Primary School Music Teaching

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Introduction

This article presents a statistical analysis of primary school music in Australia based on Irina Petrova's doctoral dissertation, published in 2012. It continues from the initial description of her work (Major Research into School Music Education) which was based on her own conclusions in two articles in Music Forum, dated November 2012 and February 2013 and dealing with primary and secondary schools, respectively. Secondary schools are the subject of Secondary School Music Teaching, the third and final article in this series.

Because one of the main challenges for this knowledge base is to assemble a comprehensive numerical picture of the music sector, the content here is primarily statistical, dealing in turn with the following topics:

  • Availability of Classroom Music
  • Teachers' Gender and Age
  • Teacher Qualifications
  • Teacher Confidence
  • Challenges
  • Meeting the Demands of Teaching.

The article takes a critical look at statistical quality, in particular in relation to the distribution across states and territories.

The table numbering starts with 2, as one table dealing with the responses to Petrova's two surveys, conducted in 2009, went into the initial article. The object is to maintain the continuity between the articles.

Classroom Music in Minority of Schools

Alt=Table 2
Alt=Table 3
Alt=Table 4
As noted, classroom music is offered in only 37% of primary schools in Australia according to the 2009 survey. The thesis does not appear to show how this varies across states and territories. The total number of primary and combined schools is known from official statistics, and Petrova provides detail for schools with classroom music. If we assume that the percentage of all primary schools reached was 81% in each state and territory, as in Australia as a whole, we gain the impression that above-average proportions of primary schools in Tasmania, Western Australia and Queensland have classroom music, with NSW about the average or slightly higher, and the rest of the states and the two territories below average proportions of classroom music. This can only be a rough indication, and should be supported with data that must have been collected when the survey was analysed.

Similar considerations apply to government, Catholic and independent schools discussed below. In total, the percentage of schools with classroom music seems to be similar between government and non-government schools (the published 2009 statistics from the Australian Bureau of Statistics did not distinguish Catholic from independent schools).[1]


Australian schools are classified into three groups.

Government schools operate under the direct responsibility of the relevant state or territory minister. Non-government schools are established and operate under conditions set by state or territory government regulatory authorities. They can be either Catholic or independent schools. The former are generally administered by Catholic education offices; independent schools comprise other non-Catholic, non-government schools.[2]

Tables 2 to 4 highlight an important difference between states, relating to NSW compared with the rest of Australia: 45% of classroom teachers in government schools in that state were generalists rather than specialist music teachers. The proportion as well as the absolute number of non-specialists is highest in NSW government schools, but 22% of primary music teachers in NSW Catholic schools were also non-specialists. The proportion was 36% for all primary schools surveyed in the state.

A minority of primary schools with any classroom music teaching employed more than one specialist music teacher. Only 2% of government schools did so, compared with 4% of Catholic schools, and 16% of independent schools.[3]

Teachers' Gender and Age

Alt=Table 5
Primary music teachers were identified for four age groups as well as gender.[4] The top of Table 5 shows the actual numbers surveyed in each of four age groups. Each age group had a preponderance of female teachers ranging for three age groups from about 82% to 86%. The 30-39 age group had relatively more males but females still accounted for three-quarters of the total sample in that age group. Women made up 82% of the total teaching staff surveyed.

Across the age groups, only 12.3% of females and 10.9% of males were in their 20s. There was a strong increase in the percentage towards the older age groups, with 37% of females being 50 and over. The distribution for males was probably similar; the higher proportion in the 30-39 group may be due to sampling error in a small sample — or it may have a real basis though it is unclear what that might be.

Irina Petrova made the point in her Music Forum article on primary school music teaching that a significant number of teachers have taught for more than 16 years. "This suggests a high level of music teaching experience in the profession. The older teachers were more educated in music compared to younger teachers; musical training of primary teachers was routine and much more extensive." (p 58)

Alt=Box 2
The risk, as she observes, is that these qualified and experienced teachers will leave the workforce without being replaced in sufficient numbers by teachers who have similar qualifications.

Her point is well made.[5] The box to the left compares the percentage distribution of age groups between 20 and 64 years which we estimate to be in the Australian workforce at a similar age range as teachers.[6] The difference between the fairly constant shares of around 25% for each age bracket in the total workforce, and the rise in the percentage from young to older age groups in the teacher sample, is quite dramatic. Some may be due to teachers joining the workforce later than the average worker, but this can't explain the difference.

