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“There must be an ideal solution…”
Assessing training methods of knife defense performance of police recruits
Swen Koerner, Mario S. Staller & André Kecke
Policing: An International Journal
Special Issue: “What works in police training?”
This is a post-peer-review, pre-copyedit version of an article published in Policing: An
International Journal. The final authenticated version is available online at:
https://www.emerald.com/insight/content/doi/10.1108/PIJPSM-08-2020-0138/full/html
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Purpose
The study compares the impact of two different pedagogical approaches in police training by
assessing the knife defense performance of German police recruits against different types of
knife attacks. Linear or nonlinear – which pedagogical approach leads to more efficient knife
defense performance?
Design
20 German state police recruits (w = 5, m = 15) were assigned to linear and nonlinear group.
The linear and nonlinear groups’ performance on knife defense was assessed on a pretest, after
a 3-week training intervention, on a posttest and 8 weeks thereafter on a retention test, utilizing
a mixed method design (Sendall et al., 2018).
Findings
Quantitative data on knife defense performance suggest a lastingly better performance of the
nonlinear group: On retention test, participants of the nonlinear group were hit less (p = .029),
solved the attack faster (p = .044) and more often (81,8%) than participants of the linear group
(55,6%). In contrast, qualitative data reveal that, despite of evidences for a high level of
perceived competence, the nonlinear teaching of knife defense skills has been accompanied by
considerable uncertainties, effected by the lack of techniques and the focus on principles and
operational parameters only.
Originality
It is the first study assessing the impact of different pedagogical approaches in police training.
For the practice of police trainers, the results provide empirical orientations for an evidence-
based planning of and reflection on pedagogical demands within their training (Mitchell and
Lewis, 2017).
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Introduction
While police training in Germany in general is far from being a well-researched area (Körner
and Staller, 2020a), evidence-based findings on its effectiveness is scarce. However, national
(Jager et al., 2013) and international studies (Preddy et al., 2019; Rajakaruna et al., 2017;
Renden et al., 2015) raise important questions regarding the role, police training is expected to
have as an integrative mechanism for the transfer of skill to the field. More recent empirical
(Cushion, 2018) and conceptual (Körner and Staller, 2017) studies have argued, that next to
contextual factors such as the time spend on learning (Jager et al., 2013; Renden, Landman, et
al., 2015) or the content taught (Renden et al., 2017), pedagogical aspects of training design
play a decisive role for police officer´s skill development.
Based on latest empirical findings on police training, the following study investigates the role
of pedagogy in police training by assessing the impact of two different pedagogical approaches.
Since especially knife attacks on police officers have been a recurring topic in the public and
policing debate in Germany for years, in this explorative field study knife defense performance
of German police recruits against different types of knife attacks has been compared: One group
was taught using the currently predominant linear approach and the other using key principles
of nonlinear pedagogy. By assessing the impact of two available approaches, the article
provides evidence-based orientations for an informed decision-making of police trainers as well
as for the further professionalization of police (self-defense) training (Mitchell and Lewis,
2017).
Police training revisited
Police training serves as an integrative mechanism between police education and professional
practice, aiming to equip police officers with operational skills meeting the complex demands
encountered in the field (Nota and Huhta, 2019). For instance, for recruits of the Hessian state
police in Germany, the academy curriculum states, that training should lead to a competent "use
of situation-specific access techniques in combination with physical means, the use of aids and
weapons within the framework of proportionality" and the "mastering of the individual self-
defence concept" (HfPV, 2016). Whilst there is little empirical evidence available to date on
the extent to which police training generally meets its goals, recent international (Renden,
Nieuwenhuys, et al., 2015) and national studies (Jager et al., 2013; Körner and Staller, 2019)
point to a lack of transfer between training and the field.
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In the study by Jager and colleagues on "Violence against police officers" (Jager et al., 2013),
the interviewed police officers report that the "techniques" (p. 347) dealt with in the training do
not transfer to the operational context in a desired, causing "feelings of helplessness" (p. 351).
Findings of a recent pilot study focussing on violent conflicts experienced by German federal
police officers in deployment (Körner and Staller, 2019) point to the same direction: 20 out of
21 police officers reported that police training had not adequately prepared them for the conflict
dynamics that have occurred.
According to the view of police officers, the problem of transfer between police training and
the field is mainly due to a lack of time spent on learning, leading to insufficient automatization
of techniques (Buttle, 2007; Jager et al., 2013; Renden, Nieuwenhuys, et al., 2015).
