The task you will be doing is called the Tower Of London. Basically what you will be doing is looking at this ‘goal’ set of three pegs on which are placed five coloured discs. You will then move the coloured discs on the second ‘start’ set of three pegs to exactly match the positions of those on the first set in as few moves as possible using the mouse.” Plan instructions: As for the control instruction, plus “Each trial is in two parts. In the first part look carefully at the ‘goal’—and plan in your head the moves you have to make to the bottom set of discs to make them match those of the goal set in the fewest possible moves. When you have planned your moves and are confident that they will achieve the goal position you can go onto part two which is use the mouse
6 PHILLIPS ET AL. to move the discs on the bottom set of pegs as quickly as you can to match those of the goal set. It is very important that you have planned what you have to do before beginning to move the actual discs.” Inform instructions: As for the plan instructions, plus “You will be told the minimum number of moves required to match the goal at the beginning of each trial.” In each of these conditions, the following measures were recorded: time spent preplanning (from the appearance of the discs to the first move made), mean move times, and the number of moves made. Also recorded was the number of trials solved in the minimum number of moves possible. However, due to computer problems this last variable was only available for 49 participants: 15 in the informed group, 17 in the plan group, and 17 in the control group. The TOL trials were split into four difficulty levels, each with five trials, and the effects of trial type on planning, moving, and accuracy analysed: Level 1: trials ranging from one to five moves, with no indirect moves. Level 2: trials ranging from three to seven moves, with one or two indirect moves, and one or two subgoal chunks. Level 3: trials with five to nine minimum moves, two to four indirect moves, and one to four subgoal chunks. Level 4: trials with seven to ten minimum moves, three to five indirect moves, and three subgoal chunks. Results Figure 2 shows the mean preplan times, move times, excess moves made, and number of trials solved in the minimum number of moves in each of the three experimental conditions, aver- aged across all 20 trials. An analysis of variance (ANOVA) revealed a significant difference between the instruction groups in terms of time spent preplanning, F(2, 91) = 10.81, p < .0001. A post hoc test of significance (LSD test) showed that the control group was signifi- cantly faster than either the planning or the informed group. There was no significant differ- ence between the planning and informed groups. However, despite these large differences in preplanning time, there were no group differences in time spent moving the discs, F(2, 91) = 1.28. The next question is whether the increased planning times in plan and inform conditions resulted in fewer moves being made on the TOL task. Analysis of the number of moves made showed no significant difference between the three different instruction conditions, F(2, 91) = 1.09. There was also no effect of the different instruction conditions on the number of trials solved in minimum moves, F(2, 46) = 1.24. Analysis across the four difficulty levels Further analyses compared the effects of the three experimental conditions on perfor- mance at the four difficulty levels of the TOL task (see Figure 3). In terms of planning time, there were effects of both condition, F(2, 91) = 10.68, p < .001, and trial type F(3, 273) = 28.8, p < .001, with significant increments in plan time between all levels (except Levels 3 and 4). A significant interaction between condition and trial type in predicting planning time was also found, F(6, 273) = 5.16, p < .001. Tukey’s HSD test showed that trial type significantly affected planning times for both inform and plan groups, but did not affect planning time for the control group. Inform and plan groups did not differ in terms of preplanning time at any
