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Moving your eyes to solution: Effects of movements on the perception of a problemsolving task a
K. Werner & M. Raab
ab
a
Department of Performance Psychology, German Sport University Cologne, Institute of Psychology, Cologne, Germany b
Department of Applied Sciences, London South Bank University, London, UK Accepted author version posted online: 05 Feb 2014.Published online: 11 Mar 2014.
To cite this article: K. Werner & M. Raab (2014) Moving your eyes to solution: Effects of movements on the perception of a problem-solving task, The Quarterly Journal of Experimental Psychology, 67:8, 1571-1578, DOI: 10.1080/17470218.2014.889723 To link to this article: http://dx.doi.org/10.1080/17470218.2014.889723
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THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014 Vol. 67, No. 8, 1571–1578, http://dx.doi.org/10.1080/17470218.2014.889723
Moving your eyes to solution: Effects of movements on the perception of a problem-solving task K. Werner1 and M. Raab1,2
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1 Department of Performance Psychology, German Sport University Cologne, Institute of Psychology, Cologne, Germany 2 Department of Applied Sciences, London South Bank University, London, UK
There is ample evidence suggesting a bidirectional connection between bodily movements and cognitive processes, such as problem solving. Current research suggests that previous movements can influence the problem-solving process, but it is unclear what phase of this process is affected. Therefore, we investigated participants’ gaze behaviour in the first phase of arithmetic problem solving with two groups (plus group, minus group) to explore a spatial bias toward the left or the right while perceiving a problem-solving task (the water-jar problem) after two different movements—that is, for the plus group, sorting marbles from two outer bowls into one in the middle, and for the minus group, sorting marbles from the middle bowl to the outer ones. We showed a right shift of spatial bias for the plus and to the left for the minus group in the perception and problem tasks. Although movements affected gaze, the groups did not differ in their overall problem-solving strategies; however, the first correct solutions did differ. This study provides further evidence of sensorimotor effects on problem solving and spatial bias and offers insight into how a two-phase problem-solving process is guided by sensorimotor information. Keywords: Arithmetic problem solving; Embodied cognition; Movement; Spatial bias.
Over the last decades of research in the field of embodied cognition, ample evidence of a bidirectional link between bodily movements and cognitive processes has been obtained (for a review see Goldin-Meadow & Beilock, 2010). However, to date it is still unclear how action influences cognition and how the basic phases of a cognitive process such as problem solving are affected. Two basic phases of problem solving have been identified (Newell & Simon, 1972). First, the problem solver has to create his or her own problem space (Duncker, 1935/1963; Simon & Newell, 1971). The problem space is “the way a particular subject represents the task in order to
work on it” (Simon & Newell, 1971, p. 151). Second, based on the defined problem space, the problem solver starts generating solutions to the problem. Recent research has suggested that at least the solution to a problem-solving task can be affected by movement (Litchfield & Ball, 2011; Thomas & Lleras, 2007, 2009a, 2009b; Werner & Raab, 2013). Here we wanted to investigate whether specific movements affect the problem space phase, as well, by analysing participants’ gaze behaviour. Initially, we explore how movements can affect at least one of the two basic phases of the problem-solving process. It has been argued that
Correspondence should be addressed to Karsten Werner, German Sport University Cologne, Institute of Psychology, Am Sportpark Müngersdorf 6, 50933 Köln, Germany. E-mail: [email protected] © 2014 The Experimental Psychology Society
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it is not the movement per se but the goal of the movement that is causal for the effect of sensorimotor information on cognitive processes (Engel, Maye, Kurthen, & König, 2013; Raab & Green, 2005). For example, when a hand is raised to a particular position the sensorimotor information “up” is activated, and when the hand is dropped to the original position the sensorimotor information “down” is activated. Accordingly, activation of sensorimotor information is understood as the activation of action simulation (Alibali & Kita, 2010). This action simulation activates specific information, enabling the problem solver to generate solutions or affecting the perception of the task environment. For example, Thomas and Lleras (2007) asked their participants to solve a computerized version of Duncker’s (1945) radiation problem. The task was to destroy a tumour with lasers, without injuring the healthy tissue around it. “The correct solution to this problem entails firing multiple low-intensity lasers from different locations around the tumor so that they converge at the tumor” (Thomas & Lleras, 2007, p. 663). Participants’ gaze behaviour was manipulated prior to the problem presentation. They were instructed either to fixate on the tumour or to make saccadic eye movements between the tumour and different locations outside the image on the screen. These different instructions guided the participants’ attention, and thus they perceived the task environment in different ways that led to their creation of different problem spaces. As a result, participants in the tumour fixation condition solved fewer problems correctly than those who had made the saccadic eye movements. Comparable results revealed the original study by Grant and Spivey (2003) using the same problem task. Participants’ gaze behaviour in their study was guided by highlighting either the central tumour or the surrounding tissue. Through highlighting the tissue, more saccades between tumour and tissue were observed; this led to more correct solutions. From an embodied cognition view, the eye movements themselves could have influenced the generation of solutions by activating sensorimotor information that led to a focus on specific information. How can we affect spatial bias via an
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implicit gaze manipulation using arm movements to affect the problem space phase? Understanding the relation between cognitive concepts (e.g., good vs. bad or high vs. low numbers) and spatial attribution might be helpful to answer this question. For example, participants generally attributed the concept of good to up and of bad to down (Casasanto, 2009). Such spatial attribution of a concept can guide attention. For instance, participants detected stimuli in a stimulus–response (S–R) task faster on the right side than on the left side when a high number was presented (Fischer, Castel, Dodd, & Pratt, 2003). The opposite was true for low numbers. Further, it was found that the effect works in the opposite direction; thereby, the eye position can serve as a predictor of whether a number called out by a participant in a random number generation task will be higher or lower than the last one (Loetscher, Bockisch, & Brugger, 2008). Thus if participants look to the right, the probability of calling out a higher number than the last one increases and vice versa for looking to the left. If high and low numbers are linked with spatial bias, the same effects may occur for similar concepts, such as addition and subtraction, given that numbers increase during addition and decrease during subtraction (Knops, Thirion, Hubbard, Michel, & Dehaene, 2009). We will test this prediction of a spatial bias to the right for addition and to the left for subtraction in the following study. In a nutshell, sensorimotor information activated by movements can prime related cognitive concepts (e.g., addition or subtraction), and these concepts are spatially attributed (e.g., right or left). Based on the relation of movements and cognitive concept and their spatial attribution, we predict that movements can guide spatial bias (e.g., to left or right) and, thus, the perception of a problem-solving task. Testing this prediction, we used a perception task and a computerized variation of Luchins’s (1942) water-jar problem to test the spatial bias (see Figure 1). In the perception task, we were interested whether movements affect the spatial bias when no cognitive tasks were presented. In the water-jar problem,
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Figure 1. Examples of the perception task (left) and the problem-solving task (right) in our version of the water-jar problem.