Interestingly, studies on the structure and delivery of police training examined that the time
resources available have not been approached efficiently. For instance, a time-on-task analysis
of 16 consecutive training hours of police self-defence and arrest training with German police
recruits revealed an active time of 23% (=03:40h), meaning that an average of 13.75 minutes
per hour was spent on learning activities relevant to the job (Körner and Staller, 2020a; Staller,
2020). For police training in UK, a recent case study yielded, that the police officers trained
spent 54% of the training time passively “watching demonstrations, receiving briefings for
tasks, and getting feedback on previous practice“ (Cushion, 2018) p. 5), and when active, they
were occupied with content been poorly linked to real-life scenarios.
Besides presumably insufficient time resources, the police officers in Jager et al. (2013) and
Renden, Nieuwenhuys, et al. (2015) articulate discrepancies between the selected contents of
their training and operational requirements. This concerns the area of single techniques (e.g.
leverage techniques (Jager et al., 2013) and technical self-defense systems (Renden,
Nieuwenhuys, et al., 2015), but above all the non-treatment of constitutive contextual factors
of the use of techniques in deployment (Rajakaruna et al., 2017). In the view of police officers,
violent encounters in duty are inherently characterized by complexity, surprise and a high
degree of aggressiveness, leading to physiological arousal, emotional stress and the demand for
rapid decision making under pressure (Renden, Landman, et al., 2015).
Both, the economic use of time resources as well as the functional integration of training content
cannot be considered independently of the chosen teaching method and the underlying
pedagogy. The extent to which an official hour of police training turns out being an active hour
of training for the learner (time-on-task) or the training content is gradually linked to contextual
factors of deployment (surprise, dynamics, aggressiveness, etc.), is primarily a question of
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training design. Police training as an institutionalized teaching and learning setting is essentially
a pedagogical process, containing the design, delivery and reflection of training. Consequently,
the transfer problem between training and deployment turns out being a pedagogical issue
addressing special demands on police trainers (Körner & Staller, 2020b). If contents are served
"in a piecemeal and disjointed fashion" (Cushion, 2018, p. 7) and participating police officers
are engaged to listen, absorb and imitate the trainer (ibid.), then this exactly is the expression
of a linear pedagogical approach to learning.
Linear pedagogy
Linear pedagogy is underpinned by the assumption that a) learning is a process induced by the
trainer, b) training literally consists of a transfer of information which are c) applicable as ideal
solution detached from situational and individual prerequisites (Körner and Staller, 2017).
Accordingly, linear teaching is trainer-centered: it is the trainer who demonstrates the desired
standard solution for a known problem, explains important features of execution, breaks down
the overall solution into parts and let them rehearse in isolated repetition (Brown, 2013). Ideally
the learners' individual performance increasingly corresponds to the given standard (Moy et al.,
2015). Since linear approaches to teaching are concerned with the reproduction of an ideal
technical solution, instructions and feedback of the trainer address learners internal focus of
attention (Moy et al., 2013) by emphasizing single technical aspects of (movement) execution,
e.g. the correct angular position of a defensive movement. Learners are challenged to
technically optimize their solution and therefore concerned with the how-decision of
performance (how to execute).
Recent data on structure and delivery of police training in Germany clearly indicate the
dominance of a linear approach to teaching (Körner and Staller, 2020a): 16.75% of total time-
on-task (23.13%) was devoted to the reproduction of techniques, while trainer-centered
activities accounted for 26.09%. Although prevalent in other fields of modern society too,
especially in sports training and physical education (Brown, 2013), linear pedagogy is by no
means without alternatives (Isaieva, 2019). Recent approaches to nonlinear pedagogy (Chow
et al., 2016) are worth being recognized in the police domain.
Nonlinear Pedagogy
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Nonlinear pedagogy is based on the argumentative premise that human behavior is nonlinear in
nature. Due to empirically given biomechanical degrees of freedom (Bernstein, 1967) and the
principle of (neuro-)biological degeneracy (Edelman and Gally, 2001), same effects can be
achieved in different ways, i.e. consistency in the result does not require consistency in cause
or in the course of action. As known from research in high performance sports, functional
movements can be performed by the coordination of different motor components, observable
as different motor executions and different solutions to the problem at hand (Schöllhorn and
Bauer, 1998). The nonlinearity in individual learning and performance is taken serious in the
widely cited Constraints-led approach (CLA, Renshaw et al., 2010). Since slight changes can
cause maximum changes in action and outcome, CLA aims at manipulating key constraints on
performance in a representative manner (Pinder et al., 2011), meaning that characteristics of
the application context (e.g. moments of surprise in deployment) are resembled in training so
that learners (e.g. police officers) can attune to action-specific information (functionality) and
are allowed to act in training as they have to in the field (action fidelity). Nonlinear approaches
to teaching like CLA reach for variability and individuality of problem solving (Arajo et al.,
2017), finally, learners are capable of (Körner & Staller, 2020b). Therefore, instructions and
feedback of the trainer address learners external focus of attention (Moy et al., 2013): They
emphasize the overall goal of a (movement) solution instead of technical aspects of execution
(internal focus of attention). In nonlinear training design learners have to recognize what to do
and how and are therefore concerned with coupled what- (what to do) and how- (how to execute)
decisions.