MENTAL PLANNING 7 Figure 2. Mean plan time, move time, number of moves, and number of trials solved in the minimum moves possi- ble in plan, control, and inform conditions in Experiment 1. Bars indicate standard deviations. level of trial difficulty, whereas both of these conditions resulted in longer planning times than did the control condition at Levels 3 and 4 TOL trials. Next, move times across the different trial types were analysed. There was no effect of experimental condition on moving times, F(2, 91) = 0.960, but a strong effect of trial type, F(3, 273) = 60.6, p < .001, such that the trials with no indirect moves were performed quicker than the more difficult trials. There was also a significant interaction between condition and trial type, F(6, 273) = 3.86, p = .001, see Figure 3. The conditions generally did not differ in move
Figure 3. Effect of planning instruction condition and trial type on plan times, move times, number of excess moves, and trials solved in minimum moves in Experiment 1. Trial type: Level 1 = one to five moves, with no indirect moves; Level 2 = three to seven moves, with one or two subgoal chunks; Level 3: five to nine minimum moves, one to four subgoal chunks; Level 4: seven to ten minimum moves, and three subgoal chunks. 8
MENTAL PLANNING 9 times, except that those in the inform condition moved the discs more slowly than those in the control condition at Trial Levels 3 and 4. The effects of condition and trial type on the number of excess moves made above the mini- mum possible for solution were analysed. There was no effect of condition on the number of moves made, F(2, 91) = 1.30, but there was a significant effect of trial type, with more complex trials resulting in higher numbers of excess moves, F(3, 273) = 72.5, p < .001. There was no interaction between condition and trial type in determining the number of excess moves, F(6, 273) = 1.80. In terms of the number of trials (out of five) solved in the minimum number of moves, there was no effect of instruction condition, F(2, 46) = 1.24, or interaction between trial type and condition, F(6, 138) = 1.60. There was an effect of condition, F(3, 138) = 27.2, p < .001, with significant decrements in number of trials solved across all difficulty levels except Levels 2 and 3. The trials so far have been classified roughly in terms of difficulty, however, Ward and Allport (1997) specify that number of “chunks” of indirect moves best identifies the difficulty of planning required, so another analysis examined the effects of subgoal chunks on accuracy of performance. Four of the trials could not be unambiguously classified in terms of number of chunks. Of the remaining trials, five had no indirect moves, four had one subgoal chunk, two had two subgoal chunks, and five had three subgoal chunks. The effect of planning condition and number of subgoal chunks on the probability of solving a trial in the minimum number of moves was examined. There was a substantial effect of chunks on the probability of correct solution, F(3, 138) = 47.3, p < .001. There was no effect of planning condition on accuracy of solution, F(2, 46) = 0.536, nor an interaction between condition and subgoal chunks, F(6, 138) = 1.29. In order to investigate potential influences on planning time, correlations between plan- ning time and other performance measures are reported in Table 1. These results collapse per- formance across difficulty levels to avoid reporting excessive numbers of correlation coefficients. There was little indication that TOL difficulty had directional effects on the rela- tionships reported. There was no significant relationship between the amount of time spent planning and number of excess moves or trials solved in the minimum number of moves in any of the experi- mental conditions. In the control condition the positive relationship between planning time and trials solved in the minimum number of moves approached significance (r = .47). Plan TABLE 1 Correlations between preplanning time and other performance indices in the three different instructions conditions of Experiment 1 Correlation between plan time and: —————————————————————————– Move time Excess moves Trials solved in min. moves Condition correlation (n) correlation (n) correlation (n) Plan 0.19 (33) −0.03 (33) −0.08 (17) Inform –0.07 (29) −0.23 (29) 0.30 (15) Control 0.80* (32) −0.09 (32) 0.47 (17) Notes: n indicates number of participants for whom correlation reported (numbers in parentheses). *indicates correlation significant at p < .05.