participants had “to obtain a required volume of water given certain empty jars for measure” (Luchins, 1942, p. 2). We manipulated the volume of the jars to create two possible ways participants could solve the problem—that is, by either addition or subtraction. Two different movements were developed to prime the addition (plus group) and subtraction (minus group) solutions and their spatial bias in the problem space phase to the right (plus group) or the left (minus group). Thus, the way a problem solver creates the problem space should differ if the spatial bias is affected. The jar in Figure 1 that was placed on the left side was needed for the subtraction solution and the one on the right side for the addition solution. The middle jar had to be used for both solutions. Taking the embodied cognition perspective, we argue that movements can induce a focus on cognitive concepts, consequently leading to spatial attention and movement-specific solutions to a problem-solving task. Given the results provided by studies on cognitive concepts and spatial bias, we hypothesize differences in the gaze distribution—that is, a right-shifted gaze distribution for the plus group and a left-shifted gaze distribution for the minus group. We further hypothesize an influence of movement on how a problem solver generates solutions that is more addition solution for the plus group and more subtraction solution for the minus group. Yet the studies to date did focus on the solutions to a problem-solving task and how movement affects them, but not on the early information processing,
so we empirically validated an influence on the problem space phase.
Method We used a between-subjects design with the groups (plus vs. minus) as the between-subjects factor. The dependent variable for the perception task was distribution of gaze behaviour (left vs. right), and for the problem-solving task the variables were number of correct solutions, type of solution, and the distribution of the gaze behaviour during the first 3 s after all jars were presented. The decision for the 3 s was based on findings of an automatic binding for stimuli to a perceptual unit of 3 s that is called the subjective present (Pöppel, 1997). Given our focus is on how the early problem space phase is affected by previous movements, we decided to investigate the subjective present. Participants We tested 40 students aged from 19 to 28 years (M = 23.68 years, SD = 2.41; 27 women, 13 men). An a priori G-Power (Version 3.1.5) analysis revealed a test power of .81. Concerning handedness, only one participant self-reported being left-handed. All participants participated voluntarily in this study and were unfamiliar with the presented problem. The participants were assigned randomly to one of the two groups. The study complied with the Declaration of Helsinki and was approved by the ethics committee of the local university.
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Materials The experiment was programmed with Inquisit 3 (Millisecond Software, Seattle, WA) and was presented on a 55′′ monitor at a distance of 1.20 m to the participants. To prime the participants in the two movement groups, we used blue glass marbles and three glass bowls (one big and two smaller bowls), which participants had to manipulate before each trial for 30 s. Participants’ gaze behaviour was measured with the eye-tracking system Tobii Glasses (Tobii Technology, Stockholm). Task In the perception task, four identical jars (three at the top and one at the bottom) were presented to the participants on a computer screen without any additional information (see Figure 1). Participants were instructed to look at the screen while these jars were presented. This task was performed to analyse the influence of movement on spatial bias without an interfering cognitive task (e.g., reading numbers or mental calculation). For the problemsolving task we adapted a paradigm that has been successfully implemented in a previous study showing more general effects of movements on problem solving (Werner & Raab, 2013). We also used Luchins’s (1942) water-jar problem but changed the order of the jars. In this version of the problem task, the volume of water in the different jars allows two possible ways to solve this problem due to mental calculation. The first option was to subtract the amount of water held by one of the jars with less water twice from the one with the highest amount (1 – 2 – 2). The second option was to add the amount of water held by the jars with less water (2 + 2 + 3; see Figure 1). In all trials both solutions were possible. After the problem tasks, participants had to solve four arithmetic equations to check for their general skill in mental arithmetic. Mean number of correct solutions in the arithmetic equations serves as a control variable. Procedure Each participant was individually tested in about 40 min. First the participant was told a cover
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story: “The aim is to investigate how breaks during problem solving influence your ability to solve this problem.” The experiment started with the task instructions and two examples that explained the problem. Participants were instructed to reach the target volume (displayed in millilitres) by spillover of the volumes of the jars in the top line, allowing refilling of the top jars at any time. Thereafter, the participants had to solve two simple water-jar problems with only two jars at the bottom line to become familiar with the procedure. As we used a computerized version of Luchins’ (1942) task, the participants had to mentally calculate the different numbers representing the volumes. After the examples, the experimenter placed three glass bowls in front of the participants and silently demonstrated the movement. For the addition movement, the blue glass marbles were equally distributed in the two smaller bowls. Participants had to use both hands to simultaneously move a marble from each of the side bowls to the biggest bowl in the middle. For the subtraction movement, all the marbles were placed in the biggest bowl in the