Supplementary files are available for this work. For more information about accessing
these files, follow the link from the Table of Contents to "Reading the Supplementary Files”.
Table of Contents
Go Back
System dynamics of learning processes
- comparing apples with pears
Mats G E Svensson
Centre for Environmental Studies
Lund University, P O Box 170,
SE-221 00 Lund
Email: mats.svensson@ chemeng.lth.se
2002-05-15
Page 1 of 25
Abstract Despite fundamental changes in how people work, live, and entertain themselves,
education systems at the beginning of the new millennium would be familiar to anyone who
attended school 50-60 years ago. While most of the business world has changed with the
introduction of information technology, the academic educational curriculum is remarkably
unchanged. This paper presents a model of how leaming is influenced by the major intemal
factors such as motivation, metacognitive skills, prior knowledge and extemal factors such as
study time, support, teaching and infrastructure, including information technology. The
outcome of the leaning model is subordinate the path towards the results. These major
intemal and external influencing factors are affecting each other in several ways, and the
modelling process is forcing and enhancing viewpoints on how they are influencing each
other - thus the comparison of apples and pears. The model also suggests how improvements
in teaching, support and infrastructure may improve the learning process, including how
changes in the infrastructure i.e. with the introduction of information technology are affecting
the learning process and the achievements.
Keywords: Learning, knowledge, education, metacognitive skills, motivation, learning
technology, soft variables, loop analysis
Page 2 of 25
Introduction
Life is about continuous learning. Most of us learn new things every day. We call it “a
stimulating environment”. We are getting more and more competent each day. For years it has
been attempted within educational science to establish the process of learning. A lot is known
about instruction but as to leaning and acquiring knowledge and insight we still know
relatively little about. Much research is carried out into methods of instruction but very little
into learning with learning tools. How can a learning process be turned into a model and how
can leaming be modelled? A model can help educators to better understand the strengths and
telationships between each of the components. It provides a basis for understanding and
utilising compensatory relationships among the components, as well. It will also enable a
more systemic view on learning systems, and the orchestration of resources for learning.
The aim is to investigate how we best can support learning. It also gives possibilities to
distinguish the separate extemal components from internal components, and assumes a few
basic principles that can be distinguished in the leaming process. The model should also
establish a background about how learning takes place with leaming tools and how learning
can be enhanced by learning technology.
The field of systems analysis has produced few learning models so far. Some attempts have
been made (Eftekhar & Strong, 1995; Min et al., 2000). There might be several reasons for
this. First, one obvious reason is that leaning is still a not a fully understood process. This
seldom stops system dynamics modellers. The role of modelling is also emphasized as a way
of generating testable hypotheses (Roberts et al., 1983)). Second, learning is influenced by
both external factors; teaching system, subject matter, organizational structure, etc, as well as
intemal factors such as motivation, cognitive processes, memory, behaviour, skills etc.
It is generally agreed that students construct their own knowledge. One “ism” that addresses
knowledge construction is constructivism. Teaching strategies based upon constructivism tend
to be inquiry oriented. Learners are encouraged to discover rules without a great deal of
specific teacher input. Inquiry strategies often include tasks explicitly aimed at uncovering
misconceptions. Metacognitive skills play a central role in constructivist leaning models.
Thus much emphasis is put on teach learners to leam. We have all been taught through
lecturing or in classroom environments. This is not likely to be the only and/major learning
environment as we learn continuously, also outside “learning environments”. Instead concepts
as e-Learning, a k a web-based leaming and Blended learning, a combination of conventional
Page 3 of 25
teaching/training and web-based learning will be more common in the future (Rosenberg,
2001). More time will also be devoted to own learning, individualised and self-paced, and
thus self-efficacy will be emphasised (Zimmerman et al., 1994). It also means that more
access to learning material and increased opportunities to learn by self-studies, practices,
simulations has to be given. It has to be emphasized that leaming environments are not
necessarily the same as a teaching/instruction environment.
Leaming can be briefly conceptualized as: a) increasing one’s knowledge, b) memorizing and
teproducing, c) applying, d) understanding, e) seeing something in a different way and f)
changing as a person (Marton et al 1993). The first three categories describe learning as a
reproduction of information, whereas the last three depict leaming as knowledge
transforming. This study does not distinguish these, but of course the latter three categories is
what learning efforts should aim for.
Some of the problems that this modelling approach is trying to direct:
¢ How can motivation be supported?
* What are the effects of increased infrastructure, e.g. introduction of a learning
management system?
* What is the relationship between study time and leaming achievements?
* Whatis the relationship between leaming achievements and prior knowledge?
* How is prior knowledge affecting leaming?
* Can decreased teaching be substituted by an increase in infrastructure?
¢ What is the relationship between metacognition and leaming achievements?
