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Individual differences in the exploration of a redundant space-time motor task
Neuroscience Letters 529 (2012) 144–149
Contents lists available at SciVerse ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Individual differences in the exploration of a redundant space-time motor task Adam C. King a,∗ , Rajiv Ranganathan b , Karl M. Newell a a b
Department of Kinesiology, Pennsylvania State University, United States Sensory Motor Performance Program, Rehabilitation Institute of Chicago, United States
h i g h l i g h t s
Individual differences are rarely assessed in motor learning studies. Examined variation in preferred movement strategies in a redundant space-time task. Three clusters of individuals varied in initial performance and search strategy. Exploration was influenced by task constraint, feedback and intrinsic dynamics. Adaptive learning should include skill level, task difficulty, and search strategies.
a r t i c l e
i n f o
Article history: Received 18 July 2012 Received in revised form 1 August 2012 Accepted 7 August 2012 Keywords: Redundancy Search strategies Motor learning Intrinsic dynamics
a b s t r a c t Individual differences in learning a motor task are rarely assessed even though they can potentially contribute to our understanding of the problem of motor redundancy—i.e., how individuals can exploit multiple different strategies to realize the task goal. This study examined individual variations in the preferred movement strategy of a redundant motor task. Thirty-two participants performed a star tracing task on a digitizing tablet with the goal of minimizing a performance score that was given as feedback. The performance score was a weighted combination of spatial error and movement time, meaning that multiple strategies could yield the same score. A cluster analysis revealed three distinct groups of individuals based on their initial movement strategy preferences. These groups were not only different on their initial performance, but also exhibited differences in both local (trial-to-trial change) and global (average change) search strategies that were reflected through differential modification of spatial and temporal components. Overall, the results in this space-time task reveal that the intrinsic dynamics of the individual channel the initial exploratory solutions to learning a redundant motor task. © 2012 Elsevier Ireland Ltd. All rights reserved.
1. Introduction The uniqueness of each individual has classically been attributed to variability in intellectual capacity or in a single general motor ability [1] and presents several challenges to the study of group differences that use standard inferential statistics. Indeed, individuals possess a unique set of movement capacities and preferences based on a variety of factors that include anatomical organization, physiological structure, learning style and previous movement experiences. However, in the search for group differences, most studies in motor control and learning typically attempt to minimize or filter out the effects of these individual differences by selecting simple motor tasks and using techniques such as random group assignment and averaging. These procedures can mask
∗ Corresponding author at: Department of Kinesiology, The Pennsylvania State University, 23 Rec Building, University Park, PA 16802, United States. Tel.: +1 814 863 4037; fax: +1 814 863 7360. E-mail address: [email protected] (A.C. King). 0304-3940/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.neulet.2012.08.014
important characteristics of inter-individual variability that may reveal qualitatively and quantitatively distinct pathways of change [9,17]. One perspective to motor learning that emphasizes the notion of individual differences is the dynamical systems framework [10,13]. Differences between individuals are captured in the construct of intrinsic dynamics [11] that can be viewed as a dynamic landscape of movement capabilities that influence the trajectory of performance change relative to the to-be-learned action [10]. It is well established that individuals acquire new movement patterns on the background of pre-existing capacities; however, uniformity of this history across individuals is likely not the case. For example, using a scanning paradigm to assess individual differences, Kelso and Zanone [12] demonstrated that individuals possess different stable coordination patterns prior to any influence of practice and learning. However, this framework has so far been restricted to examining a class of motor tasks where the goal is to produce a particular relative phase between two effectors, meaning that the number of ways in which this motor task could be solved was limited.
A.C. King et al. / Neuroscience Letters 529 (2012) 144–149
Although the individual performance levels may converge with practice, the potential sources contributing to inter-individual variability during the initial stages of acquisition has been one of the primary emphases in the study of individual differences [24]. The importance of these individual differences may be especially critical in motor tasks that afford redundancy. Redundancy offers the opportunity to solve a particular motor problem with an infinite number of solutions [4], thereby increasing the potential variation between individuals in how they solve the task. However, most approaches to redundancy have typically examined highly constrained motor tasks where in spite of the presence of redundancy there is very little variation between individuals (e.g., reaching in straight lines with bell-shaped velocity profiles) [8,14,25]. While these approaches have been successful in revealing features of welllearned movements patterns, they can be rather limiting when investigating the acquisition of new movement skills where individual differences likely play a much larger role in influencing how participants explore the perceptual-motor workspace in the process of achieving improved performance (i.e., “search strategies” cf. [18]). The present study sought to examine the role of individual differences during the exploration of a redundant space-time motor task on the search strategies used to realize performance improvements. The redundancy in the task was created by using a feedback score that was the linear weighted combination of two scores—a score that reflected the spatial accuracy (i.e., the spatial component) and a score that reflected the movement time (i.e., the temporal component). Using this redundant task offered two advantages in the attempt to identify individual differences during the initial exploration process. First, a variety of spatial and temporal solutions can be used to achieve the same outcome measure, which allowed us to examine individual’s initial movement preferences for this task. Second, because of the speed-accuracy trade-off [5] between the spatial and temporal components, the task allowed exploration of multiple strategies before participants could settle on a consistent solution. As a result, we examined how individual differences channeled the preferred movement strategies during initial practice. We hypothesized that the redundancy in this task would result in participants choosing distinct pathways of exploration, that would not only impact their initial performance, but also their subsequent search strategies [18].
