Nonlinear Pedagogy

Nonlinear Pedagogy: Encouraging Exploratory Learning in Physical Education (PE)

What is Nonlinear Pedagogy? (2:38)

  • Develops more effective game play characteristics in students

  • Facilitates students’ exploration of individualized and creative movement solutions in the learning of motor skills

  • Allows students to better acquire opportunities for movement in game like contexts

  • Encourages interactions with peers through more problem-solving and collaborative learning platforms

  • Helps students achieve success while reducing pedagogical emphasis on prescriptive instruction and drill

A Nonlinear Pedagogy (NP) approach involves the application of key pedagogical principles with the focus on manipulating task constraints (e.g., introducing different ball sizes, ball textures and grid sizes etc.) and creating representative learning designs to enhance skill-learning.

Since NP behaviours emerge at various levels (e.g., individual, game, and physical education context) in the learning of game skills, it makes sense for PE teachers to adopt a pedagogy that considers nonlinear interactions occurring in teaching and learning interventions (Davids, Button, & Bennett, 2008).

How is Nonlinear Pedagogy different from traditional approaches?

In contrast to the technique dominated, one-size-fits-all PE pedagogical approaches that include the use of prescriptive instructions and repetitive skills, NP is student-centric and emphasises exploratory learning on the part of the students.

Instead of limiting students learning opportunities when developing movement skills, NP facilitates students exploration of individualized and creative movement solutions and allows students to better acquire opportunities for movement in game like contexts. NP also encourages interactions with peers through more problem-solving and collaborative learning platforms (Chow, 2013; Chow et al., 2007; Chow, Davids, Button & Renshaw, 2016).

Learning success (e.g., better control and consistency outcome in sport skills) is also achieved despite reduced emphasis on prescriptive instruction and drill.

A PE class that engages in Nonlinear Pedagogy (NP) has the following features:



  • PE teacher manipulates key task constraints to form boundaries within which students explore functional movement solutions (Chow et al., 2009; Renshaw, Chow, Davids & Hammond, 2010) (e.g., changing the dimension of the playing area in an invasion game like soccer can impact time and space constraints: allowing the emergence of different playing behaviours).

  • PE teacher creates representative learning designs in which learning is situated in real-game contexts and is more outcome-focused (e.g., practicing dribbling against an opponent rather than with stationary cones)

  • Teaching cues are guided by movement outcomes (e.g. a firm and accurate pass in football) instead of movement forms (e.g. to kick the football at a specific angle by using a specific part of the foot).

  • While students’ learning is exploratory in nature, NP also allows more room for movement variability (Chow et al., 2007; Davids, Bennett & Newell., 2005; Renshaw, Davids, Shuttleworth & Chow, 2009) (e.g., using rackets with different lengths or ball so varying sizes).



To illustrate, a NP teaching episode may unfold like this:

Step 1: PE teacher demonstrates the task goal (e.g., forehand tennis stroke) but without direct instruction on how it is to be done.

Step 2: Learners explore their individualized movement solutions, including trying different forms, different equipment, playing competitive games etc.

Step 3: PE teacher facilitates students’ learning by asking questions (e.g. “Can you do it in a different way?”, “Can you show it again?”).

There were three phases in the research design:



Phase Nature of study Level of analysis
Phase 1
  • Intervention study

  • Controlled experimental school setting

  • 24 students randomly assigned to either NP or Linear Pedagogy (LP) group

Individual Individual
Phase 2
  • Intervention study
  • Quasi-experimental design

  • 24 students forming 12 pairs were assigned to the NP or LP intervention group

Individual Groups of individuals
Phase 3
  • Intervention study
  • Quasi-experimental design

Individual Within a class setting and on individual teacher
How did students respond?

Phase 1: Compared to the LP group


  • NP group performed as well as the LP group.

  • NP group found more individualized movement solutions.

  • NP group’s exploratory learning did not result in less effective acquisition of the game skill.


Phase 2: Compared to the LP group


  • NP group’s demonstration of extra rallies related to their improved ability in the application of game concepts.

  • NP group possessed slightly better control and consistency to hold a rally (i.e. a series of back and forth tennis shots).


Phase 3: Compared to the LP group


  • NP group performed longer rallies than the LP group post-intervention.

  • NP group was able to hold longer cooperative rallies.


In addition, key findings from interviews also found that LP participants were more rigid in their approach to acquire movement skills while NP participants were more outcome-focused and could find alternative and creative solutions to the game challenges.

Question-Icon
How did teachers respond?

