












































AUSTRALIAN POPULATION STUDIES 2017 | Volume 1 | Issue 1 | pages 26–40 
 

© Raymer, Biddle and Guan 2017. Published under the Creative Commons Attribution-NonCommercial licence 3.0 Australia 
(CC BY-NC 3.0 AU). Journal website: www.australianpopulationstudies.org 

A multiregional sources of growth 
model for school enrolment projections 

James Raymer*  The Australian National University 
Nicholas Biddle  The Australian National University  
Qing Guan  The Australian National University 

*Corresponding author. Email: james.raymer@anu.edu.au. Address: School of Demography, ANU 
College of Arts and Social Sciences, The Australian National University, 9 Fellows Road, Acton 
ACT 2601, Australia 

Paper received 9 May 2017; accepted 17 July 2017; published 20 November 2017 

Abstract 

Background 

Education planning requires accurate and efficient projection models. Current projection models 
either do not make use of all available information and are reliant on idiosyncratic expert judgement, 
or are too complex to be maintained and explained. 

Aims 

To test whether a multiregional projection model performs better than current methodology in 
explaining and projecting school enrolments in a school system with student mobility. 

Data and methods 

A multiregional cohort model was developed for projecting enrolments for multiple schools or 
districts simultaneously. For illustration, data were obtained for all government schools in the 
Australian Capital Territory (ACT) for the years 2008–2016. Multiregional projections were compared 
with a cohort transition model and the ACT Education Directorate’s own projections. 

Results 

(i) There is great diversity in the sources of school enrolment growth that need to be accommodated 
in enrolment projections; and (ii) multiregional projections perform slightly better than traditional 
methods with less effort and more transparency. 

Conclusion 

A sources of growth approach guides the understanding of enrolment change, which is critical for 
making informed projections. 

Key words 

Enrolment projections; cohort transition; multiregional demography; Australian Capital Territory; 
Australia. 
  

 

http://www.australianpopulationstudies.org/
mailto:james.raymer@anu.edu.au


Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 27 

 

1. Introduction 

School districts require information about the expectation of future school enrolments so that they 
can plan the supply of classrooms, teachers, materials and facilities. School enrolments are also 
important for understanding the education system within a larger social and economic context 
(Stone 1965). Without accurate projections, education may be disrupted because of inadequate 
facilities or a lack of teachers or other resources. Alternatively, education may be over-budgeted in 
the provision of teachers, infrastructure and resources, thus causing a misallocation of public funds.  

While projections are never entirely certain due to unobserved factors influencing student mobility 
decisions (Morrison 2000), there are a variety of demographic tools that can be applied to increase 
projection certainty and help better judgements to be made. Surprisingly, in our review we find that 
most education jurisdictions neglect investments in testing or improving projection methodology and 
instead rely on relatively crude projection models with ad-hoc assumptions built in. 

In this paper, we assess a method to project future enrolments for multiple schools or school districts 
simultaneously. Our method is illustrated with data obtained for the Australian Capital Territory 
(ACT) from the ACT Education Directorate for the period 2008–2016. Our aim is to provide better 
understanding of the demographic drivers enrolment change, and to develop more efficient 
projection systems. The multiregional projections are designed to study transitional changes that 
have occurred over time across school levels, as well as between schools and school regions.  

2. Review of methods used to project school enrolments  

Sweeney and Middleton (2005, p. 366) list several distinct approaches used to project school 
enrolments. These include cohort survival and regression methods that use past enrolment data and 
birth records, as well as extended versions of these methods which incorporate other information 
such as migration and student drop-out rates. They also list the modifiable spatial filter method 
(Rushton, Armstrong and Lolonis 1995), which combines cohort survival methods with residential 
address data to determine the size of future school attendance areas. These methods can incorporate 
birth records, past and future housing unit data and the number of students each housing type 
yields. Webster (1971) provides a similar list of projection approaches but also includes those based 
directly on age-specific population counts. Johnstone (1974) further distinguishes between models 
that are deterministic (including Markov Chain models), stochastic and constrainable.  

One key issue is whether projections should be focused at the school level or at the broader district 
level. This also applies to projections for subgroups in heterogeneous populations (Grip 2009). A 
bottom-up (school level) approach can be tailored to fit each school’s composition and needs; 
however, this approach may not consider wider demographic changes in the region around the 
school. A top-down (district level) approach, on the other hand, is often considered pragmatic 
because projections for large areas tend to be more accurate and less prone to rapid population 
changes (Berk & Associates 2008; Grip 2009; Schellenberg and Stephens 1987, p. 13; Stronge and 
Schultz 1981; Swanson and Tayman 2012, p. 281). It can also incorporate wider demographic 
changes which are occurring in the region of interest. The main disadvantage is that a top-down 
approach may produce unrealistic results for schools which have trends or student profiles that are 
substantially different from other schools within their district.  



28 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

In order for projections to be understood and utilised, the methodology and assumptions need to be 
transparent and replicable. The projection approach must also be flexible and able to be adapted to a 
variety of situations and changes that occur to enrolment patterns if the time-consuming process of 
developing specific projection models for each school or school district is to be avoided (Gould 1993; 
Johnstone 1974; Stone 1965). This includes schools in established neighbourhoods, as well as those 
in areas that are currently being developed or planned.  

At times, it may be necessary to incorporate expert judgements or scenarios to account for future 
change possibilities (Morrison 2000). Furthermore, the projection methodology should be regularly 
assessed in terms of accuracy (how well it predicts the truth) and efficiency (amount of time and 
effort required to produce results) (Swanson and Tayman 2012).  

In most developed countries, including Australia, there tends to be very high rates of grade 
progression (close to 100 per cent) in most schools. This implies the expectation that, for example, 
nine years from now nearly all students enrolled in academic level 1 today will be enrolled 
somewhere in level 10. Moreover, there tends to be high retention of students at particular schools. 
The exception, of course, is for students transitioning between primary and secondary school or, in 
jurisdictions such as the ACT, from a government high school (years 7 to 10) to a secondary college 
(years 11 and 12). Current bulges or dips in student numbers can be expected to move through the 
academic levels over time. If primary school enrolments are lower in one year, secondary or high 
school enrolments will follow at predictable times in the future.   