2. Methods Thirty-two right hand dominant healthy individuals volunteered to participate in this study. The participants gave informed consent to the experimental procedures that had been approved by the Pennsylvania State University Institutional Review Board. The participants were seated in front of a graphics tablet (Wacom Cintuq 21Ux, Vancouver, WA) and instructed to trace a sixpointed star pattern displayed directly on the tablet screen using a digital stylus (Fig. 1). The diameter of the star shape (i.e., the distance between opposite vertices) was 30 cm. The 2D position of the stylus was sampled at 120 Hz. Participants started each trial on the right apex of the star, traced the pattern in a counter-clockwise direction and finished the trial at the same point. Following each trial, a visually displayed performance score was presented and participants were instructed to minimize the score throughout practice. The performance score (PS) was the sum of a weighted temporal component (WT ) and a weighted spatial component (WE ) that was calculated using the following equation: PS(n) = WT (n) + WE (n)
(1)
145
Fig. 1. Experimental setup. Participants traced the star on a digitizing tablet in a counter-clockwise direction using a stylus pen and started/finished each trial on the right apex of the six-pointed star.
where WT (n) =
aT (n) aTnorm + bEnorm
and WE (n) =
bE(n) aTnorm + bEnorm
and where n indicates the nth trial, T and E represent movement time and spatial error, and a and b represent the weighting coefficients for movement time and spatial error components, respectively. Pilot data provided the basis for determining the parameters of Eq. (1). Three pilot participants each performed 200 trials that were channeled by instructions over different segments of the speed-accuracy function so as to provide scores (i.e., movement time and spatial error) across the whole speed-accuracy range. The Tnorm and Enorm parameters were defined relative to the fastest movement time and least spatial error obtained in pilot data, respectively. The criterion used for this report was the speedaccuracy relation that had an equal emphasis of temporal and spatial components to the performance outcome. Participants were aware that the performance score reflected both speed and accuracy components but did not have knowledge regarding the weighting coefficients. Each participant completed 50 practice trials during each of two practice session. The original impetus of the investigation was to examine the practice distribution effects of massed/distributed sessions (unpublished results); however, here we only focus on the first 50 trials in the first session for this report to examine the initial exploration of a redundant motor task. 2.1. Data analysis The WT and WE components were used for all data analyses. A cluster analysis was used to determine the distinct number of
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would indicate a rather direct path (i.e., simply moving monotonically from one end of the workspace to the other). Finally, for the local search strategy (i.e., the trial-to-trial change), we examined how the performance score on a particular trial resulted in a change in the strategy on the next trial. This was done using two separate correlation analysis—(a) between PS and WE [i.e., between PS(n) and WE (n + 1)–WE (n)], (b) between PS and WT . A more negative correlation indicated that a high (low) performance score on a particular trial was associated with a systematic decrease (increase) in the time/error component on the next trial. All dependent variables were assessed through separate ANOVAs with group assignment as the between-subject factor. All correlations were Fisher z-transformed to satisfy assumptions of normality. A significance level of p < 0.05 was used for all analyses. When necessary, post hoc pairwise multiple comparisons with Bonferroni correction were used. All statistical analyses were run using SPSS v17 (IBM, Armonk, NY).
3. Results
Fig. 2. Initial and final performance. (A) Breakdown of one-dimensional performance score measure into movement time (WT ) and spatial error (WE ) components. Circle and triangle symbols indicate performance on trial 1 and trial 50, respectively. (B) Mean performance score on trial 1 and trial 50 as a function of group. Error bars indicate standard error.
