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Complex and nonlinear pedagogy andthe implications for physical educationJia Yi Chowa & Matthew Atenciob
a Department of Physical Education and Sports Science, NationalInstitute of Education, Nanyang Technological University,Singaporeb Department of Curriculum Teaching and Learning, NationalInstitute of Education, Nanyang Technological University,SingaporePublished online: 08 Oct 2012.
To cite this article: Jia Yi Chow & Matthew Atencio (2014) Complex and nonlinear pedagogyand the implications for physical education, Sport, Education and Society, 19:8, 1034-1054, DOI:10.1080/13573322.2012.728528
To link to this article: http://dx.doi.org/10.1080/13573322.2012.728528
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Complex and nonlinear pedagogy and
the implications for physical education
Jia Yi Chowa* and Matthew Atenciob
aDepartment of Physical Education and Sports Science, National Institute of Education,
Nanyang Technological University, Singapore; bDepartment of Curriculum Teaching and
Learning, National Institute of Education, Nanyang Technological University, Singapore
There is increasing support to describe and examine the teaching of game skills in physical
education from a complex and nonlinear perspective. The emergence of game behaviours as a
consequence of the dynamic interactions of the learner, the game environment and the task
constraints within the game context highlights the nonlinear and complex nature of how learning of
game skills can occur. While there is increasing recognition that teaching and learning should be
seen from a complex and nonlinear perspective, the challenge is to provide teachers with ideas on
how to deliver lessons and activities that are underpinned by specific pedagogical practices from
this perspective and in alignment with emerging curricular guidelines. In this paper, key features of
complex and nonlinear pedagogy are discussed and exemplified through a Singaporean PE context.
Practical implications are shared on how lessons/activities (soccer) based on aspects of complex
and nonlinear pedagogy can be delivered in the school.
Keywords: Complexity; Nonlinear pedagogy; Physical education; Game skills; Singapore
Introduction
In this paper, we illustrate how teachers can support students’ learning of
movement skills and accompanying construction of knowledge regarding game
skills in ways that are underpinned by the similar yet differentiated theoretical
principles of complexity and dynamical systems. These theoretical perspectives
dovetail in the sense that they both suggest that student learning in PE does not
follow a pre-set pathway that unfolds in a straightforward manner; instead it is
proposed within these theoretical perspectives that student learning emerges
within diverse and nonlinear trajectories in complex and dynamic environments.
In this paper, we explicate how this view of student learning arguably aligns with
recent holistic curricular guidelines that now underpin the Singaporean PE
curriculum and education system more broadly as an example. Our analysis is
supported by several case descriptions of soccer lessons that can be used in
Singaporean secondary schools. These examples serve to illustrate how practical
*Corresponding author. Department of Physical Education and Sports Science, National Institute
of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore.
Email: [email protected]
Sport, Education and Society, 2014
Vol. 19, No. 8, 1034�1054, http://dx.doi.org/10.1080/13573322.2012.728528
# 2012 Taylor & Francis
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lessons might be underpinned by both complexity and dynamical systems
conceptual thinking.
Our analysis initially highlights how PE teachers might come to embrace
pedagogies reflecting the tenets of complex learning theory, an approach acknowl-
edged by Light (2008). This approach is concerned with the dynamic, spontaneous
and even unpredictable interactions that reflect students’ movement and game sense
learning. Indeed, a complex approach to PE pedagogy is increasingly being seen as a
viable alternative to more technical-focused and discipline mastery oriented
approaches (see Jess et al., 2011; Butler et al., 2012; Light et al., in press). As noted
by Butler et al. (2012), within the traditional approach of teaching games in PE,
‘mastery is valued, teachers deliver knowledge, the curriculum emphasizes correct
and efficient ways to carry out skills, and ideal learners are compliant, responsive,
and able to memorize information’ (p. 4). Moving away from simply teaching
students to learn the technical aspects of skills and games by breaking them down
into parts through mechanistic and linear teaching practices (Light, 2008), a
complex view of learning in PE instead proposes that teachers can foster learning
conditions that reflect greater authenticity. Subsequently, PE students are positioned
as being more flexible and constructivist learners who might better engage with
complex phenomenon and ‘real-life’ conditions that require them to engage with
higher states of adaptability and responsiveness. Indeed, Jess et al. (in press) state
that teachers invoking this complex learning approach attempt to enable PE students
with the capacity to encounter a range of physical activities and physical cultures that
exist within and outside of curricular PE, and over the course of their lifetime. For
this to occur, teachers should arguably scaffold learning experiences that require
diverse and unexpected responses in terms of physical movement, cognitive
reasoning and social interaction. We take up this view and go further in suggesting
that a dynamical systems perspective adds to our understanding of complex learning
in PE. It lends itself to teachers more specifically creating and evaluating complex
learning conditions, whereby teachers come to manipulate tasks and environmental
boundaries or ‘constraints’, with the aim of facilitating learning opportunities that
lead to adaptive and exploratory movement and game reasoning. For example, Chow
et al. (2007) posit that games can be taught through a nonlinear pedagogical
approach, with teachers modifying task constraints and using facilitative instruction
in order to enhance students’ knowledge of skills, movement and tactical decision
making.
Physical education: a Singaporean perspective
Before embarking on a more specific discussion of complex and dynamical systems
principles in order to foreground the ways in which teachers might create lessons that
enhance Singaporean students’ learning of soccer, we first outline the key influences
that structure Singaporean PE and education system more generally.
Complex and nonlinear pedagogy 1035
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In relation to the quality of educational experience that can be offered, Singapore
has arguably one of the world’s best education systems (McKinsey Report, 2010)
where the government has invested heavily in the education sector. The annual
education budget for education was S$9.7 billion in 2010 (MOE Corporate
Brochure, 2010). It is often explained by the Singaporean government that the
development of human capital is crucial, and thus the government has traditionally
expended a huge amount of its financial budget on education. With such financial
outlay, clear objectives for the education system have been set out to provide the key
shareholders (especially the teachers and school leaders) guidelines to support a
sound and relevant learning experience for the students. On the whole, the education
experience is intended to be broad-based with recent focus on holistic learning. This
is so students can be equipped with key competencies and mindsets to thrive in the
twenty-first century. In this aspect, the role of PE is considered pivotal, with the
Ministry of Education (MOE) clearly emphasising how PE is instrumental in helping
students build up useful and relevant knowledge and skills that translate within their
broader education and their lives (MOE, 2006).
