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Traditional learning approaches are typically based on a linear understanding of causality where the same cause leads to the same effect. In recent years there has been increasing interest in the complexity of nature and living phenom-ena, with significant insights provided by models of change that are based on a nonlinear understanding of causality, where small causes can lead to big effects and vice versa. In this vein, learning processes seem to be more successful for inducing behavioral change when teaching processes deviate from a linear approach. The differential learning approach takes advantage of fluctuations in a complex system by increasing them through 'no repetition' and 'constantly changing movement tasks' which add stochastic perturbations. Previous research has provided much evidence on the superiority of a differential learning approach for learning single movement techniques, in comparison to repetition-and correction-oriented approaches. In this pilot study, the parallel acquisition and learning of two movement techniques in the sport of football are the objective of investigation. One traditionally trained group and two differentially trained groups (blocked and random) trained for 4 weeks, twice a week, on ball control and shooting at goal tasks. Results supported previous work and revealed significant advantages for both differential groups in the acquisition phase as well as in the learning phase, compared to the traditional group. These data suggest that, instead of following a direct linear path towards the tar-get of a 'to-be-learned' movement technique by means of numerous repetitions and corrections, a differential approach is more beneficial because it perturbs learners towards more functional movement patterns during practice. INTRODUCTION Traditional models of learning have recently been ques-tioned because of their principles that all learners typically start with the same exercise followed by other identical teaching exercises in order to build up a methodical sequence of exercises followed by all students in order to achieve stip-ulated learning goals [1]. A similar logic underpins the inter-pretation of traditional pedagogical principles that all learn-ers need to progress "from easy to hard" or "from simple to complex" exercises. In principle this logic implies the under-standing of linear causality as fundamental basis for a linear pedagogy. In a weak version of this approach to learning, linear causality assumes that same causes will lead to same effects. In the strong version (because much more mathe-matical conditions have to be fulfilled) similar causes will lead to similar effects. In reality these assumptions are asso-ciated with models of linear equations in which the result is just a sum of weighted parameters of influence. In practice this approach is accompanied by the breaking up of a sports movement into certain phases or anatomical focuses that are all trained separately and put together at the end. From a structural point of view traditional learning ap-proaches in general, and motor learning specifically, can be considered as being similarly based on a few latent
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100 The Open Sports Sciences Journal, 2012, 5, (Suppl 1-M11) 100-112
1875-399X/12 2012 Bentham Open
Open Access
The Nonlinear Nature of Learning - A Differential Learning Approach
W. I. Schöllhorn*,1, P. Hegen1 and K. Davids2
1University of Mainz, Institute for Sport Science, Albert Schweitzer Straße 22, 55099 Mainz, Germany
2Queensland University of Technology, Australia
Abstract: Traditional learning approaches are typically based on a linear understanding of causality where the same cause
leads to the same effect. In recent years there has been increasing interest in the complexity of nature and living phenom-
ena, with significant insights provided by models of change that are based on a nonlinear understanding of causality,
where small causes can lead to big effects and vice versa. In this vein, learning processes seem to be more successful for
inducing behavioral change when teaching processes deviate from a linear approach. The differential learning approach
takes advantage of fluctuations in a complex system by increasing them through ‘no repetition’ and ‘constantly changing
movement tasks’ which add stochastic perturbations. Previous research has provided much evidence on the superiority of
a differential learning approach for learning single movement techniques, in comparison to repetition- and correction-
oriented approaches. In this pilot study, the parallel acquisition and learning of two movement techniques in the sport of
football are the objective of investigation. One traditionally trained group and two differentially trained groups (blocked
and random) trained for 4 weeks, twice a week, on ball control and shooting at goal tasks. Results supported previous
work and revealed significant advantages for both differential groups in the acquisition phase as well as in the learning
phase, compared to the traditional group. These data suggest that, instead of following a direct linear path towards the tar-
get of a ‘to-be-learned’ movement technique by means of numerous repetitions and corrections, a differential approach is
more beneficial because it perturbs learners towards more functional movement patterns during practice.
Keywords: Differential Learning, complex systems, fluctuations, football, movement variability.
INTRODUCTION
Traditional models of learning have recently been ques-
tioned because of their principles that all learners typically
start with the same exercise followed by other identical
teaching exercises in order to build up a methodical sequence
of exercises followed by all students in order to achieve stip-
ulated learning goals [1]. A similar logic underpins the inter-
pretation of traditional pedagogical principles that all learn-
ers need to progress “from easy to hard” or “from simple to
complex” exercises. In principle this logic implies the under-
standing of linear causality as fundamental basis for a linear
pedagogy. In a weak version of this approach to learning,
linear causality assumes that same causes will lead to same
effects. In the strong version (because much more mathe-
matical conditions have to be fulfilled) similar causes will
lead to similar effects. In reality these assumptions are asso-
ciated with models of linear equations in which the result is
just a sum of weighted parameters of influence. In practice
this approach is accompanied by the breaking up of a sports
movement into certain phases or anatomical focuses that are
all trained separately and put together at the end.
From a structural point of view traditional learning ap-
proaches in general, and motor learning specifically, can be
considered as being similarly based on a few latent
*Address correspondence to this author at the University of Mainz, Institute
for Sport Science Albert Schweitzer Straße 22, 55099 Mainz, Germany;
Tel: 06131 3923583; Fax: 06131 3920643;
E-mail: schoellw@uni-mainz.de
assumptions. Two of these underlying assumptions with the
biggest influence on the practical consequences in motor
learning are discussed in this paper. These assumptions can
be considered as simplified projections of reality on models.
One model serves as a ‘to-be-achieved target’ that is primar-
ily prescribed by an external instructor. The second model is
related to the path along which the target movement is to be
achieved. In most cases both models imply latent assump-
tions that restrict possible practical consequences and limit
the possible potential of the learning system. Here we dis-
cuss these mainly latent assumptions with respect to their
plausibility and subsequently we will suggest consequences
that can be drawn from slightly revised, but experimentally
verified, more plausible assumptions. The consequence of
our analysis is to end up with the differential learning ap-
proach which considers rather movement variations as the
basis of learning than movement repetitions, realizing it by
adding stochastic perturbations to a central movement pat-
tern in order to ensure no precise movement repetitions and
no corrections during the skill acquisition process [2, 3].
Several studies have compared the effectiveness of different
interventions on the basis of training single sport techniques
[4, 5]. In summary, the interventions which added stochastic
perturbations during learning were at least as successful as
traditional training methods. In the majority of cases, the
differential learning approach resulted in better skill acquisi-
tion and better learning rates in participants [6, 7]. The prac-
tical consequences of the revised assumptions have been
tested in a study of skill acquisition in the team sport of foot-
ball. This football experiment extends previous work since
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 101
two techniques are learned with nonlinear methods in paral-
lel and are compared with a classical linear learning ap-
proach.