Modelling soft variables - comparing “apples with pears”
Modelling of processes involved in learning require involvement with variables that are
intemal to the human being. Variables like motivation and knowledge or quality of instruction
are not things that can be computed. They do not get numeric or precise value. This simplified
learning model is an attempt to compare such variables, and contains both intemal “soft”
variables as well as external, “hard” and “soft” variables. Can these by compared and
combined in a model? And why attempt to do it? If we follow the dimension-based taxonomy
of systems suggested by Jordan (1968; in Checkland 1993), three principles lead to three pairs
of properties: Rate of change - Structural (static) and Functional (dynamic), purpose -
Purposive and Non-purposive, connectivity - Mechanistic and Organismic. All systems can
be categorized with these parameters, according to Jordan. These bipolar dimensions describe
the information needed to specify any given example of a system. If we look at the model
Page 4 of 25
presented in this paper and the two major types of parameters included in the model. How do
they differ? Soft variables, e g variables that are not possible to define on a generally agreed
scale, are usually functional in terms or rate of change, purposive and organismic in its
connectivity. Hard variables, on the other hand, are often easier to at least define what type of
scale to use, and can be structural as well as functional, purposive, but often mechanistic in its
connectivity. When including or utilising soft variables in a model, the focus is merely on
behaviour than on structure (Checkland, 1993). The suitability of the chosen soft variables can
often be questioned. However, they are often more interesting, and even defining the scales of
soft variables can initiate a good discussion. Soft variables are just as valid to graph as hard
variables, but are more challenging. Forrester and Senge (1980) mention three classes of
system dynamic model tests— system structure, system behaviour and policy improvement
tests. System dynamic model validation is not an ‘‘accept’’ or ‘‘reject’’ statistical
significance exercise, but rather a confidence building process resulting from model
development and use. Any system dynamic model is a more or less informative parsimonious
Tepresentation whose results are implicit in the structure chosen.
Model structure and parameter assumptions
A learning model is defined as a theoretical statement outlining the conditions by which
students lean and develop with respect to a particular educational goal. A learning model is
analogous to a blueprint of the curriculum; it provides a conceptual foundation to guide the
selection and arrangement of experiences intended to promote goal achievement. Explicitly
acknowledged in a learning model are statements about the structure, process, and content of
the curriculum that will lead to achievement of the goal. Each academic programme goal has
an associated learning model, although it is seldom expressed. The definition of system
structure and parameter estimation remedies this. Below is a causal loop diagram of the
model. Leaming and learning outcomes (as “A chievements”) are the central parts of the
model. Below these two parameters are the extemal factors; Study time, Support, Teaching,
and Infrastructure. A bove the two central parameters the three major internal parameters are
found; Motivation, Metacognitive skills, and Prior knowledge. The three major external
factors, outside the system boundaries of this model, are depicted with dotted lines;
Goal/purpose, Personal capability, and Resources.
Page 5 of 25
~--Goal/P urpose*~
Prior
knowledge “
bss
Metacognitive#”
skills
Motivation
/ oN
Learning Achievements
+
—— As)
Study time
capability
Infrastructure
esources
__ wane Pe a
Figure 1. Causal loop diagram showing the model and the relationships between the learning
model’s parameters. Loops where the external factors; Study time, Support and Teaching are
included, are all balancing loops, i.e. e limiting, while the loops where the internal factors
Motivation and Metacognitive skills are Reinforcing. The parameters Goal/Purpose, Personal
capability and Resources are external factors not included in the model.
Learning
Leamers use a variety of integrated skills and attitudes to regulate their leaming. Learning
encompasses cognitive abilities, e g one’s capacity to leam. Included in Leaming, for
simplicity reasons, are cognitive ability, knowledge and strategies. Cognitive ability affects
learning directly and indirectly through knowledge and regulation of strategy development.
Strategies refer to the mental tactics used to make a cognitive task easier to understand or
Page 6 of 25
perform. Even a modest repertoire of strategies can improve leamming and performance
significantly. In addition, strategy instruction increases positive motivational beliefs and may
compensate for lack of intellectual ability or knowledge. There are not any empirical
evidences for any clear relationship between cognitive ability and metacognition (Pressley &
Ghatala, 1990).
The following parameters are considered as the most important internal factors:
Motivation
Motivation is a primary factor in any theory or model of learning. Motivation refers to beliefs
about one's ability to successfully perform a task, as well as one's goals for performing a task.
Motivation as used here refers to a number of beliefs and attitudes that affect learning. It is
now clear that students do not use existing knowledge and strategies effectively if they do not
believe they will improve leaming. The sources of motivation dimension ranges from
extrinsic (i.e. outside the learning environment) to intrinsic (i.e. integral to the leaming
environment) (Pintrich & Schunk, 1996).