According to the Singapore PE syllabus (MOE, 2006), the desired education
outcome of PE is to, ‘Develop students’ motor and game skills and equip them
with the knowledge, skills and attitudes to pursue and enjoy a physically active
and healthy lifestyle’ (p. 2). On a more specific level, key objectives of
Singaporean PE are to educate students to understand how to engage with
problems and to apply thinking skills to PE (MOE, 2006). Accordingly, a variety
of physical activities have been selected to ensure that PE lessons are purposeful,
engaging, developmentally appropriate and stimulating (MOE, 2006). It is
proposed that these activities challenge students both physically and cognitively
so that they can continue to be active in a lifelong sense, when they leave school.
The teaching of games which are categorised as territorial, net/wall, striking and
fielding was established as an approach to teach specific sports (e.g. soccer,
basketball, tennis, badminton, softball), under the purview of these game
categories. The recommendation from MOE is to begin teaching these games
from the Primary 3 level (approximately nine years of age) all the way to
Pre-university level (17 years of age).
However, while the structure of ‘what’ to teach in terms of games is explicitly listed
in the PE syllabus, the specific methods underpinning ‘how’ to teach these games are
unclear. That is, the pedagogical approach that should be undertaken to construct
students’ learning in line with the PE curriculum is not discussed in the syllabus.
Currently, PE teachers in Singapore are trained at the National Institute of
Singapore (NIE), the only teacher preparation institute in the country to teach
these games using strategies associated with Teaching of Games for Understanding
(TGfU). The assumption here is that teachers leaving the NIE should have the
adequate competency to deliver PE lessons in the ways mandated within the MOE-
created curriculum. However, research suggests that there remains a tendency for
most teachers to focus on the need for students to achieve technical competency in
terms of the skills required to play these games within a games teaching context
1036 J. Y. Chow and M. Atencio
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(known as Games Concepts Approach) (McNeill et al., 2004). Rossi et al. (2007)
have also found that while TGfU is sometimes considered useful by Singaporean
teachers, technique-based teaching is still their preferred method of teaching PE.
However, PE graduates showed strong support for the adoption of TGfU in their
teaching with students being highly motivated and clearly enjoying their lessons
(Rossi et al., 2007).
From our point of view, adequately meeting the desired education outcomes of PE
as outlined in the national Singaporean PE syllabus requires that teachers create rich
learning conditions where students can explore different movement solutions.
Furthermore, as discussed below, our position is that a games-based approach
incorporating elements of both complex and nonlinear pedagogies can be used to
frame and enhance student learning of movement skills in a more holistic manner in
line with recent Singaporean curricular guidelines. Indeed, Forrest et al. (2012) pose
that games-based learning has recently gained currency within Australia, for
instance, because of the belief that this model supports higher levels of student
engagement, whereby ‘students in the class bring their own understandings to games
and are active participants in both the learning process and construction of games
and sport knowledge’ (p. 147).
Developing a complex and nonlinear PE pedagogy
Although these conceptual thoughts are inextricably linked in terms of reflecting an
epistemological view of learning that is process-oriented and constructed, rather
than simply internally representing a fixed external world that can be broken down
into reducible knowledge (Light, 2008), various authors have used slightly different
terms to describe both complex and nonlinear principles in the realm of PE. For
example, numerous authors conceptualise students’ learning about the body,
movement and games occurs within dynamic and interactive conditions and
relative to teacher-enacted boundaries and constraints, leading to diverse student
learning outcomes and identities. For instance, Hopper et al. (2009) tend to use
the term ‘Complexity thinking’, Light et al. (in press) propose the use of a
‘Complex Learning Theory’ (CLT) framework, while Jess (2012) has recently
advocated for a ‘Complex Ecological Model’. Chow et al. (2007) subscribe to the
term ‘Nonlinear Pedagogy’ that is underpinned by the principles emerging from
dynamical systems theory. However, while there are indeed nuances that exist in
relation to how these conceptual frameworks are defined, it is not the purpose or
the scope of this paper to engage in a debate on the slight differences that might
exist with regard to their nomenclature. Going forward, our focus is to extend the
theoretical propositions set forth within these conceptual thoughts in order to
examine how a practical lesson underpinned by complex and nonlinear considera-
tions might support the teaching and learning needs of PE teachers and students.
Complex and nonlinear pedagogy 1037
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Complexity theory and PE pedagogy
Recently, scholars such as Morrison (2008) and Davis and Sumara (2006) have used
complexity theory in order to describe how teachers can actively embed the values of
unpredictability and self-organisation within classroom lessons. These lessons, in
contrast to traditional scenarios reflecting behaviourist and ‘top-down’ instruction,
are considered to be highly exploratory in nature, privileging students’ creative
processes, as well as the open-ended generation of diverse knowledge. High states of
‘connectivity’ and ‘cross-fertilization’ (Doll, 2008) are features of these lessons,
whereby student and teacher relationships become highly valued and seen as vital for
the emergence of rich and productive learning outcomes. According to Doll (2008),
learning in this type of complex environment does not occur through the direct
transmission of fixed knowledge ‘from expert to novice, or from teacher to student,
but in a nonlinear manner through all in a class exploring a situation/problem/ issue
together (and indeed from multiple perspectives)’ (p. 202).
Advocates of complex teaching in PE have instigated a ‘shift in thinking, reflecting
the notion that teachers should facilitate children’s active exploration and self-
organisation through reflection, critical thinking, and collaboration’ (Jess et al., in
press, p. 4). In terms of coming to understand the movement, a complex view
suggests that ‘knowledge is co-constructed in unpredictable, multi-factored, and
nonlinear ways’ (Jess et al., in press, p. 4). Light et al. (in press) sympathises with this
view, proposing that involvement in games ‘does not occur only at an intra-individual
level but is, instead, also distributed, among teammates and inextricably linked to the
physical and socio-cultural environment within which it takes place’ (p. 6). Thus,
within a complex classroom, rather than being conceptualised as discrete entities
within a complicated and mechanistic system, participants are instead positioned as
co-constructors of knowledge and practices that taken together lead to the
emergence of rich, productive and even unpredicted outcomes (Morrison, 2008).
