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close this bookCounting the Cost of Teacher Education: Cost and Quality Issues (CIE, 1999, 37 p.)
View the document(introduction...)
View the documentMulti-Site Teacher Education Research Project (MUSTER)
View the documentAbstract
View the document1. Introduction
View the document2. Some Common Approaches to Initial Teacher Education
View the document3. Some Methodological Issues
View the document4. Analysing Costs
Open this folder and view contents5. A Framework for Exploring Costs Before, During and After Training
View the document6. A Note on Organisational Patterns and Costs
View the document7. Concluding Remark
View the documentReferences
View the documentAppendix 1: Researchable Questions Related to Entry, Training Process, Outcomes and Deployment of New Teachers

4. Analysing Costs

There are two obvious ways to begin to explore costs and subsequently effectiveness. The first focuses on different types of costs (or more generally resource issues). The second seeks to unpack the training pathway to minimum competence for a publicly licensed teacher into three domains - before, during and after the core training experience. This section addresses the first focus.

First, some general observations. At a macro level the main cost drivers related to teacher training systems are self-evident and can be separated into recurrent salary and non-salary costs6 and into fixed and variable costs.

6 Capital costs fall outside the scope of this discussion. These are costs which should rightly be apportioned over the lifetime of physical assets i.e. predominantly buildings. It is problematic to analyse capital costs in the absence of knowledge of building stock, utilisation rates, and methods of financing capital expenditure which typically is separately treated in national accounts.

Recurrent salary costs arise from teaching faculty and support staff (which include non-teaching administrators and service personnel). The costs of training in full-time institutions will normally be most heavily influenced by salary costs which will typically account for between 50% and 90% of all recurrent costs per trainee in post-school training institutions. The distribution between teaching and non-teaching salary costs can vary over a wide range - it is possible to find institutions where non-teaching salary costs may exceed those of teaching salaries per trainee, especially where training is residential.

In principle it is easy to identify factors that will tend to increase salary costs and those which will reduce them. Low student-staff ratios (10:1 or less?) will inflate costs, as will a high proportion of non-teaching staff salaries (more than 25%?). Relatively high and growing lecturers' salaries (in relation to GDP/capita and other comparable groups of professionals) will increase costs unless coupled with higher levels of student-staff ratios. Younger average ages of college staff will reduce costs, high and increasing average seniority will inflate costs. School-based training, if it substitutes teachers' time for that of lecturers, may reduce average costs per trainee.

The main determinant of recurrent salary costs per student is the student-teacher ratio7 (STR). This can be expressed formally as follows.

7 Assuming non-teaching salaries are small in relation to teaching salaries - this may not be true in some systems.

Where Ns = number of students and Nt = number of teachers (lecturers).

Re-arranging we have Ns = STR x Nt

The salary cost per student for teaching staff (Cs) is represented by

Cost per Student

Where = the sum of all teachers (lectures) salaries

By substitution

If is approximately equal to the Average of all Teachers Salaries (AvTs) x Nt

then

This mathematical representation leads to the fairly obvious point that recurrent teaching costs per student rise with average teachers' salaries and fall as the STR increases.

However, the more precise relationships over time will depend on whether average and total salary bills change at rates different to the STR as a result of pay awards, incremental drift and differential retirement and recruitment rates at the top and the bottom end of the salary scales. On the margin the relationship between AvTs, and STs/Ns, may not remain constant if the mean and the median salaries do not coincide with the arithmetic average.

It might seem as simple as arguing that if AvTs is minimised and STR maximised in ways consistent with maintaining quality, the economic concern with cost efficiency would be satisfied. It is not quite that simple. What is delivered to students in the training curriculum will not only depend on salary costs per student. These have to be translated into staff contact hours with students and the work which surrounds these contact hours. Higher salary costs per student and lower student-staff ratios, can co-exist with low student contact hours depending on how work is organised. Lower salary costs per student and higher student-staff ratios can be achieved without necessarily diminishing student contact time.

The key point here is that the STR is a function of the number of teaching staff thought to be needed (Ts). This of course ultimately determines S Ts. Formally the relationships can be represented as follows.

and

It is now clear that what is delivered in terms of taught time (taught hours per week) for a particular cost, is a function of the number of students per teacher (STR), the amount of teaching associated with teaching posts and the average teaching group size.

Table 2a is suggestive of some possible relationships between variables. It shows that for Colleges with the same number of students and staff, which therefore have similar costs per student, different mixes of group size, student learning time and teaching loads are possible.

Table 2a: Four Different Patterns with Similar Costs

College

Number of Students

Number of Staff

Student-teacher Ratio

Cost per Student (Av Salary per Teacher 15000).

