This article was downloaded by: [Anadolu University]On: 20 December 2014, At: 15:07Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Physical Education and Sport PedagogyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/cpes20

Complexity thinking in PE: game-centred approaches, games as complexadaptive systems, and ecological valuesBrian Storey a & Joy Butler ba Sport Science Department , Douglas College , 700 Royal Avenue,New Westminster , BC , Canada , V3L 5B2b Department of Curriculum and Pedagogy , University of BritishColumbia , Vancouver , CanadaPublished online: 08 Mar 2012.

To cite this article: Brian Storey & Joy Butler (2013) Complexity thinking in PE: game-centredapproaches, games as complex adaptive systems, and ecological values, Physical Education andSport Pedagogy, 18:2, 133-149, DOI: 10.1080/17408989.2011.649721

To link to this article: http://dx.doi.org/10.1080/17408989.2011.649721

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Complexity thinking in PE: game-centred approaches, games ascomplex adaptive systems, and ecological values

Brian Storeya∗ and Joy Butlerb

aSport Science Department, Douglas College, 700 Royal Avenue, New Westminster, BC, CanadaV3L 5B2; bDepartment of Curriculum and Pedagogy, University of British Columbia, Vancouver,Canada

(Received 18 July 2010; final version received 30 September 2011)

Background: This article draws on the literature relating to game-centred approaches(GCAs), such as Teaching Games for Understanding, and dynamical systems viewsof motor learning to demonstrate a convergence of ideas around games as complexadaptive learning systems. This convergence is organized under the title ‘complexitythinking’ and gives rise to a comprehensive model of game-based learning thataddresses theoretical and practitioner considerations relevant to researchers andteachers. Complexity thinking is also partnered with an ecological integration valueorientation to reinforce the dominant purposes of game-based learning in physicaleducation.Key concepts: The study of game-based learning from a complexity thinking perspectiverelies on the foundational alignment of game characteristics with those of complexlearning systems. Both complex learning systems and games are (a) comprised of co-dependent agents, (b) self-organizing, (c) open to disturbance, (d) sites of co-emergent learning, (e) open to varying experiences or interpretations of time, and (f)able to evolve their structures in response to feedback. Considering games as learningsystems opens the door to consideration of the system being as sustainable andadaptable as it can. Sustainability, adaptation potential, and engagement levels emergefrom the ‘game as learning system’ discussion in order to provide insight into thefunctioning of the game. High levels of engagement and sustainability are thepresented goals for teachers working from a complexity thinking perspective. Anumber of key concepts from systems literature, such as attractors, affordances,attunement, and disturbances, are discussed as identifiable and manipulatabledimensions of game-based learning.Implications for the PE profession: Physical educators are well positioned to noticelearning as it emerges and to construct environments that focus learning withoutforcing learning. Complexity thinking concepts such as flow, coupling, engagement,attractors, affordances, attunement, and disturbance, in combination with thepedagogical principles advocated by GCAs, provide a robust set of analytical andteaching tools. It is to be hoped that a deepening of understanding of how game formsand game play lead to learning during games will improve the quality of learningexperiences in games and foster increasing and prolonged engagement by students.

Keywords: physical education; complexity thinking; complex learning systems; games;sport; flow; constraints; teaching games for understanding (TGfU); game-centredapproach (GCA); value orientations

# 2013 Association for Physical Education

∗Corresponding author. Email: storeyb@douglas.bc.ca

Physical Education and Sport Pedagogy, 2013Vol. 18, No. 2, 133–149, http://dx.doi.org/10.1080/17408989.2011.649721

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

Introduction

Physical education (PE) teachers are held responsible for supporting the motor-skill devel-opment of children and youth while simultaneously fostering the joy of movement and life-long personal and social responsibility. This ‘prepare-it-forward’ role of the PE teachers hasbecome a constant motivation for teachers and researchers interested in comprehensivemodels for understanding game-based learning. Consistent with this vein of work, thisconceptual article explores the convergence of language and theories occurring betweenphysical educators using game-centred approaches (GCAs) and movement researchersworking from dynamical systems views of contextualized learning. Complexity thinking,based on an understanding of games as complex adaptive systems, is presented as acentre for this convergence. From this centre, this article describes how complexity thinkinglanguage can be used to understand the nature of learning during physical games andhow complexity thinking may inform the desired purposes and outcomes of games in PEsettings.

In attempts to explain and study how movement is internally organized and learned inrelation to one’s environment, researchers working with disciplinary foci such as motorlearning and biomechanics, as well as researchers seeking applied sport performance andskill acquisition ends, are increasingly employing the language and terminologies of com-plexity thinking theories, such as dynamical systems theory (see Arzamarski et al. 2010;Bourbousson, Seve, and McGarry 2010; Chow et al. 2006; Davids and Araujo 2010;McGarry et al. 2001; Renshaw et al. 2010; Wagman et al. 2001). The desired end ofmuch of this research is to aid teachers, coaches, and researchers in their efforts to helpstudents learn more effectively and efficiently.

Concurrently, research on curriculum and pedagogy relating to game-based learning inschool and coaching settings is increasingly investigating the efficacy and nuances ofGCAs. Harvey and van der Mars (2010) remind us that the many variations of GCAs,such as Game Sense (den Duyn 1997), the Tactical Games Model (Mitchell, Oslin, andGriffin 2006), Play Practice (Launder 2001), and the Tactical Decision Learning Model(Grehaigne, Wallian, and Godbout 2005), all followed the Teaching Games for Understand-ing (TGfU) model (Bunker and Thorpe 1982). Furthermore, all GCAs share the goal ofkeeping the ‘delights of human movement’ (Kretchmar 2005) at the centre of game-based learning so that students ultimately want to play again (Waring and Almond1995). In the original TGfU model, the delight of human movement, although not specifi-cally named as such, was an underlying theme connecting game appreciation and themodel’s cyclical design resulting in game play at the beginning and end of the learningcycle.