10 PHILLIPS ET AL. times did not relate to move times in the plan and inform conditions. However, in the control condition those who planned faster also moved the discs faster. Discussion Those in plan or inform conditions spent considerably longer preplanning on the TOL task than those in the control condition. The major difference in planning strategies between the experimental groups occurred on the most difficult trials. Despite these substantial differ- ences in time spent preplanning, there was no effect of task condition on the time spent moving the discs. This suggests that plan and control instructions did not result in differences in the amount of time spent planning “on-line”—that is, during the moving phase of the task. Is the extra time spent preplanning by those in the plan condition—an extra 12 s for each of the most demanding trials—wasted time? The current results suggest that even if participants spend a reasonable length of time preplanning, the same amount of on-line planning will occur as when no preplan was made. These results concur with findings from Phillips et al. (1999) that concurrent secondary tasks substantially reduced time spent preplanning, but did not increase the time spent moving the discs. Further, despite the substantially shorter planning times in the control condition, there was no effect of planning condition on the accuracy of solving TOL trials. This suggests that long preplanning times in the plan condition were not utilized to make effective plans of action. The groups took very similar numbers of moves to solution, even on the most difficult trials. In fact, the average number of moves made in plan and control conditions was remark- ably similar: An average of 129.64 moves over all trials in the planning instructions group, compared to 129.66 moves across all trials in the control instructions group. When left to determine a strategy for attempting the TOL task (i.e., in the control condition) individuals do not spend much time preplanning (4.34 s per trial). Perhaps this is a prudent strategy to use on the TOL, the extra time spent during plan or inform conditions appears to bring no benefit in terms of speed or accuracy of performance. At least on the version of the task used here, it appears that the task is best solved by intermittent bursts of planning and execution, rather than full preplanning where all subgoals are defined and solved mentally in advance. One interpretation of the results might be that those in both plan and control conditions made quite full plans, but those in the plan condition spent more time (ineffectively) checking the plan that they made. This seems unlikely because if monitoring of plans was a major cause of differences in preplanning time, it would be expected that those in the inform condition, where there was a clear criterion against which to check plans, would have shown significantly longer planning times. However, if anything, planning times were shorter in the inform condi- tion. There was also no effect of the inform condition in terms of number of moves made, sug- gesting that people were either unable to identify how many moves were in their own mental plans, or not concerned when plans exceeded the minimum number of moves. Those in the inform condition did take longer to execute moves in the most difficult trials than those in plan or control conditions. This extra time during the move phase may have been used to check their executed plans one line against the informed number of moves. In relation to the different planning instructions that have been given to participants in previous neuropsychological studies, it appears that the instructions given do influence planning behaviour, that is, being told to make a full mental plan affects behaviour prior to
MENTAL PLANNING 11 moving discs on the TOL task. However, these different instruction conditions do not affect the outcome of planning, that is, trials are solved with equal accuracy under the different types of instruction. There was no significant relationship between the amount of time spent planning and the number of excess moves made in any of the experimental conditions. Relationships between planning time and trials solved in the minimum number of moves were also not significant: However, in the control condition the relationship between plan times and trials solved was close to significance (r = .47). This indicated that when no instructions to plan were given those who took longer in preplanning tended to solve more trials accurately. No such relation- ship was found in the plan condition, which suggests that more than a few seconds of planning time was not beneficial. This is in contrast with results from Ward and Allport (1997), whose instructions corresponded best with the plan condition reported here, and who found that individuals who spend longer planning make fewer errors on the TOL task. There may have been more variation in ability to carry out the TOL in the participants reported here than in Ward and Allport’s sample. The current results suggest that people do not preplan efficiently on the TOL, despite spending a reasonable amount of time apparently engaged in preplanning prior to execution of the task. This could be because memory limitations prevent individuals from being able to mentally carry out problem analysis, subgoal definition, subgoal solution, and evaluation of the action plan, at least on lengthy trials with multiple subgoals. Alternatively, inefficient planning may occur because carrying out such a sequence mentally is unpleasantly demanding and unlikely to occur without substantial incentive to do so. The next experiment addresses the issue of whether people can