Therefore, in a simplistic sense, the complex learning system reflects and creates
more than simply the sum of knowable parts as purveyed within the mechanistic and
linear learning model.
Jess et al. (2011) posit that a behaviourist approach to teaching movement and
games in the aforementioned mechanistic way reveals a ‘compartmentalized’ and
‘de-contextualised’ curriculum often associated with the transmission of ‘expert’
knowledge in a linear way. In contrast, a complexity perspective aligns with more
exploratory, yet connected, curricular guidance. Likewise, Light et al. (in press)
suggest that rather than breaking up game components into discrete parts, in a
mechanistic way, a more ‘player-centred, inquiry-based approach’ (p. 15) that aligns
with complex learning theories enables games participants to learn in more holistic
ways.
The teacher plays a critical role in fostering these conditions of complexity. Light
et al. (in press) discuss how teaching rugby to participants requires that the instructor
design and manipulate the learning environment, as well as ‘the complexity of the
situation and the degree of pressure that he/she places players under when they are
1038 J. Y. Chow and M. Atencio
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making decisions’ (p. 14). This means that the instructor needs to regularly ‘read the
situation’ (p. 14) and make varying and appropriate adjustments. Adding to this
sentiment, Jess et al. (in press) pose that adjusting the learning environment at the
micro-level of the gym or classroom is not an ad hoc practice, but is instead one that
requires a knowledgeable understanding of existing macro-level factors. The ‘nested’
curriculum thus provides flexible parameters or ‘boundaries’ that teachers must
interpret at a more localised level in order to construct adaptive learning
environments at the level of practice that might reflect proliferating student
movements and outcomes:
Viewing primary PE from this perspective reveals a more structured phenomenonthan may originally be assumed as the notion of ambiguous bounding can bewitnessed in many ways. National guidance, school facilities, equipment, children’sages, the amount of curriculum time and the nature of PE activities create some ofthe different boundaries influencing children’s learning experiences. More speci-fically, teachers (and children) regularly modify PE learning experiences byreducing or extending the complexity of tasks being attempted. (Jess et al., inpress, p. 5)
Teaching PE in this vein can be aligned with the view of Phelps and Hase (2002),
whereby, in a non-deterministic manner, learning conditions are set up in ways that
‘are rich with learning possibilities’ and teachers come to interact with students in
diverse and shifting learning systems as part of the ‘unfolding of understandings’
(p. 512). Phelps and Hase further suggest that actively introducing ‘noise’ or
‘dissonance’ is vital to creating more unpredictable learning conditions that more
closely resembles ‘real-life’ experience. In this way, teachers deliberately challenge
students ‘to reflect on new ideas, concepts and theories and to engage in action’
(p. 515). Taking up this view, Atencio et al. (2012) have described how PE teachers
themselves have even been pushed to re-examine their practices and identities when
faced with new curricular principles and theoretical models. The introduction of this
new knowledge into a PE professional learning group often contradicted the
teachers’ previous beliefs and understandings and arguably led the system towards
the ‘edge of chaos’. This re-evaluation was reflected in regular states of emotional
‘stirring up’ (Lewin, 1947/1951) and in general the learning group moved away from
a state of stability as they grappled with how to improve their pedagogical practices.
Dynamical systems and human movement
Complexity thinking, as we have demonstrated above, can be relevant to improve
understanding of the context of how students can be taught to acquire game skills
and understanding in a PE context. We further propose that a complex view of the
learning process can also be reflected in a nonlinear perspective that takes into
account complex conditions and more specifically addresses students’ unique and
specific movement learning processes (Tan et al., 2011). We now discuss how, at the
level of individual movement taking place within a complex and integrated learning
environment, the process of acquiring game skills exhibits key features of how a
Complex and nonlinear pedagogy 1039
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complex system behaves. Chow et al. (2011) have highlighted the key features of
human learning from a nonlinear perspective where such a system is: (1) subjected to
non-proportional change in response to inputs in a learning environment; (2) multi-
stable such that a single cause can have multiple effects; (3) open to external factors
altering the behaviour of the individual learner; and (4) able to harness the presence
of functional variability inherent in the learning process to acquire new movement
patterns.
With the feature of non-proportionality, it is espoused that a learner will
demonstrate small/large changes in performance when provided with inputs in a
learning context such as instructions or a change in equipment. These changes in
performance by the learner are not proportionate to the amount of ‘inputs’. Renshaw
et al. (2012) reiterated how the level of change resulting from exposure to a key
specific constraint, such as a new training method, higher quality practice partners or
a minor rule change is sometimes difficult to predict and will be determined by the
intrinsic dynamics (current predispositions) of the individual. As a consequence,
there is considerable indeterminacy by which learners achieve similar performance
outcome levels. Learners remain poised on the edge of stability and instability ready
to produce creative movement solutions to performance challenges when exposed to
a significant constraining influence (Kauffmann, 1995; Phillips et al., 2010).
A second key feature of human learning from a nonlinear perspective on multi-
stability highlights how a single cause (e.g. instructions or a change in rules of an
activity) can lead to multiple behavioural effects. With multi-stability, it will not be
surprising to expect the emergence of different and varied movement solutions
demonstrated by the students or even the same learner to achieve the same
performance outcome (Chow et al., 2011). For example, when a shuttlecock is
played high to a badminton player, the high trajectory of the shuttlecock affords
several possible strokes (e.g. smash, clear, drop or the drive) that could be executed
by the receiver in an attempt to win a point. In other words, there are multiple stable
preferred patterns of behaviours available or afforded by to the receiver.
Parametric control suggests that by manipulating certain parameters, physical
educators can guide learners to explore various functional organisational states
within the learning context. For example, the manipulation of instructions or the
change in equipment enables learners to display new or different movement
behaviours in learning situations. A soccer coach who wants to emphasise changing
the direction of attack (i.e. switching play) can easily manipulate the nature of the
game by keeping the width and shortening the length of the playing area and also by
introducing scoring zones in the corners of the pitch to afford to the players greater
opportunities to switch the direction of play when on the offensive. Such a
manipulation of practice task constraint is clearly an example of utilising the
pedagogical principles of modification by exaggeration to influence the emergence of
different movement behaviours among the learners (Tan et al., 2011).