preferred strategy groups and to identify the individual differences shown in Fig. 2A. The clustering analysis used the ‘k-means’ function in MATLAB v7.11 (Mathworks, Natick, MA) which includes an iterative process that defines the minimum distance of withincluster centroid distances for each data point in determining the respective cluster index assignment [21]. The outcome of the cluster analysis determined the number of groups and group assignment for each individual. The dependent variables of PS, WE and WT were analyzed in separate mixed model ANOVAs with group as the between-subject factor repeated over initial (trial 1) and final (trial 50) performance. The global (i.e., the average change over all 50 trials) search strategy in the WE –WT space was examined through a principal component analysis to quantify the primary dimension of exploration. The slope of the first principal component defined each individual’s global search strategy. A slope close to 0 indicated a strategy that involved exploration along the WT dimension whereas a slope close to 90 indicated a strategy that involved exploration along the WE dimension. To measure the degree of exploration, we computed an exploration index that effectively quantified the path length of the search process. The Euclidean distance in WE –WT space was computed between successive trials for the entire session. The exploration index was defined by the cumulative distance traveled across the 50 trials and normalized by the maximum Euclidean distance between any two trials in WE –WT space. An exploration index close to 1
The data shown in Fig. 2A illustrate large inter-individual variability in WT and WE components of the task on the first practice trial. For example, one group of subjects exhibit a fast movement time accompanied by high spatial error. Conversely, another group used a strategy that consisted of a slower movement time and less spatial error. The results of the cluster analysis determined that there were 3 groups—a movement time (MT) group (n = 6), a mixed (MIXED) group (n = 18) and a spatial error (SE) group (n = 8). Analysis of PS revealed significant main effect of group [F(2,29) = 16.35; p < 0.001] and trial [F(1,29) = 217.56; p < 0.001]. A significant interaction between group and trial was observed [F(2,29) = 14.93; p < 0.001]. Post hoc comparisons revealed that PS was significantly lower on trial 50 than trial 1 [p < 0.001] and that on trial 1 the MIXED group had lower PS than the other groups [ps < 0.01], but there were no differences at trial 50. A similar pattern of findings were observed between the WT and WE results. Analysis revealed a significant main effect of group [WT : F(2,29) = 86.55; p < 0.001; WE : F(2,29) = 54.77; p < 0.001] and trial [WT : F(2,29) = 82.12; p < 0.001; WE : F(2,29) = 52.20; p < 0.001] and a significant interaction between group and trial [WT : F(2,29) = 44.93; p < 0.001; WE : F(2,29) = 36.86; p < 0.001]. Post hoc comparisons revealed significantly lower WT and WE on trial 50 than trial 1 [ps < 0.01]. Also, WT and WE on trial 1 was significantly different for all groups [ps < 0.01] and on trial 50 the MT group had a lower WT than the other groups [ps < 0.05] but that WE was similar for all groups. Fig. 3 illustrates the performance trajectory of a representative subject from each group. An individual in the MT group predominantly changed spatial error as a function of practice (Fig. 3A). Conversely, an individual from the SE group primarily changed movement time while maintaining a similar level of accuracy as a function of practice (Fig. 3C), while an individual in the MIXED group varied both components (Fig. 3B). The results from the PCA slope analysis revealed a significant main effect of group [F(2,29) = 30.46, p < 0.001]. The MT group exhibited significantly steeper slope values than both MIXED and SE groups [ps < 0.001] and a difference was observed between the latter two groups [p < 0.01]. Fig. 4A shows the mean exploration index as a function of group. There was a significant main effect of group [F(2,29) = 9.12, p < 0.001] on the exploration index. Post hoc comparisons revealed that the SE group had a significantly lower exploration index than MT and MIXED groups [ps < 0.001].
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Fig. 3. Performance score trajectory. Representative examples of outcome score trajectory from an individual subject in the MT (A), MIXED (B) and SE (C) groups. Dark filled symbols indicate early trials in practice that progress to lighter symbols near the end of practice. Slope of first principal component (D) as a function of group. Error bars indicate standard error.
Fig. 4B displays the mean correlation between PS and WE and PS and WT as a function of group. There was a significant main effect of group on the PS–WE correlation [F(2,29) = 4.41, p < 0.05] and on the PS–WT correlation [F(2,29) = 7.94, p < 0.01]. Post hoc comparisons showed that the SE group had a higher negative correlation between PS and WE than MT and MIXED groups [ps < 0.05] and the PS–WT correlation revealed that the MT group exhibited the highest negative correlation and that the SE group had a lower negative correlation than the other groups [p < 0.01]. 4. Discussion This study examined individual differences in the exploration of a redundant motor task where the feedback score was a linear combination of a spatial component and a temporal component. We found distinct differences in how participants initially explored a solution to this redundant task. A cluster analysis procedure identified 3 general strategies used to solve the task. These corresponded to (i) a “maintain speed strategy” (MT group), (ii) a “maintain
accuracy” (SE group) strategy and (iii) a mixed strategy (MIXED group). The exploration index indicated that all groups searched the workspace extensively during this initial exploration phase (i.e., they simply did not move directly from one end of the workspace to the other as would be predicted by a simple gradient descent type search process). An important result was that even though individuals were classified into distinct groups based only on the performance of their first trial, there were sustained differences between these groups in how they subsequently explored the perceptual motor workspace. The global and local search strategies showed that the MT group tended to change their strategy mostly along the spatial error dimension whereas the SE group tended to change along the movement time dimension. The persistent difference in search strategies suggests that the groups identified by the cluster analysis were reflective of the individual’s intrinsic dynamics and not simply a statistical artifact. The results have important theoretical implications for the study of skill acquisition and motor learning. In attempting to formulate a theory of learning that can generalize across individuals, the
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Fig. 4. Local search process. (A) Exploration index as a function of group and (B) correlation of performance score (PS) with WT and WE as a function of group. See text for definitions. Error bars indicate standard error.
