Phillip Conatser

Eric James

This article describes how differential learning and dynamical systems theory can be used by physical educators to help students better learn motor skills that are adapted to their own physical needs and skills. Physical educators are concerned with finding optimal ways for students to learn and improve their motor skills. However, this objective is complicated by the fact that children differ in various physical characteristics (e.g., height, weight, strength, body composition, flexibility etc.), and each child possesses different preexisting motor skills. Some children also require special adaptations to participate in physical education.

While principles of biomechanics suggest that certain general movement forms are more effective in sports skills, nonetheless differences between individual students’ bodies make it likely that different movement patterns will be optimal for each child. Even elite athletes vary in the details of the techniques they use. Therefore, it is not surprising that individual differences should exist between our students. In the case of students with disabilities, optimal movement patterns for different children may differ widely.

In addition to accounting for biomechanical differences between students, the optimal practice conditions for learning sports skills should also be used. Ideal conditions for learning physical skills would facilitate each student learning the motor patterns that are best suited to him or her. And, even if ideal movement patterns are known, it isn’t necessarily the case that the best way to learn these skills is to repeat the exact movement pattern as closely as possible over and over. The discovery of optimal learning and practice conditions is the subject of study in the field of motor learning.

A relatively old concept in motor learning is that of ‘variable practice’. The concept of variable practice comes from Schema theory (Schmidt, 1975). This concept, which has received experimental support, indicates that better learning and retention of motor skills occurs if the movement patterns are practiced at different scaling ratios. For example, basketball shooting will improve more if students practice shooting from different distances and locations on the court as opposed to always shooting from the same distance and location on the court.

However, more recently a different theoretically-based principle has shown that other forms of variation in the practice of movement skills can benefit learning. This principle is ‘differential learning’ and is based on the theory of “dynamical systems.” When using differential learning in the practice of movement skills, the movement patterns themselves are intentionally varied during practice. For example, during practice of the shot put for track and field, one could have athletes alter the timing between the upper and lower body, change the way they hold the shot, project the shot in different directions, and/or shoot different weighted shots.

This theoretical principle suggests that by having students perform a variety of movement patterns, a self-organized process of learning is initiated. Through the process of experimentation with different movement patterns, target goals, and by learning alternative means of performing a task (rather than only practicing the supposedly ‘correct’ movement form), students learn an individualized motor solution that works best for themselves given the environmental context and constraints of their own bodies.

The process of adding ‘noise’ to performance by having students produce different movement patterns induces a bifurcation in the child‘s motor dynamics. That is, the student is perturbed from (i.e., pushed out of) their previously used less efficient movement patterns and begins a self organized learning process that leads to the emergence of a more skillful movement pattern. The idea is that without inducing the student to leave their habitual movement patterns, they will be less likely to actually engage in learning.

Taking advantage of the self organizing process of differential learning, educators should have students perform movement skill in a variety of different ways, rather than by only having them mimic the ‘perfect’ or ‘right’ way to perform each motor skill. For example, performing a tennis serve without bending or straightening their elbow or performing the tennis serve turned 90 degrees to the right or left of the direction they would usually face can serve this purpose. Creativity is “key” to finding different variations of motor skill movements to perform, leaving habitual patterns behind and beginning the self organized process of learning. Students may find this method more motivating, interesting, and enjoyable. If differential learning makes practice more interesting, this may also increase on-task time and skill development.

Let’s take a quick look at the underlying proposition behind differential learning which is dynamical systems. Here we present some important terminology, how dynamical system works, and suggestions to change behavior more effectively.

Dynamical system: System that changes over time. They are complex (many degrees of freedom) and nonlinear (abrupt change to completely new behavior) but characterized by relatively simple mathematical formulations.

Degree of Freedom: All the independent elements of the system (e.g., all the muscle fibers, muscles, tendons, ligaments, and bones in the musculoskeletal system).

Self-Organization: Under certain physical and thermodynamic conditions, independent elements of the system cease acting individually and come together to act cooperatively as one unit. There is no predetermined plan or blueprint for this pattern formation.

Complex Behavior: Seemingly simple physical systems consisting of uniform molecular elements can self-organize into wonderfully complex patterns that change over time in ways that can be mathematically defined.

Collective Variables: Under certain physical and thermodynamic conditions, the resulting organized behavior can be described in terms of one or more variables (order parameters) that appear to organize the previously disorganized system.

Attractor States: Particular patterns shown by systems over time out of the enormous number of possible patterns. Basically, complex systems autonomously prefer certain patterns of behavior strictly as a result of the cooperativeness of the participating elements in a particular context (i.e., function). Attractor states are not encoded or programmed beforehand. Rather, attractors are emergent phenomena.

Phase Transition: The ability of complex systems to change from one pattern to another in a seemingly sudden or discontinuous (nonlinear) manner. The system shifts between qualitatively different attractor states. Phase transitions occur due to changes in system sensitive variables (control parameters, constraints, rate limiters).