The reconciliation of GCA literature and complex systems literature is underway. Light(2008, 2009) contributed an important piece of conceptual alignment between TGfU andcomplex learning systems theories by demonstrating the consistency of both frameworkswith underlying social constructivist learning theories and an epistemological positionbased on internal constructions of reality and knowledge. Laboratory-based and appliedresearch supporting the alignment of GCAs and complex learning systems theory hasalso been driven by developments in motor-learning studies. Motor-learning researchbased on dynamical systems theory is contributing to an increasingly nuanced view ofhow specific teacher actions in the form of creating or removing constraints from individ-uals, tasks, and the surrounding environment during games foster the emergence of situa-tionally relevant and efficacious movement (see Chow et al. 2006; Renshaw et al. 2010).Dynamical systems theory, the underlying complexity theory from which the constraint-

134 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

led approach has emerged, works from a position of organism/environment symmetry(Davids and Araujo 2010). Organism/environment symmetry forces recognition thatplayer development, movement choices, and learning cannot be considered in isolationfrom game characteristics and other player abilities. To bring this and other dynamicalinsights into the realm of teacher practices, Renshaw et al. (2010) have proposed a ‘con-straint-led pedagogy’ wherein they advocate for a balanced understanding of learner devel-opment in relation to task, performer, and environment constraints. Interestingly, GCAs,which were born from a tradition of reflective practice, had already intuited the role ofthe environment and constraints in game manipulation and learner development.Whether manipulating rules, scaling equipment, adjusting the number of players, or resiz-ing boundaries, all GCAs deploy some form of taxonomy for organizing aspects of gamesthat can be changed by teachers or students to prioritize the learning of certain movementpatterns and decision-making over others.

The new dimension added to GCAs by motor-learning research based on dynamicalsystems theory is a deeper understanding of the characteristics of the environment/learner and task/learner interactions that surround player development. Examples of theadded depth emerging from dynamical systems literature include more detailed expla-nations and study of complex system phenomena, such as degeneracy (Davids andAraujo 2010; Liu, Mayer-Kress, and Newell 2006), coupling (Bourbousson, Seve, andMcGarry 2010), self-organization and phase shifts (McGarry et al. 2001), perturbationand disturbance, attunement, attention, and perception (Arzamarski et al. 2010; Wagmanet al. 2001). These concepts are developed further during the discussion of the ‘Complexitythinking model of game-based learning’ presented later in this article.

In addition to the language of dynamical systems theory being used in motor-learningliterature, language associated with what can generally be described as ‘complexity think-ing’ has emerged across subject areas. This literature has its roots in a biological and evol-utionary world view (Doll 1993) and is exemplified by work such as Mennin’s (2007),which articulated the characteristics of small problem-based learning groups with thecharacteristics of complex adaptive systems. The shift to complexity thinking acrosssubject areas represents a paradigm shift in organizing the knowledge of learning(Mennin 2007, 303). At the heart of this language shift is the acceptance of the fact thatlearning is not predictable, is not linear, nor is it best explained through simple rationalmodels.

For example, motor-learning studies looking at the reproducibility of motor perform-ance while limiting environment and task variation have shown that degeneracy is avalid concept for understanding adaptation throughout the biological world, includingthe study of human movement. Davids and Araujo (2010) highlight Pinder, Renshaw,and Davids’ (2009) study of cricket batting as an example of this phenomenon. Liu,Mayer-Kress, and Newell’s (2006) study of rotating a roller-ball (gyro-ball) in one handis another study that explicitly uses the concept to describe motor coordination variabilityleading to similar outcomes. ‘Degeneracy is the ability of elements that are structurallydifferent to perform the same function or yield the same output’ (Edelman andGally 2001, 13764). For this discussion of focused student learning and games teachingin PE, Liu et al.’s (2006) description of degeneracy as the ‘many-to-one mapping frommovement coordination space to performance space’ (392) provides a succinct explanation.Each time a subject in their study successfully rotated the roller-ball, the neurological andmuscular–skeletal patterns noted were slightly different and yet, from a performancemeasurement point of view, subjects produced trial after trial of similar performanceoutcomes. To describe these and other observations in motor learning, closed models

Physical Education and Sport Pedagogy 135

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

and metaphors for understanding learning are not satisfactory. For example, in therealm of human movement studies, information processing as a model for describing move-ment choice as a rationalized process has been widely challenged (Davids and Araujo2010):

A major problem with this view of decision making is that rationality only works in closedsystems (such as a computational system), where specific outcomes always derive if a rationalreasoning process is followed. (635)

A key concept in complexity thinking is that of open systems, which lie in contrast to theclosed and predictable systems described above. In the case of games, the play between playerscannot be characterized as closed or simple because there is a constant re-organization of playerrelationships occurring (Bourbousson, Seve, and McGarry 2010). Because games are opensystems, they can never be played with strictly reproducible outcomes. The events and adap-tations that occur in complex learning system, such as games, are probable but cannot be pre-determined through a process of design. The variance in learning during a game is due to thefact that ‘members of the same class of phenomenon have the capacity to respond differently tothe same sorts of influences . . . ’ furthermore, ‘. . . complex systems embody their own his-tories’ (Davis 2004, 94). In the case of games, players are capable of learning during playand, either spontaneously or in a delayed manner, of integrating that learning into subsequentplay; therefore, no two games can ever be identical. It stands to reason that if no two games canbe alike, then learning within games is also variable. Complexity thinking embraces thischaracterization of games as open systems and employs pattern analysis and relational analysis(learner to learner, learner to constraints, and learner to disturbance) in an attempt to betterunderstand what is occurring for learners. When patterns become identifiable, a pathway forcreating a more productive learning environment also emerges. For example, a skilled observerof children’s games will quickly recognize when poorly scaled equipment is keeping playersfrom successful outcomes. Once noticed, either the rules or the equipment is changed torestore a productive pattern of play.

For the remainder of this article, we adopt the term ‘complexity thinking’ as the broadumbrella under which dynamical systems theory, GCAs, and other systems theories con-verge. To demonstrate that this convergence is grounded in both theory and practice, wefirst identify the characteristics of games that are consistent with the characteristics ofcomplex adaptive learning systems. Following the articulation of games as complexadaptive systems, we present a game-based learning model that integrates key features ofGCAs and complexity thinking in an effort to provide a comprehensive view of game-based learning systems. In an effort to reconsider the purposes of game-based learning inPE, we conclude this article with the conscious alignment of complexity thinking and anecological integration value orientation (Jewett, Bain, and Ennis 1995). The purposes wepropose rely on an appreciation of games as open and complex adaptive systems, theteacher as an active agent of the system, and the emergent understanding of game function-ing assessed along the lines of sustainability, engagement levels, and adaptation potential ofa system.

Complexity thinking: seeing games as complex adaptive systems

Six criteria are now presented to assess whether a game can be considered a complex adap-tive system. Each criterion is presented in the form of a question: (a) Is the game comprisedof co-dependent agents? (b) Does the game allow for self-organization between players? (c)Is the game designed for equilibrium and open to disturbance? (d) Does the game represent

136 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

a site of nested and co-emergent learning? (e) Do the players have varying experiences orinterpretations of time during play? (f) Can the game structure evolve (Davis and Sumara2002, 2003, 2005a, 2005b; Doll 1993; Mennin 2007)?

Is the game comprised of co-dependent agents?