By saying this, e.g. scenario-based training, which is common in police training (di Nota &
Huhta, 2019), can be identified as nonlinear in nature, since problem solving in conflict
scenarios regularly requires for the nonlinear coupling of what- and how-decisions. However,
scenario training is usually used as a testing environment at the end of training in order to assess
what has been learned before. The learning phase before testing is thereby often linear in design
(Koedijk et al., 2019; Cushion, 2018). The CLA, on the other hand, offers an approach not only
for the testing but also for the design of the learning environment and thus for the whole training
unit in which the learning of the nonlinear coupling of what- and how-decisions is the focus.
Since police related training is expected to be training for the job (Koedijk et al., 2019) and the
acquisition of skill is related to the pedagogy put in place, the question arises which pedagogy
is more likely to meet the expectation. The current study compares the impact of two different
pedagogical approaches in police training by assessing the knife defense performance of
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German police recruits against different types of knife attacks. Linear or nonlinear – which
pedagogical approach leads to more efficient knife defense performance?
Design
Participants
Initially, 40 Hessian state police recruits undertaking the sixth and final stage of their police
education participated in this study. Since the intervention and had to be realized within the
context of the ongoing training process, participants were assigned to linear and nonlinear group
by the organizational authority. Lack of participation in all tests (n = 3) and training sessions (n
= 3) as well as disciplinary decisions of the police authority (independent of the intervention)
during the three months of testing and training led to the exclusion of a total number of 20
police recruits. The finale sample consists of 20 participants (w = 5, m = 15) with n = 9 (M =
25,22 years of age, standard deviation SD = 5,20; 9 male) for the linear group and n = 11 (M =
23,54 years of age, SD = 3,14; 6 male, 5 female) for the nonlinear group. The subject of knife
attacks had not been dealt within the training at the time of the study. Informed consent was
obtained from all participants before they started their involvement in the study. Ethical
approval was issued by the German Sport University Cologne.
Experimental design
The linear and nonlinear groups’ (independent variable) performance on knife defense
(dependent variable) was assessed on a pretest, after a three-week training intervention on a
posttest and eight weeks thereafter on a retention test (table 1). Each test (pretest, posttest,
retention test) took place in an indoor training hall of the police academy, prearranged for an
undisturbed procedure, and consisted of four different knife attacks. (1) Frontal stab attack: one
stab, type and line of attack known. (2) Backward stab attack: four stab, type and line of attack
known. (3). Backward slash attack: four slashes, type and line of attack known. (4) Surprise
attack: multiple attacks for at least three seconds, type and line of attack unknown. Types and
line of the attacks (1), (2) and (3) were announced to the participants and were carried out 2
seconds after announcement at a distance of 60cm. The surprise attack (4) was based on
situational characteristics of real violent dynamics, i.e. carried out surprisingly and with high
aggressiveness, and was unexpectedly applied within the three tests at different times and
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subsequent to different deceptive maneuvers (pretest: last attack, “Your shoelaces are untied”;
posttest: first attack, “Please tell us your personal study-code”; retention test: last attack, direct
after a fake surprise attack was performed). Police officers were generally asked to defend
themselves.
The attack types frontal stab (1), backward stab (2) and backward slash (3) were assigned to
the linear paradigm, where the type of attack was known in all cases and the type of execution
of the defense (how-decision) was the central challenge. Attack (2) and (3) required a transfer
of performance: With backward stab (2) the starting position related to attack (1) varies, with
backward slash (3) the starting position and attack type varies. The surprise attack (4) is
associated with the nonlinear paradigm: The defenders neither knew the moment (manipulation
of the individual) nor the type of the attack (manipulation of task), they had to make coupled
what- (what is the problem) and how- (how to execute) decisions (Körner & Staller, 2020b). In
the case of efficient performance (e.g. by impactive punches, kicks or use of the firearm/red
gun), the attacker provided appropriate feedback and signaled success of knife defense
performance by falling down, stopping, keeping the distance etc. The first author (SK), having
a martial arts and self-defense background of 30 years with additionally 20 years of coaching
experience, performed the attacks with a rubber knife wearing body protection (full head gear,
groin guard).
Training intervention
Following the pre-test, training intervention on knife defense was conducted for both groups
for 40 minutes each in three consecutive weeks. In order to ensure fidelity of teaching
approaches, SK and MS established training guidelines containing key components of both
teaching approaches and structured lesson plans for each group and class.