In the same way that bringing students to the ‘edge of chaos’ through the
introduction of ‘dissonance’ leads to productive student learning outcomes in the
complex learning framework (Jess et al., 2011), variability or noise is not always
1040 J. Y. Chow and M. Atencio
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detrimental to performance and can play a crucial role in learning a new skill (Chow
et al., 2011). For example, in multi-stable nonlinear systems, noise can play a
functional role by increasing the likelihood of a system transition between multiple
states. Specifically, the inclusion of variability can encourage the learner to explore
multiple solution possibilities for a task goal (Chow et al., 2011). For instance, it is
through executing a skill in different ways (e.g. kicking a ball with different parts of
the foot) that allows a learner to refine and acquire new movements (e.g. kicking for
height, distance or spin) that could be more effective. Variability in practice,
therefore, encourages the learner to explore and perhaps find a movement solution
that aligns the characteristics of the learner to the task objective (vice versa).
Contribution from motor learning: foundations for nonlinear pedagogy
From the motor learning literature, the understanding that learning of movement
skills exhibits clear features of nonlinear systems allows researchers and practitioners
to accept how learning needs to be situated in the context where the game skill is to
be performed. Such situated perspective on how these game skills should be taught
within the context of the game is critical as it reinforces the important role of small-
sided games that is a representation of the real game. The aim here is similar to that
espoused in the complex learning framework, i.e. to enhance students’ capacities to
be adaptive and reflective participants in both curricular and non-curricular physical
activity contexts.
Additionally, the acquisition of knowledge is imperative in the process of learning
and the Cartesian view of separating cognition and body may be a reductionist
approach that requires re-examination. Clark (1997, 1999, 2001), Port and van
Gelder (1995) and Varela et al. (1995) have emphasised the need to understand the
development of cognition from a situated and embodied perspective. As noted earlier
in the discussion of complex learning conditions that are inherently dynamic and
multi-faceted, learning in this sense takes place when the learner is in the context of
the learning environment and the acquisition of knowledge occurs as a consequence
of the interactions between the learner and the environment. Barab and Plucker
(2002) elegantly described how ability is not solely found in the ‘head’ of the learner.
Ability should be conceptualised as an entity seen as a collection of functional
relations distributed across persons and specific contexts where skilful behaviours
can then be observed (Barab & Plucker, 2002). As raised earlier, the epistemological
notion here is that the learner in PE does not simply perceive an external world of
reducible knowledge in a way that reflects linear progression. Gibson (1979) further
elucidates that perception should not be seen in silo as a property of an individual’s
mind but, importantly, is a property of the individual�environment system. In
addition, Gibson (1979) suggests that information from the environment is not
stored as it is always available and perception is more than explicit knowledge since
optical information that is present cannot be explicitly described in words. Gibson’s
concept of perception�action coupling (or information�movement coupling), which
Complex and nonlinear pedagogy 1041
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emanates from ecological psychology, lends support to online control of action which
emphasises the availability of information in the surroundings that allows the
performer to continuously use for movement control and vice versa, movement for
information. Online control of action enables the performer to use the information
for action-happening in real time and emphasises the importance of understanding
online cognition in the context of the performing situation. The concept of
perception�action coupling is critical to the understanding that PE teachers need
to plan and organise activities situated in game settings.
The organisation of representative learning and practice tasks that captures the
essence of authentic game context will need to be accounted for to ensure that these
activities are properly ‘situated’. The idea of ‘representative design’ emanates from
the work of Brunswik (1956) on probabilistic functionalism. The need for ecological
validity presents an important feature that is essential in a representative task. From
an experimental setting, ecological validity refers to the correlation between the
proximal information available to the performer and the distal stimuli of interest
(Brunswik, 1956). It also refers to the discussion centred on the extent to which
empirical findings from laboratory settings can be generalised and transferred to ‘real
world’ performance contexts. Similarly, for learning to be properly situated, the
practical tasks must provide the settings in which the learnt game skill should be
transferrable to actual game performance situations. For example, a task where a
student is required to practice chest passes to a partner for 10 minutes devoid of any
game situation in basketball is poorly representative but yet, this occurs regularly and
typically in a PE setting where ‘technical proficiency’ is emphasised. The presenta-
tion of a representative task, such as ‘practicing’ passing in a 3 versus 1 possession
catch and throw modified game, will allow greater opportunities for the students to
develop pertinent perception�action couplings that are required in game situations.
Students will become attuned to movement into space, and they will recognise the
need for a channel for pass to be present and even temporal constraints in arriving at
the space to receive a pass. The emphasis on the need for representative tasks
exemplifies the importance of understanding learning from a complex and nonlinear
perspective where the acquisition of skill emerges as a consequence of the interaction
between the performer, that task and the environment. Araujo and Davids (2011)
even suggested that skill should not be seen as an entity but rather the emergence of
an adaptive functional relationship between the performer and the environment. Skill
acquisition may more adeptly be referred to as skill adaptation or skill attunement
(Araujo & Davids, 2011).
From a constraints-led approach, which is underpinned by concepts in dynamical
systems theory, a framework is available to explain the understanding of how a
teacher can alter and take into account relevant constraints in a learning context to
facilitate the acquisition of coordination (Davids et al., 2008; Renshaw et al., 2010).
Briefly, three major categories of constraints, the performer, the environment and
task constraints interact with each other to allow the emergence of goal-directed
behaviour. Performer constraints include both structural and functional aspects of
the learner. Environmental constraints relate to the physical as well as socio-cultural
1042 J. Y. Chow and M. Atencio
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components. Task constraints incorporate rules of the activity, goals of the task and
equipment (see Chow et al., 2007 for a detailed discussion). The dynamic
interactions among the confluence of constraints in the learning situation direct
the learner to seek out functional behaviours that are likely to succeed and achieve
the goal of learning. These dynamic interactions are key phenomena of nonlinear
systems and are critical support for how learners behave as complex neurobiological
systems (Chow et al., 2009). With the confluence of these constraints, the learner
searches for a stable and appropriate movement solution present among different
possibilities for behaving (Newell, 1986).