Average Teaching Group Size

Number of Student Teaching Periods per Week

Teaching Load in Periods per Week









1

1000

67

15

1000

30

10

5

2

1000

67

15

1000

15

20

20

3

1000

67

15

1000

45

30

10

4

1000

67

15

1000

30

30

15









Thus College 1 has low teaching loads and students experience relatively few periods a week in mid-sized groups. In College 2 teaching loads are high, students have more contact time and group sizes are small. In College 3 group sizes are large, students receive a lot of teaching but teaching loads are not high. In College 4 students receive a lot of teaching in mid sized groups with mid-level teaching loads for lecturers.

Table 2b shows possible effects of varying the College intake whilst maintaining the same number of staff.

Table 2b: Four Different Patterns with Different Enrolments and Similar Staffing

College

Number of Students

Number of Staff

Student-teacher Ratio

Cost per Student (Av Salary per Teacher 15000).

Average Teaching Group Size

Number of Student teaching Periods per Week

Teaching Load in Periods per Week









1

500

67

8

2000

15

10

5

2

1000

67

15

1000

15

20

20

3

1500

67

23

667

15

20

30

4

2000

67

30

500

15

15

30









In this case the costs per student vary as the student-teacher ratio varies. College 1 has high costs and low teaching loads and taught time. Colleges 2 and 3 deliver the same number of taught hours to similar size groups of students but College 3 does so at lower cost as a result of higher teaching loads. College 4 has the lowest costs but the highest teaching loads.

These two tables and further variations on them illustrate how the key parameters interact. Most importantly they highlight the fact that, though costs per student are determined by average salaries and student-teacher ratios, what is delivered to students is also a function of teaching group sizes, and teaching loads. High costs can co-exist with low levels of contact time for students.

The discussion above focuses on teaching salary recurrent costs per student and has general applicability. Total salary costs must include non-teaching salaries, which arise from a variety of widely differing practices and expectations about staffing related to teacher education institutions. These are more difficult to generalise about. The number of non-teaching staff may or may not be related to enrolments. Some categories - e.g. Director, Vice-principals, finance officer, hostel warden etc. may exist in every training institution independent of enrolment. Other posts may be related to enrolment - e.g. the number of laboratory assistants, caretakers, and security guards. If historic budgeting is used employees may continue to be employed whether or not there is a continuing need for their services. The most that can be said about this category of expenditure is that it almost certainly is desirable to establish norms related to enrolment based on what is thought to be necessary in effectively run institutions. If this generates costs which are a small proportion of the cost per student, then analysis is of secondary importance, assuming adequate checks and balances exist to ensure what is allocated is spent as intended. If non-teaching salaries are a large proportion of the cost per student, this invites scrutiny of whether such expenditure is essential to the main training mission.

Non-salary recurrent costs per student are also difficult to generalise about. Most costs will arise from expenditure on maintenance, equipment, consumable materials, travel and subsistence, food subsidies and hostel costs, and student stipends. All of these can be examined with a view to establishing whether what is spent needs to be spent to maintain the quality of the training programme. It is of interest to compare non-salary with salary costs, to establish the extent to which non-salary costs vary per student between institutions, and to establish whether non-salary costs are or could be shared in an appropriate way which was not damaging to quality or equity. This applies both to the costs of physical assets (which may be shared with other institutions or used as community resources) and to the direct costs of training (which may be partly supported through contributions from those who benefit).

As with non-teaching salary costs, if non-salary costs are a high proportion of per student expenditure they need careful examination. If they are a very small proportion this may also suggest that there is a problem in supporting basic infrastructure and providing conditions under which effective professional development may take place.

A complementary way of analysing costs is to separate out the component parts into fixed and variable elements. The latter will be sensitive to the number of students trained and will normally not be subject to marked economies of scale. Fixed costs, as a component of costs per student, should fall with increased volume. The distinction between fixed and variable costs is clear in principle but can be blurred in practice.

In brief, fixed costs usually include central administration and other common support costs, national programme development costs, and monitoring, quality assurance and accreditation systems. These cost are likely to be fixed within a range of student numbers, but may increase stepwise when thresholds are crossed. Thus within a wide band of enrolments a fixed size teacher education secretariat may be able to administer the services needed from the centre. In some cases some of these central costs will behave more like variable costs e.g. where the costs associated with periodic inspection multiply as the number of sites that need to be inspected increases.

Variable costs include staff costs associated with teaching, tutoring and mentoring, materials for students, the direct costs of assessment, school supervision visits, and student support costs for food, accommodation and clothing. Most of these will increase linearly with the number of students. There may be areas where there are economies of scale, e.g. in textbook production, which reduce the cost of a book as the volume of production increases.