Instructional features and exercises for linear training were based on descriptions from
pedagogical research literature (Chow et al., 2016; Moy et al., 2015; Renshaw et al., 2010) and
the observational study of police training at the same training site (Körner and Staller, 2020a),
which has identified linear pedagogy to be the dominant approach applied. The structure of all
lessons followed an internationally recognized training curriculum for self-defense (Yanilov,
2003), based on key descriptors of linear pedagogy (“teaching an exercise”, p. 8), and included
a general warm-up phase, basic combative (kicks and punches on a technical level) and
awareness exercises, a main phase dealing with the lesson theme, i.e. an isolated problem (e.g.
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frontal downward stab) and the teaching of the ideal technical solution. In a final summary drill,
defense performance against the treated knife attack has been tested. According to its learning
objective, linear classes have been structured and delivered around ideal solutions for known
problems, performed by trainer-centered demonstrations of the to-be-learned technique, verbal
explanations of important features of execution (internal focus of attention, e.g. for inside-
defense: “bend the elbow at an angle between 90 and 120 degrees, rotate hip"), a chunking
down the overall solution into parts and their repetition in isolated exercises along with
corrective feedback on technical errors of the learner (e.g. for inside-defense: "extend fingers
and slightly press together”). In each linear class a different knife attack (1st downward stab,
2nd upward stab, 3rd straight stab) and solution was covered.
Instructional features and exercises for nonlinear training are based on key principles of the
Constraints-led approach (Renshaw et al., 2019; Renshaw and Chow, 2019), accounting the
nonlinear nature of learning and performance under contextual demands likely to the field and
aiming at the development of a principle-based and individualized problem-solving ability in
learners. Therefore, the structure of the training was centered around recommendations for a
representative learning design (Pinder et al., 2011): At all stages learning of a skill was
embedded in a context that resembles typical characteristics of the application environment,
e.g. in that the learners haven been attacking each other unexpectedly during a conflictual
dialogue, even during warm-up phase. According to its learning objective, in nonlinear training
police recruits were encouraged to individually explore functional solutions for problems at
hand (Körner and Staller, 2017). Therefore, training was organized as 40-minutes of “dynamic
chaos”, in which police recruits have been moving around in confined space (environmental
constraint) deliberately attacking each other (or not), including by knife (task constraint), even
right from the start (warm-up phase). The “chaotic” phases were briefly interrupted for
exercises that highlighted a certain aspect such as mindset (e.g. hitting the pad with increased
intensity until the partner signals an effective striking effect) or defending the knife-attack with
the non-dominant hand etc. In each nonlinear class different constraints on performance have
been deliberately manipulated such as number of attackers, state of awareness, starting position,
types and lines of attack, speed, physiological arousal etc. Instructions and feedback addressed
external focus of attention, emphasizing principles of successful knife defense performance
(e.g. "don't get hit", "create distance between knife and your body"). During all exercises no
technical information has been provided.
Guidelines, lesson plans and teaching style for linear and nonlinear classes were critically
discussed by SK and MS to ensure that the teaching performance was constant irrespective of
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the teaching approach used. Both authors are intensively familiar with both teaching styles. SK
has a background of 12-years in teaching self-defense to civilians, police officers` and rescue
workers and 17 years of teaching university students. MS has been a police trainer for 16 years
and as a civilian self-defense trainer for 18 years. Additionally, the linear concept was reviewed
by an experienced police trainer (AK) to ensure that the dominant pedagogical approach to
current police training has correctly been covered. AK is a police trainer with 12 years of
experience as police trainer and 13 years of operational experience in a police special force.
Due to expertise and organizational matters, training sessions have been conducted by MS (1
and 2) and SK (3).
Data collection
Prior to pretest, participants were required to individually and anonymously complete a
questionnaire on sociodemographic data. For assessing the impact of linear and nonlinear
approaches to teaching on the knife defense performance of police recruits, the study utilized a
mixed-method design (Sendall et al., 2018), see table 1).
Table 1: Study design
Design of the study
Pretest
Intervention
Posttest
Retention test
Week 1
3 weeks
Week 5
Week 13
Linear
group (n =9)
/
Nonlinear
Group (n =
11
Frontal stab
Backward stab
Backward cut
Surprise attack
Video analysis
Perceived competence
Questionnaire and
open questions
3 x 40-min knife defense
classes according to
linear / nonlinear
approaches
Surprise attack
Frontal stab
Backward stab
Backward cut
Video analysis
Perceived competence
Questionnaire and open
questions
Competence, reality and
design aspects of training
Focus group interview
Frontal stab
Backward stab
Backward cut
Fake Surprise attack
Surprise attack
Video analysis
Perceived competence
Questionnaire and open
questions
Participants knife defense performance has been recorded laterally with iPad Pro (third
generation, 4k 60fps) and with GoPro Hero5 (1080p 120fps) located behind the performer. To
assess efficiency of knife defense performance for (1) frontal stab, the number of hits (0 / 1)
equally to the (non)existence of a solution (no = got hit / yes = not got hit) has been measured.