The first assumption with respect to a to-be-learned tar-
get movement can be described by the assumption of a gen-
eral time independent model that satisfies so called objective
criteria for optimum performance. Nominal classic ‘text-
book’ movement, reported in many coaching manuals, can
be considered as general because it is provided as a model
for all learners to follow without any specifications for dif-
ferentiation by gender, age or level of performance. Accord-
ingly, textbooks or coaching manuals do not distinguish
changes to the to-be-learned target movement on a time scale
and, therefore, can be considered as time independent. Inde-
pendent of the problem of objectivity these performance
models are typically derived from research on the world’s
best athletes and it is unclear whether they can be applied to
performance of sub-elite individuals or athletes at the devel-
opment stage in elite sport.
THE ASSUMPTION OF A GENERAL VALID MODEL
The first underlying assumption for linear learning is
related to the target movement that usually has to be
achieved during a learning process. Most often the specific
target pattern within a motor learning process is prescribed
by the trainer or teacher whose knowledge is typically based
on scientific research, which often relies on measures and
scores from studies of the world’s best athletes. Performance
data from groups of world class athletes is typically chosen
as the reference system for comparison of athletes.
Previous analyses of the movement patterns of world
class male and female javelin throwers have led to an en-
forced rethink of the traditional way of training fundamen-
tally. The results of these studies revealed the identification
of athletes on the basis of a holistic movement description
during only a few milliseconds of performance [8]. Beside
nationality-specific throwing styles, the recognition proce-
dure led to the identification of highly individual throwing
patterns which were stable over several years. Most impor-
tant, and most critical, for the traditional role of a movement
archetype was the additional evidence of no identical move-
ment repetitions and the possibility of throwers performing
at world class level with different movement patterns, al-
though they were all within the area of a fictive biomechani-
cal optimum. With no evidence for an identical movement
pattern, the repetitive approach in practice is questioned due
to the low probability of being confronted with the same
performance conditions even after several thousand repeti-
tions. With no evidence for the existence of an optimal
movement pattern, the question arises: which top athlete’s
movement pattern should be copied within a learning proc-
ess? The individuality of movement patterns has been
shown, not only in high performance sports, but also in indi-
viduals performing every day movements like walking,
where even more repetitions did not lead to the repetition of
identical movements [9]. Given these findings, we are con-
fronted with the problem of how to prepare an athlete for the
next movement execution which will involve adaptation to
unknown environmental conditions. Consequently, it seems
that a movement repetition can be divided into a known and
an unknown part (Fig. 1). Traditionally, the known part of
the movement pattern is considered during the learning pro-
gress by ignoring the unknown part or assigning it a perturb-
ing influence due to noise.
Closely related to the difficulty of the characteristics of a
to-be-achieved target is the problem of how to bridge the gap
between an initial and a target state of a movement outcome.
In assumptions of a precise time independent target and a
precise initial situation it is plausible to connect the two
points linearly and to follow this path in learning. Independ-
ent of the uncertainty of the path, an even bigger problem
occurs when the target movement is reasonably assumed to
be time dependent and different for each individual. Both
assumptions increase the uncertainty of the target movement
outcome as well. If we divide the trace towards the to-be-
achieved target into arbitrary sub-units we realize that the
problem of uncertainty is accompanied with every sub-goal
and leads to an uncertain path overall. Obviously, the practi-
cal consequences are highly dependent on the assumptions of
the model of the target that are made in advance. Plausible
arguments for the assumptions of the uncertainty of a target
are given by the identification of individual movement tech-
niques as well as by the low probability of occurrence of two
identical movement repetitions. Accordingly, the probability
of linear connections between an initial and target situation
decreases enormously. Considering not just a single but sev-
eral subsystems functioning during the same task problem in
parallel, and allowing only some interactions between the
subsystems, decreases the probability of success in linear
learning approaches as well. Despite earlier indications by
Bernstein [10] with his statement about “repeating without
repetition” and extensive theoretical evidence by Hatze [11],
especially within the field of practical applications, variabil-
ity in movement repetitions has been tended to be considered
as destructive. A more constructive interpretation of move-
ment variability emerged with the system dynamic approach
followed by comprehensive descriptions and analysis of
noise [12, 13]. Due to methodological reasons the original
meaning of noise with its disturbing influence on a signal in
general is mostly limited to an equidistant disturbing influ-
ence which can be analyzed quantitatively by means of fre-
quency analysis methods. Because learning and training does
not usually follow equidistant measurements, the term sto-
chastic perturbation is applied. Meanwhile noise has become
an essential component of a few motor control theories [14,
15].
Fig. (1). Differences in the repetition of an assumingly “identical
movement”.
102 The Open Sports Sciences Journal, 2012, Volume 5 Schöllhorn et al.
DIFFERENTIAL LEARNING
However, a transfer of the structural idea of noise to
practice and therapy programs has been realized in the dif-
ferential learning approach [16]. The differential learning
approach is mainly characterized by taking advantage, for
the purpose of learning, of fluctuations that occur, without
movement repetitions and without corrections during the
skill acquisition process [3]. This approach can be consid-
ered as highly nonlinear because of learners constantly per-
forming the whole complex movement with permanently
changing stochastic perturbations. In contrast to a nonlinear
pedagogical approach, originally suggested by Davids, Shut-
tleworth and Chow [17] and Chow et al. [18], where key
tasks constraints are manipulated in order “to facilitate the
emergence of functional movement patterns and decision
making behaviors”, the differential learning approach does
not identify key task constraints. In the differential learning
approach the fluctuations in the learner’s subsystems itself
are exploited during learning, because they have the potential
to destabilize the whole system. This destabilization process
can lead to an instability that has the advantage of requiring
less energy in order to achieve a new stable state of organiza-
tion for the learner. By amplifying these observed fluctua-
tions the system is additionally confronted with the potential
limits of possible performance solutions. Consequently, a
self organizing process is initiated and exploited that forces
the system to instigate a new coordination strategy which
typically results in the emergence of more effective or more
stable movement patterns. Although in many sport tech-
niques coarse biomechanical constraints are known and can
be assumed to be valid, within a certain level of performance
and even at the highest level of performance, infinite solu-
tions are still possible. It, therefore, seems to be hard to iden-
tify key constraints that are valid for each individual learner
in each performance situation. However, these amplified
fluctuations tend to increase fluctuations in other anatomical
areas of the body and lead to a highly nonlinear adaptation
process. Several experiments have shown higher skill acqui-
sition rates for the differential learning approach in compari-
son to traditional linear approaches and, most intriguingly,
display even better performance improvements in the reten-
tion phase of learning [6, 19]. Recently, a similar influence
on physiological parameters in professional cyclists has also
been demonstrated by Bauer [4]. Two groups of cyclists
aimed to improving the efficiency of cycling movements.
