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Expertise research by Rubik's cube.

INTRODUCTION

Researchers from a number of disciplines have long been fascinated by expert performance and expertise. Expert performer is a person who, by objective standards and over a period of time, shows a superior and consistent performance in representative (typical) activities of a domain. In contrast to the everyday use of the term expert, which is applied freely to any specialised individual, expert performers must display consistent superior performance in their respective domains. Expertise refers to the cognitive, perceptual-motor, and physiological mechanism that allow expert to consistently attain superior level of performance. Webster's dictionary defines an expert as the "one who has acquired special skill in or knowledge of a particular subject through professional training and practical experience." In psychology, expertise caters a challenge to investigators interested in the structure and development of skills, because, it represents an extreme point on the spectrum of human performance (Tuffiash, Roring, & Ericsson, 2007). Moreover, the study of expert performance allows investigators to appraise the generalizability of more panoptic theories about basic cognitive processes and capacities (Tuffiash et al., 2007). Probably, that's why expertise and expert performance lure much attention of psychologists as well as researches from other domains (neuroscience, ergonomics etc.) as well. This is also well documented in numerous publications of scientific journals and series of edited books on expertise from many domains during the last 40 years (Chase, 1973; Anderson, 1981; Bloom, 1985; Ericsson & Smith, 1991; Hoffman, 1992; Starkes & Allard, 1993; Ericsson, 1996; Feltovich, Ford, & Hoffman, 1997; Starkes & Ericsson, 2003).

Expertise and Rubik's cube: Fundamental focus of the expertise research is to determine the two basic facts. First, "Who becomes an expert?" and second, "How does one become an expert?" Experimental psychologists have focused on describing the processes involved in expert performance but it is only one side of the coin. On the other side, some cognitive psychologists also emphasize on specifying the methods one should adopt for successfully acquiring expert performance. None of them were able to present a general model or a theory that would account for all of the various results. To understand more about the expertise, researchers have used different kind of model to explore the mechanism and underlying process of expertise in general. In this paper, we present a study in which the expert-performance approach (Ericsson & Smith, 1991) is applied to the domain of Rubik's cube for studying superior performance outside of the laboratory. Like other psychological phenomenon, to explain the complex cognitive behaviours such as problem solving, decision making, and memory etc. researchers have used different models like Chess (Charness, 1976; Chase and Simon, 1973), Scrabble (Tuffiash et al., 2007), Mathematics (Silver, 1981), Physics (Larkin, Dermott, Simon & Simon, 1980) etc. Chess is the most popular model for expertise research; in fact, it has been knighted "the drosophila of cognition research and psychometrics" (van der Maas & Wagenmakers, 2005). Nowadays, Rubik's cube is widely used in schools and universities to explain complex particle physics and mathematical algorithms. Rubik's cube can also be used as an expertise research model to understand complex cognitive processes. There are several factors which play crucial role in Rubik's cube solving such as selective attention, long-term memory, working memory, reasoning, decision making, planning, and motivation. Thus, in the domain of artificial intelligence, neuro-ergonomics, neuropsychology, cognitive science, as well as psychology, researchers can use Rubik's cube as a model to vindicate mysteries of experts' performance and expertise.

Why Rubik's cube? Researchers have given various theories and models on the basis of chess expertise. But these theories and models have a major problem which has not been confronted till date. Chess is basically two players' game, when we say that we are studying an expert/novice of chess as a participant, while she/he is engaged in chess playing; we are actually not studying him alone. We are actually canvassing two people as one. Two people are: one is the participant and the other one seems invisible but present in the mind of the participant. In chess every move is in respect to the opponent, so, while you're studying a participant as the participant you can't remove the effect of an opponent. That is a big problem which is being faced by chess as a model for expertise research. That demands a better and a simple model for expertise research, as effective as chess, but with the least confounding aspects. Rubik's cube has several similar properties as chess. The strong measurement properties of competitive Rubik's cube game stimulated the research interest. As in chess, every Rubik's cube game results in an objective, quantifiable outcome i.e., Solved, Not-solved (Time out or failed to solve), and time taken to solve the cube is the decisive parameter for the Rubik's cube game. Time taken to solve the cube is an indirect measure of number of moves taken place i.e. less time taken means less moves have been executed that implies better planning, shortest path searching, and good decision making skills. Every person competing in a Rubik's cube tournament receives a numerical skill rating that directly reflects his or her performance against other rated opponents. Thus, the performance metric associated with competitive Rubik's cube provides researchers with mathematically rigorous, yet ecologically valid criterion measure against which one may validate performance under standardized condition. In addition, the study of expert-performance in Rubik's cube presents an opportunity to test the generalizability of findings from studies of individual differences and superior performance in domains characteristically dominated by memory, problem solving and decision making skills.