For (2) backward stab, (3) backward slash and (4) surprise attack the number of hits and the
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existence of an attack-stopping solution (no = 0 / yes =1, for surprise attack: within three
seconds) has been determined. Additionally, for surprise attack the total time of problem
solving from first cue of attack until end (has been measured. Indicators of performance
efficiency have been determined using MAXQDA´s video coding function (sequence marker
and playback speed control, 30%). In order to assess whether the surprise attack on retention
test still has been surprisingly, participants were asked to rate their surprise value on a scale
from 0 (not surprised at all) to 25 (totally surprised). For post- and retention test of linear group,
the occurrence of the ideal technique treated in training for all types of attack has been assessed.
Immediately after test and training sessions, participants were required to complete a
questionnaire consisting of 5 items chosen from validated measures of perceived competence
taken from the corresponding subscales of a version of the Intrinsic Motivation Inventory (IMI,
Ryan, 1982), which have been successfully applied in previous studies and have proven
adequate validity and internal reliability (Koka and Hagar, 2010; Walhead and Ntoumanis,
2004). The items were suitably reworded to reflect the scope of the current task, i.e. defending
knife attacks of different kind (e.g. item1: “I think I am pretty good at in knife defense”). All
questionnaire responses were evaluated on a 7-point Likert scale from 1 (not at all true) to 7
(very true). Prior to the actual study the questionnaire items were pilot-tested with students from
German Sport University to ensure that key statements were clear. In addition, participants were
asked to answer open questions concerned their perceived competence (question A: "How do
you rate your ability to effectively defend yourself in duty against the knife attacks treated
today? Please explain why”). After posttest, focus group interviews (Sim, 1998) were
conducted with both groups (linear M = 28.93 SD = 3.36; nonlinear M = 17.11 SD = 1.53) on
design aspects of the training, the relation to reality of knife attacks and the perception of
competence. Besides participants perception, three recognized law enforcement experts were
asked to rate on a 5-point scale whether the knife defense performance seen on video would
have been effective in the field (1 = knife defense in the simulation would most likely have
been effective in the field; 5 = knife defense in the simulation would most likely not have been
effective in the field).
Results
Knife defense performance
In general, both groups showed positive progress in knife-defense performance. The problem
solving of linear and nonlinear group increased from pre- to post- to retention test: Whilst linear
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group successfully defended 32 of 36 knife attacks (4 attacks x 9 participants) at retention test,
representing an increase of 19.45% from 69.44% to 88.89%, nonlinear groups problem solving
increases by 45.45% over the same period of time: at retention test, 42 of 44 (4 attacks x 11
participants) attacks have been resolved (see table 2).
Table 2: Problem solving
At the pretest the nonlinear group showed difficulties in defending the frontal stab: six of 11
(54.5%) participants failed to clear the attack while linear groups problem solving has been
100%. In addition, for number of hits a 2 (linear, nonlinear) x3 (pre, post, retention) repeated
measures analysis of covariance (ANCOVA) yielded a statistically significant difference in
favor for the linear group at pretest, being less hit than the nonlinear group (p = .006; p < a
.05). However, the nonlinear group seemed to benefit from the training intervention: on posttest
problem solving increased to 81.98%, in the retention test all participants (100%) succeeded in
defending the frontal stab, which has been achieved by the linear group, too (see table 2).
For backward stab and backward slash, main differences in problem solving occurred at
posttest: While all participants of the nonlinear group succeeded in solving both attacks and
therefore increased their performance by 45.5% (backward stab) respectively 27.3% (backward
slash) compared to pretest, for linear group five of nine respectively three of nine participants
problem solving – nonlinear group (n=11)
Pretest
Posttest
Retention test
yes
number (%)
no
number (%)
yes
number (%)
no
number (%)
yes
number (%)
no
number (%)
Frontal stab
5 (45.5)
6 (54.5)
9 (81.8)
2 (18.2)
11 (100)
0 (0)
Backward stab
6 (54.5)
5 (45.5)
11 (100)
0 (0)
11 (100)
0 (0)
Backward slash
8 (72.7)
3 (27.3)
11 (100)
0 (0)
11 (100)
0 (0)
Surprise attack
3 (27.3)
8 (72.7)
8 (72.7)
3 (27.3)
9 (81.8)
2 (18.2)
total
22 (50)
22 (50)
39 (88.64)
5 (11.36)
42 (95,45)
2 (2.27)
problem solving – linear group (n
Pretest
Posttest
Retention test
yes
number (%)
no
number (%)
yes
number (%)
no
number (%)
yes
number (%)
no
number (%)
Frontal stab
9 (100)
0 (0)
6 (66.7)
3 (33.3)
9 (100)
0 (0)
Backward stab
6 (66.7)
3 (33.3)
4 (44.4)
5 (55.6)
9 (100)
0 (0)
Backward slash
4 (44.4)
5 (55.6)
6 (66.7)
3 (33.3)
9 (100)
0 (0)
Surprise attack
6 (66.7)
3 (33.3)
7 (77.8)
2 (22.2)
5 (55.6)
4 (44.4)
total
25 (69.44)
11 (30.56)
23 (63.89)
13 (36.11)
32 (88.89)
4 (11.11)
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failed to problem solve (see table 2). Regarding backward stab and backward slash, rmANOVA
for number of hits additionally yielded significant differences between both groups, indicating
that the nonlinear group got hit significantly less than the linear group (backward stab, p < .001;
nonlinear, M = 1.46; CI .90, 2.01; linear, M = 3.11, CI 2.50, 3.72; backward slash, p = .036,
nonlinear M = 2.18, CI 1.67, 2.69; linear, M = 3.00, CI 2.44, 3.56).