Metacognition
Metacognition refers to knowledge and regulatory skills people have about their own
learning; awareness of objectives, ability to plan and evaluate leaming strategies and capacity
to adjust leaming behaviours to accommodate needs (Alexander et al., 1995). Metacognition,
a term coined in the early 1970s, has been viewed as an essential component of skilled
learning because it allows students to control a host of other cognitive skills. According to
Brown (1987), metacognition includes two related dimensions: knowledge of cognition, and
regulation of cognition. Regarding the relationship between knowledge and metacognition, a
number of studies report a strong, positive relationship (Gamer, 1987). Scaffolding strategies
typically improves metacognitive awareness (Schraw & Mossman, 1995). Metacognitive
skills increase during studies. The increase is largest in the beginning of the studies.
Prior knowledge
Every task we undertake depends on knowledge: It is therefore also impossible to understand
and perform a task without some degree of knowledge. An important thing to keep in mind is
Page 7 of 25
that prior knowledge is the best predictor of new leaming. This means any instructional
methods offer contextual practice at the same level as that intended for testing usually give
excellent results. Prior knowledge will shorten the study time, but will also indicate higher
metacognitive skills. However, without Motivation, Prior knowledge’ s importance is less
prevalent.
The following parameters were considered as the most important extemal factors; Study time,
Support, Teaching and Infrastructure.
Study time
When we invest in learning, we pay this investment in time and efforts. Usually study time is
limiting in how much that can be achieved, but there is certainly no linear relationship
between these. In this model it is the only parameter that has any units connected to it.
Support
Support factors include peer students, family and of course tutors/teachers, whereof the most
underrated is the peer support importance. The support directly affects the learning through
helping and advising about suitable learning strategies and ways, and through strengthening
the metacognitive abilities. This is probably one of the most important issues in any leaning
situation, as it is, besides the direct teaching, the most evident feedback system. Support,
through teachers, peer students, friends and parents is strengthening the motivation but also
adds to the overall learning efficiency (Dryden & Vos, 1993).
Teaching
Teaching can be designed differently according to the role of the teacher, e.g. the traditional
didactic role or the facilitative role. The didactic role is more connected to the subject than the
latter, which is focusing more on the learning process per se, and less on the particular
subject. Effective learning includes a number of autonomous components that compensate for
each other. Teaching may exert effects on cognitive ability, choosing appropriate learning
activities in accordance with individual leaming styles and preferences, as well as improving
learning strategies and deeper understanding. For simplicity, these factors are included in the
Teaching factor. Teaching works in two major ways; first by explaining the subject, thus
Page 8 of 25
enhancing the gained achievements per time, but may also improve Motivation as well as
Metacognitive skills.
Infrastructure
Included in the Infrastructure parameter is learning facilities such as classrooms, learning
equipment, but also network and leaming management systems. Infrastructure is a typical
enhancer parameter, thus amplifying or extending other parameter, but does not provide any
value in it or alone. It is nevertheless an important parameter where much improvement has
been made throughout the history of education, and more will be done. Infrastructure
improves the effectiveness of both Teaching and Support, but is also boosting the study time,
by providing more access to leaming material as well as improves the flexibility.
Parameterisation
Detailed knowledge of a process is the prerequisite for parameterisation. All system dynamic
models need numbers to run, but where do they come from? This is a very special topic when
modelling soft variables (Graham, 1980). In the model presented in this paper, it is merely a
matter of setting the relationship between parameters by providing parameter values that will
achieve the appropriate model behaviour. What is then the “appropriate model behaviour’?
This is given by the mental model of the behaviour. This model is for policy analysis, which
is also indicating the value in the parameter estimation. According to Richardson & Pugh
(1981) parameter are value set either by knowledge about the processes involved, and from
data on individual relationships in the model, and from data on overall system behaviour. In
this model the only parameter that is possible to compare and validate from real data, is study
time. This parameter in turn is giving the size of the others. The starting values of parameters
are also set according to the ranking of factors, and thus also the amplitude of influence on the
outcome. No units were used for the intrinsic parameters such as; prior knowledge,
metacognition and motivation, and neither for support and teaching.
Judgemental parameters estimates are likely to be more uncertain (Sterman, 2000), which
indicates that model results are also uncertain. Sometimes assumptions for soft variables can
only be made to find the right relative magnitude, relative other parameters in the model. This
is the case for the internal factor this model encompasses, where it is assumed that the
increase of Motivation is a faster process than the increase in Metacognition and Prior
knowledge. For initial values of the parameters, see the Equations section below.
Page 9 of 25
Extrinsic factors
There are also extrinsic parameters that are excluded in the model but are shown in the causal
loop diagram below (Figure 1.).
Goal/Purpose is an ultimate factor that is mainly influencing the intemal factors through the
learning parameter. It signifies why students study; career move, inner wishes, visions etc.