majority of motor learning studies ignore individual differences and rely almost exclusively on examining group averages, which have been shown to result in inaccurate depictions of individual learning dynamics and mask important practice-related changes present in performance variability [9,17]. The present assessment of the individual learner’s dynamics was able to capture individual differences in global and local search strategies that may have been masked if averaging techniques were employed. For the issue of redundancy, the results point to the fact that the redundancy in the task is not only resolved by factors like task constraints and visual feedback, but that the subject’s preferred movement strategy, as defined by initial performance, plays a critical role in determining the selected solution set used to realize performance improvements. If the task is not too constrained, the preferred movement strategy may drive individuals to adopt different starting initial condition and further drive how they explore the perceptual-motor workspace for solutions that match the defined task criterion [18]. Furthermore, the sequential relation across trials during the initial exploration phase supports the notion that this pattern is not a random process but involves systematic searching [20]. Also, the trial-to-trial dynamics of the search strategies in
the redundant task space provide insight on the time-dependent properties of motor learning that are not typically captured with variance measures (e.g., uncontrolled manifold cf. [14]). A limited number of motor behavior investigations have incorporated cluster analysis in an attempt to identify movement strategies [3,21] and such classification approaches may be important in examining individual differences. One of the key methodological limitations in the study of individual differences is the difficulty in examining trends in individual data in the presence of noise. Individual learning data can be highly noisy (i.e., exhibit trial-to-trial variation) which may make it difficult to distinguish the learning strategy from other extraneous factors. In typical motor learning studies, the usual approach to minimizing the effect of this noise is to average data over trial/blocks/individuals [17], but this procedure comes at the cost of masking individual trends. By separating individuals into multiple distinct groups (rather than examine each individual as a separate entity), techniques like cluster analysis may be able to take advantage of both recognizing inter-individual differences as well as use the power of averaging within-group data. The presence of individual differences has been reported in a variety of motor actions including reaction time, complex coordination, pursuit rotor and speed-accuracy tasks [1,6]. What might be the basis of these individual differences? Individual differences are present as early as the development of reaching movement during infancy [23] and variability in growth patterns and movement experiences likely contribute to the observed variation in initial performance levels. While previous investigations have interpreted these differences from the context of variability in an intellectual ability or a general motor performance capacity [1,2,6,22], the present findings suggest an alternative interpretation. In this case, even though the level of motor performance (as indicated by the PS) was similar across individuals, there were differences in how individuals use and explore redundancy in this space-time motor task. Although understanding the basis of these individual differences requires further investigation, assessing the individual’s preferred movement strategy and intrinsic dynamics in the context of the task is a powerful way to capture this variability in a manner that can be directly related to the learning of the task. Finally, apart from theoretical implications, examining different exploration strategies has important applications in developing effective practice schedules. The current findings have implications for the approach of adaptive learning [19], where the goal is to match the demands of the learning environment to key traits of the individual learner. This requires the analysis of individual differences in solving a task that can then provide a basis to create practice schedules tailored to the individual [19]. While current approaches include customizing practice based on factors like task difficulty [7] or skill level [15], the approach adopted in this study suggests that practice schedules can also be based on the assessment of the individual’s initial movement preferences and intrinsic dynamics (e.g., in the current case whether participants chose a “maintain speed” or “maintain accuracy” strategy). In summary, individuals varied in how they initially performed in this redundant space-time task, reflecting the presence of a small set of preferred exploration strategies. The subsequent search strategies used to achieve the task solution illustrated that individuals exploit redundancy in a manner that was uniquely dependent on their intrinsic dynamics. Collectively, the findings support the notion that the construct of learning should be defined over the interaction of task, environmental and organismic constraints [16] and that examining the nature of variability at the inter-individual level may be critical for both theoretical and practical aspects of motor learning.
A.C. King et al. / Neuroscience Letters 529 (2012) 144–149
Acknowledgement The preparation of this paper was supported in part by NSF 0848339. References [1] P.L. Ackerman, Individual differences in skill learning: an integration of psychometric and information processing perspectives, Psychological Bulletin 102 (1987) 3–27. [2] J.A. Adams, Historical review and appraisal of research on the learning, retention, and transfer of human motor skills, Psychological Bulletin 101 (1987) 41–74. [3] H.U. Bauer, W.I. Schöllhorn, Self-organizing maps for the analysis of complex movement patterns, Neural Processing Letters 5 (1997) 193–199. [4] N.A. Bernstein, The Co-ordination and Regulation of Movements, Pergamon Press, Oxford, 1967. [5] P.M. Fitts, The information capacity of the human motor system in controlling the amplitude of movement, Journal of Experimental Psychology 47 (1954) 381–391. [6] E.A. Fleishman, Individual differences and motor learning, in: R.M. Gagne (Ed.), Learning and Individual Differences, Merrill, Columbus, OH, 1967, pp. 165–191. [7] M.A. Guadagnoli, T.D. Lee, Challenge point: a framework for conceptualizing the effects of various practice conditions in motor learning, Journal of Motor Behavior 36 (2004) 212–224. [8] C.M. Harris, D.M. Wolpert, Signal-dependent noise determines motor planning, Nature 394 (1998) 780–784. [9] A. Heathcote, S. Brown, D.J.K. Mewhort, The power law repealed: the case for an exponential law of practice, Psychonomic Bulletin and Review 7 (2000) 185–207. [10] J.A.S. Kelso, Dynamic Patterns: The Self-organization of Brain and Behavior, MIT Press, Cambridge, MA, 1995. [11] J.A.S. Kelso, J.P. Scholz, G. Schöner, Dynamics governs switching among patterns of coordination in biological movement, Physics Letters A 134 (1988) 8–12.