For number of hits at surprise attack, repeated measures ANOVA (Mauchly-W = .758, p = .095)
yielded a significant effect of time on performance, F(2,36) = 15.616, p < .001, hp2 = .465) but
no significant interaction effect (time*group), F(2,36) = 1.671, p = .202; hp2 = .085). Pairwise
comparisons with Bonferroni correction showed significant differences between pre- and
posttest (p = .007) and pre- and retention test (p < .001). While measures showed no effect of
time on performance F(1.266,10.126) = 2.683, p = .128, hp2 = .251) for linear group, one-way
ANOVA yielded a significant effect of time on performance, F(2,20) = 18.170, p < .001, hp2 =
.645, Mauchly-W = .729, p = .241) for the nonlinear group. More specifically, pairwise
comparisons indicate that performance against the surprise attack improved significantly from
pre- to posttest (p = .006) and from pre- to retention test (p < .001). In the retention test, the
nonlinear group got hit significantly less (p = .029, M = 3.46, CI 2.27, 4.64; linear M = 5.44, CI
4.14, 6.75, see figure 1).
Figure 1: Number of hits – surprise attack
Additionally, rmANOVA showed that the nonlinear group solved the surprise attack faster (p
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= .044, M = 3.04, CI 1.55, 4.53) than the linear group (M = 5.32, CI 3.68, 6.97, see table 3).
Surprise scores (0 = not surprised at all, 25 = totally surprised) of both groups at the retention
test revealed a mean of M = 18.11 for linear (SD = 7.10) and M = 18.64 for nonlinear group
(SD = 7.13), indicating that despite being known in principle, the surprise attack had been still
been surprisingly for both groups. T-test showed no differences (p = .871).
Table 3: Duration of solution – surprise attack
Duration of defense solution – surprise attack
Group
Pre-test
Post-test
Retention test
M (SD)
95% CI
M (SD)
95% CI
M (SD)
95% CI
duration of defense
solution
Linear
(n=9)
4.74 (1.43)
3.81 – 5.68
3.57 (0.85)
2.73 – 4.40
5.32 (3.41)
3.68 – 6.97
Nonlinear
(n=11)
5.33 (1.26)
4.48 – 6.17
4.05 (1.41)
3.29 – 4.80
3.04 (0.80)
1.55 – 4.53
M mean, SD standard deviation, 95% CI 95% confidence intervals
With regards to problem solving in the retention test, participants of the nonlinear group
succeed in defending the surprise attack in nine out of 11 cases within the first three seconds
(see table 2). In the pretest this was the case in three out of eleven cases (27.3%), which
corresponds to an increase in performance of 54,5% from 27.3% to 81.8% (see table 2). For
comparison: In the retention test the linear group solved the attack in five of nine cases (55.6%)
within the first three seconds, on pretest this was achieved in six cases (66.7%). Overall, the
data indicate that the nonlinear group performed better and achieved a comparatively higher
learning growth through the intervention than the linear group.
Perceived competence
One-way ANOVA yielded a significant effect of time on perceived competence for both
groups: (linear F(2,16) = 8.815, p = .003, hp2 = .524, Mauchly-W = .505, p = .091; nonlinear
F(2,20) = 37.289, p = .000, hp2 = .789, Mauchly-W = .768, p = .304). While for linear group
pairwise comparisons (Bonferroni corrected) showed significant differences between pre- and
retention test (p = .025), for the nonlinear group this is the case between pre- and post (p =
.001), pre- and retention (p < .001) and post- and retention test (p = .012). While perceived
competence of both groups increased with the time, results of retention test indicate that
participants of the nonlinear group (p = .040) seem to have benefitted slightly more from the
15
training intervention than the linear group. According to data of open questions, participants of
the nonlinear group cited the high variability of the exercises and the principle-based approach
as reasons for their perception of increased competence.
