Modeling Framework for Understanding the Dynamics of Learning
Performance in Education Systems
Arif Mehmood
Delsys Research Group Inc.
45 Rideau Street, Suite 400
Ottawa, Ontario, KIN 5W8
Tel: (613) 562 4077
Email: amehmood73@hotmail.com
Abstract
Both developing and developed countries allocate a substantial amount of their budgets to their
education sectors in an attempt to improve the learning performance of the students at each stage
in the education system. The stages in the system, generally, include Early Childhood
Development (ECD), Elementary and Secondary (K-12), and Post Secondary Education (PSE).
This paper illustrates that in designing effective policies to improve learning performance, it is
important to understand how stages in the education system interact over time. This paper
presents a modeling framework that can be used to evaluate the implications of success in one
stage to other stages of the education system. This research helps in understanding “where and
why” to focus education system reform efforts in order to improve the performance of the
students throughout all stages of the education system.
Keywords: Education, high school dropouts, early childhood development, parents, knowledge.
Introduction
It has been widely recognized that education provides one of the best chances to improve
economic security, job satisfaction, quality of life, and ability to enjoy a healthy lifestyle (Poveda
1999). Both developing and developed countries allocate a substantial amount of their budgets to
their education sectors in an attempt to improve education attainment of the individuals.
Education attainment takes place within a continuum process that involves learning through
different stages over an individual’s life span. These stages are typically conceived as being:
Early Childhood Development (ECD), Elementary to Secondary School (K12), Post Secondary
Education (PSE), and Adult Education and Skills Development. There are a variety of unique
issues associated with each of these stages. For example, problems at the ECD stage may include
low cognitive and social skills development, or poor motor skills. Low graduation rates, high
dropouts rates, and high retention rates (i.e., holding students back) can be matters of concern in
the K12 stage. At the later stages of the continuum, the problem may be low PSE enrollment
rates, and low skills development.
The magnitude of these problems at any point in time may varies in different countries.
However, in designing effective policies to improve learning performance, it is important to
recognize that the problems experienced in these stages are nonlinearly interconnected to each
other. Problems created in early stages of the education system can generate or intensify
problems in the later stages. For example, poor developmental foundations such as culture,
education, and health established at ECD stage could create barriers in learning at high school,
which may in turn lead to higher unemployment and lower income levels when the children
become adults. When such adults become parents, their children will likely face more
challenging learning environments and greater obstacles to success as they progress through each
stage of the education system.
Each stage of the learning continuum requires attention to address its unique problems,
particularly when each stage is viewed as a separate, isolated component. However, in real life,
the stages are not isolated. They are, in fact, elements of a single, interconnected, and integrated
system in which problems relating to one stage are nonlinearly interconnected to problems in
other stages.
Problems arising in early stages of the continuum, if not fixed, can generate or intensify
problems in the later stages. For example, poor developmental foundations such as culture,
education, and health established at ECD stage could create barriers to learning at high school,
which may in turn lead to higher unemployment and lower income levels when the children
become adults.
Similarly, problems at later stages of the continuum such as lower levels of parents’ education
attainment might create obstacles for their children to learn effectively in the ECD stage. On the
other hand, performance at one stage has also implications for other stages. For example,
physical, social and intellectual foundations developed at the ECD stage exert a powerful
influence on later well-being of the individual, build coping abilities and competencies and help
make children physically strong and emotionally healthy.
Given the fact that problems at early stages have implications for later stages and vice versa, the
question is which stage does it make sense to focus on in order to enhance the education
attainment of the individuals at a faster pace? Most research overwhelmingly confirms the
importance of the ECD stage in shaping long-term learning outcomes. The ECD stage lays the
developmental foundations in culture, education, and health, all of which influence how well
children learn as they progress through later stages of the continuum system (Berman 1984,
Walker 1991, Curie et al. 1995, Young 1996, and Donald 1997). However, to design effective
and robust strategies for establishing sound foundations for children at the EC stage, it is
necessary to fully understand the structural impediments to the success of programs focused at
the ECD stage. More specifically, in light of the interconnectedness of the education system,
policy makers need to have an understanding of how addressing the problems of other stages
could influence the likelihood and sustainability of success in the ECD stage. Furthermore, it is
necessary to develop an appreciation of how problems of one stage may evolve over time and
how those dynamics could create new challenges for the programs addressing problems in other
stages.