Co-dependence as a characteristic of complex systems refers to the fact that the system iscomprised of organisms that are inter-dependent. Without inter-dependence, there is noneed of a systems understanding of their interactions. In education, we tend not to referto our students as ‘organisms,’ but we do describe them as agents. The ‘agents’ ofgames are primarily their players, but may also include teachers, coaches, referees, andin some cases parents. Each individual player is recognized as a complex adaptive organismonto himself or herself. Once players begin to read, react, and respond (Hopper 2003) totheir teammates and opponents, they are acting as co-dependent parts of a complex learningsystem. In the simplest game with only two players, each player is co-dependent on his orher opponent for the system to operate. When one quits or is injured, the system and all theassociated learning (adaptation) potential collapse. As the example demonstrates, co-depen-dence is not restricted to teammates. Players are also coupled to opponents. Coupling refersto pairings of agents within a system. Recent research in coupling and co-dependence hasbeen undertaken in basketball by Bourbousson, Seve, and McGarry (2010) and in footballby Grehaigne, Wallian, and Godbout (2005). Systems comprised of co-dependents do notrespond in predictable ways due to the fact that changes in one part of the system lead toresponses in another. Learners’ awareness of their co-dependence on others, versus theirdomination of others, is central to the adoption of an ecological integration value orientationthat will be discussed later in this article. Helping students gain awareness of their co-dependence on opponents leads to a teaching focus that requires learning how to adjust,adapt, invent, and play games that maximize opportunities for all.

Does the game allow for self-organization between players?

Self-organization refers to the constant inter-player re-organization of play that occursduring the game. Each time an individual changes, the system must re-organize itselfaround the emergent learning at each level of consideration in the system. Self-organizationpresents a challenge for games teachers wishing to maintain control of students’ movementor to be overly prescriptive about successful movement patterns. Once a game is started,players are constantly adapting to new situations. Player re-organization is most evidentduring major phase shifts (or system evolution) in a game, such as the shift betweenoffence and defence when ball possession changes; however, self-organization is constantand ongoing between all players in a game. To visualize self-organization, consider a foot-ball game viewed from above and imagine the players moving as a team in relation to theball position and possession. In nature, the same phenomenon can be witnessed in thecomplex systems represented by flocks of birds and schools of fish in response to attractorstimuli such as predators or prey. Flocks of birds hunting insects, schools of fish avoiding apredator, and two teams trying to gain possession of a ball and score goals are all subject tothe same phenomenon of self-organization within the system. There is a constant readingand response dynamic between each agent and his or her neighbours in the system. A criti-cal step in adopting complexity thinking is recognition that self-organization occurs all thetime between players without the direct involvement of a teacher. That is not to say thatteachers do not facilitate student learning by way of co-manipulating the constraintspresent in a game or by providing direct and indirect feedback to the students on their

Physical Education and Sport Pedagogy 137

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

existing and potential movements. This shift from a control orientation to recognition oflearning as a biological adaptive process outside the teachers’ direct control but withintheir influence represents a fundamental shift in emphasis from teaching to learning(Davis and Sumara 2005a; Doll 1993; Mennin 2007).

The examples given above describe system-level self-organization, which can bedescribed at the level of agent–agent and agent–constraint interactions. For conceptualclarity, it is important to note that self-organization is also the term used within dynamicalsystems theory for studying and explaining situated human movement responses. By adopt-ing a fractal view and looking at individual movements within a game, self-organization canalso be used to explain how physiological sub-systems (skeletal, nervous, cardio-vascular,etc.) mobilize to create movement in response to events that occur during game play.Degeneracy (Davids and Araujo 2010; Edelman and Gally 2001) describes how from a per-formance measurement point of view, individual movements may look very similar fromtime to time; however, when assessing how internal sub-systems organize to create eachmovement, no two movements produced by an individual are identical. Returning fromhow individuals represent self-organization as a nested concept within the game to theself-organization of players throughout a game, the performance measures of games,such as goals, passes, outs, overs, etc., are similar from instance to instance, however,the organization of players in each manifestation may differ. Games that allow players toself-organize in an effort to create the performance outcomes that define a game are repre-sentative of complex adaptive systems both at the game play level of analysis and throughthe fractal view that looks more closely at individual movement production.

Is the game designed for equilibrium and open to disturbance?

Equilibrium in many circumstances is considered desirable; however, in complex adaptivesystems, learning does not occur when learners are maintaining their status quo (Mennin2007). Disturbances are the events that force agents in the system to adapt. They are disrup-tions to homeostasis in the individual and the flow of game play. In complexity thinkingliterature, the terms ‘disturbance’ and ‘perturbance’ are used to represent the same phenom-enon of disruption to the learner or the system. This article uses the term disturbance to rep-resent this phenomenon. Competitive games, by design, exploit the tension betweenequilibrium and disturbance in order to leverage the excitement and suspense of anunknown outcome. Equilibrium is typically established at the start of a game using equalscore and division of players between teams. This initial state of balance sets the stagefor the ensuing attempts to break and restore the equilibrium. This characteristic ofgames can be described as equilibrium by design and disturbance through play. Thischaracteristic of games creates adaptive possibilities that do not require the teacher to bethe dominant agent in a lesson. Opponents collaborate to play the game and thereby endup co-contributing to the adaptation potential of the system. The teacher is not a passiveagent in creating the disturbances that foster adaptation. The teacher is active during thedesign of games (with or without student involvement) and throughout the game play(either directly or through facilitation) by adjusting constraints and fostering attunementthrough feedback with the aim of increasing adaptation opportunities for students. Theroles of feedback, constraints, attunement, disturbance, and attractors are discussedfurther in the section titled ‘Complexity thinking model of game-based learning.’

Doll (1993) refers to systems that allow for disturbance as ‘open systems’, while ‘closedsystems’ are those that do not allow for disturbance. Games are in a continual state of dis-turbance due to the oscillating roles of players that occur during what Grehaigne, Wallian,

138 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

and Godbout (2005) call the ‘momentary configurations of play’. For example, in a 0–0football game, the team with possession of the ball is working to break the equilibrium,while the defensive team is attempting to protect the equilibrium by regaining possession.As soon as the ball is captured by the defence, the roles switch. The disturbances in thegame come from the unpredictable choices made by players with and without the ball.

Does the game represent a site of co-emergent learning?