In the following section, ideas and examples on how a complex and nonlinear
pedagogy can be infused in a PE setting to teach game skills associated with soccer in
a Singapore school will be discussed.
Practical implications for designing representative learning in a Singapore
school
Soccer has a huge following amongst the population in Singapore and is one of the
most common games taught in Singapore schools. In this section, we will highlight
how complex and nonlinear pedagogy can be incorporated into the teaching of
soccer in conditions that are designed to reflect game-like contexts.
The game of soccer encompasses many different technical and tactical compo-
nents. For the purpose of this paper, we will focus only on passing. Passing the ball to
a teammate or to open space and even into an opponent’s goal is an important
feature of the game of soccer. Key aspects of passing include the following:
. Accuracy of the pass (i.e. the pass reaching the intended target)
. Weightage of the pass (i.e. the strength of the pass and how it should be
appropriately weighted so that it allows for the pass to be completed such that
it can be comfortably received or it reaches its intended target successfully)
. Timing of the pass (i.e. the pass is made at the right moment so that it successfully
reaches the intended target)
. Selection of the pass (i.e. an appropriate choice for a pass to meet the task goal)
. Support play and channel for a pass (these are key aspects of keeping possession with
an emphasis on passing)
Below we provide several connected practical lessons covering these different
aspects of passing; these lesson examples are designed to reflect complex and
nonlinear principles as noted in the accompanying commentary. See Table 1.
As noted in the above examples from a soccer lesson, nonlinear pedagogy
encourages students to establish important perception�action couplings, where the
students can make better decisions on the conditions for the performance context
and their own affordances for action. Undoubtedly, the acquisition of game skills
needs to be situated in the game context where constructivist and more situated
learning can occur, whether in a partner or larger group scenario. Thus, the learning
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Table 1. Examples of soccer activities underpinned by a complex and nonlinear pedagogical approach
Emphasis Activity Features of complex and nonlinear pedagogical approach
Accuracy of the pass
X1
X2
Y1 Y2
End Line
End Line
(Teacher-led constraints). In groups of 4. Objective is to pass the ball across the
opponent’s end line to score a point.. Pair must stay in their respective half.
Players not allowed to move with the ball.. Rules of the activity challenges the students
to focus on accuracy by having them pass
the ball through gaps over the end line in a
game-like situation.
. No specific prescription on passing technique. Students are
allowed to explore various surfaces of the foot, including
inside and outside, as well as different ways of swinging the
leg and planting the standing foot. The focus is on the outcome
of achieving the pass successfully. Introduction of different
sized balls can be used to raise levels of complexity and
possible adaptation in relation to introduction of dissonance
to the system.. An analogy-based instruction that encourages players to point
their toes to the sky could be useful. Students asked to reflect
upon why this might or might not be useful. Other possible
techniques introduced and discussed.. The analogy used is not overly prescriptive but yet provides a
boundary to which the player can adopt a movement pattern
to execute a pass.. Situated in a game setting where players are moving and
gaps develop or diminish. Challenges the students to build
on perception�action couplings related to passing accuracy.. Self-organisation: Students to reflect upon how the physical
boundaries impacted upon time, space, movement and
technique within the complex system of the game.. Students can discuss how this fluid small-sized games
scenario relates to elements of small group and larger scale
scenarios. What does the introduction of more players do to
raise the complexity of the system, in relation to this specific
activity? This type of reflection is not intended to be
deterministic in terms of predicting the ‘best’ outcome, but
rather aims to highlight how diverse behaviours, movements
and interactions might occur when the boundaries of the
learning system change.
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Table 1 (Continued )
Emphasis Activity Features of complex and nonlinear pedagogical approach
Weightage of the pass
X1X2
Y1
Y2
. In groups of 4 or 6
. Objective is to pass the ball from different
distances to challenge students to use
different amount of strength when
executing the passes.. Students should attempt to keep the passes
going continuously with two touches on the
ball at the maximum.
. Parametric control*Varying the distances challenges students
to use different weightage to the passes made.. Also, this promotes use of different foot surfaces (e.g. instep
or top of the foot) to drive the ball for shorter or longer
distances. What happens when different foot surfaces are
used? How does this change the ways in which cooperation
takes place (e.g. does the ball go astray or on target? How
might the pairs, seen here as a complex system, learn to
adapt? In which cases might using different parts of the foot
become applicable when distances change?). Again,
emphasis is on students’ exploration of knowledge and
technique rather than ‘right or wrong’ answers per se.. Manipulate the rules such that once a pass is made, the
students have to move. This will force students to be at
different distances all the time and therefore the weight of
the passes will also have to vary each time.. Self-directed construction of knowledge: students expected
to construct understandings of how space, time, movement
and technique are impacted by the constraints introduced.
Links to both small group and full-sized scenarios should be
also raised to add authenticity, with a range of possible
patterns and scenarios discussed.
Com
plex
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agogy
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Table 1 (Continued )
Emphasis Activity Features of complex and nonlinear pedagogical approach
Timing of pass
X1X2
Y1Y2
. In groups of 4
. Objective is to pass the ball from one pair to
the opposite pair in the same grid at the
third contact of passes between the same
pair. Begin with one ball.. Introduce second soccer ball to challenge
students to value the timing of the pass.. Time the pass when your teammate is ready
to receive.
. The manipulation of instructions in this case challenges the
students to value the need to time their passes. Accuracy and
weightage are also emphasised.. Lots of variability (the addition of the second ball) can be
introduced to challenge the students to varying the timing of
the passes during the activity.. Reflection to take place in relation to how students needed
to cooperate and communicate in relation to the original
rule. Students could reflect upon the ‘noise’ introduced
when second ball is included in activity. How did the
inclusion of another ball push their complex learning
system to higher states of ‘chaos’, and push the group to
attempt to adapt and re-organise to become a more coherent
system? What were the different outcomes that emerged? It
is possible for students to experience higher level of
variability when the second ball is introduced before
transiting to a new and more stable pattern of behaviour
eventually (i.e. when students begin to better incorporate the
presence of the second ball within the passing system).. Students should reflect upon how this passing scenario
might relate to other sized group scenarios. Teaching
prompts could be used to engage students in discussion
about how the introduction of more participants and balls
would eventually add to the complexity of the learning
system. What modifications in behaviour, movement and
interaction might occur?