Personal capabilities include factors such as intelligence, other cognitive abilities, leaming
styles etc.
Resources, which is influencing the extemal factors Study time, Support and Teaching,
include limiting factors such as economic resources, budget, and of course time.
Feedback loops
The model contains several loops, whereof all except two are balancing, thus limit the
outcome of the learning process.
Loop B1 - Learning ->Achievements -> Study time->Learning: Leaming has outcomes, here
called Achievements, which could be fulfilment of objectives, or personal goals, ora
combination of these. These are usually set towards Study time. So when the Achievements
increase the remaining Study time decreases. With less Study time less Learning can take
place, thus a balancing loop.
Loop B2 - Learning ->Achievements -> Support->Leaming: When the results of the learning
is growing, usually both the demand after support as well as the planned given support is
decreasing, thus a balancing loop.
Loop B3 - Learning ->Achievements -> Teaching- >Learning: Teaching efforts are most
useful in the beginning of any leaming process, and thus the importance decreases over time
when the learning is successful and results are achieved.
Loop R1 - Learning ->A chievements ->Motivation->Learning: When the learning process
leads to increasing Achievements, the Motivation increases as a result, this in turn has a
positive effect on Learning, thus reinforcing.
Page 10 of 25
Loop R2 - Learning ->A chievements - >Metacognitive skills->Leaming: To lear is a positive
reinforcing process, which strengthen the metacognitive abilities if learning is achieved, thus
a reinforcing loop.
Loop B4 - Learning ->Achievements ->Prior knowledge->Learning: Depending on the
overall goal and purpose of the studies, Prior knowledge has a positive effect on the learning
process first, but will ultimately limit the leaning process, when the goals and the objectives
of the studies are fulfilled.
Loop B5 - Learning ->A chievements ->Support- >Motivation->Leaming: With achieved
learning results the support is decreasing, thus also affecting the motivation, and the loop is
therefore balancing.
Loop B6 - Learning ->A chievements ->Teaching- >Motivation->Leaming: As for the loop
above, the achieved learning results will lead to a decrease in teaching resources which will
lead to a decreased enhancement in Motivation.
Loop B7 - Learning ->A chievements ->Teaching- >Metacognitive skills->Leamning: The
decreases in teaching efforts with the increase in leaming achievements are also affecting the
increase in Metacognitive skills.
To summarize the feedback loop structure of the model and the consequences - the model
includes several balancing loops and any policy change for improved leaming must try to
change the limitations of these, while keeping the two dominating reinforcing loops.
As this is a model with mostly soft variables, the actual numeric output is of less interest, and
the elaboration of the parameter relationships more of interest. The results are therefore
focusing on this. In general there are three major types of parameter relationships (Figure 3.).
Page 11 of 25
@see
Pattern B . Pattern C
@e
“¥
Figure 2. Major parameter relationship types. Pattern A is a linear relationship, with
different multiplicatory effects, e g an increase in parameter x is giving a proportionally
similar increase response in parameter y, in the form of y = kx+m. This is a reinforcing
pattern. Pattern B is a saturation relationship, where an increase in parameter x is giving a
proportionally larger response in parameter y when x is small, but less when parameter x is
increasing, in the form of y = a(1-e"). This is a balancing pattern. Pattern C is an
exponential relationship of the form y=ae™, where the value of parameter y is getting
proportionally larger with a larger value of parameter x. This is a reinforcing pattern. There
are of course other relationships but these are the three major and common ones.
First, the parameter relationships can be categorized into three major positive relationship
types (Figure 2):
- Positive linear relationship (pattern A); Study time and Achievements have this type of
association. The relationship between Achievements and Prior knowledge is here assumed to
be positive and linear, but will likely also be a saturation relationship (Figure 3; pattem B)
during longer studies.
- Saturation relationship (pattern B); Support and Achievements have this association type, as
the Support is most helpful in the beginning of any studies, and then levels off at a certain
intensity. Teaching and Achievements is following the same pattem. The relationship
between Achievements and Motivation is also a positive association, but there is a certain
level of maximum motivation that is approached. Achievements and Metacognitive skills are
also similar in the pattern over time, as the previous one.
- Exponential relationship (pattern C); none of the relationships show this type of association.
Second, what combined effects on learning have these parameters? Are the effects
multiplicative or merely additive? And do they differ among different individuals?
Page 12 of 25
Moreover, how is infrastructure influencing the leaming outcome? Where should it have an
impact for best effect on leaming? It is assumed here that it is mainly via Study time, Support
and Teaching that Infrastructure has an effect on the leaning process and thus the
Achievements. Infrastructure is influencing the Study time by improving accessibility and
flexibility, thus increasing the Study time.