middle, and the participants had to move them with both hands simultaneously to the smaller bowls. We told the participants that the perception task was necessary to calibrate the eye-tracking system and to familiarize them with the experimental procedure. They started with 30 s of movement followed by the first perception trial. This simple task entailed looking at a computer screen for 10 s. This was the only instruction the experimenter gave them. Subsequently the participants again had to perform their movement for 30 s until the next perception trial was presented, for the total of three times. Thereafter the problemsolving task started with 30 s of movement followed by the first problem task. In the first 2 s, only the two middle jars and thereafter the left and right jars were presented simultaneously. We did this to reduce the effect of reading direction by centring participants’ gaze in the first 2 s. Prior to the presentation of the problem task, participants were asked to keep their head still while they tried to solve the problem. After the three problem tasks they solved four arithmetic equations to test their
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general mental arithmetic skills. At the end we asked the participants to fill out a short questionnaire about the experiment to make sure that they were not aware of the intended effect of our movement manipulation. Data analysis For the perception task we were interested in the distribution of participants’ gaze behaviour. Therefore we created two areas of interest (AOIs) around the left and the right jar, ignoring the two jars in the centre (top and bottom; see Figure 1). For the statistical analysis we used the absolute data (single fixation in the AOI) and subtracted the data for the right AOI from the data for the left AOI (left – right). This left–right difference was compared between the two groups with a t test. The same was done with the eye-tracking data of the first 3 s after all jars were presented in the problem-solving tasks. The differences in type of solution were analysed with a chi-square test. We overall analysed 120 data sets (3 trials for 40 participants) for the perception task as well as for the problem task. Regarding the analysis for the solution type, we ignored the wrong solutions (N = 56) and compared only the correct addition and subtraction solutions (N = 64). Due to a faulty SD card, we lost the eye-tracking data of seven participants (21 data sets from 120). From the 99 data sets, we analysed for gaze behaviour 70 in the perception task (in 29 sets the participants looked straight to the middle jars) and 98 in the problem task (one task could not be analysed). In Figure 2 we only show the distribution in percentage (relative frequencies of the single fixation) for easier comparison.
Results Perception task We hypothesized that inwardly sorting marbles would lead to a spatial bias to the right side and outward sorting to the left side. A spatial bias to the right was found to be higher by about 20% for the plus group (Mleft = 40.15%, Mright = 59.85%, SD = 21.33) than for the minus group and vice versa for a spatial bias to the left for the
minus group (Mleft = 58.40%, Mright = 41.60%, SD = 26.91, see Figure 2). The difference (left – right) for the number of single fixations in the AOI differed significantly between the two groups, t(28) = −2.63, p = .006, d = 0.63. Analysis of the separate trials showed a descriptive decrease of the movement manipulation. Whereas the distribution differs by about 30% in the first trial (plus group: Mleft = 34.67%, Mright = 65.33%, SD = 23.72; minus group: Mleft = 64.20%, Mright = 35.80%, SD = 32.30), it decreases to about 11% to the second trial (plus group: Mleft = 48.61%, Mright = 51.39%, SD = 29.73; minus group: Mleft = 59.94%, Mright = 40.06%, SD = 31.07) and about 16% in the third trial (plus group: Mleft = 39.00%, Mright = 61.00%, SD = 32.79; minus group: Mleft = 55.76%, Mright = 44.24%, SD = 32.16).
Problem-solving task We hypothesized that the spatial bias in the problem-solving task differs in the same direction as for the perception task for the first 3 s after all jars were presented. We found a general tendency to the left side; results reveal a difference between the plus group (Mleft = 60.44%, Mright = 39.56%, SD = 27.99) and the minus group (Mleft = 69.79%, Mright = 30.21%, SD = 24.61; see Figure 2). The difference (left – right) for the number of single fixations in the AOI was not significant between the two groups and had a small effect size, t(96) = 1.59, p = .058, d = 0.32. Further, we hypothesized more addition and fewer subtraction solutions for the plus group and vice versa for the minus group. Consistently we found more addition solutions in the plus group (14 addition vs. 13 subtraction solutions) and more subtraction solutions in the minus group (13 addition vs. 24 subtraction solutions), but the differences were not significant, χ2(1, N = 64) = 1.79, p = .091, w = .17. As 12 participants changed their solution during the three tasks, we ran a post hoc analysis for the first solution that participants named and found more addition solutions for the plus group (8 addition vs. 5 subtraction solutions) and more subtraction solutions for the
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Figure 2. Means and standard deviations for the distribution of the gaze behaviour in percentages for the perception and the problem tasks.
minus group (3 addition vs. 12 subtraction solutions), χ2(1, N = 28) = 5.04, p = .025, w = .42. Given the general tendency to adopt a subtraction solution, we analysed the time that participants needed to enter their solution and found about 20 s longer solution times for the plus group (Mplus = 84.08 s, SD = 33.37, Mminus = 64.95 s, SD = 32.76), t(37) = 1.81, p = .040, d = .58. Additionally, results revealed 10 more correct solutions in the minus group than in the plus group, χ2(1, N = 120) = 3.35, p = .034, w = .17. The number of correct solutions for the four equations showed neither any covariation on the dependent variables nor a difference between the groups.