Projections for new schools require a relational model where auxiliary information such as births, 
population projections, household composition and anticipated migration is used to estimate the 
long-term stable size and composition of future student enrolments. There are other situations 
where auxiliary information is also needed. For example, newly developed areas in middle or outer 
growth precincts may be expected to first attract young families with preschool and primary school 
aged children due to the relative affordability of land or housing for newly established household 
units. Over time, these children will progress through the school system, with the school eventually 
reaching a steady state in respect to the number of new and continuing enrolments (Herrick 1952).  

One approach which has not been considered widely in projecting future education requirements is a 
multiregional or multistate population model, which is an extension of the cohort transition model. 
Multiregional population models provide a general and flexible platform for modelling and analysing 
subnational population change over time (Rogers 1975, 1995; Land and Rogers 1982; Schoen 1988). 
They enable the combination of all the main components of population change by age with various 
transitions that each population group may experience over the life course. These transitions may be 
between academic levels (including primary to secondary or high school or high school to a 
secondary college) or between government and non-government schools.  

Despite the many theoretical and analytical advantages, multiregional models have been relatively 
unexplored because of the large amount of input data needed and requirement for matrix 
calculations to perform the projections and analyses. One exception is Sweeney and Middleton 
(2005), who applied a multiregional cohort enrolment projection method to better understand intra-
district school mobility and evaluate existing enrolment projections in Santa Barbara, California. Their 
aim was to understand intra-district school transfers in an open enrolment system for a heterogeneous 
population. In this paper, we build on their ideas to improve school enrolment projections in the ACT.  



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 29 

 

3. Analysing the sources of enrolment change  

The population of the ACT has grown substantially over the past decade and a half from 322,000 in 
2001 to 398,000 in 2016 (ACT Government 2017). This growth has been driven both by natural 
increase and net internal migration. Net internal migration contributed only a small amount despite 
large flows as levels of in-migration tended to offset out-migration. The ACT’s average annual 
population growth rate between 2001 and 2014 was 1.4 per cent with a peak of 2.2 per cent 
occurring in the 2006–2007 period.  

The ACT has seven population regions: Belconnen, Gungahlin, North Canberra, South Canberra, 
Weston Creek, Woden Valley and Tuggeranong.1 The relatively new region of Gungahlin, located in 
Canberra’s north, experienced the most rapid growth during this time, increasing from 25,000 in 
2001 to 62,000 in 2014 with an average annual population growth rate of 7.4 per cent. In Australia, 
like in many other federal systems, school planning is undertaken at the state or territory level. The 
ACT is considered a geographically small system by Australian standards with four main levels of 
public school-based education: 

• preschool – the level before full-time schooling, denoted as level P  
• primary school – the first seven years of full-time schooling, referred to as level K (Kindergarten) 

to level 6 
• high school – the next four years of full-time schooling, or levels 7 to 10 
• secondary college – the last two years of full-time schooling, or levels 11 and 12. 

The percentage of students in the ACT attending a government school increased from 57.5 per cent 
in 20082 to 59.6 per cent in 20163. The remainder were in the non-government school sector, with 
transitions between both systems as documented in this paper. 

The ACT Education Directorate is responsible for 88 public schools in the ACT comprising six early 
childhood schools (i.e., preschool to level 2), 51 primary schools (some with preschools attached), 
10 high schools, nine combined primary/high schools, eight secondary colleges and four specialist 
schools. 4 Record-level data from 2008 to 2016 taken at each year’s census in February were 
provided for this study. The data represents 611,674 student observations and contains the following 
variables: student ID (anonymised); census date; school; academic level (levels P–12); suburb; state. 
From these data, the transitions between academic levels were calculated, as well as movements 
amongst schools for all students in the ACT.  

Following Rees and Willekens (1986), data were obtained that could be used to identify the main 
sources of enrolment change. This accounting framework is outlined in Table 1. The variable gij 
represents internal migration events from one school region i to another school region j. Internal 
migration events are excluded when i = j. Instead, terms ri are entered, which are accounting balances 
that capture the result of subtracting all possible exit events from the starting enrolment population. 

                                                           
1 Note, for our analyses, the Canberra Central region is divided into North Canberra and South Canberra. A map of the 
schools and regions is available from http://www.education.act.gov.au/__data/assets/pdf_file/0005/73319/160210-ACT-
Public-Schools-Map-2016.pdf  
2 http://www.abs.gov.au/AUSSTATS/abs@.nsf/allprimarymainfeatures/FFBE2CE6D8296D21CA2576EA0011F617?opendocument  
3 http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/4221.02016?OpenDocument  
4 http://www.education.act.gov.au/publications_and_policies/publications_a-z/annual_report/annual-report-2015-
2016/section-b/b.1-organisational-overview. Specialist schools are excluded from this study. 

http://www.education.act.gov.au/__data/assets/pdf_file/0005/73319/160210-ACT-Public-Schools-Map-2016.pdf
http://www.education.act.gov.au/__data/assets/pdf_file/0005/73319/160210-ACT-Public-Schools-Map-2016.pdf
http://www.abs.gov.au/AUSSTATS/abs@.nsf/allprimarymainfeatures/FFBE2CE6D8296D21CA2576EA0011F617?opendocument
http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/4221.02016?OpenDocument
http://www.education.act.gov.au/publications_and_policies/publications_a-z/annual_report/annual-report-2015-2016/section-b/b.1-organisational-overview
http://www.education.act.gov.au/publications_and_policies/publications_a-z/annual_report/annual-report-2015-2016/section-b/b.1-organisational-overview


30 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

This number represents students who transition to the next academic level while remaining in the 
school region. Total internal out-migration from each school region are denoted by gi+ and total 
internal in-migration to each school region are denoted by g+j. The ii variable signifies the number of 
migration events from outside the system of interest and oi tabulates the corresponding number of 
persons leaving the system of interest. mi and ni denote transfers from and to non-government 
schools, respectively. The graduation events, xi, and preschool, bi, complete the flows in the table. 
Note, in this table, persons who leave the school system without graduating are included in oi.  