Teachers who participated in the research observed that:


  • Students’ learning was outcome focused and they learnt through fun, play and exploration.
  • NP helps students to develop innovation, creativity, social skills and teamwork.
  • Relative to LP, NP was actually less demanding to carry out.

In designing PE lessons, teachers can:


  • consider incorporating NP, with the understanding that it could potentially facilitate explorative learning of sports skills in students and cater for individual learning differences;

  • allow for movement variability and an emphasis on the possibility of different movement solutions to achieve the same outcome;

  • With growing empirical evidence from the NP research, PE teachers need not expect that all students conform to only one expected ‘optimal’ movement form to achieve a task goal (Chow, Davids, Button & Rein, 2008; Lee, Chow, Komar, Tan & Button, 2014; Rein, Davids & Button, 2010).


Practically, PE teachers can:


  • choose to demonstrate a desired movement outcome (e.g., getting the ball accurately to the opponent’s court) instead of prescribing a movement form (e.g. swinging the racket in a specific angle).


  • ReEd Vol 15 “Facilitating Flexible Learning” [PDF]

  • Research Brief Series, No. 14-004, “An Investigation of Nonlinear Pedagogy and its Application in Singapore Schools” [PDF]

Question-Icon
Further readings

Learn more about NP with the handbook below:

further_readings_book

Chow, J. Y., Davids, K., Button, C., & Renshaw, I. (2016). Nonlinear Pedagogy in skill acquisition: An introduction. London: Routledge [Amazon]

References
  • Atencio, M., Chow, J. Y., Tan, W. K. C., & Lee, C. Y. M. (2014). v. European PE Review, 20(2), 244-263. doi: 10.1177/1356336X14524853.

  • Button, C., Lee, C. Y. M., Dutt-Mazumder, A., Tan, W. K., & Chow, J. Y. (2012). Empirical investigations of nonlinear motor learning. The Open Sports Sciences Journal. 5(Suppl 1-M6), 49-58.

  • 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. (2013). Nonlinear learning underpinning pedagogy: Evidence, challenges and implications. Quest, 65,469-484.

  • Chow, J.Y., Davids, K., Button, C., & Rein, R. (2008). Dynamics of movement patterning in learning a discrete multiarticular action. Motor Control, 12, 219-240.

  • Chow, J.Y., Davids, K., Button, C., & Rein, R. (2009). Dynamics of multi-articular coordination in neurobiological systems. Nonlinear Dynamics, Psychology, and Life Science, 13 (1), 27-52.

  • Chow, J.Y., Davids, K., Button, C., Renshaw, I., Shuttleworth, R & Uehara, L. (2009) Nonlinear pedagogy: implications for teaching games for understanding (TGfU).

  • Chow, J. Y. (2013). Nonlinear Learning Underpinning Pedagogy: Evidence, Challenges, and Implications. Quest, 65(4), 469-484.

  • Chow, J. Y., Renshaw, I., Button, C., Davids, K., & Tan, C. W. K. (2013). Effective Learning Design for the Individual: A Nonlinear Pedagogical Approach in Physical Education. In A. Ovens, T. Hopper & J. Butler (Eds.). Complexity thinking in physical education: Reframing curriculum, pedagogy and research (pp.121-134). London: Routledge.

  • Chow, J.Y., Tan, W.K.C., Lee, C.Y.M., & Button, C. (2014). Possibilities and implications of using a motion-tracking system in physical education. European PE Review, 20(4), 444-464. doi: 10.1177/1356336X14535057.

  • Chow, J. Y., Davids, K., Button, C., & Renshaw, I. (2016). Nonlinear Pedagogy in skill acquisition: An introduction. London: Routledge.

  • Davids, K., Bennett, S. & Newell, K. eds. (2005). Movement system variability. Leeds, Human Kinects.

  • Davids, K., Button, C., & Bennett, S. (2008). Dynamics of skill acquisition: A constraints-led approach. Human Kinetics, Champaign, Illinois.

  • Lee, M. C. Y., Chow, J. Y., Komar, J., Tan, C. W. K., & Button, C. (2014). Nonlinear Pedagogy: An Effective Approach to Cater for Individual Differences in Learning a Sports Skill. PloS one, 9(8), e104744.

  • Rein, R., Davids, K., & Button, C. (2010). Adaptive and phase transition behavior in performance of discrete multi-articular actions by degenerate neurobiological systems. Experimental Brain Research, 201(2), 307-22.

  • Renshaw, I., Davids, K., Shuttleworth, R., & Chow, J.Y. (2009). Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching. International Journal of Sports Psychology, 40(4), 540-602.