Discussion The aim of this study was to investigate whether movement has a specific influence on spatial bias and therefore on how a problem solver perceives the task environment and creates a personal problem space. We analysed participants’ gaze during a perception and a problem-solving task. We hypothesized a spatial bias to the right for the plus group and to the left for the minus group for the perception task as well as for the first 3 s of the problem-solving task.
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The results for the perception task revealed a significant difference of about 20% between the two groups concerning their gaze behaviour—that is, a right shift of spatial bias for the plus group and a left shift for the minus group. Considering this difference in gaze behaviour, we find it plausible that the movements we used led to a focus on the concepts of addition and subtraction (Fischer et al., 2003; Knops et al., 2009; Loetscher et al., 2008). We argue that this effect occurred as a result of the activation of action simulation by sensorimotor information, which led to a focus on the cognitive concept that is related to the simulated action during the process of problem solving (Alibali & Kita, 2010; Alibali, Spencer, Knox, & Kita, 2011). The action simulation was activated by sensorimotor information while participants anticipated the outcome of their movement (Engel et al., 2013; Raab & Green, 2005). The anticipated outcome of the movement for the plus group when putting the marbles together was more marbles in the middle jar, and that for the minus group, when dividing the marbles, was fewer marbles in the middle jar. We assume that the anticipated outcome of more or fewer was linked to the mental number line and arithmetically guided the spatial bias to the right or left (Fischer et al., 2003).
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Further, we hypothesized for the problemsolving task the same influence on spatial bias as that for the perception task. The results showed this effect of movement on spatial bias; however, we failed shortly to show a significant difference. The lack of statistical evidence may be caused by the general tendency to the left in both groups. Thus, a search for explanations of why most of the participants focused on this side of the screen during the first 3 s is essential. First, these results might be explained by the reading direction in the culture group of our sample (Shaki & Gevers, 2011). Whenever a stimulus is presented to leftto-right reading participants they start at the upper left. This would explain why we found a tendency to the left in the gaze behaviour over all participants. Second, the left jar had a higher salience than the right one (see Figure 1)—that is, when the left and the right jars were presented, the white–black difference between the middle jar is more obvious to the left one than to the right. We argue that this leads to more attention to this stimulus based on the higher activation for the left jar on the visual map, as other visual factors (size and shape of the objects) were equal (Cave & Wolfe, 1990). We assume that both reading direction and higher salience for the left jar had a stronger influence on participants’ gaze behaviour than the implicit manipulation via movements. Concerning the type of solution, we found a tendency in the predicted direction but no significant difference between the two groups, although this was shown in a previous study. We argue that reading direction and salience also affect the type of solution. This assumption is supported by the findings for solution time and the number of correct solutions. Whereas in the minus group, reading direction, higher salience, and movement manipulation are congruent and lead to focusing on the left side and thus to an increase in the probability of choosing the subtraction solution, there is interference among these three factors for the plus group. This interference between reading direction and salience on the one hand and movement manipulation on the other slowed down the solution and led to fewer correct solutions in the plus group. Looking at the data, we suggest that the participants
started with their primed solution. The first solution differed significantly between the two groups, but 12 out of 40 switched to the alternative solution in the second or third problem task. A possible but speculative explanation is the spontaneous alternation behaviour (SAB). The SAB is an alternation of direction (e.g., left/right) in sequential, behavioural responding mainly demonstrated for animals and young children (Vecera, Rothbart, & Posner, 1991). This alternation could affect eye movements and subsequently problem space and solution. The results of the solution to the water-jar problem in our study are not fully comparable with previous results of Werner and Raab (2013). Whereas they used the same task, the jars differed in size, shape, and order when they were presented to the participants. There are two limitations of the present study. First, we were not able to show an interaction of the two phases in the problem-solving process to draw precise conclusions on how the affected spatial bias guides the manner of creating solutions to the problem task by differences in perceiving the problem-solving task. Second, in conjunction with the interaction of the phases, the task environment had to be defined more precisely, avoiding or controlling influences of, for example, reading direction (Shaki, Fischer, & Petrusic, 2009). Both aspects should be considered in further research, which should focus on how the two phases interact with spatial bias using different movements for the two phases or different times of inserting the movement. These designs would allow conclusions on how movement affects the different cognitive processes of perception and reasoning during the two phases.
Conclusion Based on the differences in the perception task, in the problem task, in first solution, and in tendencies for the number of correct solutions, we can assume that movement had an influence on spatial bias and that this influence was movement specific. We conclude that the movement-specific influence on spatial bias explains differences in how participants perceived the task environment and created their problem space. We have argued that movement
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affects the first search phase of the problem-solving process that complements recent research showing an influence on the solution to a problem-solving task, but we do not know how the whole process of solving problems is affected. For example, it is not investigated to date whether the solution is guided when the movement is inserted in the first or the second phase only. Thus, future studies should focus on the time course and investigate the influence of having only one phase of the solution process primed by a specific movement. Original manuscript received 29 July 2013 Accepted revision received 15 December 2013 First published online 11 March 2014
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Moving your eyes to solution: Effects of movements on the perception of a problemsolving task a
K. Werner & M. Raab
ab
a
Department of Performance Psychology, German Sport University Cologne, Institute of Psychology, Cologne, Germany b
Department of Applied Sciences, London South Bank University, London, UK Accepted author version posted online: 05 Feb 2014.Published online: 11 Mar 2014.