preplan efficiently if given appropriate incentive to do so. EXPERIMENT 2 Experiment 2 investigates whether people can plan ahead in the TOL task by forcing them to make judgements about whether intermediate states occurred in their plan. Only by mentally preplanning a sequence of moves can individuals be sure of whether or not a specified interme- diate disc state occurred during the plan. This experiment also re-addressed the issue of whether forcing people to preplan mentally results in more efficient subsequent execution of the TOL task, but with stronger controls placed on planning time than in Experiment 1. A final question was whether memory limitations prevent people from planning over and above a certain number of subgoals. In Experiment 2, participants were assigned to either a “plan” condition or a “5-second” condition. In the plan condition, start and goal states for a TOL trial were shown on a com- puter, and participants were asked to preplan mentally a minimum-move solution in order to work out the penultimate state of the discs before achieving the goal. They then had to choose between four plausible penultimate move states. In order to check whether these four penulti- mate states could be distinguished without making a mental plan, a 5-s condition was intro- duced to examine ability to identify penultimate move states when insufficient time was given to plan. Ability to identify penultimate move states was examined in relation to plan/5-s con- dition and trial difficulty. Participants also completed the move sequences of each TOL trial, so that move times and number of moves made could be measured. Comparison of excess moves made in 5-s and plan conditions identifies whether accurate preplanning improves
12 PHILLIPS ET AL. execution of TOL trials. The start and goal states were not present during the decision about the identity of the penultimate move state, in order that planning would be minimized during the identification stage. Method Participants A total of 40 undergraduates took part in the experiment, 26 female and 14 male, aged between 19 and 45 years of age. They were not paid for participation. Materials and procedure Half of the participants were assigned to the plan condition and half to the 5-s condition. All then completed a practice session and 12 TOL trials, as outlined in the following section. The planning phase of trials differed depending on whether participants were assigned to the plan or the 5-s condition. All subsequent stages of trials were the same in plan and 5-s conditions. Exactly the same 12 arrangements of start and goal states were used in the plan and 5-s conditions. Four difficulty levels were given; each included three trials: 5.0 trials: minimum of 5 moves to completion, 0 indirect moves. 5.2 trials: minimum of 5 moves, with 2 indirect moves in 2 subgoal chunks. 7.2 trials: minimum of 7 moves, with 2 indirect moves in 2 chunks. 9.3 trials: minimum of 9 moves, including 3 or 4 indirect moves, and either 3 or 4 subgoal chunks. Each of the start/goal set-ups used was checked through a computer program that identifies all of the different minimum move paths to solve TOL trials, in order to verify the number of moves and indirect moves required, and also to verify that only one minimum move path was possible. This was important for establishing that there was not more than one penultimate state of the discs prior to minimum move solution (see later). For the 9.3 trials it proved difficult to find suitable start-goal states that had only one minimum move solution path. Trials were therefore selected that had two different minimum move solution paths but the same penultimate state of discs. A diagrammatic version of one of the easiest trials is presented in Figure 4. Planning phase. This differed for those in plan and 5-s conditions. (1) Plan condition: Participants in the plan condition were shown the start and goal states of a TOL trial and asked to plan mentally the sequence of moves with which to solve the trial in the minimum number of moves possible. During the plan phase of the task, discs could not be moved. Emphasis was placed on the fact that participants could spend as long as they wished planning for each trial. When planning was com- plete, a mouse button was pressed to enter the next phase of the trial. (2) 5-second condition: Participants in the 5-s condition were shown a display of the start and goal states for 5 s. Once the display had been present for 5 s, the computer automatically moved on to the next phase of the trial. Pilot work established that it was not possible to plan up to the penultimate move state in 5 s, but that some information about start and goal states could be established in this time. Identification phase. This was the same in both plan and 5-s conditions. They computer displayed four different arrangements of coloured discs. Participants were asked to choose which arrangement matched the layout of the discs immediately prior to the final move of the plan being made; that is, they were to identify the penultimate state of the discs prior to the goal state being achieved. Each of the four
MENTAL PLANNING 13 Figure 4. Diagrammatic representation of TOL plan/5-s trials from Experiment 2. potential penultimate states was “one move away” from the goal state previously displayed (i.e., one disc had to be moved to achieve the goal state); however, only one of the states was the penultimate state achieved on execution of the minimum move path solution to the trial. It was emphasized to those in the 5-s condition that it was not possible for them to plan properly in 5-s so that during the identification phase of the task they would have to guess the penultimate move.