  • 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.

  • Tan, C.W.K, Chow, J. Y., & Davids, K. (2012). “How does TGfU work?”: Examining the relationship between learning design in TGfU and a nonlinear pedagogy. Physical Education and Sport Pedagogy, 17(4), 331-348.

Question-Icon
Research team

For enquiries on Nonlinear Pedagogy, please contact the Principal Investigator A/P Chow Jia Yi at jiayi.chow@nie.edu.sg.



    Principal Investigator
  • A/P Chow Jia Yi, Physical Education and Sports Science (PESS), NIE

    Co-Principal Investigator
  • Dr Clara Tan Wee Keat, Physical Education and Sports Teacher Academy (PESTA), MOE, Singapore

    Collaborator
  • A/P Chris Button, School of Physical Education, Sport and Exercise Sciences, University of Otago, New Zealand

    Consultant
  • Professor Keith Davids, Centre for Sports Engineering Research, Sheffield Hallam University, UK

Research led by
Author
Principal Investigator
A/P Chow Jia Yi
Author
Co-Principal Investigator
Dr Clara Tan Wee Keat, MOE
Collaborator:

A/P Chris Button, School of Physical Education, Sport and Exercise Sciences, University of Otago, New Zealand

Consultant:

Professor Keith Davids, Centre for Sports Engineering Research, Sheffield Hallam University, UK

For enquiries on Nonlinear Pedagogy, email: jiayi.chow@nie.edu.sg

    Collaborators

  • A/P Ng Pak Tee, Policy and Leadership Studies, NIE

  • Dr Hang Kim Hoo, MOE
  • Ms Yen Yeen Peng, MOE

M-ProSE was funded by the Education Research Funding Programme, National Institute of Education, Nanyang Technological University, Singapore (project no. OER 32/08 TTL & OER 22/12 TTL).

This knowledge resource was written by Tan Minying, Bernadine W. Sengalrayan and Tan Giam Hwee.

What teachers say

“Students can also come up with very unconventional and sometimes unpredictable ways in, in the way they actually handle the task…”

- PE teacher
Phase of education

Primary School

Academic subject

Physical Education

Research Participants

181 students

2 PE teachers

1 primary school

Contents

Research led by
Author
Principal Investigator
A/P Chow Jia Yi
Author
Co-Principal Investigator
Dr Clara Tan Wee Keat, MOE
Collaborator:

A/P Chris Button, School of Physical Education, Sport and Exercise Sciences, University of Otago, New Zealand

Consultant:

Professor Keith Davids, Centre for Sports Engineering Research, Sheffield Hallam University, UK

For enquiries on Nonlinear Pedagogy, email: jiayi.chow@nie.edu.sg

Nonlinear Pedagogy

Nonlinear Pedagogy: Encouraging Exploratory Learning in Physical Education (PE)

Question-Icon
How Nonlinear Pedagogy can help your students
  • Develops more effective game play characteristics in students
  • Facilitates students’ exploration of individualized and creative movement solutions in the learning of motor skills
  • Allows students to better acquire opportunities for movement in game like contexts
  • Encourages interactions with peers through more problem-solving and collaborative learning platforms
  • Helps students achieve success while reducing pedagogical emphasis on prescriptive instruction and drill
Question-Icon
Why Nonlinear Pedagogy?

A Nonlinear Pedagogy (NP) approach involves the application of key pedagogical principles with the focus on manipulating task constraints (e.g., introducing different ball sizes, ball textures and grid sizes etc.) and creating representative learning designs to enhance skill-learning.

Since NP behaviours emerge at various levels (e.g., individual, game, and physical education context) in the learning of game skills, it makes sense for PE teachers to adopt a pedagogy that considers nonlinear interactions occurring in teaching and learning interventions (Davids, Button, & Bennett, 2008).

How is Nonlinear Pedagogy different from traditional approaches?

In contrast to the technique dominated, one-size-fits-all PE pedagogical approaches that include the use of prescriptive instructions and repetitive skills, NP is student-centric and emphasises exploratory learning on the part of the students.

Instead of limiting students learning opportunities when developing movement skills, NP facilitates students exploration of individualized and creative movement solutions and allows students to better acquire opportunities for movement in game like contexts. NP also encourages interactions with peers through more problem-solving and collaborative learning platforms (Chow, 2013; Chow et al., 2007; Chow, Davids, Button & Renshaw, 2016).

Learning success (e.g., better control and consistency outcome in sport skills) is also achieved despite reduced emphasis on prescriptive instruction and drill.

Question-Icon
How does Nonlinear Pedagogy work?