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Table 1 (Continued )
Emphasis Activity Features of complex and nonlinear pedagogical approach
Selection of pass,
support play and
channel for a pass
X2
X1
V1
V2
. In groups of 4
. Objective is to play ball from one end to the
other. Passing to your teammate on the end
line. Player on end line able to move to
receive a pass.
. Situated in a game-like setting of 1 versus 1 and trying to get
the ball to a receiver at the end line.. Representative task design is present here. Helps to build
perception�action couplings through the modified game.. All aspects of passing will need to be incorporated here, i.e.
accuracy, weightage, timing, pass selection. Further
reflection on movements, techniques and communication
needed to achieve task. In this activity, how does the
introduction of a defensive player impact on the
complexity of the group? Within such a situated learning
context, important perception�action couplings are
established and decision-making with the appropriate
affordances for action can be strengthen.. Students then progressively link this activity with other small
group and larger group scenarios, raising points in relation to
different ways that space might be created for passes to be
played in open channels, or the different ways in which the
defender might close down channels and the attacking
player.
Com
plex
and
non
linea
rped
agogy
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Table 1 (Continued )
Emphasis Activity Features of complex and nonlinear pedagogical approach
Modified game with an
emphasis on invasion
X1
X2
X3
Y1
Direction of attack
. 3 versus 1/6 versus 2
. Team of 3 or 6 to pass ball and move the ball
from one end of grid to opposite end.. Team of 1 or 2 to attempt to stop ball from
moving into and across their end line.
. Territorial gains and invasion into opponents’ territory. Key
aspects of territorial game present.. Situated in a game setting.. Task manipulation (overload condition of greater number of
attackers to defenders; five passes before the ball can be
played across the end line) to encourage passing behaviours
but non-prescriptive. Lots of variability in a situated setting.
Many possible states of behaviours can emerge in this game
setting.. Non-proportional changes to be expected. (e.g. slight
movement off the ball can create huge opportunities for a
pass or none at all depending on positions of players involved
in the game). Students asked to reflect and consider how offensive and
defensive roles differed, as well as specific movements,
techniques and understandings that emerged. Possible
prompting could involve how the complex learning system
changes when the physical space is modified. In terms of the
learning system re-organising and adapting, what diverse
outcomes might occur when more players are introduced for
both offence and defence?
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Table 1 (Continued )
Emphasis Activity Features of complex and nonlinear pedagogical approach
Modified games with closer
similarities to the real
game context
X
XX
X
YY
Y
Y
End Zone
End Zone
. 3 versus 3 possession game.
. Five consecutive passes earns one point.
. Game changes to 4 versus 4.
. Scoring at the end zone.
. Pass ball to team mate in the end zone to
score a point.
. A 3 versus 3 game situation is set up by the teacher where the
rules could be for the students to make five consecutive
passes within the same team. This outcome will also
challenge the students to weigh their passes (with accuracy
as well) since the teammates will be in different positions all
the time in the game context to prepare themselves for a
pass.. From the possession game, another game involving a larger
number of students is set up by the teacher. Like the
possession game, this game is more game like and situated.
Notice that there are no goals in this game as passing and
support play are emphasised. In this scenario, there are lots
of opportunities to establish important perception�action
couplings required for passing.. Students asked to reflect upon the different activities in
terms of movement, space, technique and time. Students
then asked to speculate about different ways learning system
was impacted by increasing players and also moving from
‘keep away’ to end zone scoring format. Students could be
asked to reflect upon how they responded to increasing levels
of complexity when the boundaries were changed (e.g. their
movement, skills, moving into space, timing runs into space
to receive a pass and providing a channel for a pass).
Com
plex
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agogy
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task should also be representative of real game contexts to ensure student can
transfer knowledge in a more authentic sense. The teacher here is also expected to
encourage variability in the learning context to allow for exploratory behaviour in
learning. However, it is also critical that the teacher understands how to scaffold
student learning in ways that are socially inclusive, personally meaningful and
developmentally appropriate, leading to rich physical activity learning experiences
(McCaughtry & Rovegno, 2001).
An external focus of attention which emphasises the effect of the movement could
also be used to complement students’ reflection about the actual movement form
itself. In order to further challenge the students’ cognitive and contextual under-
standing of the game, it is possible to have the students reflect on each lesson and
make links with differently sized game scenarios as well as their existing knowledge of
soccer and soccer culture. They could even be prompted to reflect further upon
similar games that are in the same category. For example, the key aspects of passing
can be transferrable to basketball or even hockey where players are required to
perform passes to teammates or into space. Such opportunities for students to
engage in cognitive reflection could potentially help them to better understand and in
turn appreciate the invariant features of a common category of game (e.g. invasion/
territorial) that can be observed across different sports within the same game
category. It is also expected that this student reflection will reveal the ways in which
particular movements and skills as well as decision-making pertains to specific game-
oriented activities. At the same time, as noted by Light (2008), it is important to
emphasise here that student reflection about techniques such as passing and
receiving the ball, which is indeed important to the learning of soccer as illustrated
above, need not be conducted by direct instruction reflecting ‘right or wrong’
outcomes:
Even with a strong focus on learning technique, teachers can draw on complexlearning theory. For example, we can teach swimming or running by adopting aconceptual approach that emphasizes developing both an embodied and consciousunderstanding of the body’s movements. (p. 32)
Light states that the use of biomechanical language for secondary students or more
embodied and kinaesthetic talk with primary students would support complex and
nonlinear learning to take place. Going further, we suggest that both technical and
tactical aspects of the lesson introduced by the teacher could similarly be linked with
both biomechanical and kinaesthetic reflection by the students. As noted by
McCaughtry and Rovegno (2001), it is vital that students come to negotiate a range
of domains, including physical, cognitive and affective, in order to meaningfully
engage with movement-based learning conditions. It follows that open-ended
questions could be raised by the teacher in order to develop students’ holistic
understanding in relation to the game of soccer. A few lines of inquiry are: what does
the body feel like or move like when it is making or receiving a pass successfully or
unsuccessfully?; what about when the body has to quickly move into space to ‘get
open’ for a pass from another student, or even to defend another student?; from
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embodied or biomechanical perspectives, what does the introduction of more
participants and/or changing the physical space mean for the individual? A complex
and nonlinear pedagogy, as these initial speculations raise, requires the teacher to
organise the learning activity in such a way that the system is able to generate deeper
ways of thinking and being, and accordingly use guided reflection to probe around
students’ thought processes and feelings so as to produce more authentic and richer
knowledge.