Table 1: A sources of growth accounting framework for government school enrolments across regions 

 
Destination 

 Region Region (t+1) 
    (t) 1 2 3 4 5 6 7 NG MIG GRAD Total 

1 r1 g12 g13 g14 g15 g16 g17 m1 o1 x1 te1  
2 g21 r2 g23 g24 g25 g26 g27 m2 o2 x2 te2  
3 g31 g32 r3 g34 g35 g36 g37 m3 o3 x3 te3  
4 g41 g42 g43 r4 g45 g46 g47 m4 o4 x4 te4  
5 g51 g52 g53 g54 r5 g56 g57 m5 o5 x5 te5  
6 g61 g62 g63 g64 g65 r6 g67 m6 o6 x6 te6  
7 g71 g72 g73 g74 g75 g76 r7 m7 o7 x7 te7  
P b1 b2 b3 b4 b5 b6 b7 0 0 0 b+ 
NG n1 n2 n3 n4 n5 n6 n7 0 0 0 n+ 
MIG i1 i2 i3 i4 i5 i6 i7 0 0 0 i+ 

Total 1
1
+te  1

2
+te  1

3
+te  1

4
+te  1

5
+te  1

6
+te  1

7
+te  m+ o+ x+ 

 Notes: (1) Definitions of variables and subscripts: e = school enrolment population; r = balancing terms; g = internal 
migrations (within the ACT); P (b) = preschool enrolments; NG (m, n) = transfer to/from non-government schools; MIG (o, i) 
= migration to/from other states within Australia or overseas; GRAD (x) = exits due to graduation from government schools; 
0 = structural zeroes; t = time; i = subscript for region; and + = summation over regions. (2) Assumes zero deaths. 

The sum of the numbers in the rows of Table 1 add up to the enrolments at the beginning of the time 
interval, t

ie . The balancing term is obtained by subtracting the total number of migrations to other 
regions within the ACT, transfers to non-government schools, migrations to places outside the ACT, 
and graduations from the population at the beginning of the time interval, i.e., 

𝑟𝑟𝑖𝑖 = 𝑒𝑒𝑖𝑖𝑡𝑡 − 𝑔𝑔𝑖𝑖+ − 𝑜𝑜𝑖𝑖 − 𝑚𝑚𝑖𝑖 − 𝑥𝑥𝑖𝑖  

Similarly, the variables in the columns of Table 1 add up to the enrolments at the end of the time 
interval. We can compute these by adding to the balancing term the total in-migrations, migrations 
from outside the ACT, transfers from non-government schools and preschool entrants, i.e., 

𝑒𝑒𝑖𝑖𝑡𝑡+1 = 𝑟𝑟𝑖𝑖 + 𝑔𝑔+𝑖𝑖 + 𝑖𝑖𝑖𝑖 + 𝑛𝑛𝑖𝑖 + 𝑏𝑏𝑖𝑖  

If we combine these two equations, the balancing term cancels out and we obtain the components 
of school enrolment change:  

𝑒𝑒𝑖𝑖𝑡𝑡+1 = 𝑒𝑒𝑖𝑖𝑡𝑡 − 𝑔𝑔𝑖𝑖+ − 𝑜𝑜𝑖𝑖 − 𝑚𝑚𝑖𝑖 − 𝑥𝑥𝑖𝑖 + 𝑔𝑔+𝑖𝑖 + 𝑖𝑖𝑖𝑖 + 𝑛𝑛𝑖𝑖 + 𝑏𝑏𝑖𝑖  

Thus, the information described in Table 1 provides the basis for understanding the sources of 
enrolment change from one year to the next at the region level. 



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 31 

 

Consider Table 2, which contains the sources of growth and cohort transitions occurring across 
school regions in the ACT for levels P–11 in 2015 to levels K–12 in 2016. The row sums equal the P–11 
enrolments for schools in each of the seven ACT regions. The column sums equal the corresponding 
K–12 enrolments one year later.  

Between 2015 and 2016, 72,694 students made a transition. This included 5,393 students who moved 
out of the ACT and 6,387 students who moved to the ACT. Over 80 per cent of the transitions occurred 
within the seven regions, with non-government schools having the highest retention. The proportion of 
students leaving government schools between 2015 and 2016 in the ACT ranged from 5.6 per cent in 
Weston Creek to 10.8 per cent in Woden Valley. In-migration was greatest to non-government 
schools (n=2,142), followed by Gungahlin (n=823), Belconnen (n=788) and North Canberra (n=696). 

Table 2: Sources of enrolment change and cohort transition proportions for school regions in the ACT: levels 
P–11 (2015) to levels K–12 (2016) 

Region Enrolment Region 2016 
 2015 GUN BEL SCAN TUGG WOD WEST NCAN NG MIG Total 

 Enrolment change  
GUN 5,635 84 21 8 9 6 55 332 628 6,778 
BEL 124 8,582 27 18 20 12 124 331 722 9,960 
SCAN 12 17 3,455 32 145 3 14 129 392 4,199 
TUGG 33 32 22 6,010 146 38 32 346 706 7,365 
WOD 14 11 47 98 3,177 21 132 152 441 4,093 
WEST 8 4 10 33 121 1,612 22 77 112 1,999 
NCAN 56 88 89 21 19 2 4,319 144 558 5,296 
NG 190 133 140 214 125 30 128 23,823 1,834 26,617 
MIG 823 788 576 526 609 169 754 2,142 0 6,387 
Total 6,895 9,739 4,387 6,960 4,371 1,893 5,580 27,476 5,393 72,694 