A PE class that engages in Nonlinear Pedagogy (NP) has the following features:



  • PE teacher manipulates key task constraints to form boundaries within which students explore functional movement solutions (Chow et al., 2009; Renshaw, Chow, Davids & Hammond, 2010) (e.g., changing the dimension of the playing area in an invasion game like soccer can impact time and space constraints: allowing the emergence of different playing behaviours).
  • PE teacher creates representative learning designs in which learning is situated in real-game contexts and is more outcome-focused (e.g., practicing dribbling against an opponent rather than with stationary cones).
  • Teaching cues are guided by movement outcomes (e.g. a firm and accurate pass in football) instead of movement forms (e.g. to kick the football at a specific angle by using a specific part of the foot).
  • While students’ learning is exploratory in nature, NP also allows more room for movement variability (Chow et al., 2007; Davids, Bennett & Newell., 2005; Renshaw, Davids, Shuttleworth & Chow, 2009) (e.g., using rackets with different lengths or ball so varying sizes).


To illustrate, a NP teaching episode may unfold like this:

Step 1: PE teacher demonstrates the task goal (e.g., forehand tennis stroke) but without direct instruction on how it is to be done.

Step 2: Learners explore their individualized movement solutions, including trying different forms, different equipment, playing competitive games etc.

Step 3: PE teacher facilitates students’ learning by asking questions (e.g. “Can you do it in a different way?”, “Can you show it again?”).

Evidence from NP research

There were three phases in the research design:



Phase Nature of study Level of analysis
Phase 1
  • Intervention study
  • Controlled experimental school setting
  • 24 students randomly assigned to either NP or Linear Pedagogy (LP) group
Individual Individual
Phase 2
  • Intervention study
  • Quasi-experimental design
  • 24 students forming 12 pairs were assigned to the NP or LP intervention group
Individual Groups of individuals
Phase 3
  • Intervention study
  • Quasi-experimental design
Individual Within a class setting and on individual teacher
Question-Icon
How did students respond?

Phase 1: Compared to the LP group


  • NP group performed as well as the LP group.
  • NP group found more individualized movement solutions.
  • NP group’s exploratory learning did not result in less effective acquisition of the game skill.

Phase 2: Compared to the LP group


  • NP group’s demonstration of extra rallies related to their improved ability in the application of game concepts.
  • NP group possessed slightly better control and consistency to hold a rally (i.e. a series of back and forth tennis shots).

Phase 3: Compared to the LP group


  • NP group performed longer rallies than the LP group post-intervention.
  • NP group was able to hold longer cooperative rallies.

In addition, key findings from interviews also found that LP participants were more rigid in their approach to acquire movement skills while NP participants were more outcome-focused and could find alternative and creative solutions to the game challenges.

Question-Icon
How did teachers respond?

Teachers who participated in the research observed that:


  • Students’ learning was outcome focused and they learnt through fun, play and exploration.
  • NP helps students to develop innovation, creativity, social skills and teamwork.
  • Relative to LP, NP was actually less demanding to carry out.
Question-Icon
How can teachers get started?

In designing PE lessons, teachers can:


  • consider incorporating NP, with the understanding that it could potentially facilitate explorative learning of sports skills in students and cater for individual learning differences;
  • allow for movement variability and an emphasis on the possibility of different movement solutions to achieve the same outcome;
  • With growing empirical evidence from the NP research, PE teachers need not expect that all students conform to only one expected ‘optimal’ movement form to achieve a task goal (Chow, Davids, Button & Rein, 2008; Lee, Chow, Komar, Tan & Button, 2014; Rein, Davids & Button, 2010).

Practically, PE teachers can:


  • choose to demonstrate a desired movement outcome (e.g., getting the ball accurately to the opponent’s court) instead of prescribing a movement form (e.g. swinging the racket in a specific angle).

Question-Icon
Related links
  • ReEd Vol 15 “Facilitating Flexible Learning” [PDF]
  • Research Brief Series, No. 14-004, “An Investigation of Nonlinear Pedagogy and its Application in Singapore Schools” [PDF]
Question-Icon
Further readings

Learn more about NP with the handbook below:

further_readings_book

Chow, J. Y., Davids, K., Button, C., & Renshaw, I. (2016). Nonlinear Pedagogy in skill acquisition: An introduction. London: Routledge [Amazon]