To cite this article: K. Werner & M. Raab (2014) Moving your eyes to solution: Effects of movements on the perception of a problem-solving task, The Quarterly Journal of Experimental Psychology, 67:8, 1571-1578, DOI: 10.1080/17470218.2014.889723 To link to this article: http://dx.doi.org/10.1080/17470218.2014.889723
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THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014 Vol. 67, No. 8, 1571–1578, http://dx.doi.org/10.1080/17470218.2014.889723
Moving your eyes to solution: Effects of movements on the perception of a problem-solving task K. Werner1 and M. Raab1,2
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1 Department of Performance Psychology, German Sport University Cologne, Institute of Psychology, Cologne, Germany 2 Department of Applied Sciences, London South Bank University, London, UK
There is ample evidence suggesting a bidirectional connection between bodily movements and cognitive processes, such as problem solving. Current research suggests that previous movements can influence the problem-solving process, but it is unclear what phase of this process is affected. Therefore, we investigated participants’ gaze behaviour in the first phase of arithmetic problem solving with two groups (plus group, minus group) to explore a spatial bias toward the left or the right while perceiving a problem-solving task (the water-jar problem) after two different movements—that is, for the plus group, sorting marbles from two outer bowls into one in the middle, and for the minus group, sorting marbles from the middle bowl to the outer ones. We showed a right shift of spatial bias for the plus and to the left for the minus group in the perception and problem tasks. Although movements affected gaze, the groups did not differ in their overall problem-solving strategies; however, the first correct solutions did differ. This study provides further evidence of sensorimotor effects on problem solving and spatial bias and offers insight into how a two-phase problem-solving process is guided by sensorimotor information. Keywords: Arithmetic problem solving; Embodied cognition; Movement; Spatial bias.
Over the last decades of research in the field of embodied cognition, ample evidence of a bidirectional link between bodily movements and cognitive processes has been obtained (for a review see Goldin-Meadow & Beilock, 2010). However, to date it is still unclear how action influences cognition and how the basic phases of a cognitive process such as problem solving are affected. Two basic phases of problem solving have been identified (Newell & Simon, 1972). First, the problem solver has to create his or her own problem space (Duncker, 1935/1963; Simon & Newell, 1971). The problem space is “the way a particular subject represents the task in order to
work on it” (Simon & Newell, 1971, p. 151). Second, based on the defined problem space, the problem solver starts generating solutions to the problem. Recent research has suggested that at least the solution to a problem-solving task can be affected by movement (Litchfield & Ball, 2011; Thomas & Lleras, 2007, 2009a, 2009b; Werner & Raab, 2013). Here we wanted to investigate whether specific movements affect the problem space phase, as well, by analysing participants’ gaze behaviour. Initially, we explore how movements can affect at least one of the two basic phases of the problem-solving process. It has been argued that
Correspondence should be addressed to Karsten Werner, German Sport University Cologne, Institute of Psychology, Am Sportpark Müngersdorf 6, 50933 Köln, Germany. E-mail: [email protected] © 2014 The Experimental Psychology Society
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it is not the movement per se but the goal of the movement that is causal for the effect of sensorimotor information on cognitive processes (Engel, Maye, Kurthen, & König, 2013; Raab & Green, 2005). For example, when a hand is raised to a particular position the sensorimotor information “up” is activated, and when the hand is dropped to the original position the sensorimotor information “down” is activated. Accordingly, activation of sensorimotor information is understood as the activation of action simulation (Alibali & Kita, 2010). This action simulation activates specific information, enabling the problem solver to generate solutions or affecting the perception of the task environment. For example, Thomas and Lleras (2007) asked their participants to solve a computerized version of Duncker’s (1945) radiation problem. The task was to destroy a tumour with lasers, without injuring the healthy tissue around it. “The correct solution to this problem entails firing multiple low-intensity lasers from different locations around the tumor so that they converge at the tumor” (Thomas & Lleras, 2007, p. 663). Participants’ gaze behaviour was manipulated prior to the problem presentation. They were instructed either to fixate on the tumour or to make saccadic eye movements between the tumour and different locations outside the image on the screen. These different instructions guided the participants’ attention, and thus they perceived the task environment in different ways that led to their creation of different problem spaces. As a result, participants in the tumour fixation condition solved fewer problems correctly than those who had made the saccadic eye movements. Comparable results revealed the original study by Grant and Spivey (2003) using the same problem task. Participants’ gaze behaviour in their study was guided by highlighting either the central tumour or the surrounding tissue. Through highlighting the tissue, more saccades between tumour and tissue were observed; this led to more correct solutions. From an embodied cognition view, the eye movements themselves could have influenced the generation of solutions by activating sensorimotor information that led to a focus on specific information. How can we affect spatial bias via an
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implicit gaze manipulation using arm movements to affect the problem space phase? Understanding the relation between cognitive concepts (e.g., good vs. bad or high vs. low numbers) and spatial attribution might be helpful to answer this question. For example, participants generally attributed the concept of good to up and of bad to down (Casasanto, 2009). Such spatial attribution of a concept can guide attention. For instance, participants detected stimuli in a stimulus–response (S–R) task faster on the right side than on the left side when a high number was presented (Fischer, Castel, Dodd, & Pratt, 2003). The opposite was true for low numbers. Further, it was found that the effect works in the opposite direction; thereby, the eye position can serve as a predictor of whether a number called out by a participant in a random number generation task will be higher or lower than the last one (Loetscher, Bockisch, & Brugger, 2008). Thus if participants look to the right, the probability of calling out a higher number than the last one increases and vice versa for looking to the left. If high and low numbers are linked with spatial bias, the same effects may occur for similar concepts, such as addition and subtraction, given that numbers increase during addition and decrease during subtraction (Knops, Thirion, Hubbard, Michel, & Dehaene, 2009). We will test this prediction of a spatial bias to the right for addition and to the left for subtraction in the following study. In a nutshell, sensorimotor information activated by movements can prime related cognitive concepts (e.g., addition or subtraction), and these concepts are spatially attributed (e.g., right or left). Based on the relation of movements and cognitive concept and their spatial attribution, we predict that movements can guide spatial bias (e.g., to left or right) and, thus, the perception of a problem-solving task. Testing this prediction, we used a perception task and a computerized variation of Luchins’s (1942) water-jar problem to test the spatial bias (see Figure 1). In the perception task, we were interested whether movements affect the spatial bias when no cognitive tasks were presented. In the water-jar problem,
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Figure 1. Examples of the perception task (left) and the problem-solving task (right) in our version of the water-jar problem.