The discussion above highlights the ways in which nonlinear pedagogy, based on
the tenets of dynamical systems and scaffolded by a constraints-led approach, is a
theoretical framework that can be used by practitioners to meet the desired holistic
outcomes of Singaporean PE (Tan et al., 2011). Similar to a complex learning
perspective, nonlinear pedagogy accounts for the complex and dynamic interactions
that occur in the learning process. However, rather than simply framing this as
‘self-organisation’ or ‘self-emergence’ in the context of increasingly challenging
constraints, within the nonlinear paradigm there is an enhanced focus on
non-proportionality, multi-stability, parametric control of constraints influencing
behaviours and incorporation of the functional role of variability. Importantly, from a
nonlinear pedagogical perspective as well as complex learning approach, the tasks
must be representative and learning has to be situated authentically in the game. In
the nonlinear view, more specifically, this authenticity is necessary so that strong
perception�action couplings can be established that are relevant for effective
performances to surface when learning has taken place. Similar to the view put
forth by complexity theory, the teacher here is therefore seen as a facilitator who
guides students to construct their own movement learning outcomes, rather than to
be seen as a prescriber of knowledge or movement solutions to the students in a
linear or behaviourist sense. In nonlinear pedagogy, the teacher sets the boundaries
through effective manipulation of constraints to allow the students to search for
individualised movement solutions (i.e. optimal for the individual) that best meet the
task goal. Instructions are outcome-oriented and non-prescriptive with regards to the
specific movement requirements for the task (Chow et al., 2007). In a complex sense,
Light et al. (in press) further propose that decision-making, intrinsic to under-
standing team games such as rugby, is negatively impacted by technique-focused
approaches which utilise ‘direct-instruction coaching for developing decision-
making’ (p. 2) with pre-set outcomes to be achieved. In contrast, the authors posit
that decision making in rugby occurs in nonlinear ways, reflecting the manipulation
of the learning environment by the coach and also involving participants’ ‘adaptation
to a dynamic environment in which they draw on their existing knowledge and skill’
(p. 13). Ultimately, as illustrated in our presentation of soccer lessons incorporating
several increasingly complex activities, a complex and nonlinear perspective does not
separate skill execution from tactical understanding and decision-making that occurs
in the ‘real-life’ game environment such as 11 versus 11 soccer. Crucially, learners
are positioned in these complementary conceptual frameworks as not perceiving and
experiencing an objective world where the body, movement and knowledge can all be
distinctly separated and understood as independent components in a fixed and
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complicated system (Jess et al., 2011). On the contrary, the PE student here is
positioned as an active and reflective creator of knowledge, beliefs and practices in
line with the tasks and conditions put forth by the teacher.
Conclusion
It has been suggested that teachers, students, tasks, equipment, socio-cultural
discourses and physical environmental factors exist in a fluid and productive
relationship; this arguably leads to diverse and often unpredictable learning processes
and outcomes (Chow et al., 2007; Tan et al., 2011; Light et al., in press). This
perspective of teaching and learning in PE diverges from traditional models which
have focused on the linear perfection of movement skills. This idealistic movement
approach has been deemed problematic as students usually cannot master movement
skills in the limited timeframe afforded in the typical PE lesson. Accordingly,
students often fail to gain deeper understandings of sport and movement (Forrest
et al., 2012). Furthermore, as suggested by Forrest et al. (2012), students are often
uninvolved and disengaged during these mastery-driven lessons and, in the longer
term, tend to emerge with a lack of motivation and interest when it comes to
understanding their bodies and movement. This view regarding dominant practices
of movement-based learning, along with emerging educational guidelines advocating
for more holistic learning processes and outcomes, signalled to us the need for a
more open-ended and nonlinear PE pedagogy.
Our discussion of a soccer lesson was guided by an understanding that teachers
need to provide instructions, tasks and feedback that can make learning more
situated and personally relevant for PE students. Therefore, we are continuing to
incorporate features of nonlinear and complex pedagogical approaches to develop
teaching practices that can help our students become active learners. Crucially, this
involves providing them with ample opportunities to explore and acquire game skills
that can be used in more authentic game contexts. While we have shared a
preliminary example of how game skills in soccer (an example of a territorial game)
can be taught in nonlinear and complex ways, further elucidation is required to flesh
out the practical ways this might occur. The practical ideas and concepts raised here
can also be deployed within other categories of games (e.g. net-barrier, target or
striking games). Nevertheless, more empirical work needs to be done to examine how
features of complex and nonlinear pedagogy can be infused into the everyday
teaching practices of PE.
References
Araujo, D. & Davids, K. (2011) What exactly is acquired during skill acquisition? Journal of
Consciousness Studies, 18s(3�4), 7�23.
Atencio, M., Jess, M. & Dewar, K. (2012) It is a case of changing your thought processes, the way
you actually teach: implementing a complex professional learning agenda in Scottish Physical
Education, Physical Education and Sport Pedagogy, 17(2), 127�144.
1052 J. Y. Chow and M. Atencio
Dow
nloa
ded
by [
Uni
vers
itat P
olitè
cnic
a de
Val
ènci
a] a
t 12:
09 2
4 O
ctob
er 2
014
Barab, S. A. & Plucker, J. A. (2002) Smart people or smart contexts? Cognition, ability, and talent
development in an age of situated approaches to knowing and learning, Educational
Psychologist, 37(3), 165�182.
Brunswik, E. (1956) Perception and the representative design of psychological experiments (2nd edn)
(Berkeley, CA, University of California Press).