The Rubik's Cube: The Rubik's Cube is a 3-D mechanical puzzle, invented in 1974 by Hungarian sculptor and professor of architecture Erno Rubik. In the recent past Rubik's cube has gained popularity worldwide. In 2009 it became the top selling puzzle game in the world with the sale of 350 million cubes. In a classic Rubik's cube (3X3X3) each of the six faces is covered by nine stickers among six solid colours (traditionally white, red, blue, orange, green, and yellow). A standard '3X3X3' Rubik's Cube has 6 coloured sides, 21 pieces and 54 outer surfaces. As the centre pieces of each face of the Rubik's cube do not move, the total number of possible configurations is calculated by multiplying the number of possible arrangements of the corner pieces by the number of possible arrangements of edge pieces. This means there are more than 43 quintillion possible configurations, or 43,252,003,274,489,856,000 to be exact. But there is only one solution.

The Game of Rubik's cube: World Cube Association (WCA) is the organizing body of the Rubik's cube game all over the world. According to WCA, game of Rubik's cube has some standard rules and regulations, to maintain the quality among the players. In any WCA recognized tournament, WCA represents itself through a local/regional delegate. Generally they are present or veteran eminent players, trained by WCA. The role of WCA delegate is to supervise and maintain the sporting environment and the gaming spirit among the players. In a WCA competition, the player has to solve the scrambled cube, the scrambling is done according to the standard computer-generated algorithms. The algorithms are provided by WCA to the tournament organizer through its delegate. Now its organizer's responsibility to make sure that these algorithms will not come into the cognizance of the tournament players before the appropriate round.

During the competition standard timer is used to record the solving time (ST). The standard timer has a sheet with two touch pads for both hands. Participant has to press both the pads to start or stop the timer. As the trial begins an observer with a stopwatch will come and make sure that the timer is on zero. Then he put down the covered scrambled cube on the timer sheet, in front of the participant, and will wait for the participant's ready signal. As soon as the participant gave the ready signal to the observer, he will remove the cover of the scrambled cube and simultaneously start the stopwatch. According to WCA, every participant will get an observation time (OT), to observe the scrambled cube, of up to 15 seconds. According to games standards during the 15 seconds of OT, there will be three warnings at 8th, 10th and 12th seconds, to put down the cube to start the timer and start solving it as soon as possible. If a participant failed to do so, then he/she will be disqualified for that particular trial. This will be considered as OT of the participant in the present study. The ST will be measured from when the participants start the timer, and till the timer stopped by the participant himself. There may be several rounds to filter out the participants. Every round consisted of five trials. Average of five trial's ST will be the basis of tournament's ranking and other assessment criteria (in the present study only final round was considered).

Expert-Performance Approach in Rubik's Cube Expertise: The expert performance approach (Ericsson et. al, 1991) is an attempt to investigate the superior performance under standardized condition (inside the laboratory or under controlled conditions), in order to analyse it and to identify the relatively stable components of the performance that makes it superior. Several earlier researchers explored possible linkages between performance on standardized measures of spatial ability and skilled performance in spatially oriented game domains like Go and chess (Harre, Bossomaier, & Snyder, 2012; Waters, Gobet, & Leyden, 2002) but failed to provide a general consensus. From this theoretical perspective, based on general and basic cognitive capacities, the level of proficiency at which Rubik's cube players demonstrates superior domain-specific performance may also be dependent on their relative levels of Visuo-spatial faculties. Thus, one might posit analogous relationships between scores on standardized tests that are frequently associated with Visuo-spatial aptitude and skilled performance in the game of Rubik's cube.