Objective and scope of the model
This research involved development of a simulation model that integrates stages of the learning
continuum into a one complete system. The model maps how different system elements and
stages are interconnected to each other and helps in understanding how success/failure of
programs at one stage evolve over time and influence success/failure of programs at other stages.
The model can be used to evaluate the potential overall impact of programs designed to improve
the education attainment of Aboriginal people at specific stages of the learning continuum. For
example, in order to increase the overall education attainment of Aboriginal people, what would
be the relative leverage of a strategy that improves the performance of children at ECD stage by
20 or 40 % versus another strategy that directly focuses on improving the performance of
students at K-12 stage by 20 or 40 % or another strategy that attempts to increase the PSE
enrolment by 25 % or another strategy that assists K12 dropout students in increasing their
performance by 30 %. The model will also allow testing combinations of these different
strategies implemented at different times. The purpose of the model would be to understand what
would be the potential overall outcomes of strategies if they succeed in fulfilling their (stage-
specific objectives) by a certain percentage (e.g., 10, 20, 30, 40 etc).
Scope of the model
The model helps policy developers to understand “where and why” to focus more investment in
the continuum in order to accelerate the rate at which education attainment of Aboriginal is
enhanced. The scope of the model is broad in terms of tracking the students and their
performance as they move through stages (ECD, K12, and PSE) in the continuum. The detail
complexity has been purposely avoided in this iteration of the model in order to allow a focus
dynamic performance of the education system as a whole, arising how the underlying structure
of system. Important considerations such as family violence, gender, single parent family issues,
that may in real life influence how students perform as they progress through each stage of the
continuum are not included in the model. The impact of such factors is, however, implicitly
represented in the model by an aggregate measure at each stage in the continuum.
The model also does not focus on investigating different methods (i.e., issues of program design)
for achieving a certain degree of success under a strategy. For example, the learning performance
of K12 students can be improved by different ways such as training and hiring of more
Aboriginal teachers, Aboriginal control of education, and including courses on indigenous
curriculum. The model does not directly incorporate structure that reflects each of these
approaches. Consequently, the model in its current form cannot be used to investigate which of
these ways would provide more leverage for improving learning outcomes for K12 students.
Model Overview
Figure | depicts the model overview that maps the flow of students and their “knowledge”
through different stages of the education system. In this model, “knowledge” represents a
collection of factors such as learning ability, learning capacity, and skills or other characteristics
of an individual that help in progressing through different stages of the learning continuum.
These stages are defined as: Early Childhood Development (ECD), Elementary and High School
(K-12), K-12 Grads, K-12 Dropouts, Post Secondary Education (PSE), and parents. Students
move through these stages of the education system and eventually become parents themselves.
As shown in figure 1, four types of parents are considered in this model. These are: 1) K-12
dropout parents, 2) PSE dropout parents, 3) PSE Grads parents, and 4) K-12 Grads not enrolled
in PSE. It is assumed that these four types of parents collectively establish an environment that
influences the learning of students of new generations as they move through the ECD and K-12
stages. Students at the PSE stage mostly do not live with their parents; hence, it is assumed that
parental influence on PSE students is insignificant.
K12 Grads not enroled in
+ Number of K12 Grads not in P
* Knowledge of K12 Grads not in PSE
i
K12G
* Number of K12 Grads
+ Knowledge of K12 Grads
+ Number of students
+ Knowledge of students
+ PSE Programs
KI
* Number of students
of students
Dropouts
of PSE dropouts
dropouts
EC Stage
* Number of kids
+ Knowledge of kids
+ ECD Programs
Figure 1 Model overview
As shown in Figure 1, the stages incorporated in the model are interconnected with each other,
which allows the model to track both the movement of students as well as the knowledge that
they gain at each stage. The model incorporates an assumption that the level of knowledge
gained by students any stage depends on the level of knowledge transferred from previous stages
plus the knowledge they gain at the “current” stage. It is, admittedly, difficult to precisely
measure or even to quantify the amount of an individual’s knowledge at each stage continuum.
The focus of the model is on understanding the dynamic interaction between different factors
that influence the rate of change in the knowledge of individuals over time. Precision in
quantification of knowledge is not necessary given in this objective.
