Suppose that, in the self-reporting of time expenditure by teachers, the link between hours
reported and time expected on task is given by the following equation 4.1:
where, d = day of the week, i = teacher, = reported hours in a day, and = expected
hours in a day, and is a random error term that is assumed to be well-behaved such that
≥ 0, for ≥ 0. Within the context of the teacher’s thumbprint, this equation is equivalent to the following sentiment: “Today was my busiest day. I worked all day – 10 hours non- stop”. So = 10, but according to the Department of Education in Tasmania, teachers are expected to allocate 7.5 hours per day. Thus, = 7.5. This is the contractual time as defined,
for example, by Drago et al., (1999).
Now; a different time measurement then surfaces when teachers are asked to complete time
diaries. This measurement is the diary hours reported for any selected day of the teaching
week and is expressed as equation 4.2:
where = recorded diary hours in a day, and = reported hours in a day (as defined
earlier in equation [4.1]), and is a random error term for equation 4.2, bearing the same
assumption as in equation 4.1.
Again, in the context of the teacher’s thumbprint the sentiment is: “Today was my busiest day, I worked all day – 10 hours non-stop. Now that I have actually completed my diary entry for the day, it turns out that I have done 12 hours of work”. In this case, =10, =12, and the expectation of working a 7.5 hour day still holds: so, = 7.5. This expectation, although
allude to the fact that these times are generally measured with error. From the values of
the time recorded in teacher’s diary for each working week (Monday to Friday) can be obtained from equation 4.3
∑ ∑ ∑
where, = total time expenditure for days Monday to Friday. This equation simplifies to
∑ ∑
∑ by substituting the expression for equation [4.1], and can be expressed in the form shown in equation 4.4:
∑
This equation simply relates the total time recorded by diary entries to the expected time in
schools. The error structure is fairly complex since it is a summation of errors from other
structural equations, as well as errors peculiar to equation 4.4. For the sake of simplifying the
analysis, it is assumed that is also well-behaved, and that the errors and
will be contemporaneous (for example, Zellner, 1962; Nelson & Olson, 1978;
Dougherty, 1992; Greene, 1993; Griffiths et al., 1993; Niemi, 1993; Cameron & Trivedi,
1998).
How is equation 4.4 placed in the context of the teacher’s thumbprint? Since equation 4.4
gives the cumulative hours expended over a typical teaching week, then this equation
captures the following sentiment: “Thank God, it’s Friday – that was another big week”. It is important here to impose the restriction that: , where E is the constant E=7.5 hours that the Department of Education expects. This restriction is crucial because it allows
This is particularly important given that there are part-time and fulltime teachers, as well as
casual or relief teachers, in school systems and in the sample data analysed in thesis.
It is clear from the literature and the conceptual framework that teachers’ work extends to the weekends. In that regard, time allocation on Saturday can be thought of as some proportion of
time that has been allocation for Monday through Friday. Hence, it is prudent to argue that
Similarly, is expected that the time spent on Sunday will depend on how much time has been
spent on Saturday, as well how much time was spent during the teaching week Monday to
Friday. Hence it is also clear that Sunday times can be expressed as:
In this equation the Sunday working hours for an individual teacher are represented by .
The parameters and measure the time allocated to Sunday work as a fraction
(proportion) if time allocated to the teaching week, and Saturday, respectively. Therefore,
represents Saturday-Sunday teacher hours. Therefore the weekend hours are now
The total number of reported hours, in diary data, for the entire week are then represented as
, in equation 4.8 below:
Through a series of substitutions it is shown that an estimate of the weekly hours expended
on all activities can be represented by the following equation:
At this juncture in explaining the equation structure it is important to go back to equation 4.1
and to recall that equation 4.1 shows how the reported time may differ from what is expected
in terms of work time commitments. Unfortunately, the expression as presented in equation
4.1 does not include the interrelatedness between time-use in various days. This was a
deliberate omission earlier and designed to allow the reader to easily connect the next set of
equations to the ones derived earlier. Ideally, equation 4.1 should reflect the cumulative effect
of time-use. This creates a very complex equation structure which nonetheless needs
specifying in a form similar to that of equation 4.9.
Each of the terms on the right hand side of ∑ is dependent on a host of factors that are peculiar to the teacher (X), the school (Z), the classroom (C), the day
of the week (D), and some policy and school reform variables (SR). In expanded form,
equation 4.9 will look like this [equation 4.10]:
However, as pointed out each of the seven terms of time allocation is dependent on a host of
factors, X, Z, C, D and SR. So, ideally,
∑
In the thesis each of the daily time allocation equations is estimated, using a suite of
techniques. In using these equations, there is need to focus on the teacher as a unit of analysis
(see argument in Chapter 3, and then Section 4.3), and then show variables required for
estimating a teacher’s time-use (Section 4.4), mention and identify a suite of techniques that are good candidates for estimating time use (Section 4.5), present the estimable/estimating