participants had “to obtain a required volume of water given certain empty jars for measure” (Luchins, 1942, p. 2). We manipulated the volume of the jars to create two possible ways participants could solve the problem—that is, by either addition or subtraction. Two different movements were developed to prime the addition (plus group) and subtraction (minus group) solutions and their spatial bias in the problem space phase to the right (plus group) or the left (minus group). Thus, the way a problem solver creates the problem space should differ if the spatial bias is affected. The jar in Figure 1 that was placed on the left side was needed for the subtraction solution and the one on the right side for the addition solution. The middle jar had to be used for both solutions. Taking the embodied cognition perspective, we argue that movements can induce a focus on cognitive concepts, consequently leading to spatial attention and movement-specific solutions to a problem-solving task. Given the results provided by studies on cognitive concepts and spatial bias, we hypothesize differences in the gaze distribution—that is, a right-shifted gaze distribution for the plus group and a left-shifted gaze distribution for the minus group. We further hypothesize an influence of movement on how a problem solver generates solutions that is more addition solution for the plus group and more subtraction solution for the minus group. Yet the studies to date did focus on the solutions to a problem-solving task and how movement affects them, but not on the early information processing,
so we empirically validated an influence on the problem space phase.
Method We used a between-subjects design with the groups (plus vs. minus) as the between-subjects factor. The dependent variable for the perception task was distribution of gaze behaviour (left vs. right), and for the problem-solving task the variables were number of correct solutions, type of solution, and the distribution of the gaze behaviour during the first 3 s after all jars were presented. The decision for the 3 s was based on findings of an automatic binding for stimuli to a perceptual unit of 3 s that is called the subjective present (Pöppel, 1997). Given our focus is on how the early problem space phase is affected by previous movements, we decided to investigate the subjective present. Participants We tested 40 students aged from 19 to 28 years (M = 23.68 years, SD = 2.41; 27 women, 13 men). An a priori G-Power (Version 3.1.5) analysis revealed a test power of .81. Concerning handedness, only one participant self-reported being left-handed. All participants participated voluntarily in this study and were unfamiliar with the presented problem. The participants were assigned randomly to one of the two groups. The study complied with the Declaration of Helsinki and was approved by the ethics committee of the local university.
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Materials The experiment was programmed with Inquisit 3 (Millisecond Software, Seattle, WA) and was presented on a 55′′ monitor at a distance of 1.20 m to the participants. To prime the participants in the two movement groups, we used blue glass marbles and three glass bowls (one big and two smaller bowls), which participants had to manipulate before each trial for 30 s. Participants’ gaze behaviour was measured with the eye-tracking system Tobii Glasses (Tobii Technology, Stockholm). Task In the perception task, four identical jars (three at the top and one at the bottom) were presented to the participants on a computer screen without any additional information (see Figure 1). Participants were instructed to look at the screen while these jars were presented. This task was performed to analyse the influence of movement on spatial bias without an interfering cognitive task (e.g., reading numbers or mental calculation). For the problemsolving task we adapted a paradigm that has been successfully implemented in a previous study showing more general effects of movements on problem solving (Werner & Raab, 2013). We also used Luchins’s (1942) water-jar problem but changed the order of the jars. In this version of the problem task, the volume of water in the different jars allows two possible ways to solve this problem due to mental calculation. The first option was to subtract the amount of water held by one of the jars with less water twice from the one with the highest amount (1 – 2 – 2). The second option was to add the amount of water held by the jars with less water (2 + 2 + 3; see Figure 1). In all trials both solutions were possible. After the problem tasks, participants had to solve four arithmetic equations to check for their general skill in mental arithmetic. Mean number of correct solutions in the arithmetic equations serves as a control variable. Procedure Each participant was individually tested in about 40 min. First the participant was told a cover
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story: “The aim is to investigate how breaks during problem solving influence your ability to solve this problem.” The experiment started with the task instructions and two examples that explained the problem. Participants were instructed to reach the target volume (displayed in millilitres) by spillover of the volumes of the jars in the top line, allowing refilling of the top jars at any time. Thereafter, the participants had to solve two simple water-jar problems with only two jars at the bottom line to become familiar with the procedure. As we used a computerized version of Luchins’ (1942) task, the participants had to mentally calculate the different numbers representing the volumes. After the examples, the experimenter placed three glass bowls in front of the participants and silently demonstrated the movement. For the addition movement, the blue glass marbles were equally distributed in the two smaller bowls. Participants had to use both hands to simultaneously move a marble from each of the side bowls to the biggest bowl in the middle. For the subtraction movement, all the marbles were placed in the biggest bowl in the