According to several studies of expert performance, attaining the highest levels of achievement in a domain requires thousands of hours of "deliberate practice" (K. Anders Ericsson, 2006; Krampe & Ericsson, 1996)) during which the aspiring individual works to improve specific aspects of performance. By repeatedly modifying one's strategies, processes (according to demand of the situation), and representations over this extensive period of training, an individual may eventually achieve maximal adaptation to domain-specific task constraints (K. A. Ericsson & Lehmann, 1996). This extended adaptation to the constraints of a particular performance domain often result in the acquisition of cognitive processing mechanisms that are highly specific to a domain and, thus, are unlikely to transfer to other domains (K. A. Ericsson & Kintsch, 1995) Empirical evidence of what happens in the case of Rubik's cube is not available till date. Hence, it would be well expected that Rubik's cube, extended deliberate practice would result in superior performance only on Rubik's cube-related tasks.

Psychology of Rubik's cube solving: As discussed above there are 43 quintillion possible moves available in a 3X3 standard Rubik's cube. Rubik's Cube is a three dimensional mechanical problem. Searching the shortest and correct move requires various cognitive faculties. In a scrambled Rubik's cube one needs to remember pieces' colour and its position in the space. That will require superior memory (both short-term and long-term), it will also requires an encoding technique which can efficiently handle this huge amount of information. Not only this, but: one also needs a fast and effective process to update the intermediary moves which occurs while one is engaged in solving the cube. It is therefore reasonable to argue that deliberate practice in Rubik's cube may result in the development of specialized skills related to the retrieval of tactically important pieces positions and their visual recognition in scrambled cube without necessarily requiring superior memory or intelligence in the broader sense. The process which may create a difference between experts and novices is the encoding and retrieval technique; if encoding is better retrieval will be better. In this study it has been hypothesised that experts would have better encoding and retrieval technique. For the superior encoding process, for the experts, rather than memorising the whole pieces position in the space, it would be better to encode the cube with the help of surface colour of pieces (colour cues) and its relative positions from surface central piece (spatial cues). As the surface central piece is immovable and can be used as a reference point. We refer to the hypothesis of distinctly developed ability, to encode and access pieces positions (based on both visual (colour) cues and their position (spatial) cues) in Rubik's cube game as the Visuo-spatial colour coding and retrieval skill hypothesis. Hence better players have acquired highly specific skills relevant to Visuo-spatial colour coding and identifying and manipulating them as legal moves. This hypothesis makes several concrete predictions that can be examined using the expert-performance approach.

METHOD

Participants: Out of an original pool of 45 Indian Open Tournament players participating in the national level championship, from all over India, a sample of 30 (10 experts and 20 Novices) male players who have qualified for the final round, investigated in the study. All the participants were right handed, had normal or corrected to normal vision, and did not indicate any medical or psychological disorder. The data of 5 participants (all novices) had to be excluded from analysis because they are outliers, because they are failed to solve cube in two trials. The remaining sample consisted of 25 (10 experts and 15 novices) male Rubik's cube tournament players between the age range of 18 to 48 years (M= 23.20, SD= 8.91). Their playing strength was assessed by means of WCA National Ranking (NR) at the time of study. The expert labelled players subsample consisted of 10 participants with the NR 2 to 33 (M=16.9, SD=11.74). The Novice labelled players subsample consisted of 15 participants with the NR 80 to 163 (M= 112.63, SD= 35.29). Their educational background was under-graduate to post graduate. All participants gave the consent to participate in this study.

Task: According to the expert performance approach to assess inter-individual differences, a performance should be examined with the help of Laboratory-based task, under the standardized conditions (inside the laboratory or under controlled conditions in the field). That is how an investigator can rule out the possibility of confounding extraneous, unstable, and chance factors. As it was the first study of expertise in domain of Rubik's cube, it was difficult to develop any laboratory-based or domain representative task which is a prerequisite for expert performance approach. For this reason, in the present study only observations and interviews were taken from the standard Rubik's cube solving task itself. In the study, data collection was done in the field setting, while the Rubik's cube tournament (Indian Open 2011 at Indian Institute of Technology, Kanpur) was going on. The place was well equipped with the standard instruments required to conduct a tournament. The conditions and procedures were almost identical for each participant. The situation can be considered as the standard controlled condition, so, it fulfils almost all necessary requirements of expert performance approach.