Co-dependence leads to co-emergent learning. If you and I are playing together and youlearn a new movement that changes the way I need to respond, an opportunity for me tolearn is also created. If our play evolves together in this way, our learning is co-emergent.To expose whether co-emergence is part of the potential of a game structure, we can ask‘When one player adapts and learning is expressed through new movement patterns,does the game allow for others to adapt in response?’ If the game represents an opensystem, then the answer will be affirmative, resulting in an inevitable learning spiral thatchanges the potentialities of all other agents in the system (Mennin 2007). From a complex-ity thinking point of view, the important determinant of nested and co-emergent learning isthat learning only emerges in relation to others because it is situated within the system(Luce-Kapler, Sumara, and Davis 2002). As an example, consider children playing footballwhen one teammate is afraid to head the ball. As soon as he overcomes his fear of headingand begins to demonstrate this movement during game play, all the other players (team-mates and opposition) have the opportunity to adapt to the new ability on the field. Thenew skill affords his teammates new opportunities to experiment with chip passes andaffords defenders the opportunity to use their heading skills to oppose the player. Thenew potentiality and pattern of play are a disruption of the existing pattern creating thepossibility for co-emergent learning.

Do the players have varying experiences or interpretations of time during play?

As researchers, we are often tempted by the allure of objectivity and might thus hope thatunderstanding games as complex systems offers this promise. However, the ecologicalroots of complexity thinking and biological adaptive theories such as dynamical systemstheory remind us that the agents of games are, at their core, biological beings. Therefore,adaptation is a fully embodied experience for the player. In this regard, we contend thatit is helpful to understand complex adaptive learning systems as functioning in accordancewith their own biological clocks, not the Cartesian seconds, minutes, and hours that havelayered onto them. The focus here is on student experiences of time, not the fixed time allot-ments of PE periods or structured game segments such as ‘periods’ and ‘quarters’. As fixedand ordered components of game structure, quarters and periods tell us little about the learn-ing occurring during game play or student experience of games. Luce-Kapler, Sumara, andDavis (2002) used the expression ‘fractal time’ to describe the difference between mechan-ical time and biological time:

Fractal time, then, like fractal geometry is a more complex form. It is commonplace to speak oflife forms having their own clocks – a way that the passing of time is measured whether it is acell, a tree, or an ecosystem in a recursive process that has an identifiable rhythm or pattern. Inthe mechanical interpretations of time, humans have regularized rhythms so that quantitativelyevery second, minute, and hour is of the same length, but in doing so, human beings have lostthe sense that one moment exists within another. (360–1)

Physical Education and Sport Pedagogy 139

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

Games hold the potential to free us from artificial notions of time and to return us to therhythms of breath, heartbeat, and body that relate directly to our level of engagement, retreat,exhilaration, and disappointment. The ebb and flow of energy, focus, and effort in a game waxand wane both individually and systemically. ‘Flow’ is the word used by Csiksanetmihalyi todescribe this engagement during games. Flow ‘is a state of consciousness where one becomestotally absorbed in what one is doing, to the exclusion of all other thoughts and emotions. . . .More than just focus, however, flow is a harmonious experience where mind and body areworking together effortlessly, leaving the person feeling that something special has justoccurred. So flow is [also] about enjoyment’ (Jackson and Csiksanetmihalyi 1999, 5). Asembedded facilitators in the complex learning systems of games, we are challenged to recog-nize when flow occurs in our class from the student perspective and subsequently to learnhow to harness, redirect, replenish, and dampen it to generate student learning most effec-tively. It may take a great deal of research to frame game-based learning in ways that donot minimize the importance and subtleties of fully embodied learning. Ultimately, describ-ing experiences of play, games, and embodied learning using language may be an incongru-ent act; however, by including the criteria for biological or ecological experiences of time byparticipants, we hope to draw attention to the fact that the insider’s view of games is notmeasured in the same analytical way as the outsider’s view.

Does the game structure evolve in response to feedback?

Game structure refers to the rules, equipment, and environments, which bound or constrainmovement possibilities in games. Player–player feedback and teacher–player feedback areimplicit in the fact that games are comprised of co-dependent agents. As well, the sugges-tion that games are complex adaptive systems posits that the game structure itself is open tofeedback in order for the system to evolve. As new movement potential is achieved byplayers and old constraints give way to new, new game structures are required to permitcontinued evolution of players and push the game to its next iteration. GCAs are helpfulfor understanding this process because they predominantly adopt an open-system viewof game structures. As players gain new insights into tactical options and their abilities, tea-chers can use direct, Socratic, or democratic methods to adapt the game structure, therebyextending or expanding the adaptation potential of a game. The presentation of a complex-ity thinking game-based learning model in the following section relies on an open-systemunderstanding of game structure that sees game structure constraints evolving with playerabilities.

Complexity thinking model of game-based learning

The recognition of games as complex adaptive learning systems raises questions about howbest to utilize complexity thinking to inform day-to-day PE practices. In this section, wepresent a model for understanding learning during games that utilizes the language ofGCAs and dynamical systems theory to provide a complexity thinking view of game-based learning (see Figure 1).

The learning depicted in Figure 1 attempts to capture a number of elements present inthe complexity of game-based learning, including all the criteria relating to the definition ofgames as complex adaptive systems. Equilibrium by design and disturbance through playare represented by the balance of game structure constraints controlled by the teacher andstudents during game design on the top half of the model and game play constraints repre-senting distributed and coupled player abilities on the bottom half of the model. The game

140 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

structure constraints, depicted in the top triangle, are those represented by the physicalenvironment, rules, or equipment. In their constraint-led pedagogy approach, Renshawet al. (2010) refer to these as task and environmental constraints. These constraints rangefrom very fixed and predetermined in organized sport to open and changing in educational,inventive, and playground games. The game context, category, and form labels chosen forFigure 1 are from the game manipulation taxonomy developed by Bunker and Thorpe(1982) in the original TGfU model.

The game play constraints depicted in the bottom triangle as a collection of individuallearners represent the performer constraints (Renshaw et al. 2010) and abilities that manifestthemselves as a set of inter-related movement opportunities and challenges during anygiven ‘state of play’ (Grehaigne, Wallian, and Godbout 2005). To exemplify the role ofgame play constraints in relation to the adaptation potential present in a game, imagine abasketball game wherein no player can shoot from beyond the three-point line. The factthat this ability is not present on the floor means that the defence does not need totightly guard for a shot when play occurs outside that line. As soon as a player demonstratesthis ability, the co-dependent and co-emergent learning characteristics of games and thegames’ ability to allow for self-organization allow the defensive player coupled to theoffensive player to adjust her defensive movements in response to the newly expressedplayer ability. An important characteristic of game play constraints is that they are notfixed due to the possibility of emergent learning being instantaneously spiralled backinto the game. Furthermore, game play constraints may emerge and decay (Renshawet al. 2010) as performers’ abilities emerge and decay. Remembering the example ofthree-point shooting, it is not hard to imagine this ability coming and going for a playerthroughout the course of a game due to any number of variables, such as fatigue, concen-tration levels, and/or opponent actions.