One group was supported by specific biomechanical feed-
back about the deviation of the force that was not perpen-
dicular to the radial movement of the pedals. The second
group instead trained with two pedals that could be fixed in
an arbitrary relative left to right foot phase. After four weeks
of training the differential learning group only improved
their maximum heart rate level to the highest level of a four-
level stress test significantly from 178bpm to 164bpm and
lowered the maximum lactate production in the same test
from 7.6mmol/l down to 4,8mmol/l.
However, in all experiments the objective was the im-
provement of a single technique. Because in different sports,
especially team sports, multiple techniques are necessary for
success we decided to compare the influence of two tech-
niques trained in parallel: linearly and nonlinearly. The ob-
jective of this pilot-study is to compare a classical (linear)
training approach with the differential (nonlinear) learning
approach during the training of two techniques in football.
The single classical approach followed the repetitive and
corrective philosophy during learning, while the differential
approach was distinguished by different levels of variation.
In accordance with the contextual interference debate [20],
one approach was differentially training the two techniques
in separate blocks of trials, whereas in the second differential
approach, the two techniques followed a random order of
trial practice. Therefore, the null hypothesis was that all three
approaches would not differ with respect to the outcomes in
post and retention tests.
METHODS
Following research that has demonstrated the positive
effects of the differential learning approach when observing
a single technique in isolation, this study combined two
techniques that are essential in football within one training
session: movements for shooting a ball and for controlling it.
For this purpose, a pre-post test-design with a subsequent
retention test was applied.
Participants
The participants played in the 8th division of the German
football league and typically trained twice a week for 2 hrs.
24 participants were randomly assigned to three groups. Be-
cause only 12 participants were able to participate in every
test and training session, the learning processes of 4 partici-
pants per group could be observed. More details, including
the average age and average football experience as well as
the playing position of participants in the three groups, are
displayed in Table 1. All participants agreed to take part in
the experiment through informed consent.
Protocol
The pre-, post-, and retention-tests examined the ability
of the sample to control a ball within a minimum amount of
space [21] and the ability to shoot a ball with precision at
goal [21].
Table 1. Average age, Average Football Experience, and Players Field Specialty of the Three Experimental Groups
Average Age [Years] Football Experience [Years] Players Field Specialty of the Four Partici-
pants
Control group (CG) 23,8 ±3,9 18,5 ± 4,7 1 defender and 3 midfielders
Differential blocked group (DBG) 24,5 ± 2,1 20,8 ± 3,4 2 defenders, 1 midfielder and 1 striker
Differential random group (DRG) 24,5 ± 2,1 20,5 ± 1 2 defenders and 2 midfielders
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 103
In the ball-control test a ball was thrown towards the par-
ticipants in a parabolic flight path from an assistant who was
trained and tested to throw with a certain constancy towards
a given target. The thrower was not informed about the ob-
jective of the experiment. The ball was thrown: a) in a direct
parabolic flight at a height that forced the participant to re-
ceive the ball first with the chest; and b), with a shorter para-
bolic flight that led to the reception of a bounced ball (Fig.
2).
In the goal shooting test, participants had to shoot the ball
at goal without a goal keeper from the 16m line in 7 different
situations, with each situation repeated 5 times. Each partici-
pant performed overall 35 shooting movements in a blocked
order (7 situations x 5 times = 35 trials). The seven different
goal shooting situations were [22](Fig. 3):
1. Five immobile balls were shot towards the goal after a
short run-up from position 1.
2. Five balls were shot towards the goal after a 10m drib-
bling from position 1.
3. Five balls were shot towards the goal after a 5m drib-
bling from position 2.
4. Five balls were shot towards goal from position 1 after a
pass from the right.
5. Five balls were shot towards the goal after a 5 m drib-
bling from position 3.
6. Five balls were shot towards the goal from position 1
after a pass from the left.
7. Five balls were shot towards the goal from position 1
after crossing an obstacle of 40 cm height with a vertical
jump.
The whole time schedule for the three tests and the inter-
vention period is depicted in Table 2.
Data Acquisition
The quality of ball control was recorded by measuring
the distance of the initial contact with the foot and the resting
position of the ball after control. Each reception technique
was repeated five times in a blocked sequence.
The precision of the shots was measured by dividing the
goal into scoring zones. The zones were determined accord-
ing to plausible probability of scoring a goal. Areas that were
hard to be reached by the goalkeeper were scored higher and
vice versa. Shots that closely missed the goal scored with 1
point still (Fig. 4).
Training Intervention
A pre-test (Figs. 2 and 3) was followed by a four-week
training intervention. For four weeks, within the normal club
training program, the training intervention consisted of eight
sessions (two per week). In all eight sessions 20 exercises for
Fig. (2). Experimental set-up from the bird’s eye perspective to determine the quality of the ball’s reception (left). Direct throw of the ball
(a.) ball’s reception with the foot and indirect throw via bottom contact (b.) ball’s reception with the chest.
Fig. (3). Initial goal shooting positions with different tests.
Table 2. The Intervention Schedule
Pre-Tests Training Interventions Post-Test Break – no Training Retention Test
1st week 2nd -5th week 6th week 7th-8th week 9th week
a.)
b.)
tapemeasure
baseline
participant
throwingperson
position1position2
position3
104 The Open Sports Sciences Journal, 2012, Volume 5 Schöllhorn et al.
Fig. (4). Division of the goal in different areas with the scores 1, 3, 4, 5, 6 and the corresponding measures for each zone.
Table 3. Exemplary Trainings Plan for the CG with Orientation on the Ideal Movement Archetypes
No. Exercises Repetition Explanation
1 Goal shot with fixed ball 10 1. The supporting leg one foot beside the ball.
2. The shot leg swings linear to the ball.
3. The ankle is craned and fixed
4. The upper body is over the ball.
5. The ball should be crossed in center.
2 Ball reception with the chest 10 1. The upper body draw back when the ball is at the chest.
2. Control the ball with the foot on the ground.
3 Goal shot in motion 10 1. The supporting leg one foot beside the ball.
2. The shot leg swings linear to the ball.
3. The ankle is craned and fixed
4. The upper body is over the ball.
5. The ball should be crossed in center.
4 Ball reception with the foot 10 1. Minimize the distance from the foot to the ball.
2. Draw back during the ball is on the foot.
3.Control the ball on the ground.