14 PHILLIPS ET AL. Moving phase. Participants were shown the same start and goal states as in the planning stage and asked to move the discs one by one on-screen to convert the start state to the goal state. The measures taken from performance were preplanning time (for plan participants only), accuracy of identification of penultimate moves, decision time for identification, mean time spent per move in actually solving the TOL trials, number of excess moves made in solving the TOL trials, and number of trials (out of three) solved in the minimum number of moves. Each of these measures was calculated sep- arately for the different trial types outlined earlier (i.e., 5.0, 5.2, 7.2, 9.3). Results The results are plotted in Figure 5. A series of ANOVAs were used to explore the data. First, the effect of trial type on planning time in the initial phase of trials in the plan condition was examined. (For the 5-s condition, all plan times were controlled to be 5-s.) There was an effect of trial type, F(3, 57) = 14.6, p < .001, such that planning times incremented significantly from 5.0 to 5.2 trials, and from 5.2 to 7.2 trials. The effects of experimental condition (plan or 5 s) and trial type on the accuracy with which people identified penultimate moves were examined next. There was an overall effect of con- dition, F(1, 38) = 54.92, p < .001, such that those in the plan condition were much more likely to correctly identify penultimate moves. Further, there was an effect of trial type, F(3, 114) = 10.33, p < .001, with longer trials proving more difficult. The interaction between condition and trial type was also significant, F(3, 114) = 6.12, p < .001, as shown in Figure 5. A Tukey’s HSD test revealed that plan and 5-s conditions differed in accuracy of identification on all tri- als except those demanding nine moves (and three subgoal chunks of moves). Further, partici- pants in the plan condition were significantly worse at identifying penultimate states on 9.3 move trials than on trials of 5.0, 5.2, and 7.2 moves. Participants in the 5-s condition showed no significant differences in accuracy of identification across the different types of trial. These results suggest that people can plan with some accuracy up to seven moves (or two subgoal chunks of moves) ahead, but cannot preplan nine moves (or three chunks of moves) ahead. The effects of plan/5-s condition and trial type on time taken to make penultimate-move iden- tification decisions were also analysed. There were no effects of plan/5-s condition, F(1, 38) = 0.94, or trial type, F(3, 114) = 2.44, on decision times, nor any interaction, F(3, 114) = 0.28. Execution of TOL solutions was also analysed. There was an effect of trial type on move times, F(3, 114) = 5.50, p < .001, but no effect of plan/5-s condition, F(1, 38) = 0.03, and a non-significant interaction, F(3, 114) = 2.24. The 5.2 trials resulted in longer move times than did other trial types. There was also an effect of trial type on the number of excess moves made when solving TOL trials, F(3, 114) = 23.0, p < .001, with 9.3 and 7.2 trials resulting in more excess moves than 5.0 and 5.2 trials. However, planning condition did not affect the number of moves made, F(1, 38) = 0.06, with plan and 5-s conditions very closely matched in terms of number of excess moves made. There was no interaction between condition and trial type in determining excess moves, F(3, 114) = 0.14. The effects of plan/5-s condition and trial type on the number of trials solved in the minimum number of moves possible were also investi- gated. There was no effect of condition, F(1, 38) = 0.01. However, there were significant dif- ferences between all levels of trial difficulty in terms of the number of trials solved in minimum moves, F(3, 114) = 35.7, p < .001. No interaction was found between planning condition and trial type, F(3, 114) = 0.84.