 Transition proportions  
GUN 0.831 0.012 0.003 0.001 0.001 0.001 0.008 0.049 0.093 1.000 
BEL 0.012 0.862 0.003 0.002 0.002 0.001 0.012 0.033 0.072 1.000 
SCAN 0.003 0.004 0.823 0.008 0.035 0.001 0.003 0.031 0.093 1.000 
TUGG 0.004 0.004 0.003 0.816 0.020 0.005 0.004 0.047 0.096 1.000 
WOD 0.003 0.003 0.011 0.024 0.776 0.005 0.032 0.037 0.108 1.000 
WEST 0.004 0.002 0.005 0.017 0.061 0.806 0.011 0.039 0.056 1.000 
NCAN 0.011 0.017 0.017 0.004 0.004 0.000 0.816 0.027 0.105 1.000 
NG 0.007 0.005 0.005 0.008 0.005 0.001 0.005 0.895 0.069 1.000 
MIG 823 788 576 526 609 169 754 2,142 0 6,387 

Notes: GUN = Gungahlin; BEL = Belconnen; SCAN = South Canberra; TUGG = Tuggeranong; WOD = Woden Valley; WEST = 
Weston Creek; NCAN = North Canberra; NG = ACT non-government schools; MIG = migration to/from other states within 
Australia or overseas. 

Next, consider the cohort transitions presented in Table 3 (next page) from level 10 to level 11. The 
diagonal elements represent those who remained in schools within the region and progressed from 
level 10 to level 11. Most regions retained the majority of their students in the transition from high 
school to secondary college, except Weston Creek (0 per cent, where no secondary college is 
available) and Woden Valley (46%). Tuggeranong had the highest retention (83%). The data clearly 
show that substantial movements occurred across school regions in the transition from high school 
to secondary college. 



32 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

Table 3: Cohort transition proportions for school regions in the ACT: level 10 (2015) to level 11 (2016)  

Region Enrolment Region 2016 
 2015 GUN BEL SCAN TUGG WOD WEST NCAN NG MIG Total 

GUN 0.807 0.048 0.013 0.000 0.003 0.000 0.033 0.008 0.090 1.000 
BEL 0.056 0.789 0.016 0.004 0.007 0.000 0.047 0.005 0.074 1.000 
SCAN 0.010 0.005 0.829 0.025 0.005 0.000 0.005 0.020 0.101 1.000 
TUGG 0.009 0.009 0.018 0.826 0.055 0.000 0.000 0.005 0.078 1.000 
WOD 0.006 0.006 0.091 0.360 0.457 0.000 0.000 0.000 0.080 1.000 
WEST 0.013 0.000 0.046 0.119 0.722 0.000 0.013 0.007 0.079 1.000 
NCAN 0.038 0.077 0.162 0.031 0.198 0.000 0.396 0.018 0.080 1.000 
NG 0.048 0.023 0.043 0.042 0.026 0.000 0.016 0.747 0.055 1.000 
MIG 67 99 78 95 161 0 72 87 0 659 

Notes: GUN = Gungahlin; BEL = Belconnen; SCAN = South Canberra; TUGG = Tuggeranong; WOD = Woden Valley; WEST = 
Weston Creek; NCAN = North Canberra; NG = ACT non-government schools; MIG = Migration to/from Canberra. 

 Gungahlin 

  
 Tuggeranong 

  
 North Canberra 

  

Figure 1: Components of enrolment change for schools in Gungahlin, Tuggeranong and North Canberra, 
2008–2016 

-1200

-800

-400

0

400

800

1200

2008-09 2009-10 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16

-1500

-500

500

1500

2008-09 2009-10 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16

-1000

-500

0

500

1000

2008-09 2009-10 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16

Preschool enrolments Graduates

Net migration within ACT Net migration from outside ACT

Move to non-government schools Net gain



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 33 

 

Between 2008 and 2016 most school regions in the ACT, except Tuggeranong, experienced growth in 
enrolments each year. The sources and levels of enrolment change, however, varied considerably 
across the regions with some regions dependent on several sources of growth (e.g., South Canberra, 
Woden Valley and non-government schools) and others driven primarily by preschool enrolments 
(e.g., Belconnen, Tuggeranong and Weston Creek).  

Consider, for example, the sources of enrolment change during 2008–2016 for schools in the 
Gungahlin, Tuggeranong and North Canberra regions (Figure 1, previous page). Gungahlin grew the 
most, with this growth particularly evident from 2011 with 500 to 560 new students added each 
year. Preschool enrolments were the most significant and increasing component of growth for 
Gungahlin. However, there was a steady net loss of students to non-government schools each year. 
Preschool enrolments similarly were the only source of enrolment growth in the Tuggeranong region 
between 2008 and 2016, declining marginally in 2015–2016.  

4. Cohort transition projection models  

Three models are introduced for projecting enrolments by academic level in this section. The first is 
the standard cohort transition model based on annual enrolment numbers by academic level 
(Johnstone and Philp 1973; Gould 1993; Webster 1970). The second projection model is a 
multiregional cohort transition model that integrates all of the main sources of enrolment change 
presented in Table 1. The third projection model is that utilised by the ACT Education Directorate, 
which, at the individual school level, combines cohort transition information with assumptions on 
household compositional changes over time in relation to planned developments in the school’s 
priority intake area. Feedback from school principals on the plausibility of the results is also 
incorporated.  

To assess the accuracy of the projections, 2008–2012 data are used to predict the observed 2013–
2016 enrolments with the assumption that preschool enrolments are known. The purpose of the 
analysis is to see how well the two types of data-based projections perform against the ACT 
Education Directorate’s projections. 

4.1 Cohort transition model 

A simple and effective way to project school enrolments is to calculate the ratios of students 
progressing from one academic level to the next. While this does not explain changes to enrolment 
numbers from one year to the next, it does provide a measure of the overall change, which can be 
compared over longer periods.  