The interaction of game structure constraints and game play constraints leads to learn-ing conditions that will prioritize some adaptations over others. In keeping with the com-plexity thinking learning model for games presented in Figure 1, the terms attractors,affordances, and disturbances are used to represent the internal mechanism of gamesthat favour the emergence of some movement patterns over others. Attractors are the com-ponents of a game around which play is organized. Open space, the net, and the ball are allattractors during different states of play. McGarry et al. (2001), in describing inter- andintra-player couplings, describe how ‘the ball may be thought of as an attractor ontowhich the behaviour of each player and coupling is anchored’ (777). By using GCA tech-niques to manipulate a game, teachers or students can bring an attractor into stronger or

Figure 1. Complexity thinking model of game-based learning.

Physical Education and Sport Pedagogy 141

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

lesser focus. Rewarding players with points for passing five times before shooting is anexample of using game structure constraints to attune students to open-space consider-ations. Attunement refers to the focusing of attention on specific details or dimensions ofa phenomenon (Arzamarski et al. 2010; Wagman et al. 2001). Attunement is closelylinked to what we perceive and, therefore, has an impact on the attractors of a game.When observing young children play football, for example, their attraction to the ballcan be so great that when they finally get it, they would have lost track of what directionthey are going. For teachers, learning to perceive the dominant attractors present duringgame play opens the possibility of manipulating game structure constraints to changeplayers’ attunement, thereby strengthening or weakening the selected attractor.

Affordances are players’ opportunities to utilize their movement capacity or developnew capacity within the game structure (Renshaw et al. 2010). In an over-simplifiedexample, the affordances to develop dribbling skills in football are doubled if you halvethe number of players on a field. GCAs frequently advocate the use of small-sidedgames and use the pedagogical principles of sampling, modification representation, modi-fication exaggeration, and controlling tactical complexity (Werner, Thorpe, and Bunker1996; Butler et al. 2008) to increase specific affordances. Much like the attractors and attu-nement, affordances and attunement are also closely related. Attunement to cues that pre-cipitate effective movement will increase the likelihood that affordances are takenadvantage of by the learner. Understanding how game play constraints and game structureconstraints combine to create affordances provides insight into the adaptation potential of agame system. Seeking high adaptation potential is discussed as a goal of complexity think-ing teachers in the following section.

Attractors, affordances, attunement, and disturbance can all be considered on an indi-vidual level in order to understand how our internal self-organization contributes to themovement choices we make and how manipulation of the player environment will prioritizesome potentialities over others for us. When working with the sum total of player abilities inthe form of game play constraints as presented in Figure 1, the teacher is not only focusedon the individual, but also concerned with maximizing overall system adaptation potential.If an area of skill or attitude can be identified as holding back the evolution of game com-plexity, then the teacher has identified the game play constraint of most relevance (CMR).The CMR can be described as the skill or ability that if most players developed, the systemwould evolve to its next iteration. Using a typical GCA example, students may be asked toplay a 2v1 game of handball before being asked to try the same game with dribbling. If stu-dents can perform a give-and-go during the handball version of the game, but cannot do itduring the dribbling version, then the CMR related to evolving this particular game to itsmore complex form is dribbling. Through a process of reduction of complexity, GCAsattempt to find the CMR, overcome it, then gradually re-introduce complexity, and identifya new CMR. Throughout this process, the mode of learning is predominantly game basedand the role of the teacher is to remain emergent learning focused.

The phenomenon of recognizing CMRs for groups of learners is a core componentof practice for expert coaches and GCA advocates. The ability to discern CMRs withinan active group of learners provides complexity thinking coaches and teachers with a setof open-ended learning possibilities. Just as one CMR in the game is decaying, anotherwill be emerging. Both the emergence and decay of a CMR may represent shifts in pat-terns of play, creating an opportunity for the teacher to disturb the system and facilitateits movement to the next iteration (see the upper loop in Figure 1). As part of a reflec-tive process, students can help identify the CMR in a game which is common during thequestioning or discussion phase of a TGfU lesson. If students are given the opportunity

142 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

to reflect and adjust game structures, the system may benefit from the goal-driven motiv-ations of the students. By identifying desired movement, identifying areas to work on,and shaping the game, the students are invested in the game, which may lead to highengagement levels.

The following is an extended example of how complexity thinking and GCA techniquescan provide an open-ended pathway for assessing students during play and for creating theappropriate balance of game structure and game play constraints in an effort to create a posi-tive developmental spiral for students. Imagine a class of 32 eleven-year-old students learn-ing invasion games with a focus on football. Upon arrival at the field on the first day, theteacher divides the class into four groups of 8, then divides each group into two, andsets them off to play 4v4 football games. The students play the game without specialinstructions, while the instructor watches to assess their play. After the first five minutes,it is clear that there are two main attractors in the game (1) the ball, which is beingmobbed in all games, and (2) the net, which receives shots from everywhere and nowhas at least one if not two goalies on each team. It is also clear that a few players ineach game are making off-the-ball movements; however, there are few affordances forpassing due to the mobbing. The teacher decides to interrupt the game and, by way of adiscussion and questioning session, decides to reduce the games to 4v2 to emphasize therole of open space for offensive players. She also decides to change the scoring rules sothat each time the offensive team gets three passes, they get a point, and each time the defen-sive team kicks the ball out of the field of play, they get a point. Both game structurechanges are attempts to increase players’ attraction to open space and increase affordancesto make passes. Furthermore, the net is removed as an attractor in the reformed game. Thegames are reset to zero to create equilibrium by design. The new game continues for fivemore minutes, and in spite of the changes, the defensive teams continually kick the ballsall over the field and students become frustrated. In spite of the game structure creatingaffordances for passing, the game play constraints representing the distributed abilitieson the field may limit the success of offensive players. Equilibrium by design may notresult in the desired balance between game play and game structure constraints. At thispoint, the teacher might recognize the CMR, strong accurate passing. On the next day,she might start with a game she knows will help students develop strong and accuratepassing. After witnessing improvements in passing strength and accuracy (the decay ofthe CMR), she might retry the 4v2 game to see if the students’ attunement to passingand their recent practice have rebalanced the game play and game structure constraints.It is likely that the games would be much closer on the second day with a healthy flowof points to both offensive and defensive teams. Equilibrium by design makes student learn-ing look a lot like play again!