Equations
With the causal loop diagram of the system (Figure 1) as a blueprint, a numerical model was
built, utilising the STELLA ® software. The only parameter which has a “real” value is the
Study time, given the value of 400 hours corresponding to a semester’ s course at university
level. The following parameter equations were used in the model: Achievements, with an
initial value of zero, was assumed to be the resultant of the Learning process. The learning
process was assumed to be the product of available Study time per day times Motivation
level, Metacognitive skills, Support level and Teaching level and decreased by the inverse
value of the Prior knowledge level, assuming a base level of 0.001, with the unit Leaming
hours/day.
Learning = Study_time_per_day * Motivation_level * Support_level * Teaching level *
Metacognitive_level * (0.001/Prior_knowledge_level)
The Motivation level and the Metacognitive level were assumed to be linearly related to the
sum of Achievements and Teaching level. If no Learning occurs, no increase of Motivational
or Metacognitive levels will occur. Both levels decrease linearly with time.
Metacognitive_level(t) = Metacognitive level(t - dt) +(Metacognitive increase -
Metacognitive decrease) * dt
The Motivation and Metacognitive increase is set by Achievements and Teaching levels,
modified by a strength factor plus a base factor of 0.001. There is no increase in Motivation If
no learning is taking place.
Metacogn_increase = IF(Learning>0) THEN 0.01*(Achievements+Teaching_level) + 0.001
ELSE 0
Page 13 of 25
The Prior knowledge increase was assumed to be linearly related to Achievements with a
transfer delay of 10 time units. If no leaming takes place no change of the Prior knowledge
level will occur, as the increase is then the same as the decrease of Prior knowledge.
Prior_knowledge_level(t) = Prior_knowledge_level(t- dt) + (Prior_knowledge increase -
Prior_knowledge_decrease) * dt
Total study time was assumed to be limited to 400 hours, and decreased with 8 hours per day,
as Study time per day (h/d), plus additional time made available through Infrastructural
effects.
Study_time(t) = Study_time(t - dt) + (- Study_time_per_day) * dt
OUTFLOWS: Study_time_per_day = 8+(8*Infrastructure_effect)
Support level has an initial value of 1 and is increased per time unit by Infrastructural effects
and decreased by Achievements. The infrastructural effects on Support level is moderated by
an Infrastructure effect factor, set to 0.1. The Support level decrease is assumed to be linear
against Achievements, and also has the condition to not change if Study time is zero.
Support_level(t) = Support_level(t - dt) + (Support_change) * dt
INIT Support_level = 1
INFLOWS: Support_change = IF (Study_time>0) THEN (Support_increase-
Support_decrease) ELSE 0
The Teaching level has similar equations and relationships, except that Teaching level is
influencing Motivational and Metacognition levels.
Page 14 of 25
Results
The basic run show as expected an accumulation in Achievements with the Leaming, which
in tum is increasing the Motivation, Metacognitive and Prior knowledge levels (Figure 3).
These three parameters are increasing as long as learning takes place, which is as postulated.
They are all levelling off when the Study time is running out.
The infrastructure has a positive effect on the Learning through extending the Study time per
day, as well as increasing the Support and Teaching levels.
® motivation level 2: Metacognitive level
J * a
3 o
3
3: Prior knowledge leve!
2
7
Ly
rt
A : |
Lit
3
2
Lie \~
z |
J oda 2 je"
0.00 1250 25.00 37.50 50.00
Page 1 Days 16:04 den 15 maj 2002
XQ asar ? Levels of Motivation, Metacognitive skills, and Prior knowledge over time
SD v-achievements 2: Leaming
1: Be
2 0 |
| a
Li
| 2,
1 iJ
z a
1 iL
z , Pz -~-—— a
z 0 fale \
0.00 1250 25.00 37550 50.00
Page 1 Days 16:04 den 15 maj 2002
a ar ” Achievement and Learning over time
Page 15 of 25
3b
E® 1: study time 2: Supportlevel 3: Teaching level
1
F 4009
5]
Ri.
N.,
200 i:
.
5, |
0.00 1250 25.00 37550 50.00
Page 1 Days 16:04 den 15 maj 2002
a af ? Study time, Support level and Teaching level over time
3c
Figure 3. The diagrams show the base run of the model. Motivation and Metacognitive skills
increase with time, until the Study time has reached a value of zero. The Prior knowledge also
increases with time, but with a delay (Figure 3a). Learning (line 2 in Figure 3b) is increasing
to a peak value at time 15, and then levels off, which is setting the Achievements on a certain
level (line 1 in Figure 3b). The variables Support, Teaching, and Study time are all
decreasing with Teaching and Support as the limiting factors (Figure 3c). The limiting factor
is Study time.
The base run model show expected behaviour. The initial values and relationships are simple
and are assuming a total Study time of 400 hours is available for the Learning.