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[12] J.A.S. Kelso, P. Zanone, Coordination dynamics of learning and transfer across different effector systems, Journal of Experimental Psychology: Human Perception and Performance 28 (2002) 776–797. [13] P.N. Kugler, M.T. Turvey, Information, Natural Law, and the Self-assembly of Rhythmic Movement. Resources for Ecological Psychology, Lawrence Erlbaum, Hillsdale, NJ, 1987. [14] M.L. Latash, J.P. Scholz, G. Schöner, Toward a new theory of motor synergies, Motor Control 11 (2007) 276–308. [15] Y.-T. Liu, G. Mayer-Kress, K.M. Newell, Bi-stability of movement coordination as a function of skill level and task difficulty, Journal of Experimental Psychology: Human Perception and Performance 36 (2010) 1515–1524. [16] K.M. Newell, Constraints on the development of coordination, in: M. Wade, H. Whiting (Eds.), Motor Development in Children: Aspects of Coordination and Control, Martinus Nijhoff, Dordrecht, Germany, 1986, pp. 341–360. [17] K.M. Newell, Y.T. Liu, G. Mayer-Kress, Time scales in motor learning and development, Psychological Review 108 (2001) 57–82. [18] K.M. Newell, P.V. McDonald, Searching for solutions to the coordination function: learning as exploratory behavior, in: G.E. Stelmach, J. Requin (Eds.), Tutorials in Motor Behavior II, Elsevier, Amsterdam, 1992, pp. 517–532. [19] R.W. Proctor, A. Dutta, Skill Acquisition and Human Performance, Sage, Thousand Oaks, CA, 1995. [20] R. Ranganathan, K.M. Newell, Influence of motor learning on utilizing path redundancy, Neuroscience Letters 469 (2010) 416–420. [21] R. Rein, C. Button, K. Davids, J. Summers, Cluster analysis of movement patterns in multiarticular actions: a tutorial, Motor Control 14 (2010) 211–239. [22] R.H. Seashore, Individual differences in motor skills, Journal of General Psychology 3 (1930) 38–66. [23] E. Thelen, D. Corbetta, K. Kamm, J.P. Spencer, K. Schneider, R.F. Zernicke, The transition to reaching: mapping intention and intrinsic dynamics, Child Development 64 (1993) 1058–1098. [24] E.L. Thorndike, The effect of practice in the case of a purely intellectual function, American Journal of Psychology 19 (1908) 374–384. [25] E. Todorov, M.I. Jordan, Optimal feedback control as a theory of motor coordination, Nature Neuroscience 5 (2002) 1226–1235.
Contents lists available at SciVerse ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Individual differences in the exploration of a redundant space-time motor task Adam C. King a,∗ , Rajiv Ranganathan b , Karl M. Newell a a b
Department of Kinesiology, Pennsylvania State University, United States Sensory Motor Performance Program, Rehabilitation Institute of Chicago, United States
h i g h l i g h t s
Individual differences are rarely assessed in motor learning studies. Examined variation in preferred movement strategies in a redundant space-time task. Three clusters of individuals varied in initial performance and search strategy. Exploration was influenced by task constraint, feedback and intrinsic dynamics. Adaptive learning should include skill level, task difficulty, and search strategies.
a r t i c l e
i n f o
Article history: Received 18 July 2012 Received in revised form 1 August 2012 Accepted 7 August 2012 Keywords: Redundancy Search strategies Motor learning Intrinsic dynamics
a b s t r a c t Individual differences in learning a motor task are rarely assessed even though they can potentially contribute to our understanding of the problem of motor redundancy—i.e., how individuals can exploit multiple different strategies to realize the task goal. This study examined individual variations in the preferred movement strategy of a redundant motor task. Thirty-two participants performed a star tracing task on a digitizing tablet with the goal of minimizing a performance score that was given as feedback. The performance score was a weighted combination of spatial error and movement time, meaning that multiple strategies could yield the same score. A cluster analysis revealed three distinct groups of individuals based on their initial movement strategy preferences. These groups were not only different on their initial performance, but also exhibited differences in both local (trial-to-trial change) and global (average change) search strategies that were reflected through differential modification of spatial and temporal components. Overall, the results in this space-time task reveal that the intrinsic dynamics of the individual channel the initial exploratory solutions to learning a redundant motor task. © 2012 Elsevier Ireland Ltd. All rights reserved.
1. Introduction The uniqueness of each individual has classically been attributed to variability in intellectual capacity or in a single general motor ability [1] and presents several challenges to the study of group differences that use standard inferential statistics. Indeed, individuals possess a unique set of movement capacities and preferences based on a variety of factors that include anatomical organization, physiological structure, learning style and previous movement experiences. However, in the search for group differences, most studies in motor control and learning typically attempt to minimize or filter out the effects of these individual differences by selecting simple motor tasks and using techniques such as random group assignment and averaging. These procedures can mask
∗ Corresponding author at: Department of Kinesiology, The Pennsylvania State University, 23 Rec Building, University Park, PA 16802, United States. Tel.: +1 814 863 4037; fax: +1 814 863 7360. E-mail address: [email protected] (A.C. King). 0304-3940/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.neulet.2012.08.014
important characteristics of inter-individual variability that may reveal qualitatively and quantitatively distinct pathways of change [9,17]. One perspective to motor learning that emphasizes the notion of individual differences is the dynamical systems framework [10,13]. Differences between individuals are captured in the construct of intrinsic dynamics [11] that can be viewed as a dynamic landscape of movement capabilities that influence the trajectory of performance change relative to the to-be-learned action [10]. It is well established that individuals acquire new movement patterns on the background of pre-existing capacities; however, uniformity of this history across individuals is likely not the case. For example, using a scanning paradigm to assess individual differences, Kelso and Zanone [12] demonstrated that individuals possess different stable coordination patterns prior to any influence of practice and learning. However, this framework has so far been restricted to examining a class of motor tasks where the goal is to produce a particular relative phase between two effectors, meaning that the number of ways in which this motor task could be solved was limited.