This section describing the complexity thinking game-based learning model presentedin Figure 1 focuses on the importance of interpreting game-based learning from an open-system understanding. The model attempts to understand learner development in relationto the context. Furthermore, teachers are best understood as the catalysts of learning in con-trast to the cause of learning. An important final consideration for teachers wishing to adoptcomplexity thinking is to recognize that different GCAs afford practitioners varying degreesof control over game design, reflective processes, and subsequent game redesign. Thiscontrol exists on a continuum of teacher involvement ranging from teacher-directedgame design to problem-based learning approaches that utilize criteria and a challenge tofoster student game invention (Butler 2006; Curtner-Smith 1996). The complexity thinkinggame-based learning model can be used to analyse game function for all GCAs with open-system interpretations of game structure.

Physical Education and Sport Pedagogy 143

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

Restating the purpose of game-based learning in PE: adaptation and sustainability

The adoption of complexity thinking language to help describe game-based curriculum,pedagogy, and learning for those already working from a GCA perspective may or maynot represent a significant paradigm shift. As mentioned previously, Light (2008, 2009)articulated the underlying learning theory consistency (social constructivism) betweenGCAs and complexity thinking. For these individuals, the new knowledge may be whatGerhart and Russell (2004) refer to as an analogic act, an expansion of breadth anddepth to an existing field of meaning. However, for those working from alternate perspec-tives, such as a disciplinary mastery value orientation (Jewett et al. 1995), any considerationof games as complex adaptive systems may represent a metaphoric shift regarding howlearning occurs during games. A metaphoric shift stems from a cognitive challenge to exist-ing fields of meaning. The final challenge of this article relates to articulating the purposesof game-based learning that emerge from the adoption of complexity thinking on top of anecological integration value orientation that values the whole learner embedded in his or herlearning community.

The purpose of PE game-based learning can be articulated as the creation of adaptationopportunities through positive engagement in an ongoing effort to foster game system sus-tainability. To give meaning to this definition and relate it back to complexity thinking andGCAs, expanded explanations of engagement, system adaptation potential, and system sus-tainability are provided below. It is our view that the most successful games are identifiable bytheir high levels of engagement and the positive nature of interactions during play. Positiveengagement results from the presence of appropriate game attractors and from players sup-porting each other’s learning as well as their own. An idealized description of high/positiveengagement resulting in a self-sustaining learning system full of adaptation potential isrepresented by the upper right-hand quadrant of Figure 2.

Engagement

Between the idea of games as fluid, self-propelled, iterative learning systems and the imageof games collapsing under conflict or lack of system constraints lies the continuum ofsystem functioning characterized by the players’ level of engagement and the positive or

Figure 2. Game system engagement model.

144 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

negative dimensions of that engagement (Figure 2). Positive engagement contributes tosystem sustainability, and high levels of engagement lead to higher levels of adaptationpotential throughout the game. As an example, consider how unsupervised playgroundgames at recess and lunch collapse, restart, change players, and exclude and include bothdiscriminately and indiscriminately. These games result in positive growth for some and,at times, the stunting of others. When games fail or ‘putter along’ due to the lack of engage-ment, or worse, contain outright conflict, the game can be said to hold limited positive adap-tation potential for the players. The lack of potential is due to either high negativeengagement in the form of conflict (Figure 2, bottom right quadrant) or the low levels ofoverall engagement, possibly due to a lack of adaptive challenge in the system for many(Figure 2, bottom left).

The key differences between lunch time and recess games and PE-based games are therole of the teacher and the intended purpose of the game. It is our view that the responsi-bility of public school PE teachers is to facilitate games that aim to achieve high levelsof positive engagement. From this perspective, the complexity thinking teacher cannotaccept self-exclusion or aggressive behaviours as essentialist elements of game play. Theresponsibility of the teacher from a complexity thinking view stems from the fact thatthe teacher recognizes himself or herself as a co-dependent agent in the learning system.This acceptance carries with it the responsibility to act when games are unsustainable orlack the possibility for adaptation to accommodate and include students. The ability tomodify the game structure and influence game play constraints empowers the teacher tocontinually reflect, reset, rethink, and ultimately retry to establish equilibrium by designin games that are not representative of high/positive engagement.

System sustainability

Sustainability of game-based learning relates specifically to the aim of fostering gameswherein the learner, upon completion of the game, has (a) experienced opportunities forgrowth and (b) retained his or her desire to play again. Within ecology literature, sustain-ability refers to the deployment or consumption of a system’s resources in ways that allowsfor those resources to be regenerated in sufficient quantities to maintain system potentiality.In the learning system of games, the primary resources are its players. Unless players desireto play again, future engagement opportunities are lost and the adaptation potential of thegroup as a whole suffers.

The nature of a sports contest is competitive and cooperative. In team sports, each player on thesame team seeks to coordinate with his or her team members in the pursuit of a common com-petitive goal. Beyond this, each protagonist – individual or team – cooperates with the other tovarying extents at various times. (McGarry et al. 2001, 772)

System sustainability is perhaps the easiest link to make between GCAs and complexitythinking. All GCAs have as part of their aim the desire and ability to play again as a coreprinciple of their models. At the game system level, when games are uneven or all partici-pants are not included, the will to play of some is sacrificed as the collateral damage of apoorly functioning system. Alternatively, if we are successful in our attempts to create equi-librium by design, the ‘delight of human movement’ (Kretchmar 2005) becomes a moreprobable outcome. In contrast to the state of play described by Kretchmar, wherein joy,spontaneous movement, and energy are observable, unsustainable outcomes stem fromphysiological and/or psychological injury. Although one hopes to never facilitate gameswith negative outcomes, when they do occur, our attention to the goal of sustainability

Physical Education and Sport Pedagogy 145

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

forces reflection by the teacher on the impact of the system functioning on the individual. Ifstudents are losing interest in a game form and/or the system is starting to demonstrate lowand/or negative engagement, the pattern and relational analysis (learner to learner, learner toconstraints, and learner to disturbance) of our games should provide insight into what islimiting the adaptation potential of the game. What are the attractors in the game? Whatare the affordances for players? What is the constraint of most relevance and is it indecay or emergent? These and other questions are the analytical tools that come with a com-plexity thinking view of games. Within complexity thinking, sustainability of the system isnot based on chance. Sustainability is proactively achieved by teachers attending to inter-action of the games they facilitate and the players in their care.

System adaptation potential

The third system-level descriptor of interest to the complexity thinking teacher is the poten-tial of the learning system for adaptation. Do the game structure and game play constraintscombine to create the appropriate affordances, disturbances, and attunement to specificattractors that result in desirable adaptation (learning) opportunities for students? The adap-tation potential of the system is highest when all players are challenged near their currentlimits, resulting in the potential for new movement patterns and thought to emerge fromself-organizing responses to the events of a game. When a game is under-stimulating forsome and over-stimulating for others, the adaptation potential of the system is diminished.