Consider, for example, the observed enrolment data for schools in the Gungahlin region from 2008–
2016 (Table 4). Here, we see that there were 316 level 1 students in 2008 (shaded grey). In 2009, this 
cohort of students grew to 325 level 2 students and then to 341 level 3 students in 2010. In 2016, the 
same cohort represented 385 level 9 students. Note, as mentioned previously, Gungahlin is a 
relatively new school region and has been growing rapidly due to migration from outside the ACT 
(level 11 became available in 2011 and led to the first cohort of level 12 students in 2012). Cohort 
sizes in other school regions remained very similar or declined. 

  



34 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

Table 4: Observed enrolment data by academic level for schools in Gungahlin, 2008–2016 

Level 2008 2009 2010 2011 2012 2013 2014 2015 2016 

P 589 543 579 619 633 736 815 888 898 
K 361 402 379 432 516 538 613 699 773 
1 316 373 423 397 460 549 580 586 693 
2 326 325 346 429 428 471 531 570 598 
3 335 331 341 378 433 443 485 553 553 
4 296 350 360 316 401 459 468 494 575 
5 309 318 357 350 350 423 461 497 521 
6 309 303 319 349 390 380 440 485 502 
7 242 273 284 264 339 339 332 387 458 
8 229 259 266 295 278 354 360 367 392 
9 204 231 260 271 284 298 365 380 385 
10 203 204 245 261 289 321 316 399 415 
11 0 0 0 308 369 413 502 479 570 
12 0 0 0 0 303 311 396 489 458 

Notes: P = Preschool; K = Kindergarten.  

Transition ratios calculated from the enrolment numbers in Table 4 can be used to produce 
projections of school enrolments. The projection model is specified, in matrix form, as 

 𝐄𝐄𝑡𝑡+1 = 𝐆𝐆𝐄𝐄𝑡𝑡 + 𝐁𝐁 

where 𝐄𝐄𝑡𝑡 are vectors denoting enrolments at time t and in academic level x, G is the transition matrix 
and B is a vector including the projected preschool enrolments. In detailed form, the matrix equation 
looks like 

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡𝑒𝑒𝑃𝑃

𝑡𝑡+1

𝑒𝑒𝐾𝐾𝑡𝑡+1

𝑒𝑒1𝑡𝑡+1

𝑒𝑒2𝑡𝑡+1

𝑒𝑒3𝑡𝑡+1

𝑒𝑒4𝑡𝑡+1

𝑒𝑒5𝑡𝑡+1

𝑒𝑒6𝑡𝑡+1

𝑒𝑒7𝑡𝑡+1

𝑒𝑒8𝑡𝑡+1

𝑒𝑒9𝑡𝑡+1

𝑒𝑒10𝑡𝑡+1

𝑒𝑒11𝑡𝑡+1

𝑒𝑒12𝑡𝑡+1⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

=

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡

0 0 0 0 0 0 0 0 0 0 0 0 0 0
𝑔𝑔𝑃𝑃 0 0 0 0 0 0 0 0 0 0 0 0 0
0 𝑔𝑔𝐾𝐾 0 0 0 0 0 0 0 0 0 0 0 0
0 0 𝑔𝑔1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 𝑔𝑔2 0 0 0 0 0 0 0 0 0 0
0 0 0 0 𝑔𝑔3 0 0 0 0 0 0 0 0 0
0 0 0 0 0 𝑔𝑔4 0 0 0 0 0 0 0 0
0 0 0 0 0 0 𝑔𝑔5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 𝑔𝑔6 0 0 0 0 0 0
0 0 0 0 0 0 0 0 𝑔𝑔7 0 0 0 0 0
0 0 0 0 0 0 0 0 0 𝑔𝑔8 0 0 0 0
0 0 0 0 0 0 0 0 0 0 𝑔𝑔9 0 0 0
0 0 0 0 0 0 0 0 0 0 0 𝑔𝑔10 0 0
0 0 0 0 0 0 0 0 0 0 0 0 𝑔𝑔11 0⎦

⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡ 𝑒𝑒𝑃𝑃

𝑡𝑡

𝑒𝑒𝐾𝐾𝑡𝑡

𝑒𝑒1𝑡𝑡

𝑒𝑒2𝑡𝑡

𝑒𝑒3𝑡𝑡

𝑒𝑒4𝑡𝑡

𝑒𝑒5𝑡𝑡

𝑒𝑒6𝑡𝑡

𝑒𝑒7𝑡𝑡

𝑒𝑒8𝑡𝑡

𝑒𝑒9𝑡𝑡

𝑒𝑒10𝑡𝑡

𝑒𝑒11𝑡𝑡

𝑒𝑒12𝑡𝑡 ⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

+

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡𝑏𝑏

𝑡𝑡–4𝑔𝑔0
0
0
0
0
0
0
0
0
0
0
0
0
0 ⎦

⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

 

where 𝑒𝑒𝑥𝑥𝑡𝑡  denotes enrolments at time t, 𝑔𝑔𝑥𝑥 denotes transitions between school levels with the 

subscript marking the origin academic level, 𝑏𝑏𝑡𝑡–4 denotes births and g0 is the ratio of births at time  
t–4 to preschool enrolments. This model could be adapted further to include repetition rates as in 
Johnstone and Philp (1973).  



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 35 

 

4.2 Multiregional cohort transition model 

The enrolment transition model presented above is designed for projecting enrolments for single 
regions/schools independent of other regions/schools. To allow multiple regions/schools to be 
projected simultaneously, the matrix projection model needs to be reworked to include transitions 
amongst schools as well as academic levels. This matrix projection model is specified as:  

Et+1,x+1 = GEt,x+Ix+1   

where Et,x is a vector of enrolments of regions or schools at time t and academic level x, G contains 
the transition probabilities between levels and schools (gij), and Ix+1 is a vector of in-migration 
counts of enrolments at academic level x+1. In detailed form, the matrix equation for an eight school 
region system looks like 

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡𝑒𝑒1,𝑥𝑥+1

𝑡𝑡+1

𝑒𝑒2,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒3,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒4,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒5,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒6,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒7,𝑥𝑥+1
𝑡𝑡+1