Since Fleiss Kappa measures of experts` individual perceptions of knife defense performance
related to its likelihood of success in the field indicated only poor (3x), slight (6x) and fair (3x)
intercoder reliability (Landis & Koch, 1977), experts were asked to determine a consensual
group rating following the principles of questioning and debate (Abraham et al., 2006) while
referring to the above mentioned scale from 1 (effective) to 5 (not effective). For surprise attack
at retention test, expert rating indicated no difference between linear and nonlinear group (p =
.926), attesting both of them a good likelihood, that the performed knife defense would have
worked in the field (linear M = 2.22, CI 1.39, 3.10; nonlinear M = 2.27, CI 1.52, 3.03). One-
way ANOVA yielded a significant effect of time on performance for both groups (linear F(2,16)
= 8.493, p = .003, hp2 = .515, Mauchly-W = .649, p = .220; nonlinear F(2,20) = 18.131, p =
.000, hp2 = .645, Mauchly-W = .869, p = .531). While pairwise comparisons showed significant
improvement for both groups from pre- to posttest (linear p = .015; nonlinear p = .004)
according to experts rating, between pre- and retention test this is only the case for participants
of nonlinear training (nonlinear p < .001; linear p = .072).
Ideal technique
Despite an objectively better knife defense performance for surprise attack compared to the
linear group and a significantly improved knife defense performance compared to pretest, data
from the focus group interview at posttest point to existing uncertainties, caused by the
nonlinear intervention. According to strategies of “structured qualitative content analysis”
(Schreier, 2014) inductive coding of raw data and the grouping of meaning units led to
“uncertainty” as high-order theme within the groups` reflection of nonlinear training.
Well, I also think that we are basically well prepared [...]. But what I would have wished for was that we
had learned a technique... You didn´t quite know whether it's right or wrong or what you should do, but
you just did something and it actually works [...]. But a technique wouldn't have been bad. (section 5,
nonlinear group)
Techniques, that nonlinear training had deliberately excluded in favor of individualized and
variable solutions, led to the uncertainty of not knowing what to do and to the question of
whether the solution chosen was right or wrong. The lack of techniques, in the view of nonlinear
16
pedagogy the very solution, is perceived as a problem here. As one interviewee puts it: "There
must be some kind of ideal solution, that's where the uncertainty comes from" (section 21,
nonlinear group). Along with the desire for an ideal technical solution, nonlinear participants
wished more of typical features of linear pedagogy: demonstrations by the trainer, repetition of
isolated technique and direct verbal feedback.
I actually think it's better when one is told exactly what to do: ‘you have to do it this way or that way.’ And
that you then repeat it, a thousand times until it fits perfectly. (section 23, nonlinear group)
That one gets a feedback [...] whether the defense was already well. I think such a feedback is very
important, because you simply don't look at yourself from the outside. You are in the situation, you don't
know exactly what you have done now in retrospect. (section 45, nonlinear group)
While these qualitative data for nonlinear group reveal a perceived ‘desire for technique’ as
prerequisite for learning and performance, quantitative data of the linear group show that
concrete ideal techniques taught decrease in performance as the complexity of the attacks
increase. In the retention test the ideal solution taught was applied against the frontal stab in
seven (77.8%) out of nine cases; for defending the surprise attack it was used only once
(11.1%). Moreover, occurrence of ideal techniques applied slightly decreases between post-
and retention test from 50% to 36% (see table 4).
Table 4: Occurrence of ideal technique
Discussion
Whilst overall findings of this study reveal that both groups have benefitted from the training
intervention, data related to the attack with the highest relevance for deployment, the knife
attack which is carried out surprisingly and with high aggressiveness, suggest a lastingly better
performance and thus higher problem-solving ability of the nonlinear group: Nine weeks after
the last training, they were hit less, solved the attack faster and more often than participants of
the linear group. Additionally, the increase in the number of solved attacks between pre- and
Occurrence of ideal techniques – linear group (n=9)
Post-test
Retention test
yes
number (%)
no
number (%)
yes
number (%)
no
number (%)
Frontal stab
8 (88.9)
1 (11.1)
7 (77.8)
2 (22.2)
Backward stab
5 (55.6)
4 (44.4)
4 (44.4)
5 (55.6)
Backward slash
2 (22.2)
7 (77.8)
1 (11.1)
8 (88.9)
Surprise attack
3 (33.3)
6 (66.7)
1 (11.1)
8 (88.9)
total
18 (50)
18 (50)
13 (36)
23 (64)
17
retention test displays a steep learning curve of the nonlinear training group. Since the surprise
attack is probably the most realistic of all tested attacks due to its unexpected character, and
unlike the other three variants requires coupled what- (what to do?) and how- (how to execute?)
decisions, this result is particularly remarkable. These key findings are in accordance with
current data on the impact of nonlinear pedagogy in sports training, which have shown
remarkable effects on the retention of learning and performance (Komar et al., 2019; Lee et al.,
2014; Pizarro et al., 2019). In contrast, qualitative data reveal that, despite of evidences for a
high level of perceived competence, the nonlinear teaching of knife defense skills has been
accompanied by considerable uncertainties, effected by the lack of techniques and the focus on
principles and operational parameters only. Objectively, knife defense performance of the
nonlinear group based on principles and variation worked fairly well for all kinds of attacks.