In this study, investigators aim was to record the observation time (OT) and solving time (ST) for each participant in each trial, and after every trial a short semi structured interview were also recorded. The observers were requested to jot down the OT's of each participant in each round.

Procedure: In the Rubik's cube solving task, every participant got a pre-scrambled cube.The scrambling was done according to the computer generated standard algorithms provided by WCA. All participants get the same scrambled cube (scrambling was done by the same algorithms) for each trial.

Each participant was clearly instructed that as soon as the round begins they would get a covered scrambled cube and the cover would be opened when the participant gives the ready signal to the observer. Every participant got up to 15 seconds to observe the cube, and this observation time (OT) counting would start as soon as they give ready signal to the observer. Warnings were delivered according to the standard procedures. If the participant neglects the warnings, she/he would be disqualified for the particular trial.

The ST was measured from when the participants start the timer (started solving the cube), up to, when the participant put down the cube and stop the timer himself. That was clearly shown by the standard timer which was being used as the measure of the ST.

RESULTS

We had applied student t-test between experts and novices for ST and OT both. There was a significant difference in ST, t (23) =6.41, p<0.05 of expert (M=19.26, SD=3.12) and Novice (M=35.29, SD=7.42). On the other hand in OT, no significant difference was found t (23) =0.05, p= n.s., between experts (M=9.19, SD= 1.52) and novices (M=9.22, SD= 1.23),

Pearson product moment correlation was also calculated between OT and ST for expert and novices both. A significant correlation was found r (23) =0.55, p<0.05 between OT and ST for novices, but the same correlation was not significant r (23) =0.04, p=n.s. for experts. A Spearman rank order correlation was calculated for tournament ranking and WCA national ranking, for experts r (8) =0.69, p<0.05 it was significant but for novices r (13) = 0.45, p =n.s. it was not significant.

When the linear regression was applied, for novices, OT significantly predicted ST; [beta] =0.055, t (23) =2.39, p<0.05. OT also explained a significant proportion of variance in ST, R2 =0.31, F (1, 23) = 5.72, p<0.05. But in the case of experts [beta] =0.04, t (23) =0.12, p= n.s., OT was failed to explain a significant proportion of variance in ST, R2 =0.002, F (1, 23) =0.014, p=n.s.

There was a significant difference in the variance (standard deviation) of ST of five trials of final round, t (23) = 2.54, p<0.018 of expert (M= 2.67) and Novice (M= 7.25). On the other hand significant difference was also found in OT, t (23) = 11.61, p= 0.001, between experts (M= 0.64) and novices (M= 2.02).

Discussion: The present study was successful in demonstrating how the expert-performance approach can be applied to improve understanding of superior performance in a Rubik's cube domain. As the significant difference in ST shows that experts did better in Rubik's cube solving as compared to novices. Expert Rubik cube players outplayed novices' in each respect, they have good encoding and retrieval techniques and the way they handle the cube while they were playing/solving (rather than rotating the whole cube, they rotated only the targeted layer by their precise finger moves) is also superior. These were the skills that seem small, but had a great impact on overall ST.

On the other hand, novices spent much of the time observing the cube (after every couple of moves). By virtue, the game of Rubik's cube is dynamic in its nature. The positions and colours of the surface pieces get changed with every move. So, one had to update recent/current positions of the cube in the memory. For that, one must requires a better technique for updating the working memory. This demands a highly active visuo-spatial working memory (VWM), this can only be achieved through deliberate practice. As a Rubik's cube experts mentioned in their interview that they practice every new (better) algorithm until it became intuitive to them. Experts spent a lot of time to practice the cube solving. So, every cube position becomes a chunk, and through this practice, now they had developed a good number of chunks in their long term memory (LTM). Both LTM and VWM create an efficient Long Term Working Memory (LTWM) system. Earlier researchers have shown the importance of LTWM in the expert's superior performances ((K. Anders Ericsson, 2006).