𝑒𝑒8,𝑥𝑥+1
𝑡𝑡+1 ⎦

⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

=

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎡
𝑟𝑟1 𝑔𝑔21 𝑔𝑔31 𝑔𝑔41 𝑔𝑔51 𝑔𝑔61 𝑔𝑔71 𝑔𝑔81
𝑔𝑔12 𝑟𝑟2 𝑔𝑔32 𝑔𝑔42 𝑔𝑔52 𝑔𝑔62 𝑔𝑔72 𝑔𝑔82
𝑔𝑔13 𝑔𝑔23 𝑟𝑟3 𝑔𝑔43 𝑔𝑔53 𝑔𝑔63 𝑔𝑔73 𝑔𝑔83
𝑔𝑔14 𝑔𝑔24 𝑔𝑔34 𝑟𝑟4 𝑔𝑔54 𝑔𝑔64 𝑔𝑔74 𝑔𝑔84
𝑔𝑔15 𝑔𝑔25 𝑔𝑔35 𝑔𝑔45 𝑟𝑟5 𝑔𝑔65 𝑔𝑔75 𝑔𝑔85
𝑔𝑔16 𝑔𝑔26 𝑔𝑔36 𝑔𝑔46 𝑔𝑔56 𝑟𝑟6 𝑔𝑔76 𝑔𝑔86
𝑔𝑔17 𝑔𝑔27 𝑔𝑔37 𝑔𝑔47 𝑔𝑔57 𝑔𝑔67 𝑟𝑟7 𝑔𝑔87
𝑔𝑔18 𝑔𝑔28 𝑔𝑔38 𝑔𝑔48 𝑔𝑔58 𝑔𝑔68 𝑔𝑔78 𝑟𝑟8 ⎦

⎥
⎥
⎥
⎥
⎥
⎥
⎤

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡𝑒𝑒1,𝑥𝑥

𝑡𝑡

𝑒𝑒2,𝑥𝑥
𝑡𝑡

𝑒𝑒3,𝑥𝑥
𝑡𝑡

𝑒𝑒4,𝑥𝑥
𝑡𝑡

𝑒𝑒5,𝑥𝑥
𝑡𝑡

𝑒𝑒6,𝑥𝑥
𝑡𝑡

𝑒𝑒7,𝑥𝑥
𝑡𝑡

𝑒𝑒8,𝑥𝑥
𝑡𝑡 ⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

+

⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡
𝑖𝑖1,𝑥𝑥+1
𝑖𝑖2,𝑥𝑥+1
𝑖𝑖3,𝑥𝑥+1
𝑖𝑖4,𝑥𝑥+1
𝑖𝑖5,𝑥𝑥+1
𝑖𝑖6,𝑥𝑥+1
𝑖𝑖7,𝑥𝑥+1
𝑖𝑖8,𝑥𝑥+1⎦

⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

, 

where the diagonal elements of the G matrix is equal to the retention proportions (ri) and the off-
diagonal elements capture the movements between schools or regions (gij). This model is similar to 
the one used by Sweeney and Middleton (2005) to study enrolment transfers in the Santa Barbara 
Elementary School District in California. 

5. School enrolment projections 

5.1 School regions 

To provide an assessment of different projection models, we first focus on school regions. This allows 
us to make broad comparisons regarding expectations of change across a range of schools, and to 
work with data that tend to be more stable over time and less prone to specific situations that 
require expert assumptions or local knowledge. For the assessment, we assume that preschool 
enrolments are known. Normally these are estimated using observed or projected birth data (t–4).  

In addition to our comparison of the two projection models against the ACT Education Directorate’s 
projections and the observed data, we show the effects of different assumptions concerning the 
transitions used for the projections. The enrolment transition projection model uses the average 
annual transitions from 2008–2012. Three different transitions assumptions are used in the 
multiregional projection model. The first keeps 2011–2012 transitions constant. The second uses 
average 2008–2012 transitions and holds them constant. The third incorporates trends based on 
linear regressions of the observed transitions from 2008–2009 to 2011–2012.  



36 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

Table 5: Average observed and projected student enrolments by school region, 2013–2016 

    
Multiregional 

School 
Region 

Observed ED 
Cohort 

Transition 
2011–12 2008–12 Trend 

GUN 6,941 7,195 6,229 6,663 5,971 6,911 
BEL 10,464 10,683 10,652 10,340 10,636 10,443 
SCAN 4,633 4,766 4,517 4,501 4,471 4,789 
TUGG 7,942 7,873 7,756 8,181 7,985 8,304 
WOD  4,548 4,280 4,325 4,354 4,247 4,476 
WEST 2,063 2,178 2,083 2,071 2,041 2,210 
NCAN 5,628 5,724 5,637 5,690 5,511 5,860 
Total 42,219 42,699 41,198 41,799 40,861 42,994 

Notes: GUN = Gungahlin; BEL = Belconnen; SCAN = South Canberra; TUGG = Tuggeranong; WOD = Woden Valley;  
WEST = Weston Creek; NCAN = North Canberra; ED = ACT Education Directorate. 

Table 5 presents the average 2013–2016 results from the school region projections with the best 
performance shaded grey. Overall, the multiregional projection model with 2011–2012 transitions 
performed the best, followed closely by the ACT Education Directorate’s projections. However, the 
performance for each model varied by school region:  

• The ACT Education Directorate’s projection model did well on average for the Tuggeranong school 
region (-0.9% error), but poorly for Gungahlin (3.7%), Woden Valley (-5.9%) and Weston Creek 
(5.6%).  

• The enrolment transition method performed the best out of all the models for South Canberra 
(-2.4%) and North Canberra (0.2%), well for Weston Creek (0.9%) but poorly for Gungahlin (9.9%) 
and Woden Valley (-5.2%).  

• The multiregional model with 2011–2012 transitions performed well for Weston Creek (0.4%) but 
poorly for Gungahlin (-4.5%) and Woden Valley (-4.5%).  

• The multiregional model with 2008–2012 transitions performed well for Tuggeranong (0.5%) and 
Weston Creek (-1.1%), but very poorly for Gungahlin (-14.6%) and poor for Woden Valley (-6.9%).  