The top left quadrant of Figure 2 provides a description of games representing positiveyet low levels of engagement, meaning intensity or challenge is lacking for the players. Thissituation may be common in PE games where students play familiar games with friends andthe game structure constraints are rarely modified to challenge skilled movers or provideaffordances to those still developing their skill. Sustainability, or the will to play in thisregard, is a necessary but insufficient condition for judging the quality of game-based learn-ing. Both adaptation potential and sustainability are required to meet the educational aim ofproviding growth and development opportunities in accordance with PE teachers’ edu-cational mandate.

The adaptations that occur during games are often categorized along social, psycho-motor, cognitive, and affective dimensions; however, as complex self-organizing agentsin symmetry with their environment (Davids and Araujo 2010; McGarry et al. 2001),players do not behave and act discretely in these domains. Players demonstrate situatedexpressions of their ability during play that draw on all of their physiological sub-systems in different magnitudes in response to different disturbances or perturbations(McGarry et al. 2001; Chow et al. 2006). Positive adaptations in this light are those thatcontribute to the increasing capacity of a person’s physiological sub-systems to demonstrateflexibility and self-organization in response to a variety of movement challenges.

The adaptation potential of a system is not open ended and unlimited because thesystem is composed of individuals, and an individual’s adaptation potential is bound bystructure determinism (Davis and Sumara 2005a). ‘The manner of response is determinedby the agent’s structure, not by the perturbation. That is, a complex agent’s response isdependent on, but not determined by, environmental influences’ (p. 464). Furthermore,structural determinism impacts both the rate of learning and the limits of learning foreach player. Players new to a challenge and working far from their limits may show signifi-cant rates of adaptation, while experienced players, due to the law of diminishing returns,may appear to progress more slowly because they are working at, or near, their structurallydetermined limits. As an example, consider that it may take an elite marathon runner a year

146 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

of training to shave five minutes off her race time; in comparison, an adult who takes uprunning may complete a marathon in her first year and within her second year mayreduce her inaugural time by more than an hour. The elite runner is training and racingat, or near, her structurally determined limits, while the novice runner starts competingwhen she is far from hers. Learning is more obvious in the novice runner; however, bothare adapting by way of training. In spite of the unpredictable and sometimes unobservablenature of learning, a teacher employing complexity thinking using GCAs gains confidencein his or her ability to provide opportunities for students to adapt by attending to the engage-ment levels and sustainability of the system.

We now turn to a badminton example to demonstrate how adaptation potential andengagement are linked to the use of game structure constraints to create both equilibriumby design and specific affordances. A shot considered strategically essential in badmintonis the deep clear. This high and deep shot allows a player to slow play in an effort to re-establish court position. While designing a game for two players to practise this skill, theteacher may initially manipulate the game structure so that no points can be scored inthe front half of the court, thereby eliminating the attraction of the ‘short shot’ to gain aquick point. The affordances for deep shots are increased by this simple rule adjustment.If one player is struggling in the initial game, some additional performer-specific constraintsmay be applied to one of the players to re-establish the equilibrium by design. While watch-ing the play unfold, the complexity thinking teacher may be aware of technique; however,she is primarily interested in whether or not each player is performing the deep clear withincreasing consistency and accuracy. As long as both players are enjoying the game and theaffordances for both players to make deep clear shots are high, the game continues in a stateof high/positive engagement. Ideally, if one player needs a rule adjustment to reset the equi-librium, the players will make that adjustment on their own in order to maximize the adap-tation potential of their time together. In this example, adaptation potential as a focus for theteacher is an important anecdote to focusing on progressions that expected development onfixed timelines. By creating a system with high/positive engagement with affordances topractise the deep clear, the teacher has co-created the learning environment that allowsfor the desired skill to emerge and become more consistent through practice while respect-ing the concept of biological adaptive concept of degeneracy. In contrast, to continue toexpect players to progress on a fixed schedule without respect for individual variationsin learning represents a closed-system view of learning and is inconsistent with a complex-ity thinking view of learning.

It is with caution that we have utilized the terms ‘positive adaptation’ and ‘desirableforms of play’ in the above discussion relating to the purposes of games. Both conceptsare normative constructs and teaching choices can either reinforce or challenge the localand broader cultural norms surrounding the games. The adoption of an ecological inte-gration value orientation in support of complexity thinking represents our bias towardsPE teachers challenging overly competitive notions of games and sports and creating agame-based learning culture that values competitors as co-dependents and seeks to maxi-mize the adaptation potential of a system by seeking to provide appropriate challengesfor all students in the game.

Conclusion

Complexity thinking in PE literature is an emergent construct, and to foster sustained dia-logue and investigation around these concepts, the definition of games as complex adaptivelearning systems is seen as an important core to an emerging field of meaning. Game-based

Physical Education and Sport Pedagogy 147

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

learning can be aligned with six core characteristics of complex adaptive learning systems;they both (a) are comprised of co-dependents, (b) allow for self-organization, (c) aredesigned for equilibrium and open to disturbance, (d) are sites of co-emergent learning,(e) can be described by players using non-Cartesian expressions of time, and (f) havesystem structures that can evolve. In a complex adaptive learning system, any learningthat occurs during games is iteratively spiralled back into play and the game structuresare open to feedback in order to shape future learning opportunities. From this stance,games are open learning systems wherein learning trajectories may be probable, butprecise learning outcomes and timelines are not always predictable.

Following the characterization of games as complex adaptive systems, a comprehensivemodel for understanding game-based learning from a complexity thinking perspective out-lined key components of games learning systems. Within the model, both teacher andplayer agency are recognized as essential in creating the equilibrium by design needed topromote specific affordances, attractors, and disturbances. These identifiable componentsof game functioning are important signifiers of the adaptation potential and the actual learn-ing occurring during a game. Teachers who adopt complexity thinking and utilize GCApedagogical techniques become aware of the open-ended learning opportunities thatpresent themselves in games. Learning opportunities for a group can be focused on agame’s CMR that has either emerged through play or been designed into the game tocreate specific affordances. As the CMRs emerge and decay in games, opportunities forthe teacher to catalyze learning also emerge and decay. To take advantage of the learningopportunities present in games, complexity thinking provides analytical tools for recogniz-ing the phases and characteristics of game play. As system characteristics change or newlearning emerges, a proactive teacher is constantly assessing if the game structure andgame play constraints are creating the right balance leading to the positive and highlevels of engagement needed to foster sustainable game-based learning.