A.C. King et al. / Neuroscience Letters 529 (2012) 144–149
Although the individual performance levels may converge with practice, the potential sources contributing to inter-individual variability during the initial stages of acquisition has been one of the primary emphases in the study of individual differences [24]. The importance of these individual differences may be especially critical in motor tasks that afford redundancy. Redundancy offers the opportunity to solve a particular motor problem with an infinite number of solutions [4], thereby increasing the potential variation between individuals in how they solve the task. However, most approaches to redundancy have typically examined highly constrained motor tasks where in spite of the presence of redundancy there is very little variation between individuals (e.g., reaching in straight lines with bell-shaped velocity profiles) [8,14,25]. While these approaches have been successful in revealing features of welllearned movements patterns, they can be rather limiting when investigating the acquisition of new movement skills where individual differences likely play a much larger role in influencing how participants explore the perceptual-motor workspace in the process of achieving improved performance (i.e., “search strategies” cf. [18]). The present study sought to examine the role of individual differences during the exploration of a redundant space-time motor task on the search strategies used to realize performance improvements. The redundancy in the task was created by using a feedback score that was the linear weighted combination of two scores—a score that reflected the spatial accuracy (i.e., the spatial component) and a score that reflected the movement time (i.e., the temporal component). Using this redundant task offered two advantages in the attempt to identify individual differences during the initial exploration process. First, a variety of spatial and temporal solutions can be used to achieve the same outcome measure, which allowed us to examine individual’s initial movement preferences for this task. Second, because of the speed-accuracy trade-off [5] between the spatial and temporal components, the task allowed exploration of multiple strategies before participants could settle on a consistent solution. As a result, we examined how individual differences channeled the preferred movement strategies during initial practice. We hypothesized that the redundancy in this task would result in participants choosing distinct pathways of exploration, that would not only impact their initial performance, but also their subsequent search strategies [18].
2. Methods Thirty-two right hand dominant healthy individuals volunteered to participate in this study. The participants gave informed consent to the experimental procedures that had been approved by the Pennsylvania State University Institutional Review Board. The participants were seated in front of a graphics tablet (Wacom Cintuq 21Ux, Vancouver, WA) and instructed to trace a sixpointed star pattern displayed directly on the tablet screen using a digital stylus (Fig. 1). The diameter of the star shape (i.e., the distance between opposite vertices) was 30 cm. The 2D position of the stylus was sampled at 120 Hz. Participants started each trial on the right apex of the star, traced the pattern in a counter-clockwise direction and finished the trial at the same point. Following each trial, a visually displayed performance score was presented and participants were instructed to minimize the score throughout practice. The performance score (PS) was the sum of a weighted temporal component (WT ) and a weighted spatial component (WE ) that was calculated using the following equation: PS(n) = WT (n) + WE (n)
(1)
145
Fig. 1. Experimental setup. Participants traced the star on a digitizing tablet in a counter-clockwise direction using a stylus pen and started/finished each trial on the right apex of the six-pointed star.
where WT (n) =
aT (n) aTnorm + bEnorm
and WE (n) =
bE(n) aTnorm + bEnorm
and where n indicates the nth trial, T and E represent movement time and spatial error, and a and b represent the weighting coefficients for movement time and spatial error components, respectively. Pilot data provided the basis for determining the parameters of Eq. (1). Three pilot participants each performed 200 trials that were channeled by instructions over different segments of the speed-accuracy function so as to provide scores (i.e., movement time and spatial error) across the whole speed-accuracy range. The Tnorm and Enorm parameters were defined relative to the fastest movement time and least spatial error obtained in pilot data, respectively. The criterion used for this report was the speedaccuracy relation that had an equal emphasis of temporal and spatial components to the performance outcome. Participants were aware that the performance score reflected both speed and accuracy components but did not have knowledge regarding the weighting coefficients. Each participant completed 50 practice trials during each of two practice session. The original impetus of the investigation was to examine the practice distribution effects of massed/distributed sessions (unpublished results); however, here we only focus on the first 50 trials in the first session for this report to examine the initial exploration of a redundant motor task. 2.1. Data analysis The WT and WE components were used for all data analyses. A cluster analysis was used to determine the distinct number of
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would indicate a rather direct path (i.e., simply moving monotonically from one end of the workspace to the other). Finally, for the local search strategy (i.e., the trial-to-trial change), we examined how the performance score on a particular trial resulted in a change in the strategy on the next trial. This was done using two separate correlation analysis—(a) between PS and WE [i.e., between PS(n) and WE (n + 1)–WE (n)], (b) between PS and WT . A more negative correlation indicated that a high (low) performance score on a particular trial was associated with a systematic decrease (increase) in the time/error component on the next trial. All dependent variables were assessed through separate ANOVAs with group assignment as the between-subject factor. All correlations were Fisher z-transformed to satisfy assumptions of normality. A significance level of p < 0.05 was used for all analyses. When necessary, post hoc pairwise multiple comparisons with Bonferroni correction were used. All statistical analyses were run using SPSS v17 (IBM, Armonk, NY).