• The multiregional model with trend transitions did very well for Gungahlin (-0.5%) and Belconnen 
(-0.2%), but not well for South Canberra (3.5%), Tuggeranong (4.5%), Weston Creek (7.2%) and 
North Canberra (4.2%).  

The year-to-year projection results and observed enrolment numbers for Gungahlin, Tuggeranong 
and North Canberra are presented in Figure 2 (next page). 

In summary, the multiregional models applied to school regions appear to work best overall 
(especially considering the objective nature of the information required). Average transition models 
work well when the school regions are relatively stable but poorly when regions are growing, such as 
Gungahlin and Belconnen. Here, incorporating trends or auxiliary information on planning 
developments in the transitions makes sense. The big advantage of the multiregional projection 
models is that the patterns of change (and error) can be explained and linked to observed trends. 
There is also consistency in the projection framework for school region moves within the ACT. That 
is, a departure from one school region must be an entry into another. This is particularly important 
when considering the transition between primary and high school levels and between high school 
and secondary college levels. The other factor to consider is efficiency.  



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 37 

 

  Gungahlin 

 

 Tuggeranong 

 
 North Canberra 

 

Figure 2: Observed and estimated enrolments for schools in Gungahlin, Tuggeranong and North Canberra, 
2008–2016 
Notes: ACT ED = ACT Education Directorate’s projection; CT = cohort transition; MR = multiregional projection; Obs = 
observed values. 

3,500
4,000
4,500
5,000
5,500
6,000
6,500
7,000
7,500
8,000

2008 2009 2010 2011 2012 2013 2014 2015 2016

ACT ED CT MR 11-12

MR 08-12 MR Trend Obs

7,500
7,700
7,900
8,100
8,300
8,500
8,700
8,900
9,100
9,300
9,500

2008 2009 2010 2011 2012 2013 2014 2015 2016

ACT ED CT MR 11-12

MR 08-12 MR Trend Obs

4,900

5,100

5,300

5,500

5,700

5,900

6,100

6,300

2008 2009 2010 2011 2012 2013 2014 2015 2016

ACT ED CT MR 11-12

MR 08-12 MR Trend Obs

% Error  MR 11-12   1.1 
ACT ED 1.8 MR 8-12  -3.5 
CT  0.2 MR Trend   6.9 

% Error  MR 11-12   3.3 
ACT ED -3.2 MR 08-12  -0.3 
CT  -4.3 MR Trend   6.8 

% Error  MR 11-12    -7.1 
ACT ED    0.9 MR 08-12  -23.4 
CT  -13.7 MR Trend     0.6 



38 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

5.2 School projections for North Canberra 

The multiregional projection method is particularly useful for capturing students transitioning 
between primary and high schools and between high schools and secondary colleges. This is further 
illustrated with schools in North Canberra, an area with a relatively stable total population in terms 
of age composition and growth.  

Table 6: Observed and projected enrolments for schools in North Canberra, 2013–2016 

 
2013 2014 2015 2016 

School Obs ED MR Obs ED MR Obs ED MR Obs ED MR 

A. Observed and projected enrolments 

A 424 436 442 410 432 434 405 443 420 396 480 412 

B 315 344 331 327 335 343 350 345 345 350 336 338 

C 421 429 426 432 423 432 471 456 446 480 471 439 

D 567 632 591 585 662 604 598 675 614 600 656 621 

E 483 425 443 554 436 447 556 456 466 611 462 466 

F 77 84 79 76 84 78 70 85 74 77 84 72 

G 545 587 541 553 588 544 562 600 532 573 622 515 

H 718 744 711 741 797 721 723 823 719 721 842 710 

I 1,068 1,064 1,059 1,054 1,064 1,082 1,050 1,064 1,073 1,065 1,064 1,084 

J 848 854 809 866 841 805 919 837 824 871 833 835 

Total 5,466 5,599 5,433 5,598 5,662 5,490 5,704 5,784 5,510 5,744 5,850 5,491 

B. Difference between projected and observed 

A 

 
12 18 

 
22 24 

 
38 15 

 
84 16 

B 

 
29 16 

 
8 16 

 
-5 -5 

 
-14 -12 

C 

 
8 5 

 
-9 0 

 
-15 -25 

 
-9 -41 

D 

 
65 24 

 
77 19 

 
77 16 

 
56 21 

E 

 
-58 -40 

 
-118 -107 

 
-100 -90 

 
-149 -145 

F 

 
7 2 

 
8 2 

 
15 4 

 
7 -5 

G 

 
42 -4 

 
35 -9 

 
38 -30 

 
49 -58 

H 

 
26 -7 

 
56 -20 

 
100 -4 

 
121 -11 

I 

 
-4 -9 

 
10 28 

 
14 23 

 
-1 19 

J 

 
6 -39 

 
-25 -61 

 
-82 -95 

 
-38 -36 

Total 

 
133 -33 

 
64 -108 

 
80 -194 

 
106 -253 

Notes: Obs = observed values; ED = ACT Education Directorate projection; MR = multiregional projection. 

The school level projections for North Canberra focus on the level and between-school movements 
across seven primary schools (schools A–G), two high schools (schools H–I) and one secondary 
college (school J). In this illustration, only schools in North Canberra are included, but the model 
framework could be extended to include any set of schools. Also, for illustration purposes, we apply 
the average 2008–2012 transitions as the basis for estimating transitions for 2013–2016.  



Australian Population Studies 1 (1) 2017 Raymer J, Biddle N and Guan Q 39 

 

The projection results for schools in North Canberra are presented in Table 6 (panel A). Also included 
are the corresponding observed values and the projections made by the ACT Education Directorate 
(panel B) with the closest value to the observed value shown in grey. The multiregional projection 
model out-performed the ACT Education Directorate’s projections for seven out of the 10 schools in 
each of the four projection years. These differences, however, are fairly modest. The real benefits of 
the multiregional model are that: (i) less assumptions are required; and (ii) there is a capacity to 
disaggregate the projection error. 