Order of the exercises
Explanation of the technique goal shot
10 goal shots
Explanation of the ball reception with the chest
10 ball receptions
Explanation of the technique goal shot
10 goal shots
Explanation of the ball reception with the foot
10 ball receptions
Important: Corrections 5 seconds after completing the task and only every third trial!
the goal shooting technique and 20 exercises for the ball con-
trol technique were performed. Each intervention lasted
about 25 minutes. In summary, each participant performed a
total of 160 exercises for both techniques. The CG trained
according to the classical training approach oriented on ideal
movement archetypes for goal shooting and ball control
movements (Table 3). Both techniques were trained in a
blocked order: the goal shooting technique in the first half of
the training session followed by the ball control task in the
second half. Methodological sequences of exercises on goal
shots and ball’s control with numerous repetitions and error
corrections were conducted. Criteria for the optimum per-
formance of the goal shooting movement included the posi-
tion of the standing leg, orientation of the head, amplitude of
the kicking leg, sequence of the maximum velocity in the
limbs of the kicking leg, stiffness of the kicking leg at ball
contact and arm movements during the approach and during
the kicking movement. Main criteria for functional technique
in ball reception were fixation of the approaching ball, soft
first ball contact.
The two other groups trained (DBG and DRG) according
to the differential learning approach, one group with both
techniques in blocked order and the other group with random
order in one training session (see Tables 4 and 5). The core
idea of the two differential training groups was to increase
the fluctuations of both techniques in order to make the ath-
letes more stable against disturbances and in order to provide
the athletes the possibility to seek and explore functional
movement patterns. The fluctuations were increased by infi-
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 105
nite variations in each technique as well as by avoiding
movement repetitions and by providing no corrective feed-
back. Movement variations were characterized by variations
in the standing leg, in the kicking leg, in the arms, in the
trunk, in the head and the ball, referring to the angles, the
angular velocity and the rhythm of each joint movement. To
exemplify: the standing leg had to be placed well before the
ball, well behind it, or well to the side of the ball; the knee
joint in one shot had to be stiff, in the other it was kept very
flexible or alternating between stiffness and flexibility after
each shot.
Table 4. Exemplarily Trainings Plan for the DBG
No. Exercise
1 Ball reception with the chest (indirect) (r. eye closed + l. arm straight up + r. arm straight lateral)
2 Ball reception with the chest (indirect) (prostrate the standing leg + r. eye closed)
3 Ball reception with the chest (indirect) (feet close together + head nod forward and backward)
4 Ball reception with the chest (indirect) (feet on the inner edge + turn the head to right and left)
5 Ball reception with the chest (indirect) (feet cross + tend the upper body to right and left)
6 Ball reception with the chest (indirect) (circle the hip + both arms straight lateral)
7 Ball reception with the chest (indirect) (stand on tiptoe + rotate both arms against the same)
8 Ball reception with the chest (indirect) (feet on the inner edge + rotate the arms forward)
9 Ball reception with the chest (indirect) (feet close together + r. arm close to the body)
10 Ball reception with the chest (indirect) (stand on the left feet + rotate both arms forward)
11 Ball reception after a throw with ground contact (inner surface + hips back and forth + arms lateral)
12 Ball reception after a throw with ground contact (upper surface + ball reception wide in front of the body)
13 Ball reception after a throw with ground contact (exterior surface + ball reception wide lateral of the body)
14 Ball reception after a throw with ground contact (exterior surface + hips back and forth)
15 Ball reception after a throw with ground contact (inner surface + stand on tiptoe)
16 Ball reception after a throw with ground contact (inner surface + prostrate the standing leg + upper body to the left)
17 Ball reception after a throw with ground contact (upper surface + stand insight)
18 Ball reception after a throw with ground contact (exterior surface + rotate the arms backward + upper body to the right)
19 Ball reception after a throw with ground contact (upper surface + legs hard + rotate the arms forward)
20 Ball reception after a throw with ground contact (inner surface + behind the body + rotate the arms against the same)
21 Goal shot after a short dribbling (inner surface + head to the left and the right + heel off)
22 Goal shot after a short dribbling (exterior surface + full rotation before the shots)
23 Goal shot after a short dribbling (upper surface + r. knee upwards and lateral)
24 Goal shot after a short dribbling (inner surface + r. heel to the back + arms forward)
25 Goal shot after a short dribbling (inner surface + rotate arms forward)
26 Goal shot after a short dribbling (upper surface + rotate arms forward + head to the left)
27 Goal shot after a short dribbling (upper surface + rotate arms against the same + head to the right)
28 Goal shot after a short dribbling (inner surface + l. knee upwards lateral)
29 Goal shot after a short dribbling (upper surface + rotate arms against the same + head to the left and right)
30 Goal shot after a short dribbling (exterior surface + head to the right +arms lateral)
31 Goal shot a jumping ball (exterior surface + run up lateral)
106 The Open Sports Sciences Journal, 2012, Volume 5 Schöllhorn et al.
Table 4. Contd…..
No. Exercise
32 Goal shot a jumping ball (upper surface + upper body to the right + run up with little jumps)
33 Goal shot a jumping ball (inner surface + run up cross + both arms up)
34 Goal shot a jumping ball (exterior surface + circle the hip + bot arms up)
35 Goal shot a jumping ball (upper surface + both arms forward + hip to the left and right)
36 Goal shot a jumping ball (inner surface + sidesteps; + head nod forward and backward)
37 Goal shot a jumping ball (exterior surface + standing leg wide beside the ball + eyes blinking)
38 Goal shot a jumping ball (inner surface + standing leg before the ball + eyes blinking)
39 Goal shot a jumping ball (inner surface + run up with jumps + arms lateral)
40 Goal shot a jumping ball (exterior surface + upper body forward and backward)
Table 5. Exemplarily Trainings Plan for the DRG. The Different to the DGB is the Order of the Exercises
No. exercise
1 Ball reception with the chest (indirect) (r. eye closed + l. arm straight up + r. arm straight lateral)
2 Ball reception with the chest (indirect) (prostrate the standing leg + r. eye closed)
3 Ball reception with the chest (indirect) (feet close together + head nod forward and backward)
4 Ball reception with the chest (indirect) (feet on the inner edge + turn the head to right and left)
5 Ball reception with the chest (indirect) (feet cross + tend the upper body to right and left)
6 Ball reception with the chest (indirect) (circle the hip + both arms straight lateral)
7 Ball reception with the chest (indirect) (Stand on tiptoe + rotate both arms against the same)
8 Ball reception with the chest (indirect) (feet on the inner edge + rotate the arms forward)
9 Ball reception with the chest (indirect) (feet close together + r. arm close to the body)
10 Ball reception with the chest (indirect) (stand on the left feet + rotate both arms forward)
11 Ball reception after a throw with ground contact (inner surface + hips back and forth + arms lateral)
12 Ball reception after a throw with ground contact (upper surface + ball reception wide in front of the body)
13 Ball reception after a throw with ground contact (exterior surface + ball reception wide lateral of the body)
14 Ball reception after a throw with ground contact (exterior surface + hips back and forth)
15 Ball reception after a throw with ground contact (inner surface + stand on tiptoe)
16 Ball reception after a throw with ground contact (inner surface + prostrate the standing leg + upper body to the left)
17 Ball reception after a throw with ground contact (upper surface + stand insight)
18 Ball reception after a throw with ground contact (exterior surface + rotate the arms backward + upperbody to the right)
19 Ball reception after a throw with ground contact (upper surface + legs hard + rotate the arms forward)
20 Ball reception after a throw with ground contact (inner surface + behind the body + rotate the arms against the same)
21 Goal shot after a short dribbling (inner surface + head to the left and the right + heel off)
22 Goal shot after a short dribbling (exterior surface + full rotation bevor the shots)
23 Goal shot after a short dribbling (upper surface + r. knee upwards and lateral)
24 Goal shot after a short dribbling (inner surface + r. heel to the back + arms forward)
25 Goal shot after a short dribbling (inner surface + rotate arms forward)
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 107
Table 5. Contd…..