MENTAL PLANNING 15 Figure 5. Experiment 2 results. Effect of plan/5-s condition and TOL trial type on: planning time per trial, num- ber of penultimate states correctly identified, identification time per trial, average time to make each move in solving TOL trials, number of excess moves made on TOL trials, and number of trials solved in minimum moves. White col- umns indicate plan condition, shaded indicate 5-s condition. Trial types: 5.0 = trials requiring a minimum of five moves, none indirect; 5.2 = trials requiring a minimum of five moves, two indirect; 7.2 = trials requiring a minimum of seven moves, two indirect; 9.3 = trials requiring a minimum of nine moves, three indirect. Finally, the relationships between planning time and other task variables in the plan con- dition only were examined. Significant correlations indicated that longer planning time was related to: poorer accuracy of identification (r = –.45), longer time spent identifying
16 PHILLIPS ET AL. penultimate move states (r = .44), longer to move discs on the TOL (r = .46) and a greater number of excess moves (r = .56). The correlation between plan time and number of trials solved in the minimum number of moves was non-significant (r = −.26). Discussion The results of Experiment 2 provide support for the hypothesis that people can mentally con- struct a TOL plan; however, as the complexity of the task increases planning becomes more difficult, and many individuals seem unable or unwilling to plan with complete efficiency. Most individuals are able to formulate plans up to seven moves or two subgoal chunks ahead, as seen in the accurate identification of penultimate moves by those in the plan conditions compared to those in the 5-s condition. However, participants could not plan nine moves (three or four subgoal chunks) ahead. Indeed the average of 56 s spent preplanning on 9.3 trials did not result in better ability to identify penultimate moves than did guessing. One potential problem with the task might be that the mental image of the penultimate-move states gener- ated by participants would not easily map onto the computer-generated image of the move states. However, the high level of performance on the 5.0 trials in the plan condition suggests that most individuals were capable of recognizing the correct choice of allowed time to plan. Performance during Experiment 2 suggests that the major factor determining difficulty of planning in TOL trials is the number of subgoal chunks, rather than the number of moves made, concurring with the findings of Ward and Allport (1997). This can be seen from Figure 5, where the number of correct decisions made on penultimate states by those allowed to plan is higher in 5.0 than in 5.2 trials, but does not differ between 5.2 and 7.2 trials. In agreement with the results from Experiment 1, there was no effect of planning condition on move times in solving TOL trials, despite the substantial differences in planning times between plan and 5-s conditions. Spending a long time preplanning (e.g., on 7.2 trials, 53 s per TOL problem in the plan condition compared to 5 s) does not reduce the amount of time spent planning on-line when carrying out a TOL trial. Further, there was no effect of planning con- dition on the number of excess moves made, or trials solved in the minimum number of moves, suggesting that the extensive time spent making apparently accurate plans is of little benefit when carrying out the motor moves. Although it is possible to construct a mental preplan to solve two subgoal TOL trials, this plan does not appear to prove very helpful when actually executing a solution to the task. This finding concurs with evidence that making a full think- aloud plan for a TOL trial does not benefit the subsequent execution of a solution to the trial (Gilhooly et al., 1999). Summarizing across the different types of trial, a very similar number of trials (out of 12) were solved in minimum moves in the plan condition (6.96 trial) and 5-s condition (7.00 trials). There are a number of different explanations for the finding that accurately identifying the last stage of a plan did not assist subsequent execution of that plan. For example, it is possible that at least on some trials individuals planned move paths that took more than the minimum number of moves but still included the correct penultimate state. However, this would not explain the majority of correct identifications of penultimate stages, because many non-mini- mum move paths result in a different layout for the last stage of the plan. Alternatively, the demands of the plan condition emphasized the production and memorization of the endpoint of the plan. Perhaps this meant that memory resources were prioritized towards storage of the
MENTAL PLANNING 17 penultimate state, rather than the full plan. Our preferred explanation is that participants may indeed have produced an effective minimum move plan during the planning phase and cor- rectly identified the penultimate state, but could not readily translate the mental plan into a full sequence of moves because of incompatibility between the representational format of the men- tal plan and motor execution, or because of memory failures. This fits with the evidence that people construct on-line plans from scratch during execution of the TOL, even when they have attempted to produce a full mental preplan (Gilhooly et al., 1999). GENERAL DISCUSSION The current results suggest that most individuals can mentally plan up to seven moves (or two subgoals) ahead in the TOL task, but not nine moves (three or four subgoals) ahead. Further, both experiments provide evidence that carrying out mental preplanning on TOL trials does not assist subsequent execution of a plan of action: Time invested in preplanning