For simulation purposes, an index scale is utilized that represents an assumed initial average
level of knowledge for individuals at each stage. For example, it is assumed that the average
knowledge of children at the ECD stage is 10 Units; at the K12 stage the assumed average
knowledge is 40 Units, the average knowledge of K12 graduates is 80 Units, while the average
knowledge for K12 dropouts is 70 Units. The assumed differences in the initial level of
knowledge for individuals at each stage of the education system is premised on the fact that, on
average, the knowledge of individuals at any stage will be greater than the knowledge of
individuals at preceding stages. For example, a PSE graduate has relatively more knowledge
than a K12 graduate.
The model also incorporates structure and logic for establishment and discontinuation of ECD,
K12, and PSE programs (as distinct from the ECD, K12 and PSE stages of the continuum). The
model increases or decreases the number of these programs available to ECD, K12, and PSE
students respectively, depending on the need of these programs based on the current number of
individuals at these stages. For example, if the current number of individuals increases at a stage,
the model adds incrementally more programs to that stage until the desired need of the programs
is reached. The number of programs available to ECF, K12, and PSE students represent the
“productive capacity” of the school system at each stage and is one factor that influences the rate
at which individuals are able to add knowledge at that stage of the learning continuum.
Dynamic hypothesis of the model
Figure 2 illustrates the dynamics hypothesis of the modeling framework presented in this paper.
This dynamic hypothesis describes the positive feedback processes of the education system that
demonstrates the interconnections of the different stages. As shown in the figure, it is assumed
that the level of knowledge at any stage depends on the level of knowledge transferred from
previous stage plus the knowledge gained at that stage. The gain in knowledge for children at
ECD and K-12 stages, however, can also be influenced by their parents’ knowledge.
Knowledge of
lads at K12
__ Rnowledge of kids RS
at ECD
renowicdae of
Wr students af PSE
Gain in Inowledge by lads
as in K12 ©
Gain in parents
Gain in knowledge by knowledge
lads in ECD
Gain in knowledge
foe by PSE students
hz)
Knowledge of
parents
Figure 2 Dynamic hypothesis of the model
As shown in figure 2, the knowledge gained at each stage in the education process is determined
by the relative strength of the positive feedback loop operating at that stage. The level of
knowledge or learning that students acquire at earlier stages of the education system can affect
their learning outcomes in later stages. Similarly, knowledge gained at later stages would
influence the rate of gaining knowledge at early stages by students in succeeding generations.
For example, learning at the ECD stage can affect the performance of students in elementary and
high school. Low literacy level in high school can be a barrier to acquiring knowledge at the
University and college level. Conversely, high literacy rates in PSE can increase the gain in
knowledge at ECD and K-12 stages.
The relative strength of a positive feedback loop at a certain stage in figure 2 also depends on the
number of individuals at that stage. Figure 3 shows the concept of the number of individuals to
determine the average knowledge of an individual for only ECD and K-12 stages. Figure 4
repeats the same concept illustrated in figures 2 and 3 for all of the stages considered in this
paper.
aii
Knowledge of lads
ai ECD ‘, is wiledge of
Ae mee
‘e af - avetagtie é \
Ave owl ofa aad Gainin mowed by his
yin ee
Aes)
Gain in cae by ak
ledsin ECD _ A t outs: Ty Ae) a) \ s
5 ae
Knowledge of 12
PS, in ze 6) / z Ee y ts
o Ss PO / i
os KL2 drop out
—— parenis
°
— pe Knowledge of 8
a parents
mes
Figure 3 Model structure for ECD and K-12 stages
As shown in Figure 3, average knowledge of a child at the ECD stage depends on the number of
children in ECD and total knowledge of all children at ECD. The average knowledge of a child
at ECD, in turn, influences the rate at which knowledge is gained in ECD. In the case of the K-12
stage, the average knowledge of a child at K-12 not only influences the gain in knowledge at K-
12 but also affects the dropout or graduation rate.
seul eS
elSgubntosane Seeker ‘Ea.
ens ar \
a Deer Pees \ ees
(fo) Xe \ Sug Me
2); sella
; ee td
Figure 4 Structure of the model
Simulation Model
The structure of the model (Figure 4) is converted into a mathematical model using the System
Dynamics methodology. Figures 5, 6, and 7 illustrate the stock-flow structure of the model.