No. Exercise
26 Goal shot after a short dribbling (upper surface + rotate arms forward + head to the left)
27 Goal shot after a short dribbling (upper surface + rotate arms against the same + head to the right)
28 Goal shot after a short dribbling (inner surface + l. knee upwards lateral)
29 Goal shot after a short dribbling (upper surface + rotate arms against the same + head to the left and right)
30 Goal shot after a short dribbling (exterior surface + head to the right +arms lateral)
31 Goal shot a jumping ball (exterior surface + run up lateral)
32 Goal shot a jumping ball (upper surface + upper body to the right + run up with little jumps)
33 Goal shot a jumping ball (inner surface + run up cross + both arms up)
34 Goal shot a jumping ball (exterior surface + circle the hip + bot arms up)
35 Goal shot a jumping ball (upper surface + both arms forward + hip to the left and right)
36 Goal shot a jumping ball (inner surface + sidesteps + head nod forward and backward)
37 Goal shot a jumping ball (exterior surface + standing leg wide beside the ball + eyes blinking)
38 Goal shot a jumping ball (inner surface + standing leg before the ball + eyes blinking)
39 Goal shot a jumping ball (inner surface + run up with jumps + arms lateral)
40 Goal shot a jumping ball (exterior surface + upper body forward and backward)
Order of the excercises for DRG:
33, 17, 6, 15, 2, 11, 16, 3, 1, 19, 9, 12, 26, 23, 35, 5, 37, 32, 27, 31, 10, 8, 14, 40, 28, 13, 24, 30, 4, 38, 39, 21, 34, 20, 18, 29, 25, 22, 36, 7
Statistical Analysis
Nonparametric tests were used to analyze the data. The
statistical tests selected for use were especially developed for
clinical experiments with low case numbers involving rare
diseases. They included the H-Test from Kruskal and Wallis,
followed by a single comparison test [23]. The H-Test results
in H-values (H) comparable to t-values in the t-test. Once the
H-values are below a critical value (χ2) the results are con-
sidered to be significant. The first test provides information
about the global trend and the second test compares the indi-
vidual group results. At the comparison test the calculated
values are Demp and the critical values for the decision of
significance are Dcrit. The significance level for both tests
was set to 0.05.
RESULTS
The results of the pre-, post- and retention-test of the
three training groups are displayed in Fig. (5) for the shoot-
ing movement and in Fig. (6) for the reception movement.
The results of the ball’s reception test within the post-test did
not reveal any significant difference in the global trend be-
tween the three groups (H = 0.76 < χ2t = 5.69). A significant
difference (α =0.05) can be discerned when comparing the
classical group and both differential groups separately (Demp
= 7.5 > Dcrit = 5.27). No significant difference could be iden-
tified between both differential trained groups (Demp = 2 <
Dcrit =4.13). The retention-test data analysis of the ball’s re-
ception test did not indicate statistically significant differ-
ences in the global trend between the three groups (H = 1.86
< χ2 = 5.62). When comparing the three groups separately, a
significant difference between the classical group and the
two differential groups can be identified (Demp = 12 > Dcrit =
5.27). The comparison between the differential trained
groups 1 and 2 does not reveal a significant difference (Demp
= 0 < Dcrit = 5.27). Table 6 and Fig. (5) illustrate the data and
their time course.
The test results of the goal shooting test reveal a signifi-
cant global trend (H = 7.38 > χ2=5.69). When comparing the
results of the classic trained group and both differential
trained groups a statistical difference can be stated again
(Demp = 24 > Dcrit = 5.27). The test results of both differential
trained groups were clearly different to the results of the
classic trained group. A relevant difference between the dif-
ferential trained groups cannot be detected (Demp = 0 < Dcrit =
4.13). The statistical analysis of the goal shot test points out
a significant difference between the three groups in the glob-
al trend (H = 7.87 > χ2 = 5.62). Again the individual com-
parison shows a significant difference between the classic
trained group and both differential trained groups (Demp = 24
> Dcrit = 5.27). A significant difference can also be deter-
mined when comparing the two differential trained groups.
Thus the performance of the differential trained group DRG
is significantly better than the performance of the differential
trained group DBG (Demp = 7 > Dcrit = 4.13). Table 7 and
Fig. (6) show the data and the course. Table 8 gives an over-
view on all results. Hereby the standard deviations of the
goal shooting results have to be interpreted carefully because
of the nonlinearity of the chosen scoring.
In summary, the results of the study revealed a signifi-
cant difference between the CG and both the differential
trained groups (DBG and DRG), with respect to the tasks of
ball control and ball shooting (Table 8). Only in the reten-
108 The Open Sports Sciences Journal, 2012, Volume 5 Schöllhorn et al.
Table 6. Mean and Standard Deviation of the Pre-, Post-, and Retentiontest Results of the Reception Task
pre-test (Mean±STD) [cm] post-test (Mean±STD) [cm] retention-test (Mean±STD) [cm]
Control group (CG) 654±308 465±142 506±153
Differential blocked group (DBG) 568±192 424±152 418±144
Differential random group (DRG) 660±222 416±143 393±115
Table 7. Mean and Standard Deviation of the Pre-, Post-, and Retentiontestresults of the Goal Shooting Task
pre-test (Mean±STD) [score] post-test (Mean±STD) [score] retention-test (Mean±STD) [score]
Control group (CG) 32±9,3 29,5±1,3 30,8±4,6
Differential blocked group (DBG) 32,5±4,8 39,8±1 41±3,4
Differential random group (DRG) 41±3,6 42,8±14 45±6,1
Fig. (5). Pre-, Post-, and Retentiontest of the reception performance.
Note: The total distance is fomed by the sum of the individual participants at five receptions with the foot and five receptions with the chest
and subsequentliy with the foot.
Fig. (6). Pre-, Post-, and Retentiontest scores of the goal shooting performance.
tion-test of the goal shooting technique was a significant
difference between the DBG and the DRG groups also ob-
served. An interesting observation is that the DRG was ex-
posed to more fluctuations than the DBG.