Study time and Achievements show a decreasing curvilinear relationship, indicating that the
Learning is decreasing in the end of the available study time. Learning shows its highest
value at day 15 and is then decreasing. The Support and Teaching levels are first increasing
and then decreasing as the Study time is used. The Metacognitive skills are first increasing
rapidly and then level off, with increasing Achievements, which is also the pattem for
Motivational level. The relationship between Achievements and Prior knowledge is also
showing the same pattern, but with defined delay.
Infrastructure effects
Infrastructure effects, which in the model are directly affecting the Support and Teaching
level, as well as the Study hours per day, are leading to more Learning per time unit and thus
Page 16 of 25
higher levels of Achievements. A tenfold increase in Infrastructure effects, from 0.01 to 0.1
lead to 80% higher levels in A chievements, indicating the nonlinearity in the base model.
BP achievements: 1-2-3
A 49 |
— it
L: er +
0.00 12.50 25.00 37.50 50.00
Page 2 Days 17:13 den 15 maj 2002
XN aa 7? ‘Achievements versus Infrastructure effects (0.001, 0.01 or 0.1)
Figure 4. A sensitivity analysis where, the Infrastructure effect was varied with the values of
0.01, 0.1 and 1.0, which can be interpreted as no infrastructure effect (0.001, or 0.1%), a
slight effect (0.01, or 1%, and a 10% effect (0.1), increases the Achievements over time.
Teaching level effects
Teaching level has an additative effect on the Motivation and Metacognitive levels in this
model. An increase in Teaching level will thus not show any major increases in the
Motivation and Metacognition levels. If the Teaching level instead would have been
multiplicatory in its effect together with the level of Achievements, the result is rather
unexpected, shown in Figure 5. The Motivation and Metacognition levels will then never
increase and no Learning will take place. This could be suspected to be an artefact due to that
the level of Achievement starts at a value of zero, but even if the starting value of
Achievement is set to a higher value, the same result will prevail.
Page 17 of 25
&® =v actievements 2: Learning
1 04
a
aoe
re
.
|—-2
a
0.00 1250 25.00 37.50 50.00
Page 1 Days 18:39 den 15 maj 2002
aaFr ? ‘Achievement and Learning over time
1 0
2 0.
Figure 5. The effect of Teaching level as a multiplicatory factor affecting Motivation and
Metacognition, together with Achievement level.
Achievement effects
With an increase in Achievements the model will give a linear decrease in Support and
Teaching levels. If the relationship is assumed to be nonlinear, pattern B or C in Figure 2, the
overall result will be the same, but the timing will be different with a faster learning but also
that the dedicated Study time will be finished sooner.
Prior knowledge level is a limiting Leaming factor in this model, and by decreasing the effect
of Prior knowledge with a factor of 10, will improve the level of Achievements 10-fold, not
unexpected.
The delay in the transformation of Achievements to Prior knowledge, set to 10 time steps in
the base model, merely influences the constraining effect of Prior knowledge. If the delay is
even larger, the constraining effect of Prior knowledge on Learning will accordingly will be
later in time. However that will lead to that Support and Teaching levels will be limiting the
Leaming instead, and will stop further learning before the allocated Study time is running out.
Discussion and Conclusions
Effective learning includes a number of more or less autonomous components that
compensate for each other. The purpose of this paper was to describe a model that includes
both external factors of both quantitative as well as of qualitative characteristics, with intemal
qualitative factors, and propose one way of investigate how these factors are enhancing or
inhibiting each other. The learning process is of course more complicated than depicted in this
Page 18 of 25
model, involving memory types, cognitive abilities, information processing, etc, but is was
not in the scope of this model. The scope was merely to propose a way of combining factors
that everyone knows are related but do not know how - a perfect but difficult research topic.
Internal factors affecting learning
This model uses four major internal factors; Learning, Motivation, Metacognition and Prior
knowledge. These four parameters do of course not cover all internal factors, but I suggest
that these are the most important ones. No single factor can do all the work, and it is the
orchestration of all that makes learning possible. It is also possible to compensate for
weaknesses in one factor using strengths in other. This aspect has not been covered by this
model. It is also different combinations that are used for different leaming purposes. This is
another omitted aspect.
Motivation is often defined as the processes that initiate and sustain certain behaviour
(Pintrich & Schunk, 1996). Motivation to lea is about engagement and willingness to learn,
to master concepts and skills, and to keep being curious. How can motivation be supported? It
is obvious from other investigations as well as from this model that teaching activities that
promote motivation is highly awarding in terms of improved learning. What this model is
omitting is the clear cross connection between metacognition and motivation that can enhance
each other.
How metacognitive abilities are best supported? A gain the obvious answer lies in the
combinatory effects, and how teaching is defined (Kluwe et al., 1987; Schraw & Mossman,
1995). Maybe teaching shall focus more on teaching on how to lear than the teaching the
subject in itself (Brown,1987; Dryden & Vos, 1993; Hattie et al. 1996).