Figure 5 shows the flow of individuals through the various stages from ECD to parents while
figure 6 tracks the flow of knowledge of those individuals as they move from one stage to
another. For illustration purpose the interaction between individuals and their knowledge for K-
12 stage is shown in Figure 7 and is discussed in this paper. The interaction between individuals
and their knowledge for other stages is not depicted, but is the same as described for the K-12
stage.
Dewthsteof12
net gj 112 Oras ot ag 0 Tne ar 12 ae
secon paces ‘abesane pets cule prals
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Beni
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ee ~
et enlbng PSE PSE drew
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Figure 6 Flow of knowledge through different stages
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| 7 pees
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Figure 7 Interaction between children in K-12 and their knowledge
As shown in figure 7, children from the K-12 stock move to either the stock of K-12 dropouts or
to the stock of K-12 graduates. The number of K-12 dropouts or graduates is assumed to vary
every year based on the average knowledge of children enrolled in K-12. This relationship is
defined as:
Fraction of K12 dropouts = Normal fraction of K12 dropouts x Effect of Ave knowledge of kids
on K12 dropout (dd)
Where
Fraction of K12 dropouts is assumed to vary from 0.02 to 0.45.
Normal fraction of K12 is assumed equal to 0.3.
Effect of Ave knowledge of kids on K12 dropout is an assumed nonlinear function
of the Ave knowledge of kids in K12.
Figure 8 shows a hypothesized relationship based on author’s heuristic understanding between
Ave knowledge of kids in K12 and Effect of Ave knowledge of kids on K12 dropout. The vertical
axis in figure 8 represents the assumed values for Effect of average knowledge of kids on K12
dropout while the horizontal axis represents the normalized values of the Ave knowledge of kids
in K12. As shown in figure 8, it is assumed that when Ave knowledge of kids in K12 increases to
more than one, then the effect of average knowledge of kids on K12 dropout will decrease, in
10
turn, Fraction of K12 dropout will decrease. It is also assumed that when Ave knowledge of kids
in K12 decreases to less than one, the Fraction of K12 dropouts will also increase.
Effect of Ave knowledge of kids at K12
on knowledge gain
i)
°
0 1 2 3 4 5 6 7 8
Normalized values of Ave knowledge of kids in K12
Figure 8 Heuristic relationship for effect of ave. knowledge of children on K-12 dropout.
The variable Ave knowledge of kids in K12 depends on Knowledge of kids in K12 and Kids in
K12. The Knowledge of kids in K12 increases by knowledge transferred from ECD and
knowledge gained during K-12 stage, and decreases by knowledge transferred by K-12 dropouts
and graduates.
It is assumed that a child gains a certain amount of knowledge at K-12 stage. This amount of
knowledge endogenously varies by the average knowledge of parents and average knowledge of
kids at K12. In the model, Gaining knowledge during K12 is defined as:
Gaining knowledge during K12 = Fraction of knowledge gained during K12 x Kids in K12 x
Effect of ave knowledge of kids on knowledge gain during K12
x Effect of parents ave knowledge on knowledge gain during
K12
Where
Fraction of knowledge gained during K12 is an assumed value of knowledge that
kids gain from school and home during K12 period.
Effect of ave knowledge of kids on knowledge gain during K12 and Effect of
parent's ave knowledge on knowledge gain during K12 both are assumed
11
nonlinear functions of Ave knowledge of kids in K12 and Ave knowledge of
parents respectively. A similar shape is assumed for these functions, as shown in
Figure 9.
4.0 Lh ]
3.5
nN
a
a
on knowledge gain
nN
Oo
oof
ou oO
1
°
1 2 3 4 5 6 7 8
Normalized values of Ave knowledge of kids in K12
Figure 9 Heuristic relationship for effect of Ave knowledge of children at K-12 on knowledge gain
As shown in Figure 9, it is assumed that when Ave knowledge of parents increases to more than
one, then its effect on the gain in knowledge by children in K-12 will also increase. On the other
hand, when Ave knowledge of parents decreases to less than one, the gain in knowledge by
children in K-12 will also decrease.
The process for gain in knowledge by individuals at other stages such as ECD and PSE is similar
as described for the K-12 stage, however, the strength of the nonlinear relationships is considered
to be different for each stage. For example, it is assumed that effect of parents’ knowledge on
knowledge gain at the ECD stage is stronger than at the K-12 stage because at ECD stage
children are more dependent on their parents.