Because the differential learning approach supports per-
formance individuality the results of the individual partici-
pants were analyzed visually as well [16]. Figs. (7 and 8)
display the individual results in all tests. Three out of four
participants in the classical group improved their perform-
ance within the ball’s control test from pre- to post-test
(Fig. 7a). Only one participant was not able to keep the start-
ing level. Because this participant had already started at the
1300
1500
1700
1900
2100
2300
2500
2700
2900
pretest posttest retentiontest
totaldistance[cm]
CG
DBG
DRG
100
110
120
130
140
150
160
170
180
190
200
pretest posttest retentiontest
points
CG
DBG
DRG
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 109
Table 8. Summary of the Significant Test Results between the Groups
post-test retention-test
ball’s reception goal shot ball’s reception goal shot
CG Sig. to DBG
Sig. to DRG
Sig. to DBG
Sig. to DRG
Sig. to DBG
Sig. to DRG
Sig. to DBG
Sig. to DRG
DBG Sig. to CG
Sig. to CG Sig. to CG Sig. to CG
Sig. to DRG
DRG Sig. to CG
Sig. to CG Sig. to CG Sig. to CG
Sig. to DBG
Note: Sig. = significant difference at the 5% level (α = .05).
highest performance level, he may have been demonstrating
decreasing progress with increasing levels of performance.
From the differential learning point of view in this case the
fluctuations were decreasing with the number of trial repeti-
tions as performance was increasing and it becomes increas-
ingly harder to enlarge the area of possible solutions that are
more successful. The largest performance increase was 45%
achieved by the participant with the lowest starting level.
After the two-weeks of break in the retention phase the re-
sults of all participants from the classic trained group de-
creased in the retention-test. This observation corresponds to
classical memory effects that follow learning procedures that
are mainly characterized by performance repetitions. In
comparison all participants of the differential blocked and
differential random group improved their performance or
kept the level of performance independent of the starting
level from the pre- to the post-test. In contrast to the classical
group, three out of four participants were able to increase or
equalize their posttest level in the retention test. Finally, all
participants ended up with increased performance levels in
comparison to the pretest. Most intriguingly, in the differen-
tial random group, all participants improved their perform-
ance in all tests in comparison to the pretest independent of
their starting level. There were similar reactions during the
retention phase, three participants even improved their per-
formance after the break, and one maintained it. The results
indicate that in both differentially trained groups the majority
of the participants were able to improve their performance in
all tests following the pretest, independent of the initial level,
indicating additional evidence for supporting the effect of
individuality by the differential learning approach.
Within the goal shooting test only two out of four in the
classical group were able to improve performance from pre-
to post-test, the other two participants even decreased their
pretest result. Participant 4 had the largest performance in-
crease of 36%. When comparing the results of the post- and
the retention-test it can be noticed that three participants im-
proved and one worsened.
The test results of the differential blocked (Fig. 8b) and
random (Fig. 8c) group were more homogeneous than the
results of the classic trained group. All participants within
the DBG improved their goal shooting performance from
pre- to posttest. Therefore, three out of four participants were
even able to increase the ability for precise kicks in the reten-
tion test. In the DRG the most heterogeneous results can be
Fig. (7). Performance of test persons regarding the development within the ball’s reception test: CG (left), DBG (middle) and DRG (right).
110 The Open Sports Sciences Journal, 2012, Volume 5 Schöllhorn et al.
Fig. (8). Performance of test persons regarding the development within the goal shot test: CG (left), DBG (middle) and DRG (right).
observed. Two participants improved their performance with
in the first interval whereas the other two even decreased
their level. In the subsequent retention phase the two partici-
pants who decreased the test score in the first interval in-
creased the test score during the second. The participant who
had the largest increase during the first interval decreased his
performance during the second interval. Only one athlete
could show an increase in performance in both intervals.
DISCUSSION
In contrast to a classical repetition and correction-
oriented teaching methodology, a nonlinear pedagogical ap-
proach to teaching two football techniques was investigated
in this study. The training intervention had to be included
into the normal training program and life schedule of the
members of the football club and, therefore, provided a high
external validity. Unfortunately, only 50% of the participants
were able to complete their participation in all test and inter-
vention events. The small number of participants gave the
study the character of a pilot study. Because of the similar
ages and football experience levels of the participants, the
groups can be considered as homogenous. Due to the number
of participants the individual results in all tests were espe-
cially important in this study. Considering the results of both
technique tests together, for groups as well as for individu-
als, offers clear evidence for the superiority of the differen-
tial learning approach in comparison to the classical training
approach. The results of the classical group and its individu-
als can be interpreted traditionally [24] as follows. In most
cases an increase during the acquisition phase is followed by
a decrease in the learning phase during the retention test. In
contrast to the classical group, both differential training
groups in general showed a clear advantage in learning two
techniques in parallel. Both differential groups showed, on
average, an increase in performance during the acquisition
period, and at least maintenance of performance at the post-
test level. In the majority of participants, an increase in per-
formance during the retention phase can be observed as well.
Taking the individual results into account as well, only one
participant in the DRG group during the ball reception tests
showed extraordinary differences in behavior, compared to
the rest of the group. In this case the group results have to be
interpreted with care. In comparison to data from earlier
studies on differential learning of singular sport techniques,
the present results verify the observed tendencies. The ten-
dency shows an increase in learning and skill acquisition rate
when differences between two subsequent movements are
exploited during training. Because both differentially trained
groups ended up with comparable improvements, further
research is demanded for the optimum amount of differences
that would be functional during training. In addition, these
results need to be verified with larger and other samples be-
cause in the present study design only the probability of data
with the assumption of a true hypothesis was tested but not
the hypothesis it self. In this context it has to be mentioned
from a stochastic and epistemological point of view that not
only the size of sample is of interest in future but rather the
number of investigations related to the research topic, and
therefore the number of hypothesis in order to pursue the
question for the probability of a hypothesis (=p(H0)) [25,
26].
Somewhat surprising is the higher learning rate of the
differential random group, despite their higher initial per-
formance level. But this observation was in accordance with
earlier findings in which the more advanced participants re-
sponded even acutely to the differential learning approach. In
supplementing earlier research, results of the present pilot
study of differential learning led to improved skill acquisi-
tion and learning rates when participants were confronted
with two techniques to learn. How sensitive these results are
with respect to the relative similarity of the two to-be-
learned techniques is a question that needs further research.
With respect to the individual results, the differential
blocked group showed the most consistent performance. All
participants were able to improve their performance in both
tests and in both techniques. In comparison the differential
f
The Nonlinear Nature of Learning - A Differential Learning Approach The Open Sports Sciences Journal, 2012, Volume 5 111
blocked group only showed homogenous improvements over
all three tests in the ball control task, whereas in the goal
shooting task, two participants were not able to increase their
overall score in comparison to the initial state. Obviously,
only some participants could take advantage of the increased
system variability to enhance performance and learning. Per-
haps for these participants the optimum amount of system
variation needed for learning was exceeded.