middle, and the participants had to move them with both hands simultaneously to the smaller bowls. We told the participants that the perception task was necessary to calibrate the eye-tracking system and to familiarize them with the experimental procedure. They started with 30 s of movement followed by the first perception trial. This simple task entailed looking at a computer screen for 10 s. This was the only instruction the experimenter gave them. Subsequently the participants again had to perform their movement for 30 s until the next perception trial was presented, for the total of three times. Thereafter the problemsolving task started with 30 s of movement followed by the first problem task. In the first 2 s, only the two middle jars and thereafter the left and right jars were presented simultaneously. We did this to reduce the effect of reading direction by centring participants’ gaze in the first 2 s. Prior to the presentation of the problem task, participants were asked to keep their head still while they tried to solve the problem. After the three problem tasks they solved four arithmetic equations to test their
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general mental arithmetic skills. At the end we asked the participants to fill out a short questionnaire about the experiment to make sure that they were not aware of the intended effect of our movement manipulation. Data analysis For the perception task we were interested in the distribution of participants’ gaze behaviour. Therefore we created two areas of interest (AOIs) around the left and the right jar, ignoring the two jars in the centre (top and bottom; see Figure 1). For the statistical analysis we used the absolute data (single fixation in the AOI) and subtracted the data for the right AOI from the data for the left AOI (left – right). This left–right difference was compared between the two groups with a t test. The same was done with the eye-tracking data of the first 3 s after all jars were presented in the problem-solving tasks. The differences in type of solution were analysed with a chi-square test. We overall analysed 120 data sets (3 trials for 40 participants) for the perception task as well as for the problem task. Regarding the analysis for the solution type, we ignored the wrong solutions (N = 56) and compared only the correct addition and subtraction solutions (N = 64). Due to a faulty SD card, we lost the eye-tracking data of seven participants (21 data sets from 120). From the 99 data sets, we analysed for gaze behaviour 70 in the perception task (in 29 sets the participants looked straight to the middle jars) and 98 in the problem task (one task could not be analysed). In Figure 2 we only show the distribution in percentage (relative frequencies of the single fixation) for easier comparison.
Results Perception task We hypothesized that inwardly sorting marbles would lead to a spatial bias to the right side and outward sorting to the left side. A spatial bias to the right was found to be higher by about 20% for the plus group (Mleft = 40.15%, Mright = 59.85%, SD = 21.33) than for the minus group and vice versa for a spatial bias to the left for the
minus group (Mleft = 58.40%, Mright = 41.60%, SD = 26.91, see Figure 2). The difference (left – right) for the number of single fixations in the AOI differed significantly between the two groups, t(28) = −2.63, p = .006, d = 0.63. Analysis of the separate trials showed a descriptive decrease of the movement manipulation. Whereas the distribution differs by about 30% in the first trial (plus group: Mleft = 34.67%, Mright = 65.33%, SD = 23.72; minus group: Mleft = 64.20%, Mright = 35.80%, SD = 32.30), it decreases to about 11% to the second trial (plus group: Mleft = 48.61%, Mright = 51.39%, SD = 29.73; minus group: Mleft = 59.94%, Mright = 40.06%, SD = 31.07) and about 16% in the third trial (plus group: Mleft = 39.00%, Mright = 61.00%, SD = 32.79; minus group: Mleft = 55.76%, Mright = 44.24%, SD = 32.16).
Problem-solving task We hypothesized that the spatial bias in the problem-solving task differs in the same direction as for the perception task for the first 3 s after all jars were presented. We found a general tendency to the left side; results reveal a difference between the plus group (Mleft = 60.44%, Mright = 39.56%, SD = 27.99) and the minus group (Mleft = 69.79%, Mright = 30.21%, SD = 24.61; see Figure 2). The difference (left – right) for the number of single fixations in the AOI was not significant between the two groups and had a small effect size, t(96) = 1.59, p = .058, d = 0.32. Further, we hypothesized more addition and fewer subtraction solutions for the plus group and vice versa for the minus group. Consistently we found more addition solutions in the plus group (14 addition vs. 13 subtraction solutions) and more subtraction solutions in the minus group (13 addition vs. 24 subtraction solutions), but the differences were not significant, χ2(1, N = 64) = 1.79, p = .091, w = .17. As 12 participants changed their solution during the three tasks, we ran a post hoc analysis for the first solution that participants named and found more addition solutions for the plus group (8 addition vs. 5 subtraction solutions) and more subtraction solutions for the
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Figure 2. Means and standard deviations for the distribution of the gaze behaviour in percentages for the perception and the problem tasks.
minus group (3 addition vs. 12 subtraction solutions), χ2(1, N = 28) = 5.04, p = .025, w = .42. Given the general tendency to adopt a subtraction solution, we analysed the time that participants needed to enter their solution and found about 20 s longer solution times for the plus group (Mplus = 84.08 s, SD = 33.37, Mminus = 64.95 s, SD = 32.76), t(37) = 1.81, p = .040, d = .58. Additionally, results revealed 10 more correct solutions in the minus group than in the plus group, χ2(1, N = 120) = 3.35, p = .034, w = .17. The number of correct solutions for the four equations showed neither any covariation on the dependent variables nor a difference between the groups.