It is, admittedly, difficult to measure or quantify the amount of an individual’s knowledge at
each stage of the education process. However, the focus of this paper is on understanding the
interaction between different factors that influence the rate of change in the knowledge of
individuals over time. For simulation purpose, a scale is assumed that represents an initial level
of the average knowledge of individuals at each stage. For example, it is assumed that the
average knowledge of children at the ECD stage is 10 Units; at the K-12 stage the assumed
average knowledge is 40 Units, the average knowledge of K-12 graduates is 80 Units, while the
average for K-12 is 60 Units. The assumed differences in the initial level of knowledge for
individuals at each stage of the education system is premised on the fact that, on average, the
knowledge of individuals at any stage will be greater than the knowledge of individuals at
12
preceding stages. For example, a PSE graduate has relatively more knowledge than a K12
graduate.
Simulation results
Base run
Initially the model is parameterized in a way that equilibrium exists in all stocks. To test the
dynamic hypothesis articulated in this paper, the model is driven from equilibrium by an
exogenous disturbance. The step input, a sudden one-shot disruption of the system’s equilibrium
state, is a very simple and uncomplicated, yet informative, disturbance (Lynies, 1988). Such a
test is important for understanding any tendency internal to the system (Saeed, 1987). The
equilibrium of the model is disturbed by a 20 percent step increase in the Net increase in Kids at
ECD at time 10. All other parameters and nonlinear relationships remain unchanged. Figures 10
(a), (b), (c), and (d) show a base run simulation of the model over a hypothetical 300 year period
starting in equilibrium at year one.
As a consequence of the step increase in the number of children at ECD, the number of
individuals at all stages increases proportionally throughout the remainder of the simulation. For
example, Figure 10 (a) and (b) show an increase in the number of K/2 dropout parents and PSE
graduated parents respectively. As the number of individuals at each stage increases, so does the
knowledge of these individuals at that stage. The average knowledge of individuals at a stage
captures the relative change in the number of individuals and their respective knowledge. For
example, Figure 10 (c) shows variations in the Ave knowledge of kids at ECD that reflect the
relative change in the number of Kids in ECD and Knowledge of Kids at ECD. Similarly, Figure
10 (d) reflects the changes in the total number of all types of parents considered in this paper and
changes in total knowledge of these parents.
13
E12 crop cut parenis PSE graduated parents
1,000
300
800
700
600 200
GQ 30) 60 «90120, 150 180-210 240-270 300 6 30 60 90 120 150 180 219 240 270 300
Time (Year) Time (Year)
K.12 drop out parents: Base. 7-7 +++ pretsons PSE graduated parents Base —t—-t—+—+—_ persons
(a) (b)
Ave knowledge of kids at ECD Ave knowledge of parents
u 130
105 125
as BNGHRRHRARABEAeee
95 NE 115
4 AN LL sid
0 3 6 9% 120 150 180 210 240 270 300 0 30 60 90 120 150 180 210 240 270 300
Time (Year) Time (Year)
Awe knowledge of kids at ECD : Base ——+—4_ Knowledge/person Ave knowledge of parents : Base ——+——+— _ Knowledge/persen.
(c) (d)
Figure 10 Simulation results of base runs
Policy runs
A number of policy experiments are carried out on the base run of the model to understand the
implications of different strategies aimed at improving overall education attainment such as
increasing the average knowledge of parents, reducing K-12 dropout rates, and increasing PSE
graduates. This section describes four of these policy experiments, implemented at time 15 in the
simulation. These policy experiments are:
1) Investment in ECD: making ECD programs more effective than its present situation is an
effort to increase the gain of knowledge of children at the ECD stage. This policy is
implemented by stepping up the normal increase in ECD programs. This would represent
an additional improvements in the ECD programs including, for example, extending
services and facilities at preschool daycare centers, hiring more qualified and experienced
staff, and introducing new, more effective approaches to learning. Similarly, examples of
external factors at elementary and secondary school (K-12) stage would include
curriculum, qualification of teachers, and facilities provided at school.
14
2) Investment in K-12: improving the performance of high schools to increase the gain in
knowledge by high school students. This policy is tested by stepping up the normal
increase in K12 programs. This would represent an additional improvements including,
for example, improving standard student to teacher ratios, improving methods of
teaching, increasing teacher competency through training programs, and introducing
modern technology in the K12 programs that would help students to gain more
knowledge.