3. Results
Fig. 2. Initial and final performance. (A) Breakdown of one-dimensional performance score measure into movement time (WT ) and spatial error (WE ) components. Circle and triangle symbols indicate performance on trial 1 and trial 50, respectively. (B) Mean performance score on trial 1 and trial 50 as a function of group. Error bars indicate standard error.
preferred strategy groups and to identify the individual differences shown in Fig. 2A. The clustering analysis used the ‘k-means’ function in MATLAB v7.11 (Mathworks, Natick, MA) which includes an iterative process that defines the minimum distance of withincluster centroid distances for each data point in determining the respective cluster index assignment [21]. The outcome of the cluster analysis determined the number of groups and group assignment for each individual. The dependent variables of PS, WE and WT were analyzed in separate mixed model ANOVAs with group as the between-subject factor repeated over initial (trial 1) and final (trial 50) performance. The global (i.e., the average change over all 50 trials) search strategy in the WE –WT space was examined through a principal component analysis to quantify the primary dimension of exploration. The slope of the first principal component defined each individual’s global search strategy. A slope close to 0 indicated a strategy that involved exploration along the WT dimension whereas a slope close to 90 indicated a strategy that involved exploration along the WE dimension. To measure the degree of exploration, we computed an exploration index that effectively quantified the path length of the search process. The Euclidean distance in WE –WT space was computed between successive trials for the entire session. The exploration index was defined by the cumulative distance traveled across the 50 trials and normalized by the maximum Euclidean distance between any two trials in WE –WT space. An exploration index close to 1
The data shown in Fig. 2A illustrate large inter-individual variability in WT and WE components of the task on the first practice trial. For example, one group of subjects exhibit a fast movement time accompanied by high spatial error. Conversely, another group used a strategy that consisted of a slower movement time and less spatial error. The results of the cluster analysis determined that there were 3 groups—a movement time (MT) group (n = 6), a mixed (MIXED) group (n = 18) and a spatial error (SE) group (n = 8). Analysis of PS revealed significant main effect of group [F(2,29) = 16.35; p < 0.001] and trial [F(1,29) = 217.56; p < 0.001]. A significant interaction between group and trial was observed [F(2,29) = 14.93; p < 0.001]. Post hoc comparisons revealed that PS was significantly lower on trial 50 than trial 1 [p < 0.001] and that on trial 1 the MIXED group had lower PS than the other groups [ps < 0.01], but there were no differences at trial 50. A similar pattern of findings were observed between the WT and WE results. Analysis revealed a significant main effect of group [WT : F(2,29) = 86.55; p < 0.001; WE : F(2,29) = 54.77; p < 0.001] and trial [WT : F(2,29) = 82.12; p < 0.001; WE : F(2,29) = 52.20; p < 0.001] and a significant interaction between group and trial [WT : F(2,29) = 44.93; p < 0.001; WE : F(2,29) = 36.86; p < 0.001]. Post hoc comparisons revealed significantly lower WT and WE on trial 50 than trial 1 [ps < 0.01]. Also, WT and WE on trial 1 was significantly different for all groups [ps < 0.01] and on trial 50 the MT group had a lower WT than the other groups [ps < 0.05] but that WE was similar for all groups. Fig. 3 illustrates the performance trajectory of a representative subject from each group. An individual in the MT group predominantly changed spatial error as a function of practice (Fig. 3A). Conversely, an individual from the SE group primarily changed movement time while maintaining a similar level of accuracy as a function of practice (Fig. 3C), while an individual in the MIXED group varied both components (Fig. 3B). The results from the PCA slope analysis revealed a significant main effect of group [F(2,29) = 30.46, p < 0.001]. The MT group exhibited significantly steeper slope values than both MIXED and SE groups [ps < 0.001] and a difference was observed between the latter two groups [p < 0.01]. Fig. 4A shows the mean exploration index as a function of group. There was a significant main effect of group [F(2,29) = 9.12, p < 0.001] on the exploration index. Post hoc comparisons revealed that the SE group had a significantly lower exploration index than MT and MIXED groups [ps < 0.001].
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Fig. 3. Performance score trajectory. Representative examples of outcome score trajectory from an individual subject in the MT (A), MIXED (B) and SE (C) groups. Dark filled symbols indicate early trials in practice that progress to lighter symbols near the end of practice. Slope of first principal component (D) as a function of group. Error bars indicate standard error.