does not result in quicker move times or fewer moves to solution. Models of performance on the TOL often emphasize the importance of full mental preplanning (Owen, 1997; Ward & Allport, 1997). The current experimental results provide converging evidence alongside that of proto- col analysis (Gilhooly et al., 1999) and dual task studies (Phillips et al., 1999) that mental pre- planning is not a major determinant of the efficiency of performance on the TOL. Instead, accurate performance depends largely on on-line planning. Most everyday tasks demanding planning involve on-line modification of plans, and interspersed episodes of planning, evalua- tion, and execution (Cohen, 1996). Decisions made during planning may be influenced by moment-to-moment changes in the state of relevant attributes. Also, in real-life planning it is often prudent to have a number of sketchy alternative or back-up plans, given unexpected contingencies. The finding that mental preplanning does not benefit subsequent solution of TOL trials supports the idea (Phillips et al., 1999) that the representational coding involved in preplan- ning and execution of TOL trials is not compatible. Task demands requiring preplanning may result in verbally rehearsed plans being made. This is supported by the finding that verbal dual tasks cause greater reductions in mental planning time than do visuospatial secondary tasks (Phillips et al., 1999). During the execution phase of TOL trials, these verbal plans have to be translated into motor movements and evaluated on-line in relation to a visual display; so visuospatial memory is likely to be more important. Again, this is supported by findings from dual-task manipulations. During execution, it might be difficult to translate a verbal plan into spatial movements and to relate the plan to any unexpected intermediate visual states (for example, where a plan was inaccurate). It has been argued by a number of authors that working memory is heavily involved in TOL performance (Joyce & Robbins, 1991; Morice & Delahunty, 1996; Owen, 1997). Such memory limitations make it unlikely that people will make full preplans because in response to an effortful cognitive task most individuals adapt or develop strategies that demand as few resources as possible (Belmont, Freeseman, & Mitchell, 1988), and on-line planning is less resource intensive than mental preplanning. Although idealized performance on the TOL might require full mental preplanning (a cognitive process with a high working-memory load), those taking part in cognitive tests often find ingenious ways to avoid loading memory (Phillips & Forshaw, 1998).
18 PHILLIPS ET AL. These results have some implications for the interpretation of executive tasks in general. Often, such tasks involve many different cognitive components and many potential strategies to attempt the task. Small variations in task instructions may influence the way people carry out the task. Caution is needed in interpreting performance on such tasks as reflecting a par- ticular executive deficit. Unless reliable information is available that indicates the strategies used by individuals to attempt such tasks, assumptions should not be made about the cognitive processes involved. In the current experiments, when no specific instructions were given to preplan, there were considerable individual differences in the length of time spent planning. One influence on planning time might be level of impulsivity (Owen, 1997). There is evidence that degree of impulsivity—the extent to which an individual shows preference for speed over accuracy—is somewhat stable across different cognitive tasks (Phillips & Rabbitt, 1995). Evidence relevant to this comes from an unpublished study (McGowan, 1998) in which participants completed the TOL, and questionnaire measures of impulsivity such as the Barratt Impulsivity Scales (BIS: Barratt & Patton, 1983). When participants were given no particular instructions about planning the correlation between planning time and BIS score was −.44: Those who self- reported as more impulsive spent less time planning on the TOL task. However, impulsivity did not relate to TOL excess moves made. Choosing to spend a long time preplanning may reflect personality characteristics rather than the efficiency of planning. CONCLUSIONS This paper aimed to address three questions: 1. Does time invested in preplanning result in more efficient solution of TOL trials? The results from both experiments indicate that time spent preplanning does not result in more efficient solution of the TOL in terms of either accuracy of solution or time spent carry- ing out the solution. 2. Can people make accurate mental plans? Evidence from Experiment 2 indicates that peo- ple can make mental plans if forced to do so. However, participants rarely follow a strat- egy of full preplanning unless given no choice by task parameters. Investing time in creating full mental preplans of TOL solution paths does not appear to be an efficient method of tackling the task. Conditions in which people were requested or forced to make full preplans did not result in quicker move times, or fewer moves made, com- pared to conditions discouraging or preventing planning. 3. Are there limitations on the length of mental plans? There do appear to be limitations on mental plans—the evidence here suggests that on the TOL task people have substantial difficulty in mentally planning more than two subgoals ahead. REFERENCES Barratt, E.S., & Patton, J.H. (1983). Impulsivity: Cognitive, behavioural and psychophysiological correlates. In M. Zuckerman (Ed.), Biological bases of sensation seeking, impulsivity and anxiety. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
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