Butler, J. I., Storey, B. & Robson, C. (2012) Emergent learning focused teachers and their
ecological complexity worldview. Sport, Education and Society. doi:10.1080/
13573322.2012.680435
Chow, J. Y., Davids, K., Button, C., Rein, R., Hristovski, R. & Koh, M. (2009) Dynamics of multi-
articular coordination in neurobiological systems, Nonlinear Dynamics, Psychology and Life
Sciences, 13(1), 27�52.
Chow, J. Y., Davids, K., Button, C., Shuttleworth, R., Renshaw, I. & Araujo, D. (2007) The role of
nonlinear pedagogy in physical education, Review of Educational Research, 77(3), 251�278.
Chow, J. Y., Davids, K., Hristovski, R., Araujo, D. & Passos, P. (2011) Nonlinear pedagogy:
learning design for self-organizing neurobiological systems, New Ideas in Psychology, 29,
189�200.
Clark, A. (1997) Being there: putting brain, body and world together again (Cambridge MA, MIT
Press).
Clark, A. (1999) An embodied cognitive science? Trends in Cognitive Sciences, 3(9), 345�351.
Clark, A. (2001) Mindware. An introduction to the philosophy of cognitive science (New York, Oxford
University Press).
Davids, K., Button, C. & Bennett, S. J. (2008) Coordination and control of movement in sport: an
ecological approach (Champaign, IL, Human Kinetics).
Davis, B. & Sumara, D. (2006) Complexity and education: inquires into learning, teaching and research
(London, Lawrence Erlbaum).
Doll, W. (2008) Complexity and the culture of curriculum, Educational Philosophy and Theory,
40(1), 190�212.
Forrest, G., Wright, J. & Pearson, P. (2012) How do you do what you do? Examining the
development of quality teaching in using GCA in PETE teachers, Physical Education & Sport
Pedagogy, 17(2), 145�156.
Gibson, J. J. (1979) An ecological approach to visual perception (Boston, MA, Houghton- Mifflin).
Hopper, T., Butler, J. & Storey, B. (2009) TGfU . . . simply good pedagogy: understanding a complex
challenge (Ottawa, Physical Health Education Association (Canada)).
Jess, M. (2012) The developmental physical education project: complex ecological innovation in action.
Ph.D. thesis, University of Edinburgh.
Jess, M., Atencio, M. & Carse, N. (in press) Introducing conditions of complexity in the context of
Scottish PE, in: A. Ovens, T. Hopper, & J. Butler (Eds) Complexity in physical education:
reframing curriculum, pedagogy and research (London, Routledge).
Jess, M., Atencio, M. & Thorburn, M. (2011) Complexity theory: supporting curriculum and
pedagogy developments in Scottish physical education, Sport, Education and Society, 16, 179�199.
Kauffmann, S. A. (1995) At home in the universe: the search for laws of complexity (London, Viking).
Lewin, K. (1947/1951) Field theory in social science (New York, Harper).
Light, R. (2008) Complex learning theory: its epistemology and its assumptions about learning:
implications for physical education, Journal of Teaching Physical Education, 27(1), 21�37.
Light, R. L., Harvey, S. & Mouchet, A. (in press) Improving ‘at-action’ decision-making in team
sports through a holistic coaching approach, Sport, Education and Society. doi:10.1080/
13573322.2012.665803
McCaughtry, N. & Rovegno, I. (2001) Meaning and movement: exploring the deep connections to
education, Studies in Philosophy and Education, 20(6), 489�505.
McKinsey Report. (2010) How the world’s most improved school systems keep getting better (London,
McKinsey and Company).
Complex and nonlinear pedagogy 1053
Dow
nloa
ded
by [
Uni
vers
itat P
olitè
cnic
a de
Val
ènci
a] a
t 12:
09 2
4 O
ctob
er 2
014
McNeill, M. C., Fry, J. M., Wright, S. C., Tan, W. K. C., Tan, K. S. & Schempp, P. G. (2004) In
the local context: Singaporean challenges to teaching games on practicum, Sport, Education
and Society, 9(1), 3�32.
Ministry of Education. (2006) Physical education syllabus (Singapore, Ministry of Education,
Curriculum Planning and Development Division).
MOE Corporate Brochure. (2010) Education in Singapore (Singapore, Ministry of Education).
Morrison, K. (2008) Educational philosophy and the challenge of complexity theory, Education
Philosophy and Theory, 40(1), 19�34.
Newell, K. M. (1986) Constraints on the development of coordination, in: M. G. Wade &
H. T. A. Whiting (Eds) Motor development in children. Aspects of coordination and control
(Dordrecht, Martinus Nijhoff), 341�360.
Port, R. F. & van Gelder, T. (1995) Mind as motion: explorations in the dynamics of cognition
(Cambridge, MA, MIT Press).
Phelps, R. & Hase, S. (2002) Complexity and action research: exploring the theoretical and
methodological connection, Educational Action Research, 10(3), 507�524.
Phillips, E., Davids, K., Renshaw, I. & Portus, M. (2010) Expert performance in sport and the
dynamics of talent development, Sports Medicine, 40(3), 1�13.
Renshaw, I., Chow, J. Y., Davids, K. & Hammond, J. (2010) A constraints-led perspective to
understanding skill acquisition and game play: a basis for integration of motor learning
theory and physical education praxis? Physical Education and Sport Pedagogy, 15 (2), 117�137.
Renshaw, I., Davids, K., Phillips, E. & Kerherve, H. (2012) Developing talent in athletes as
complex neurobiological systems, in: J. Baker, S. Cobley & J. Schorer (Eds) Talent
identification and development in sport: international Perspectives (New York, Routledge), 64�80.
Rossi, T., Fry, J. M., McNeill, M. & Tan, C. W. K. (2007) The Games Concept Approach (GCA)
as a mandated practice: views of Singaporean teachers, Sport, Education and Society, 12(1),
93�111.
Tan, C. W. K., Chow, J. Y. & Davids, K. (2011) ‘How does TGfU work?’: examining the
relationship between learning design in TGfU and a nonlinear pedagogy, Physical Education
and Sport Pedagogy. doi:10.1080/17408989.2011.582486
Varela, F. J., Thompson, E. & Rosch, E. (1995) The embodied mind. Cognitive science and human
experience (London, MIT Press).
1054 J. Y. Chow and M. Atencio
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