This model establishes a negative relationship between learning and prior knowledge. This is
not always true, but is a sacrifice to achieve simplicity. Prior knowledge will often have a
positive effect, especially in situations where already known techniques and methods can be
applied to a new field or knowledge arena, and thus enhance the learning process.
External factors affecting learning
This model suggest four major external factors; Study time, Support level, Teaching level and
Infrastructure, whereof the first and the last are factors that do not encompass any direct
feedback mechanism. There is of course a direct relationship between amount of available
study time and leaming. This model assumes a linear relationship. This is of course only true
within certain values, and is probably individually variable, and dependent on the study
subject (Ackerman, 1988) . It might be possible to derive certain subject-specific patterns.
Page 19 of 25
This is probably one of the major factors that restrict the use of this model, as being learning
domain- unspecific.
Teaching increases knowledge. But how to make this process as effective as possible, in a
limited amount of time and in ways that promote deeper conceptual understanding? This
model is not covering such qualitative aspects of teaching, although it could be included.
What are the effects of increased infrastructure, e.g. introduction of a leaming management
system? Can decreased teaching be substituted by an increase in infrastructure? This model
actually shows that this is possible, however it is not a one-to-one relationship. By providing
better support, increased accessibility to leaming resources and further teaching and training
in metacognitive skills and motivation amplifying activities, teaching activities can be cut,
and this is possible to test with this model. Self-efficacy will likely be a quality that pays off
in the future education systems (Zimmerman et al., 1994; Butler & Winne, 1995; Bandura,
1997).
Conclusions - Comparing apples with pears
Is it then possible to compare apples with pears? Y es it is, and sometimes it is inevitable, but
often do we not know how. Checkland (1993) addresses this particularly and also compares
“hard” and “soft” systems thinking. However, he avoids elegantly the problem of
parameterisation of soft variables. It is one thing to define the parameters, and another to
define a value for the particular parameter. The model presented here emphasizes this as the
values are not important and meaningful, which may be typical for soft variables. I would also
argue that the apple versus pear comparison is the quintessence of systems thinking. Many
systems are of the transboundary type, not clearly fitting in any systems typology, but
nevertheless are resolvable. However, they are challenging and different approaches will
always be disputable. Or as Piet Hein been putting it: “Problems worthy of attack, prove their
worth by hitting back”.
Page 20 of 25
List of equations
Achievements(t) = Achievements(t - dt) + (Learning) * dt
INIT Achievements = 0
INFLOWS:
Learning =
study time _per_day*Motivation_level*Support_level*Teaching level*Metacognit
ive_level*(0.001/Prior_ knowledge level)
Metacognitive level(t) = Metacognitive level(t - dt) +
(Metacognitive increase - Metacognitive decrease) * dt
INIT Metacognitive level = 0.001
INFLOWS:
Metacognitive increase = Metacogn_ increase
OUTFLOWS:
Metacognitive decrease = 0.001
Motivation level(t) = Motivation level(t - dt) + (Motivation increase -
Motivation decrease) * dt
INIT Motivation level = 0.001
INFLOWS:
Motivation_increase = motivn_increase
OUTFLOWS:
Motivation decrease = 0.001
Prior knowledge level(t) = Prior knowledge level(t - dt) +
(Prior knowledge increase - Prior knowledge decrease) * dt
INIT Prior knowledge level = 0.001
INFLOWS:
Prior knowledge increase = Prior _knowl_increase
OUTFLOWS:
Prior_knowledge decrease = 0.001
Study time(t) = Study time(t - dt) + (- study time _per_ day) * dt
INIT Study time = 400
OUTFLOWS:
study time _per_day = 8+(8*Infrastructure effect) {h/d}
Support_level(t) = Support_level(t - dt) + (Support_change) * dt
INIT Support_level = 1
INFLOWS:
Support_change = IF (Study time>@) THEN (Support_increase-Support_decrease)
ELSE 0
Teaching level(t) = Teaching level(t - dt) + (Teaching change) * dt
INIT Teaching level = 1
INFLOWS:
Teaching change = IF(Study time>0) THEN Teaching increase-Teaching decrease
ELSE 0
Achievement_to_knowledge transfer_delay_ = DELAY(Achievements,
transfer delay term)
infrastructure effect = 0.05
Metacogn increase = IF(Learning>0) THEN 0.01*(Achievements+Teaching level)
+ 0.001 ELSE 0
motivn_ increase = IF(Learning>0) THEN
0.01*(Achievements+Teaching level)+0.001 ELSE 0
Page 22 of 25
Prior_knowl_increase = IF(Learning>0) THEN
@.01*Achievement_to knowledge transfer delay +0.001 ELSE 0
Support_increase = infrastructure effect*S increase multiplier
S_increase multiplier = 0.1
Teaching increase = infrastructure _effect*T_ increase multiplier
transfer delay term = 10
T_increase multiplier = 0.1
Support_decrease = GRAPH(Achievements)
(0.00, 0.001),
(5.00, 0.051),
(10.0, 0.101)
(1.00, 0.011),
(6.00, 0.061),
(2.00, 0.021),
(7.00, 0.071),
Teaching decrease = GRAPH(Achievements)
(0.00, 0.001), (1.00, 0.011), (2.00, 0.021), (3.00, 0.031), (4.00,
(5.00, 0.051),
(10.0, 0.101)
(6.00, 0.061),
(7.00, 0.071),
Page 23 of 25
(3.00, 0.031),
(8.00, 0.081),
(8.00, 0.081),
(4.00,
(9.00
0.041),
00, 0.091),
(9.00,
0.041),
0.091),
References
Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition:
Cognitive abilities and information processing. Journal of Experimental Psychology: General,
117, 288-318.