3) Investment in PSE: improving the performance of the Universities and colleges so as to
increase the gain in knowledge by PSE students. This policy is implemented by stepping
up the normal increase in PSE programs. For example, this policy could be implemented
by hiring more qualified professors in Universities or by offering advanced technologies
facilitate learning at the PSE level.
4) Increasing PSE Enrollment: This policy is implemented by stepping up the fraction of K-
12 graduates that enroll in PSE. The stepping up of the PSE enrollment could be achieved
by measures such as expanding the capacity at Universities and colleges or by offering
scholarships to help support students involved in studies at the PSE stage.
These four policy experiments are conducted using typical goal-gap structure for the time period
(0 to 500). The simulation results of these experiments are shown in Figure 11 (a), (b), (c), and
(d).
As shown in figure 11 the policy run,“K12” which focuses on improving learning outcomes in
high schools is relatively more effective as a strategy for improving the average knowledge of
parents and reducing dropouts from K-12 and PSE stages of the education system. The K12
policy is more effective because of a cascading leverage effect within the education system.
Strengthening the positive loop (R2) in figure 2 has the compounding effect of strengthening the
other positive loops shown in figure 2. However, one can imply that increasing the strength of
any loop in figure 2 would result in increasing the strength of all other loops. The question is on
which loop should efforts be focused and why? The reasons why intervention focused on the K-
12 stage is found to be more effective are: number of individuals at K-12 stage is relatively more
than to the number of individuals at any stage, and the location of the K-12 stage in the system is
such as to contribute relatively more in increasing the knowledge of parents for a longer period
of time.
15
K12 drop out parents PSE gradhated parents
1,000 1,000
150 4
500 500
ve
250 [a =
8
D 5D 100 150 200 250 300 350 400 450 500 °
0 50 100 150 200 250 300 350 400 450 S00
Tine (Yea)
PSegutocelpeat Ee
‘Tine (Yea)
10 dep naman “BED 22 a a ae a 5 a
aiepoeie 2 tee | : a
tp mapents2SEBm1 ———§———§——§——~§ spars | jopSenilt tery; gg gi
(a) (b)
Ave knowledge of kids at ECD Ave knonledge of parents
200 ey 300 T
150 ra 600
100 { i 7
: Thee dl
200
pees = — =
0 r pa
0 50 100 150 200 250 300 350 400 450 soo | °
0 530. 100 150-200 250 300 350 400-450 500.
Time (Year)
‘Aue lowed ofits BCD : Base ———}———+-_ + Khwrledgepatson
‘Ave laweedge ofits 2 ECD ; ECD 22 3- Khrwledgepatson,
‘Ave lawrledge ofits @ ECD: E12. —3———3—3_— Fouvedgefpason
‘Ave lnwwmledge of ide ECD : PSE Hnovledee person,
‘Ave lowwredge ofkide ECD : PSE Bool —S—§——5— Iinowhdgvpason.
Tine (Year)
Figure 11 Simulation results of policy runs
Policy runs in the long run
In this section the same four policy experiments described above are repeated for an extended
period of time (0 to 1000) to explore the long-term consequences of these four strategies. The
simulation results of these experiments are shown in Figure 12 (a), (b), (c), and (d). As shown in
16
figure 12, the strategy of making ECD programs more effective will, in the long term, produce
education system performance outcomes that match the outcomes achieved under the “K12”
strategy.