Question-Icon
References
  • Atencio, M., Chow, J. Y., Tan, W. K. C., & Lee, C. Y. M. (2014). v. European PE Review, 20(2), 244-263. doi: 10.1177/1356336X14524853.
  • Button, C., Lee, C. Y. M., Dutt-Mazumder, A., Tan, W. K., & Chow, J. Y. (2012). Empirical investigations of nonlinear motor learning. The Open Sports Sciences Journal. 5(Suppl 1-M6), 49-58.
  • 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. (2013). Nonlinear learning underpinning pedagogy: Evidence, challenges and implications. Quest, 65,469-484.
  • Chow, J.Y., Davids, K., Button, C., & Rein, R. (2008). Dynamics of movement patterning in learning a discrete multiarticular action. Motor Control, 12, 219-240.
  • Chow, J.Y., Davids, K., Button, C., & Rein, R. (2009). Dynamics of multi-articular coordination in neurobiological systems. Nonlinear Dynamics, Psychology, and Life Science, 13 (1), 27-52.
  • Chow, J.Y., Davids, K., Button, C., Renshaw, I., Shuttleworth, R & Uehara, L. (2009) Nonlinear pedagogy: implications for teaching games for understanding (TGfU).
  • Chow, J. Y. (2013). Nonlinear Learning Underpinning Pedagogy: Evidence, Challenges, and Implications. Quest, 65(4), 469-484.
  • Chow, J. Y., Renshaw, I., Button, C., Davids, K., & Tan, C. W. K. (2013). Effective Learning Design for the Individual: A Nonlinear Pedagogical Approach in Physical Education. In A. Ovens, T. Hopper & J. Butler (Eds.). Complexity thinking in physical education: Reframing curriculum, pedagogy and research (pp.121-134). London: Routledge.
  • Chow, J.Y., Tan, W.K.C., Lee, C.Y.M., & Button, C. (2014). Possibilities and implications of using a motion-tracking system in physical education. European PE Review, 20(4), 444-464. doi: 10.1177/1356336X14535057.
  • Chow, J. Y., Davids, K., Button, C., & Renshaw, I. (2016). Nonlinear Pedagogy in skill acquisition: An introduction. London: Routledge.
  • Davids, K., Bennett, S. & Newell, K. eds. (2005). Movement system variability. Leeds, Human Kinects.
  • Davids, K., Button, C., & Bennett, S. (2008). Dynamics of skill acquisition: A constraints-led approach. Human Kinetics, Champaign, Illinois.
  • Lee, M. C. Y., Chow, J. Y., Komar, J., Tan, C. W. K., & Button, C. (2014). Nonlinear Pedagogy: An Effective Approach to Cater for Individual Differences in Learning a Sports Skill. PloS one, 9(8), e104744.
  • Rein, R., Davids, K., & Button, C. (2010). Adaptive and phase transition behavior in performance of discrete multi-articular actions by degenerate neurobiological systems. Experimental Brain Research, 201(2), 307-22.
  • Renshaw, I., Davids, K., Shuttleworth, R., & Chow, J.Y. (2009). Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching. International Journal of Sports Psychology, 40(4), 540-602.
  • 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.
  • Tan, C.W.K, Chow, J. Y., & Davids, K. (2012). “How does TGfU work?”: Examining the relationship between learning design in TGfU and a nonlinear pedagogy. Physical Education and Sport Pedagogy, 17(4), 331-348.
Question-Icon
Research team

For enquiries on Nonlinear Pedagogy, please contact the Principal Investigator A/P Chow Jia Yi at jiayi.chow@nie.edu.sg.



    Principal Investigator
  • A/P Chow Jia Yi, Physical Education and Sports Science (PESS), NIE
    Co-Principal Investigator
  • Dr Clara Tan Wee Keat, Physical Education and Sports Teacher Academy (PESTA), MOE, Singapore
    Collaborator
  • A/P Chris Button, School of Physical Education, Sport and Exercise Sciences, University of Otago, New Zealand
    Consultant
  • Professor Keith Davids, Centre for Sports Engineering Research, Sheffield Hallam University, UK

This research on Nonlinear Pedagogy was funded by Singapore Ministry of Education (MOE) under the Education Research Funding Programme (OER 15/09 CJY & OER 21/14 CJY) and administered by National Institute of Education (NIE), Nanyang Technological University, Singapore. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Singapore MOE and NIE.

This knowledge resource was written by Li Sze Yan and Tan Giam Hwee.

What is Nonlinear Pedagogy? (2:38)

What teachers say

“Students can also come up with very unconventional and sometimes unpredictable ways in, in the way they actually handle the task…”

- PE teacher
Phase of education

Primary School

Academic subject

Physical Education

Research Participants

181 students

2 PE teachers

1 primary school