However, there was no significant difference in the OT between experts and novices. That surprises initially but when we see the table-1 and table-2 together, it gives an interesting explanation. On an average experts take almost same OT as novices, but the individual variance of five trials of final round (sd) explain that, average of sd of experts was less than the novices and the mean difference of 'sd' was significant, that reveals, experts shows less variance in time to explore the cube and to encode it with their encoding technique, in each trial. To validate the current findings, interview data of experts' provides a reasonable basis, that, experts coding and retrieval technique was so efficient that they can encode any scrambled cube, with little variance in OT. On the contrary, novices admitted, that, as they lack the efficient encoding and retrieval skills, that's why they use different encoding approach to encode the cube in each trial. That's why they need different time to observe the cube in different trials. This finding also suggests that over the period of extensive training, experts developed an economical cognitive mechanism, which seems intuitive to others and also they are able to handle any situation in the domain, in which they are expert.

The correlations of novices showed strong relationship that also between OT and ST which is supported by the regression coefficient. The novice's interviews give a basis to explain these findings. As the novices lack the efficient coding technique that is why, they put more emphasis to remember the whole cube. It creates cognitive overloading that affects their timing quotient and hampers the overall performance. On the other hand, the correlations showed that, there was no significant relationship between OT and ST for experts. It also explained that experts have better understanding of problem space that is why they need the same duration to understand different problems of a domain. The proposed visuo-spatial colour coding skill hypothesis was supported by this view.

The deliberate practice factor has an important role also in Rubik's cube domain; novices need well-structured practice schedule to improve their cognitive factors as well as their fine motor movements specially the finger movements. Because, if they remember the surface colours of pieces and their positions in the cube, they need not view the colour and position every time, and faster and precious finger movements will give an edge and can save more time.

Accounting for the superior performance of experts in everyday life appears to require a different approach, where performance is captured by carefully designed representative tasks and then systematically investigated with process-tracing techniques and experimental manipulations. Previous applications of this approach have tended to focus on domains like chess, music, and sports, because they readily permit the direct observation and reproduction of superior performance by experienced individuals under controlled conditions.

However, the challenges faced by contemporary expert-performance researchers was to demonstrate how the principles and mechanisms proposed to explain high achievement in these kinds of skill domains can be used to explain human performance more generally. Although; some studies, have already taken important steps in this direction (Ackerman, 2000; Ericsson, 2004). There is clearly a need for more research synthesizing the findings from studies of elite performance in competitive domains like Rubik's cube and chess with the findings from field studies of skilled performance in occupational or everyday realms as well as from controlled laboratory studies of unskilled performance by novice learners. Nevertheless, we believe that by directly investigating the essential properties of superior performance researchers can derive generalizable predictions about the development and nature of human abilities that both meet the traditional standards of scientific measurement while providing useful information about learning in real-world contexts. Hence, studies designed in the spirit of the expert-performance approach can satisfy both basic and applied cognitive research goals allowing academic scientists to generate and test theoretically driven hypotheses about fundamental cognitive processes in the laboratory, while simultaneously permitting applied practitioners interested in improving real-world achievement to benefit from cognitive psychology's powerful methodological toolbox.

Conclusion: These results reveal substantial difference between experts and novices. Experts exceed novices in solving cubes. The trend (mean and variance (sd) in five trials of final round) in ST suggests that experts were extremely competent and had developed a rapid and efficient mechanism to solve the cubes. The novices have higher OT as compared to the experts, which signifies that they need more time to understand the problem space. This was also affirmed by the variance (sd) in OT in five trials of final round, of the novices. interviews reveals that, expert's had developed a highly efficient colour coding techniques. Due to their unique coding technique and vast experience they need almost fixed time to encode the cubes.

At the same time, it is clear that the first studies in a domain will never account for all of the potentially relevant information about the structure and acquisition of expert performance in that domain. There will always be the need for subsequent studies to replicate the initial analyses, refine the measurement instruments, explore theoretically incongruent findings, and develop practical applications..