Discussion The aim of this study was to investigate whether movement has a specific influence on spatial bias and therefore on how a problem solver perceives the task environment and creates a personal problem space. We analysed participants’ gaze during a perception and a problem-solving task. We hypothesized a spatial bias to the right for the plus group and to the left for the minus group for the perception task as well as for the first 3 s of the problem-solving task.
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The results for the perception task revealed a significant difference of about 20% between the two groups concerning their gaze behaviour—that is, a right shift of spatial bias for the plus group and a left shift for the minus group. Considering this difference in gaze behaviour, we find it plausible that the movements we used led to a focus on the concepts of addition and subtraction (Fischer et al., 2003; Knops et al., 2009; Loetscher et al., 2008). We argue that this effect occurred as a result of the activation of action simulation by sensorimotor information, which led to a focus on the cognitive concept that is related to the simulated action during the process of problem solving (Alibali & Kita, 2010; Alibali, Spencer, Knox, & Kita, 2011). The action simulation was activated by sensorimotor information while participants anticipated the outcome of their movement (Engel et al., 2013; Raab & Green, 2005). The anticipated outcome of the movement for the plus group when putting the marbles together was more marbles in the middle jar, and that for the minus group, when dividing the marbles, was fewer marbles in the middle jar. We assume that the anticipated outcome of more or fewer was linked to the mental number line and arithmetically guided the spatial bias to the right or left (Fischer et al., 2003).
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Further, we hypothesized for the problemsolving task the same influence on spatial bias as that for the perception task. The results showed this effect of movement on spatial bias; however, we failed shortly to show a significant difference. The lack of statistical evidence may be caused by the general tendency to the left in both groups. Thus, a search for explanations of why most of the participants focused on this side of the screen during the first 3 s is essential. First, these results might be explained by the reading direction in the culture group of our sample (Shaki & Gevers, 2011). Whenever a stimulus is presented to leftto-right reading participants they start at the upper left. This would explain why we found a tendency to the left in the gaze behaviour over all participants. Second, the left jar had a higher salience than the right one (see Figure 1)—that is, when the left and the right jars were presented, the white–black difference between the middle jar is more obvious to the left one than to the right. We argue that this leads to more attention to this stimulus based on the higher activation for the left jar on the visual map, as other visual factors (size and shape of the objects) were equal (Cave & Wolfe, 1990). We assume that both reading direction and higher salience for the left jar had a stronger influence on participants’ gaze behaviour than the implicit manipulation via movements. Concerning the type of solution, we found a tendency in the predicted direction but no significant difference between the two groups, although this was shown in a previous study. We argue that reading direction and salience also affect the type of solution. This assumption is supported by the findings for solution time and the number of correct solutions. Whereas in the minus group, reading direction, higher salience, and movement manipulation are congruent and lead to focusing on the left side and thus to an increase in the probability of choosing the subtraction solution, there is interference among these three factors for the plus group. This interference between reading direction and salience on the one hand and movement manipulation on the other slowed down the solution and led to fewer correct solutions in the plus group. Looking at the data, we suggest that the participants
started with their primed solution. The first solution differed significantly between the two groups, but 12 out of 40 switched to the alternative solution in the second or third problem task. A possible but speculative explanation is the spontaneous alternation behaviour (SAB). The SAB is an alternation of direction (e.g., left/right) in sequential, behavioural responding mainly demonstrated for animals and young children (Vecera, Rothbart, & Posner, 1991). This alternation could affect eye movements and subsequently problem space and solution. The results of the solution to the water-jar problem in our study are not fully comparable with previous results of Werner and Raab (2013). Whereas they used the same task, the jars differed in size, shape, and order when they were presented to the participants. There are two limitations of the present study. First, we were not able to show an interaction of the two phases in the problem-solving process to draw precise conclusions on how the affected spatial bias guides the manner of creating solutions to the problem task by differences in perceiving the problem-solving task. Second, in conjunction with the interaction of the phases, the task environment had to be defined more precisely, avoiding or controlling influences of, for example, reading direction (Shaki, Fischer, & Petrusic, 2009). Both aspects should be considered in further research, which should focus on how the two phases interact with spatial bias using different movements for the two phases or different times of inserting the movement. These designs would allow conclusions on how movement affects the different cognitive processes of perception and reasoning during the two phases.
Conclusion Based on the differences in the perception task, in the problem task, in first solution, and in tendencies for the number of correct solutions, we can assume that movement had an influence on spatial bias and that this influence was movement specific. We conclude that the movement-specific influence on spatial bias explains differences in how participants perceived the task environment and created their problem space. We have argued that movement
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affects the first search phase of the problem-solving process that complements recent research showing an influence on the solution to a problem-solving task, but we do not know how the whole process of solving problems is affected. For example, it is not investigated to date whether the solution is guided when the movement is inserted in the first or the second phase only. Thus, future studies should focus on the time course and investigate the influence of having only one phase of the solution process primed by a specific movement. Original manuscript received 29 July 2013 Accepted revision received 15 December 2013 First published online 11 March 2014
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