CONCLUSION
Based on the theoretical considerations of the differential
learning approach and the empirical results observed, a non-
linear learning process can be assumed, with important im-
plications for practice. The differential learning approach
exploits these ideas and puts them into practice. After having
proven the effectiveness and efficiency of an isolated tech-
nique in various sports, this pilot study extends the differen-
tial learning approach to two techniques within one training
session. The practical consequence of the study presented is
that two techniques can easily be trained within one training
session by applying the differential learning approach. Nega-
tive influences regarding both techniques, like decrease in
performance or boredom were not observed, implying that
skill and performance in both techniques was developed in a
positive way.
Regarding the sequence of exercises it can be stated that
there is merely a difference between both differential trained
groups. The results showed that it makes no difference
whether the exercises are trained en bloc or random. Within
one training session two differential training blocks for two
separate techniques may well be applied. A switch between
the two techniques at random has only caused a statistically
significant positive effect within the goal shooting test. Con-
sequently, it can be assumed that this procedure has only a
minimal positive effect on memory performance respectively
learning capacity of the participants. The participants who
constantly switched between both techniques could achieve
better goal shooting test results at the retention-test. The re-
sults at the ball’s reception test do not differ between the two
differential trained groups. Due to these findings a distinct
statement regarding a recommendation for an exercise se-
quence cannot be made.
Either way, both differential trained groups performed
significantly better than the classic trained group. Due to the
nonlinearity of motor learning it seems reasonable to expe-
dite training with stochastic perturbations. Monotonous repe-
titions of movements should be abandoned whereas large
variations should be produced in order to initiate self-
organization so that a more effective and more efficient
learning process can be designed.
CONFLICT OF INTEREST
The authors confirm that this article content has no con-
flicts of interest.
ACKNOWLEDGEMENT
Declared none.
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Received: August 14, 2011 Revised: May 25, 2012 Accepted: May 30, 2012
© Schöllhorn et al.; Licensee Bentham Open.
This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.
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Chapter
Kontingenz bedeutet, dass etwas so ist, wie es ist, aber auch anders sein könnte. In Bezug auf die Wissenschaft bezieht sich Kontingenz auf die grundlegende Beziehung zwischen Forschung und Forschungsgegenstand. Wissenschaft macht sichtbar, was die gewählten Theorien und Methoden sichtbar machen können. Wechseln wir die Instrumente der Forschung, ändert sich auch der Gegenstand. Im vorliegenden Artikel thematisieren wir die erkenntnistheoretische Verschränkung von Forschung und Gegenstand am Beispiel eines unserer eigenen aktuellen Forschungsprojekte. Im Hinblick auf eine empirische Studie zu trainingspädagogischen Aspekten und hier besonders des Ansatzes des Constraints-Led-Approach (CLA) im polizeilichen Selbstverteidigungstrainings werfen wir einen reflexiven Blick auf die Auswahlentscheidungen auf verschiedenen Ebenen des Forschungsprozesses. Im Ergebnis betonen wir dessen Kontingenz. Dem Bedürfnis nach Kontrolle im Verfahren und auch im Gegenstandsbereich der Trainingspädagogik verorten wir in der Einsicht in den Forschungsprozess; eine Einsicht, die besonders durch Forschungsparadigmen mit wechselnden Beobachtungsperspektiven gefördert werden kann. Wir plädieren daher für die Reflexion der Kontingenz als Anregung für trainingspädagogische Forschungsprozesse.
... According to Maynard and colleagues [74], the intervention period and number of sessions should be sufficient to find possible cognitive effects. The duration of intervention and number of sessions was oriented on previous studies on DL [75,76]. Additionally, it was aligned with the school's curriculum, which typically calls for exams after the fourth to sixth week of a learning module, and we wanted to avoid clashing with an exam period due to the increased stress level of the participants. ...
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Numerous studies have shown cognitive enhancement through sport and physical exercise. Despite the variety of studies, the extent to which physical activity before or after a cognitive learning session leads to more effective cognitive enhancement remains largely unresolved. Moreover, little attention has been paid to the dependence of the motor learning approach then applied. In this study, we compare the influence of differential with uniformly rope skipping directly succeeding an acquisition phase in arithmetic mathematics. For three weeks 26 pupils, 14 female, 12 male, and 13.9 ± 0.7 years old, completed nine 15 min exercises in arithmetic math, each followed by 3 min rope skipping with heart rate measurement. Arithmetic performance was tested in a pre-, post-and retention test design. The results showed a statistically significant difference between the differential and the control groups within the development of arithmetic performance, especially in the retention test. There was no statistical difference in heart rate. It is suggested that the results provide evidence for sustainable improvements of cognitive learning performance by means of highly variable rope skipping.
... Following this argument, it becomes clear that it is necessary to support the athlete's ability to adapt to changing surrounding conditions. Taking this into account, Schöllhorn, Hegen and Davids (2012) argued in favor of a theory of differential learning, in which the form of teaching and the learning process can be adjusted individually in consideration of the personal abilities and needs of the athlete. These Processes and adjustments are undertaken in order to enable the athletes to perform a general technique. ...
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Approach runs in order to maximize approach velocity are an inherent component in many sports. The goal of the study was to investigate the regulation of a complex motor task in gymnastics vaulting and the impact of the visual system within these processes. It was hypothesized that a visual perception-based strategy incorporating time-to-contact information derived from the variable tau is used to optimize the run-up in particular. Kinematic parameters of 10 gymnasts performing handsprings were examined. The analysis revealed that, on average, onset of visual control took place three steps prior to the hurdle. Linear regression showed that tau margin is dependent on the velocity of the approach run. The study supports the idea of a regulation of the run-up that is based on a visual strategy in which the influence of the vaulting table is crucial. The gymnasts were able to adapt the step length and duration respective to the movement velocity in order to facilitate an optimal transition of the run-up towards the take-off board and subsequent the vaulting table. In the process the influence of run-up velocity relating to the value of tau at the onset of visual control is of utmost importance.
... 114 Variability refers to the variations that are observed between individuals and emerge within individuals in different reiterations of a performance task over time. 115 The variability within complex dynamical systems is useful in allowing movement outcomes to be accomplished in a variety of ways by dynamical movement systems. For example, variability empowers field-based performers to discover a multitude of coordination solutions to complete a successful pass while space between defenders changes at different rates. ...
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Coaching behaviours often derive from sporting traditions, instinct and previous experiences. Practitioners tend to follow traditional, inherited methods rather than adopt new evidence-based approaches associated with athlete development. This article reviews literature relating to theoretical constructs of a novel coach education framework (CEF) developed by the Irish Rugby Football Union. The three constructs included are: self-determination theory (SDT), explicit learning theories (ELT) and implicit learning theories (ILT). A total of 82 publications met the inclusion criteria (SDT: n = 18, ELT: n = 28, ILT: n = 36). This review supports the efficacy of these constructs in isolation for promoting effective coaching practices and provides a justification for future implementation of the framework and its evaluation. This framework may have the potential to address a shortfall in current coach education formats, which have traditionally focused on What content should be used for athlete development as opposed to How practitioners can coach more effectively.