References

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Viveka Nand Tripathi (*) and Anurag Upadhyay (**)

(*) Ph.D., Department of Psychology, University of Allahabad., (**) Ph.D., Department of Psychology, Lecturer, Government College, Uttar Pradesh, India

Received: January 07, 2018

Revised: February 09, 2018

Accepted: April 14, 2018
Table-1: Mean and SD of OT and ST (individual) of Experts

Experts  M and SD of OT  M and SD of ST

E1       (10.45) 0.48    (14.31) 1.39
E2        (8.69) 0.58    (21.59) 1.67
E3       (12.25) 0.40    (17.92) 1.77
E4        (9.01) 0.60    (21.26) 2.04
E5        (9.83) 0.69    (22.63) 2.05
E6        (6.62) 0.71    (16.64) 2.24
E7        (9.15) 0.53    (20.34) 2.28
E8        (7.61) 0.75    (20.41) 3.00
E9        (8.82) 0.76    (15.56) 3.12
E10       (9.51) 0.94    (24.35) 7.19

Table-2: M and SD of OT and ST (individual) of Novices

Novice  M and SD of OT  M and SD of ST

N1       (7.54) 2.39    (27.23) 2.84
N2       (8.66) 2.06    (22.24) 2.91
N3      (11.35) 1.33    (45.87) 3.57
N4       (9.78) 1.72    (36.19) 4.00
N5       (9.28) 1.98    (42.79) 4.08
N6       (6.69) 2.33    (34.73) 4.30
N7      (10.14) 1.75    (41.37) 4.31
N8      (10.07) 2.19    (37.39) 5.56
N9      (10.37) 1.67    (29.64) 5.64
N10      (9.68) 1.94    (36.42) 5.69
N11      (8.62) 1.89    (31.30) 7.40
N12     (10.23) 2.07    (51.34) 8.10
N13      (8.80) 1.90    (39.14) 13.76
N14      (7.67) 2.68    (29.99) 14.19
N15      (9.49) 2.50    (42.12) 22.51

Interview Summary

Major themes        Experts

performance         Felt satisfied and happy with their performance.
Satisfaction

Algorithm Based     Cube was solved on the basis of large number of
Solving             pre-learned algorithms.

Better Algorithms   Used faster and more efficient (in term of less
                    no. of moves) algorithms

Deliberate/Focused  Had practiced a specific problem/weak points/new
Practice            techniques until it became intuitive/automatic
                    /reflexive.

Enhancement of      With the help of rigorous training they had
Cognitive           expanded large memory span, faster thinking style,
Skills/Resources    and better access to their experience stored in
                    memory.

Visuospatial        In the process of solving, cube encoding includes
Encoding and        colors of the pieces and its relative positions
Retrieval           with reference to center piece of targeted surface.
Technique           Encoding process differed from person to person.

Full                While solving the cube paid full attention and
Attention/Keen      displayed keen observation skills.
Observation

Performance         Felt less/no pressure of peer competitors
Pressure

Fine Motor          Gave credit to their fast and precise finger
Control             movements. Rather than rotating the whole cube the
                    used fingers to rotate the targeted layer that made
                    their solving faster.

Memory              No/minimum memory interference reported
Problems/Retrieval
Interference

Proceduralization   Reported that as they saw the constellation of the
                    cube, they started solving intuitively.

Strategic and       While observing the cube they started planning from
tactical planning   small moves to larger goals.

Major themes        Novices

performance         Felt good but not satisfied with their performance.
Satisfaction

Algorithm Based     Learned only few algorithms.
Solving

Better Algorithms   Felt confused and reported mixing of algorithms
                    while using them.

Deliberate/Focused  Lacked focused practice.
Practice

Enhancement of      Lacked large memory span, and reported interference
Cognitive           while accessing learned rules and algorithms.
Skills/Resources

Visuospatial        Were still learning the process.
Encoding and
Retrieval
Technique

Full                Tried to pay full attention but were easily
Attention/Keen      distracted by memory interference or noise present
Observation         in the environment.

Performance         Felt pressure from top ranking players and the
Pressure            other competitors

Fine Motor          Tried to use their fingers to rotate the targeted
Control             layer but lack of practice hindered performance.

Memory              Recollection of past experience to solve the cube
Problems/Retrieval  was hampered by memory interference.
Interference

Proceduralization   Reported more declarative memory/knowledge
                    regarding solving the cube.

Strategic and       Lack of planning, only short term goals were set.
tactical planning
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Author:Tripathi, Viveka Nand; Upadhyay, Anurag
Publication:Indian Journal of Community Psychology
Date:Sep 1, 2018
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