Subjectively, however, in nonlinear participants perception the need of an ideal technique has
been a recurrent subject, along with the wish for technique-based instruction, feedback and
repetition of isolated techniques. While an analysis of the reasons for this perception lays behind
the scope of the current study, it can at least be assumed that the socialization of learners in of
predominant linear teaching settings in school, training and possibly also within police training
itself (Körner & Staller, 2020a) provides a plausible explanation.
The finding of a ‘desire for technique’ is barely being found nor discussed in current nonlinear
research literature (Atencio et al., 2013; Chow et al., 2016, 2011; Chow and Atencio, 2014;
Moy et al., 2015; Renshaw et al., 2010). However, as an (un)intended side effect of non-linear
training it deserves full attention. On the other hand, data of the current study show, that
although “an ideal solution” has been the prominent subject of linear class, it's occurrence in
performance slightly decreases as time and complexity increase. This finding is in line with
results of recent studies on police self-defense training for high pressure situations
(Nieuwenhuys et al., 2009; Renden et al., 2017), indicating the functionality of reflex-based
movements instead of ideal techniques.
Results of the study are related to important limitations. Designed as a field study, the
investigation accounted for the call for a higher ecological validity of nonlinear intervention
studies (Renshaw et al., 2019). The ‘natural’ integration into the ongoing training process of
police recruits however led to a central restriction though: During the three months of testing
and training, the final sample was reduced by half mainly due to organizational decisions. In
addition, it is unclear which factors may have influenced the willingness (not) to participate in
training. Participation in terms of frequency, reasons of absence etc. of German police recruits
in mandatory police training has not been investigated yet. Furthermore, the difference between
18
objective markers of performance efficiency and expert judgement raises questions that need
to be followed: Are the number of hits, resolution time, and existence of the solution false or
incomplete indicators of effective knife defense performance within the field? Possibly, a
qualitative inductive analysis on how knife attacks have been defended (specificity of defense
actions) provides more detailed information. Particularly in view of the grievous differences in
evaluation between the experts (intercoder reliability) in the first round, the general question
arises too, as to what exactly experts base their judgement on and why.
Practical implications
The pedagogy of police training has gathered small scientific attention so far (Körner and
Staller, 2020). The current study aimed at investigating whether the use of linear and nonlinear
pedagogical training interventions leads to differences in the performance of German police
recruits in knife defense. It is the first study assessing the impact of different pedagogical
approaches in police training. Since "mastering of the individual self-defense concept" (HfPV,
2016, p. 98) is fixed as key goal of mandatory training for German police recruits, the subject
of knife defense can be viewed as valuable component.
Concerning the question on which pedagogical approach police training should be based on,
the results of this study suggest that the answer is less of an either-or. Rather, from a practical
point of view, police training requires a conceptual and situational trade-off between the
subjective need of participants for orientation through technique, calling for a more linear
approach, and the objective need for performance capabilities that are robust to the demands of
the field, calling for a more nonlinear approach to learning. For trainers, the qualitative finding
that a trainee may feel uncomfortable in nonlinear learning but may improve and retain
information more quickly than in linear settings leads to the important question of which
outcome should be given greater weight at the moment: the trainees' feelings or the adoption of
functional behavior? From the perspective of professional practice, in training needs of learners
and objective requirements constantly have to be weighed against each other (Staller, 2020).
Linear pedagogy is based on the concept of ideal technical solutions, however results of the
present study suggest that it is at least not the only option for training design. With non-linear
pedagogy there exists a remarkable variant that could complement the training practice within
the police. For the practice of police trainers, the current study provides empirical orientations
for an evidence-based planning of and reflection on pedagogical demands within their training
(Mitchell and Lewis, 2017), sensitive to both, participants needs and operational requirements
19
of deployment. It is important to note that the impact of both, linear and nonlinear approaches
to learning ultimately depends on the quality of their implementation by the trainers. However,
for the further professionalization of police trainer and police trainer education, more empirical
research on the impact of different pedagogical approaches on the development of police
performance (including related aspects, e.g. participation, engagement and safety in training) is
needed.
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