One of the reasons why the ECD-focused strategy takes a longer time than the K-12 strategy is
the time lag involved in increasing the knowledge of parents. Children in K-12 influence the
average knowledge of parents more quickly they become parents more quickly than children in
the ECD stage. Once the knowledge level of parents begins to increase, the rate of knowledge
gain at ECD and K-12 stages also increases, which in turn further increases the knowledge of
parents as the children move out of the education system and start families. Conversely, if
policies are adopted that delay improvements in the knowledge of children in the K-12 stage, the
learning environment for their children will be more challenging than it would otherwise have
been,
E12 drop out parents
1,000
500
12 dup out peas : Base. f+ parsons
K12 dup ou pats : ECD. a3. 3. parsons
E12 atop ot panes : KI]. 3 ——3- ——3.— parsons
Ki2 drop ow peat: PSE 4 4
2 op ou pets : PSE Bol ———§———5 5 5 pss
(a)
PSE graduated parents
1,000
500
0
0 150 «300 «450 «600750900
Time (Year)
PSE gadueed parats : Base. —}————_+_ +. parsons
PSE guduted praes : ECD) 233-3. parsons
PSE gaduted paees : KI2). ———3———3- —- 3. _— parsons
PSE guduted paws : PSE
PSE gudited puss : PSE Bao). ———§———§ 5 5 — parsons
(b)
Ave knowledge of kids at ECD
Ave knowledge of parents
0 150300 450-600
Time (Year)
750 900
1,000
ne
Ave lawaledge ofits ¢ BCD
‘Ae lawwledge ofits ¢ BCD
Ave lawaledge ofits ¢ ECD
Ave laweledge ofits ¢ ECD
Ave lawaledge ofits ¢ ECD
Base ——+—} + — owtedgepasn,
Ec) 32 2 todas
Kl) —}——3 3. 1 oedgeasn,
PSE i Hovrledgupaeon
PSE Birol —S ——5 5 — Hnowledgeasn,
(c)
‘Ave nowledgeofparats
‘Ave nowledg ofparats
‘Ave nove ofp
‘Ave ovmedgeofpurate
‘Ave ovedgeofpurate
Buse —}-—- ——}- + fhoohdgepason
Ee). —2—2_2 3. Frowhedgepason
1. ——3——3 3 3 Fhrowhdgepason
PSE 4444 Bourmedevparon
PSE Bool ——§———§§- ——§ Huodgupasen
(d)
Figure 12 Simulation results of policy runs for extended period of time
17
Discussion
Each stage of the education system requires resources to tailor the solutions of specific problems.
For example, the ECD stage needs support to run programs for mitigating problems such as poor
health, and low cognitive development and motor skills of young children. The effectiveness of
these ECD programs generally depends on the qualifications, experience of mentors and
facilities provided at these programs. Most research overwhelmingly confirms the importance of
the ECD stage, as early experience exerts a powerful influence on later well-being, builds coping
abilities and competencies and helps make children physically strong and emotionally healthy. It
has been argued that the ECD stage could provide strong developmental foundations in culture,
education, and health, all of which influence how well children learn as they progress through
later stages of the education system (Berman 1984, Walker 1991, Curie et al. 1995, Young 1996,
and Donald 1997). Armed with this knowledge how important ECD is on educational attainment,
governments naturally will tend to emphasize investment in programs targeted to the ECD stage.
However, the high leverage investment, that taps the power of ECD and that generates the
greatest overall learning performance gain in the shortest possible time may actually lie in other
stages of the education system.
The policy experiments described in this paper identify that improving learning outcomes for
students in the K-12 stage would yield more benefits than policies aimed at improvement of any
other stage. The improvement of K-12 learning performance increases the number of K-12
graduates and enrollment in PSE. The resulting improvement in the knowledge of parents
increases their ability to provide a sustainable and effective learning environment for the kids of
next generations. It is important to note that the model assumes that parents do participate in
their kid’s learning and that such participation is beneficial. In addition to effectiveness of the
ECD programs, the environment that parents provide at home has a powerful influence on how
well a child progresses at the ECD stage. The environment that parents establish usually depends
on their learning from different stages including ECD, K-12 and/or PSE.
Experimentation with the model suggests that performance problems of one stage influence the
magnitude of problems of other stages, and that solving problems at one stage can fix the
problems of other stages. Because the education system appears to be characterized by a number
of inter-connected self-reinforcing structures it is important to design policies that reflect an
understanding of how the whole system behaves, rather than focusing on problems of each
individual stage. In particular, policies aimed at improving overall education performance
should take into account the likelihood that the most effective solutions for resolving problems in
one stage of the system may be found by intervening in other stages of the system that, due to the
systems structure, provide greater leverage for change.
Limitations of the model and future work
The modeling framework presented in this paper is based on many assumptions that need to be
investigated in more depth using empirical evidence. For example, the shape and strength of the
nonlinear relationships are based on author’s intuitive or heuristic understanding about these
relationships. As noted by (Lagasto et al. 1980) cause and effect relationships could be
incorporated in the model to represent essential phenomena, which might otherwise be omitted
18
due to lack of sound empirical evidence. However, any such relationships initially defined in the
model should be later investigated in more depth using available empirical evidence.
In addition, extending the model by including more loops might enhance the understating about
interaction between stages of the education system.
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