... The long-term basketball player development should include diversified motor experiences (DiFiori et al., 2018). Movement variability can be promoted using differential learning approach (Schöllhorn, 2012), it was beneficial for physical performance in basketball players (Arede et al., 2021). Notwithstanding, little is known how sports-specific experience influence training response following this approach. ...
... The goal-shooting test scores(Schöllhorn et al., 2012). ...
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Zusammenfassung Ziel : Das richtige Zähneputzen ist für Kinder ein komplizierter Prozess. Ziel dieser Studie war es daher, die Wirkung des häuslichen, differenziellen Lernens zur Verbesserung des Zähneputzens zu untersuchen. Methoden : In dieser prospektiven, kontrollierten, einfach verblindeten, randomisierten klinischen Studie wurden 44 Kinder (Alter: 5,6 ± 1,6 Jahre; 24 weiblich, Baseline QHI [Quigley-Hein-Index] > 3, PBI [Papillenblutungsindex] > 0,3, mittlerer dmft = 9 bzw. DMFT = 1,6) zufällig einer Test- und einer Kontrollgruppe (jede Gruppe n = 22) zugeteilt, indem das Kind selbst einen unbeschrifteten Umschlag aus einer Kiste zog. Alle Kinder erhielten die Anweisungen und Informationen zur Mundhygiene in diesen verschlossenen Umschlägen und wurden aufgefordert, diese Anweisungen zu Hause zu befolgen. Lediglich die Kinder der Testgruppe erhielten Instruktionen mit Übungen nach der Methodik des differenziellen Lernens, während die Kinder der Kontrollgruppe Instruktionen zum Putzen nach der KAI-Putztechnik erhielten. Bei Studienbeginn und Follow-ups nach 4 und 12 Wochen wurden Plaque- und Gingivaindizes (QHI, PBI) in beiden Gruppen durch 2 kalibrierte und verblindete Untersucher (L.L. und M.K.) erhoben. Ergebnisse : Zu Studienbeginn gab es keine signifikanten Unterschiede zwischen der Test- und der Kontrollgruppe in Bezug auf Plaque- und Gingivaindizes (QHI: 4,2 ± 0,5 und 4,2 ± 0,5; p = 0,9; PBI: 0,7 ± 0,4 und 0,6 ± 0,2; p = 0,8). Bei den Follow-ups nach 4 und 12 Wochen zeigten beide Gruppen bessere Mundgesundheitsindizes, die Testgruppe aber insgesamt deutlicher. Der Unterschied bei den Plaqueindizes verfehlte knapp die statistische Signifikanz (4-Wochen-Recall; QHI/Test: 2,1 ± 0,9; Kontrolle: 2,6 ± 0,9; p = 0,1). Dagegen zeigte sich im 4-Wochen-Recall bereits ein statistisch signifikanter Unterschied bezüglich der Gingivaindizes (PBI/Test: 0,1 ± 0,2 vs. Kontrolle: 0,4 ± 0,2; p <0,001). Beim 12-Wochen-Recall zeigte die Testgruppe statistisch signifikante und klinisch relevante bessere Mundgesundheitsindizes als die Kontrollgruppe (12-Wochen-Recall, QHI/Test: 1,9 ± 0,8 vs. Kontrolle: 3,3 ± 0,9; p <0,001; PBI/Test: 0,1 ± 0,1 vs. Kontrolle: 0,5 ± 0,2; p <0,001). Schlussfolgerungen : Schlussfolgernd kann festgestellt werden, dass das differenzielle Lernen auch bei Kindern mit hohem Kariesrisiko und initial schlechter Mundhygiene zu Mundhygieneverbesserungen führt, die der konventionellen Lernmethode durch Wiederholung mittelfristig überlegen ist.
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72 college students learned 3 motor tasks under a blocked (low interference) or random (high interference) sequence of presentation. Retention was measured after a 10-min or 10-day delay under blocked and random sequences of presentation. Subsequent transfer to a task of either the same complexity or greater complexity than the originally learned tasks was also investigated. Results showed that retention was greater following random acquisition than under changed contextual interference conditions. Likewise, transfer was greater for random acquisition groups than for blocked acquisition groups. This effect was most notable when transfer was measured for the transfer task of greatest complexity. Results are considered as support for W. F. Battig's (1978) conceptualization of contextual interference effects on retention and transfer. (13 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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In this position paper we examine whether performance and learning of basic motor skills in football can be enhanced by adding noise in the form of random components to target movements during training. To support our argument we examine data on performance and learning of fundamental target skills such as passing and shooting. Evidence emerged from these studies that the addition of random variability during performance and learning of football skills benefited participants of differenct skill levels, compared to players engaged in traditional practice programmes emphasizing continuous repetition of target movements. The ubiquitous phenomenon of stochastic resonance is proposed as a potential mechansim for the counterintuitive benefits of adding noise to learning and performance enviornments. further research is needed to verify our interpretation of these data from football suggesting that stochastic resonance may form an umbrella explanatory framework on the role of variability in extant theories of motor learning.
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In physical education, the Teaching Games for Understanding (TGfU) pedagogical strategy has attracted significant attention from theoreticians and educators alike because it allows the development of game education through a tactic-to-skill approach based on the use of modified games. However, it has been proposed that, as an educational framework, it currently lacks adequate theoretical grounding from a motor learning perspective to empirically augment its' perceived effectiveness by educators. In this paper we examine the literature base providing the theoretical underpinning for TGfU and explore the potential of a nonlinear pedagogical framework, based on Dynamical Systems Theory, as a suitable explanation for TGfU's effectiveness as a strategy in physical education teaching. The basis of nonlinear pedagogy involves the manipulation of key task constraints on learners to facilitate the emergence of functional movement patterns and decision-making behaviors. We explain how interpretation of motor learning processes from a nonlinear pedagogical framework can underpin educational principles of TGfU and provide a theoretical rationale for guiding implementation of learning progressions in physical education.
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In this paper, the major assumptions of influential approaches to the structure of variability in practice conditions are discussed from the perspective of a generalized evolving attractor landscape model of motor learning. The efficacy of the practice condition effects is considered in relation to the theoretical influence of stochastic perturbations in models of gradient descent learning of multiple dimension landscapes. A model for motor learning is presented combining simulated annealing and stochastic resonance phenomena against the background of different time scales for adaptation and learning processes. The practical consequences of the model's assumptions for the structure of practice conditions are discussed, together with their implications for teaching and coaching.