Control Parameters: Any organic or environmental variable that, when changed, leads to corresponding changes in the collective behavior of the system. Control parameters do not contain instructions for the change (nonspecific information), but rather drive the system into a new attractor state (behavioral pattern). Understanding the developmental process includes a characterization of the control parameters that cause phase transitions.

People are characterized by many degrees of freedom, and behaviors are characterized by the compression of these degrees of freedom into collective variables. This coming together of degrees of freedom is a self-organizing process in that behaviors emerge strictly as a cooperative function of the subsystem within a particular context. Thus, behaviors are not hardwired or predetermined. However, certain patterns or behaviors are preferred, and deviations from these patterns will tend to be attracted back to these stable attractor states. Phase transitions between attractor states or developmental changes that are qualitatively different from previous behavioral states (nonlinear change) are caused by the scaling up or down (linear change) of critical control parameters.

• The human system is very complex with many "degrees of freedom" (independent elements).
• Joints, muscles (620 pairs), muscle fibers, etc...
• To walk or perform any movement, one has to control all degrees of freedom.

• The same motor commands from the central nervous system will not always produce the same movement.
• When the body is in different orientations in space, and if the body is currently moving, it is either being moved passively, or if external forces are acting on the body (e.g., wind), then different movement commands interfere with the one-to-one mapping between motor commands and the movements that will be produced by these commands.

• Lead to coordination between the elements of the system.
• This constraint of degrees of freedom is termed a "coordinative structure" or "synergy."

• A group of muscles, often spanning several joints, that are constrained to act as a single, functional unit (e.g., all fingers of the hand working together as a unit to grasp a ball).
• Not hardwired, emerges to meet needs of task.
• Self-organizing rather than prescriptive.
• Because it is emergent, it allows more flexibility to meet CCV.
• Elements are constrained to act together, rather than each element being individually controlled.
• Each element can be part of multiple coordinative structures.
• Functionally defined (meaningful in context).
• Reduces the number of degrees of freedom that need to be controlled.

• Gaits of a horse (walk, trot, gallop,). As speed changes (scaled up) new behaviors (gaits) appear.
• Walking to running on treadmill.
• Water boiling on stove (no mechanism in pot that made executive decisions).
• Arms moving in- and out-of-phase.

Key Points

• No one subsystem contains instruction for the organization of behaviors (no a priori code).
• No one system has priority over other systems. All systems interact in the self organizing process to determine emergent behavior.
• The emerging behavior will vary depending on the task and environmental context.
• The system "prefers" certain patterns (attractor states), but these patterns are not pre-specified (not determined by motor programs reflex chains).

Skill Develops in an Asynchronous and Nonlinear Manner

• Some elements of the system may show accelerated development and be available in advance of the emergence of a behavior or skill (e.g., alternating kicking pattern precedes upright walking).
• Since all components are necessary for the performance of a skill, faster developing components must wait for slower developing (rate limiting) components.
• At any time in development, an organism will prefer certain behaviors based on developmental status and context (attractive state).

Attractors and Stability

• Attractors - preferred behavior/pattern of system.
• The strength (stability) of behavioral attractors determines the degree of flexibility in behavior and how easily and quickly changes between attractors (patterns) will occur.
  • Strong attractors = stable behavior that is less likely to be interfered with and will quickly return to the stable state after a perturbation.
  • Weak attractors = highly variable behavioral patterns that will easily be interfered with and will rapidly transition to another attractor state.
• Due to the role of the environment, certain behaviors will be masked (not appear) or manifested (demonstrated).

Three Major Types of Constraints

• Organismic: internal or within body (height, weight, body proportion, linkage of bones, muscle strength, central nervous system, etc..) The organism has to accommodate to changes associated with growth.
• Environmental: external to organism but not manipulated by experimenter (gravity, temperature, light, altitude).
• Task: goal and specific requirements of the activity.
  • goal of task (specific or nonspecific pattern)
  • rules specifying (constraining) response
  • implements used that constrain the response

What Do We See Developmentally When Learning a Skill?

• Initial Stage: a pattern is initially produced that oftentimes contain co-contractions.
• Intermediate Stage: degrees of freedom begin to be released and performance improves.
• Skilled Stage: passive forces are exploited to produce more skilled performance.

What can we do to change behavior?

• ID possible rate limiters (3 types of constraints) or possible control parameters.
• Habilitate (when possible) organismic constraints (rate limiters.)
• Help children learn new behavioral attractors.
• Modify task/environmental constraints to allow behaviors to emerge.
• Exploit instability at transitions to ID possible control parameters to change behavior (readiness).
  • Higher levels of behavior will only appear when organism and task demand a change.

Summary:
Physical educators can use the properties of dynamic systems to enhance the learning experience of students. Utilizing the properties of movement pattern (attractor) formation, the properties by which these patterns stabilize and destabilize as well as the process through which the learning of new behavioral patterns occurs will assist students to more readily engage in the self-organizing process of learning new skills. The differential learning principle of having students practice multiple movement variations for each motor skill will jump-start their learning process. This type of practice can also help students stay motivated through their interest and enjoyment of classes that are always fresh with new variations of movement skills to be practiced.

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