Fig. 4B displays the mean correlation between PS and WE and PS and WT as a function of group. There was a significant main effect of group on the PS–WE correlation [F(2,29) = 4.41, p < 0.05] and on the PS–WT correlation [F(2,29) = 7.94, p < 0.01]. Post hoc comparisons showed that the SE group had a higher negative correlation between PS and WE than MT and MIXED groups [ps < 0.05] and the PS–WT correlation revealed that the MT group exhibited the highest negative correlation and that the SE group had a lower negative correlation than the other groups [p < 0.01]. 4. Discussion This study examined individual differences in the exploration of a redundant motor task where the feedback score was a linear combination of a spatial component and a temporal component. We found distinct differences in how participants initially explored a solution to this redundant task. A cluster analysis procedure identified 3 general strategies used to solve the task. These corresponded to (i) a “maintain speed strategy” (MT group), (ii) a “maintain
accuracy” (SE group) strategy and (iii) a mixed strategy (MIXED group). The exploration index indicated that all groups searched the workspace extensively during this initial exploration phase (i.e., they simply did not move directly from one end of the workspace to the other as would be predicted by a simple gradient descent type search process). An important result was that even though individuals were classified into distinct groups based only on the performance of their first trial, there were sustained differences between these groups in how they subsequently explored the perceptual motor workspace. The global and local search strategies showed that the MT group tended to change their strategy mostly along the spatial error dimension whereas the SE group tended to change along the movement time dimension. The persistent difference in search strategies suggests that the groups identified by the cluster analysis were reflective of the individual’s intrinsic dynamics and not simply a statistical artifact. The results have important theoretical implications for the study of skill acquisition and motor learning. In attempting to formulate a theory of learning that can generalize across individuals, the
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Fig. 4. Local search process. (A) Exploration index as a function of group and (B) correlation of performance score (PS) with WT and WE as a function of group. See text for definitions. Error bars indicate standard error.
majority of motor learning studies ignore individual differences and rely almost exclusively on examining group averages, which have been shown to result in inaccurate depictions of individual learning dynamics and mask important practice-related changes present in performance variability [9,17]. The present assessment of the individual learner’s dynamics was able to capture individual differences in global and local search strategies that may have been masked if averaging techniques were employed. For the issue of redundancy, the results point to the fact that the redundancy in the task is not only resolved by factors like task constraints and visual feedback, but that the subject’s preferred movement strategy, as defined by initial performance, plays a critical role in determining the selected solution set used to realize performance improvements. If the task is not too constrained, the preferred movement strategy may drive individuals to adopt different starting initial condition and further drive how they explore the perceptual-motor workspace for solutions that match the defined task criterion [18]. Furthermore, the sequential relation across trials during the initial exploration phase supports the notion that this pattern is not a random process but involves systematic searching [20]. Also, the trial-to-trial dynamics of the search strategies in
the redundant task space provide insight on the time-dependent properties of motor learning that are not typically captured with variance measures (e.g., uncontrolled manifold cf. [14]). A limited number of motor behavior investigations have incorporated cluster analysis in an attempt to identify movement strategies [3,21] and such classification approaches may be important in examining individual differences. One of the key methodological limitations in the study of individual differences is the difficulty in examining trends in individual data in the presence of noise. Individual learning data can be highly noisy (i.e., exhibit trial-to-trial variation) which may make it difficult to distinguish the learning strategy from other extraneous factors. In typical motor learning studies, the usual approach to minimizing the effect of this noise is to average data over trial/blocks/individuals [17], but this procedure comes at the cost of masking individual trends. By separating individuals into multiple distinct groups (rather than examine each individual as a separate entity), techniques like cluster analysis may be able to take advantage of both recognizing inter-individual differences as well as use the power of averaging within-group data. The presence of individual differences has been reported in a variety of motor actions including reaction time, complex coordination, pursuit rotor and speed-accuracy tasks [1,6]. What might be the basis of these individual differences? Individual differences are present as early as the development of reaching movement during infancy [23] and variability in growth patterns and movement experiences likely contribute to the observed variation in initial performance levels. While previous investigations have interpreted these differences from the context of variability in an intellectual ability or a general motor performance capacity [1,2,6,22], the present findings suggest an alternative interpretation. In this case, even though the level of motor performance (as indicated by the PS) was similar across individuals, there were differences in how individuals use and explore redundancy in this space-time motor task. Although understanding the basis of these individual differences requires further investigation, assessing the individual’s preferred movement strategy and intrinsic dynamics in the context of the task is a powerful way to capture this variability in a manner that can be directly related to the learning of the task. Finally, apart from theoretical implications, examining different exploration strategies has important applications in developing effective practice schedules. The current findings have implications for the approach of adaptive learning [19], where the goal is to match the demands of the learning environment to key traits of the individual learner. This requires the analysis of individual differences in solving a task that can then provide a basis to create practice schedules tailored to the individual [19]. While current approaches include customizing practice based on factors like task difficulty [7] or skill level [15], the approach adopted in this study suggests that practice schedules can also be based on the assessment of the individual’s initial movement preferences and intrinsic dynamics (e.g., in the current case whether participants chose a “maintain speed” or “maintain accuracy” strategy). In summary, individuals varied in how they initially performed in this redundant space-time task, reflecting the presence of a small set of preferred exploration strategies. The subsequent search strategies used to achieve the task solution illustrated that individuals exploit redundancy in a manner that was uniquely dependent on their intrinsic dynamics. Collectively, the findings support the notion that the construct of learning should be defined over the interaction of task, environmental and organismic constraints [16] and that examining the nature of variability at the inter-individual level may be critical for both theoretical and practical aspects of motor learning.
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