ReferencesArzamarski, R., R. Isenhower, B. Kay, M. Turvey, and C. Michaels. 2010. Effects of intention and

learning on attention to information in dynamic touch. Attention, Perception & Psychophysics72, no. 3: 721–35.

Bourbousson, J., C. Seve, and T. McGarry. 2010. Space–time coordination dynamics in basketball:Part 1. Intra- and inter-couplings among player dyads. Journal of Sports Sciences 28, no. 3: 339–47.

Bunker, D., and R. Thorpe. 1982. A model for teaching of games in secondary schools. Bulletin ofPhysical Education 18, no. 1: 5–8.

Butler, J. 2006. Curriculum construction of ability: Enhancing learning through teaching games forunderstanding. Sport, Education and Society 11, no. 3: 243–58.

Butler, J., J. Oslin, S. Mitchell, and L. Griffin. 2008. The way forward for TGfU: Filling the chasmbetween theory and practice. Physical & Health Education Journal 74, no. 2: 6–12.

Chow, J., K. Davids, C. Button, R. Shuttleworth, I. Renshaw, and D. Araujo. 2006. Nonlinear peda-gogy: A constraints-led framework for understanding emergence of game play and movementskills. Nonlinear Dynamics, Psychology, and Life Sciences 10, no. 1: 71–103.

Curtner-Smith, M. 1996. Teaching for understanding: Using games invention with elementary chil-dren. Journal of Physical Education, Recreation and Dance 67, no. 3: 33–7.

Davids, K., and D. Araujo. 2010. The concept of ‘Organizmic Asymmetry’ in sport science. Journalof Science and Medicine in Sport 13, no. 6: 633–40.

Davis, B. 2004. Inventions of Teaching. New York, NY: Lawrence Erlbaum Associates.Davis, B., and D. Sumara. 2002. Constructivist discourses and the field of education: Problems and

possibilities. Educational Theory 52, no. 4: 409–28.Davis, B., and D. Sumara. 2003. Why aren’t they getting this? Working through the regressive myths

of constructivist pedagogy. Teaching Education 14, no. 2: 124–40.

148 B. Storey and J. Butler

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14

Davis, B., and D. Sumara. 2005a. Complexity science and educational action research: Toward a prag-matics of transformation. Educational Action Research 13, no. 3: 453–64.

Davis, B., and D. Sumara. 2005b. Challenging images of knowing: Complexity science and edu-cational research. International Journal of Qualitative Studies in Education 18, no. 3: 305–21.

Den Duyn, N. 1997. Games sense: Developing thinking players. Canberra, Australia: AustralianSports Commission.

Doll, William. 1993. A post-modern perspective on curriculum. New York, NY: Teachers CollegePress.

Edelman, G., and J. Gally. 2001. Degeneracy and complexity in biological systems. Proceedings ofthe National Academy of Sciences, USA 98, no. 24: 13763–8.

Gerhart, M., and M. Russell. 2004. Metaphor and thinking in science and religion. Zygon 39, no. 1:13–8.

Grehaigne, J.F., N. Wallian, and P. Godbout. 2005. Tactical-decision learning model and students’practices. Physical Education & Sport Pedagogy 10, no. 3: 255–69.

Harvey, S., and H. van der Mars. 2010. Teaching games using “Play Practice” part 1: Designing theright games. Journal of Physical Education, Recreation and Dance 81, no. 4: 26–33, 54.

Hopper, T. 2003. Four Rs for tactical awareness: Applying game performance assessment in net/wallgames. Teaching Elementary Physical Edudation 14, no. 2: 16–21.

Jackson, S., and M. Csiksanetmihalyi. 1999. Flow in sports: The keys to optimal experiences and per-formances. Champaign, IL: Human Kinetics Inc.

Jewett, A.E., L.L. Bain, and C.D. Ennis. 1995. The curriculum process in physical education.Dubuque, IA: Brown and Benchmark.

Kretchmar, S. 2005. Teaching games for understanding and the delights of human activity. InTeaching games for understanding: Theory, research, and practice, ed. L. Griffin and J.Butler, 199–212. Windsor: Human Kinetics.

Launder, A.G. 2001. Play practice: The games approach to teaching and coaching sports.Champaign, IL: Human Kinetics.

Light, R. 2008. Complex learning theory – It’s epistemology and its assumptions about learning:Implications for physical education. Journal of Teaching in Physical Education 27, no. 1: 21–37.

Light, R. 2009. Understanding and enhancing learning in TGfU through complex learning theory. InTGfU . . . simply good pedagogy: Understanding a complex challenge, ed. T. Hopper, J. Butlerand B. Storey, 23–34. Ottawa, ON: Physical and Health Education Canada.

Liu, Y., G. Mayer-Kress, and K. Newell. 2006. Qualitative and quantitative change in the dynamics ofmotor learning. Journal of Experimental Psychology: Human Perception and Performance 32,no. 2: 380–93.

Luce-Kapler, R., D. Sumara, and B. Davis. 2002. Rhythms of knowing: Toward an ecological theoryof learning in action research. Educational Action Research 10, no. 3: 353–72.

McGarry, T., D. Anderson, S. Wallace, M. Hughes, and I. Franks. 2001. Sport competition as a dyna-mical self-organizing system. Journal of Sports Sciences 20, no. 10: 771–81.

Mennin, S. 2007. Small-group problem-based learning as a complex adaptive system. Teaching andTeacher Education 23, no. 3: 303–13.

Mitchell, S., J. Oslin, and L. Griffin. 2006. Teaching sport concepts and skills: A tactical gamesapproach. 2nd ed. Champaign, IL: Human Kinetics.

Pinder, R., I. Renshaw, and K. Davids. 2009. Information-movement coupling in developing crick-eters under changing ecological practice constraints. Human Movement Science 28, no. 4:468–79.

Renshaw, I., J. Chow, K. Davids, and J. Hammond. 2010. A constraints-led perspective to understand-ing skill acquisition and game play: A basis for integration of motor-learning theory and praxis?Physical Education & Sport Pedagogy 1, no. 21: 1–21.

Wagman, J., K. Shockley, M. Riley, and M. Turvey. 2001. Attunement, calibration, and exploration infast haptic perceptual learning. Journal of Motor Behaviour 33, no. 4: 323–7.

Waring, M., and L. Almond. 1995. Game-centered games: A revolutionary alternative for gamesteaching? European Physical Education Review 1, no. 1: 55–66.

Werner, P., R. Thorpe, and D. Bunker. 1996. Teaching games for understanding: Evolution of model.JOPERD 67, no. 1: 28–33.

Physical Education and Sport Pedagogy 149

Dow

nloa

ded

by [

Ana

dolu

Uni

vers

ity]

at 1

5:07

20

Dec

embe

r 20

14