6. Discussion and conclusion 

Understanding the demographic drivers of enrolment change is essential for making accurate and 
informed projections. Variables influencing change include the birth of children in school intake 
areas, movements between government schools in a city or district, migration into or out of a city or 
region, and movements to or from non-government schools. The multiregional cohort projection 
model presented in this paper provides a flexible platform for including the main transitions affecting 
school enrolment change. By grouping schools in a multiregional model, understanding about 
student movements is increased and projection bias reduced. 

In order to make and assess projections, some understanding of the components of enrolment 
change and their trends is required. There is no single projection model that performs best in all 
situations. School districts should consider a variety of assumptions when developing projection 
models and adapt them to meet local differences. They need also to incorporate proposed or new 
housing developments and land releases which may result in increased migration by young families 
into the area and rapid population growth impacting education provision for the areas affected.  

As projections are often heavily scrutinised, the ability to explain trends in terms of the sources of 
growth provides a stronger evidence base and argument for school infrastructure, personnel and 
resource requirements. It also allows the projections producer to understand where the sources of 
error occurred in relation to changing enrolments over time. This is the main motivation underlying 
the multiregional cohort projections.  

We have demonstrated the variability in the sources of student enrolment change across the ACT 
and the relative stability in the different sources of enrolment change and cohort transitions. 
Movements within and outside the ACT government school system can have large effects and are 
more difficult to predict. The multiregional school enrolment projection model captures these 
movements and may be applied to a wide array of situations. However, the transition data must be 
available. 

Key messages 

• Accurate projections of school enrolments and understanding of sources of error are essential 
for good school planning. 

• The multiregional projection model used in our study performed as well or better than a cohort 
transition model and current projection model used by the ACT Education Directorate. 

• A multiregional model that interrogates enrolment change can be used for short- to medium-
term enrolment projections in the ACT. 



40 Raymer J, Biddle N and Guan Q Australian Population Studies 1 (1) 2017 

 

Acknowledgements 

This paper is drawn from a previously commissioned review of school enrolment projection 
methodology prepared for the ACT Education Directorate. The authors would like to thank the 
Directorate for their comments and suggestions, and Xujing Bai for her research assistance. 

References 

ACT Government (2017) Estimated Resident Population – September Quarter 2016, viewed 19 December 
2016, http://apps.treasury.act.gov.au/__data/assets/pdf_file/0008/644813/ERP.pdf/_recache.  

Berk & Associates (2008) Office of Superintendent of Public Instruction K–12 School Enrollment Projections 
Study: final report, viewed 19 December 2016, www.k12.wa.us/SchFacilities/Publications/pubdoc
s/EnrollProjectionMethodologiesFinalReport2008.pdf.  

Gould E (1993) An interactive flow model for projecting school enrolments. International Review of 
Education 39(4): 319–332. 

Grip R S (2009) Does projecting enrollments by race produce more accurate results in New Jersey school 
districts? Population Research and Policy Review 28(6): 747–771.  

Herrick J H (1952) Estimating future school enrollments in rapidly growing communities. Educational 
Research Bulletin 31(4): 92–94.  

Johnstone J N (1974) Mathematical models developed for use in educational planning: a review. Review of 
Educational Research 44(2): 177–201. 

Johnstone J N and Philp H (1973) The application of a Markov Chain in educational planning. Socio-
Economic Planning Science 7(3): 283–294. 

Land K C and Rogers A (eds) (1982) Multidimensional mathematical demography: proceedings of the 
conference on multidimensional mathematical demography held at the University of Maryland, 
College Park, Maryland, March 23–25, 1981, sponsored by the National Science Foundation. New 
York: Academic Press. 

Morrison P A (2000) Forecasting enrollments for immigrant entry-port school districts. Demography 37(4): 
499–510. 

Rees P H and Willekens F J (1986) Data and accounts. In: Rogers A and Willekens F J (eds) Migration and 
Settlement: A Multiregional Comparative Study. Dordrecht: D. Reidel Publishing Company; 19–58.  

Rogers A (1975) Introduction to Multiregional Mathematical Demography. New York: John Wiley & Sons. 
Rogers A (1995) Multiregional Demography: Principles, Methods and Extensions. Chichester: Wiley. 
Rushton G, Armstrong M P and Lolonis P (1995) Small area student enrollment projections based on a 

modifiable spatial filter. Socio-Economic Planning Science 29(3): 169–185. 
Schellenberg S J and Stephens C E (1987). Enrollment projection: variations on a theme, paper presented 

at the Annual Meeting of the American Educational Research Association. Washington DC, 20–24 
April 1987, viewed 19 December 2016, http://files.eric.ed.gov/fulltext/ED283879.pdf. 

Schoen R (1988) Modeling Multigroup Populations. New York: Plenum Press. 
Stone R (1965) A model of the educational system. Minerva 3(2): 172–186. 
Stronge W B and Schultz R R (1981) Models for projecting school enrollment. Educational Evaluation and 

Policy Analysis 3(5): 75–81. 
Swanson D A and Tayman J (2012) Subnational Population Estimates. Dordrecht: Springer. 
Sweeney S H and Middleton E J (2005) Multiregional cohort enrolment projections: matching methods to 

enrolment policies. Population, Space and Place 11(5): 361–380. 
Webster W J (1970) The cohort-survival ratio method in the projection of school attendance. The Journal 

of Experimental Education 39(1): 89–96.   
Webster W J (1971) An empirical comparison of selected enrollment projection formulas. The Journal of 

Educational Research 64(8): 375–381. 

http://apps.treasury.act.gov.au/__data/assets/pdf_file/0008/644813/ERP.pdf/_recache
http://www.k12.wa.us/SchFacilities/Publications/pubdocs/EnrollProjectionMethodologiesFinalReport2008.pdf
http://www.k12.wa.us/SchFacilities/Publications/pubdocs/EnrollProjectionMethodologiesFinalReport2008.pdf
http://files.eric.ed.gov/fulltext/ED283879.pdf