Alexander, J. M., Carr, M., & Schwanenflugel, P. J. (1995). Development of metacognition in
gifted children: Directions for future research. Developmental Review, 15, 1-37.
Bandura, A. (1997). Self-efficacy: The exercise of control. New Y ork: W. H. Freeman..
Brown, A. (1987). Metacognition, executive control, self-regulation, and other more
mysterious mechanisms. In F. Weinert & R. Kluwe (Eds.), Metacognition, motivation, and
understanding (pp. 65-116). Lawrence Erlbaum, Hillsdale, New Jersey.
Butler, D., & Winne, P. (1995). Feedback and self-regulated learning: A theoretical synthesis.
Review of Educational Research, 65, 245-281.
Checkland, P. 1993. Systems thinking, systems practice. Wiley’s, London.
Dryden, G. & Vos, J. 1993. The learning revolution. Jalmar Press, Rolling Hills, California.
Eftekhar, N.& Strong, R. (1995) Dynamic modelling of a learning process. A pproved for
publication in The Intemational Journal of Engineering Education.
http://www ijee.ditie/articles/999981 /article.htm
Forrester, J.W. & Senge, P. M.1980. Tests for Building Confidence in System Dynamics
Models. In A. A. Legasto Jr. (Ed.), System Dynamics . Studies in the Management Sciences.
(pp. 209-228). North-Holland, New Y ork.
Garner, R. (1987). Metacognition and reading comprehension. A blex Publishing, Norwood,
New Jersey.
Graham, A.K. 1980. Parameter estimation in system dynamic modelling. In Randers, J. (ed.)
Elements of the system dynamics method. The MIT Press, Cambridge, Massachussetts.
Hattie, J., Biggs, J., & Purdie, N. (1996). Effects of learning skills interventions on student
leaming: A meta-analysis. Review of Educational Research, 66, 99-136.
Kluwe, R. H. (1987). Executive decisions and regulation of problem solving. In F. Weinert &
R. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 31-64). Lawrence
Erlbaum Press, Hillsdale, New Jersey.
Marton, F. Dall’Albam G. & Beaty, E. 1993. Conceptions of learning. International Joumal of
Educational Research 19: 277-300.
Min, R., Vos, H., Kommers, P. & van Dijkum, C. 2000. A concpet model for learning.
Journal of Interactive Learning Research 11(3-4): 485-506.
Page 24 of 25
Pintrich, P. R., & Schunk, D. H. (1996). Motivation in education: Theory, research, and
applications. Prentice Hall, Englewood Cliffs, New Jersey.
Pressley, M., & Ghatala, E. S. (1990). Self-regulated leaming: Monitoring leaming from text.
Educational Psychologist, 25, 19-33.
Richardson, G. P. & Pugh III, A. L. 1981. Introduction to system dynamics modelling.
Productivity Press, Portland, Oregon.
Roberts, N., Andersen, D., Deal, R., Garet, M. & Shaffer, W. 1983. Introduction to computer
simulation. A system dynamics modeling approach. Productivity Press, Portland, Oregon.
Rosenberg, M. J. 2001. e-Leaming. McGraw & Hill, New Y ork.
Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational Psychology
Review, 7, 351-373.
Sterman, J. 2000. Business dynamics. McGraw & Hill, New Y ork.
Zimmerman, B. J., Greenberg, D., & Weinstein, C. E. (1994). Self-regulated academic study
time: A strategy approach. In D. Schunk & B. J. Zimmerman (Eds.), Self-regulation of
learning and performance: Issues and educational applications (pp. 181-201). Lawrence
Enbaum, Hillsdale, New Jersey.
Back to the Top
Page 25 of 25
CC BY-NC-SA 4.0