Teacher Qualifications

Qualification or musical attainment is a central concept in Irina Petrova's thesis. She distinguishes between "high", "moderate" and "low" (including no) qualifications.[7] The measure of qualification is supplemented by whether the teacher had prior musical training and whether she or he took music while in secondary school, and for how long, and whether they were currently playing musical instruments or singing, and for how long.

Alt=Table 6

Table 6 shows actual number of observations to the left and percentage distributions across the three qualification levels to the right. Just under half of the total sample of primary school teachers (48.4%), were highly qualified in terms of the music education they had received, while 22.5% were moderately qualified, and the remaining 29.1% had low qualifications, or none.

Relatively more men than women were highly qualified to teach classroom music (65.2% as against 44.8%), and a smaller proportion had low or no qualifications to do so (23.9% compared with 30.2%).

The percentage of teachers with high qualifications tended to fall with age, though a high proportion of highly qualified persons in the 30-39 group may be at least partly associated with a biased sample of males (refer box comparing the sample with the total Australian workforce for each age group and sex).

Alt=Table 7
Table 7 shows the distribution by states and territories of primary school teachers' musical qualifications. Among the five mainland states represented by samples of 30 observations or more, Queensland was well ahead on highly qualified teachers (69%). In Victoria, South Australia and Western Australia, the proportion was around 57%, leaving NSW as the odd mainland state out with only 27% of primary school music teachers having achieved high musical attainment. In Tasmania, 10 of 19 teachers (53%) were highly qualified; in the ACT, of a sample of six only, 50%.

Conversely, of the five mainland states, NSW had the highest proportion of primary music teachers with low or no musical attainment (49%), and in South Australia, despite its relatively high proportion of highly qualified teachers, the proportion was 40%. No explanation has been found for the polarised distribution in South Australia.[8] Victoria also had a relatively high percentage of teachers with low musical attainment (25%). The two remaining mainland states, Queensland and Western Australia, both had about 13% in the "low" category, and in Tasmania only one of the small sample of 19 respondents (5%).

Alt=Table 8
In independent primary schools, as would probably be expected, 65% of music teachers were highly qualified — but even here 11% fell in the low category. In government and Catholic schools, the percentages were roughly similar with the "high" category among Catholic schools having a small lead (47% compared with 44%). The "low" group was represented by about one-third of music teachers in either group.

Prior Exposure to Music

Alt=Table 9
Seven out of eight of primary music teachers in the sample had undertaken musical training before they began their formal teacher training (Table 9). This included 94% of those with high musical attainment based on their educational achievements, every one of those with moderate, and two-thirds of those with low qualifications (or none)[9]

Whether music was chosen as a subject when these teachers went to secondary school is an additional indicator of past musical exposure. Table 10 was derived from a more detailed presentation in Petrova's thesis (p 257).

To put these figures into perspective, the reader is reminded that 48.4% of respondents had high, 22.5% moderate, and 29.1% low musical qualifications (Table 6). Perhaps surprisingly, 21% of those with high music attainment had not taken music in secondary school — the same proportion as in the total sample. This compared with only 10% of those with moderate qualifications not choosing music as a secondary school subject (and 31% of those with low attainment, which is less surprising — as well as being roughly comparable with the 33% in Table 9 who didn't undertake musical training prior to their teacher training).[10]

Alt=Table 10

Those who did undertake music as a subject in secondary school were classified into four groups: those who did every year from 7 to 12, Year 12 only, two years or more including Year 12, and one year or more excluding Year 12. This seemed to be the best indicator of any intentions to choose music as a teaching career:

  • 28% of all those achieving high musical attainment (including those who didn't do music in secondary school) studied music in every school year, compared with 21% of the moderate and 11% of the low group
  • About 9% of the two top groups studied music in Year 12 only (indicating awakening career ambitions?), compared with only 3% of teachers with low musical attainment
  • A few teachers with high qualifications (5%) had done two to five years (not all six years) of secondary school music including Year 12, compared with 14% of the moderate category and one sole member (1%) of the bottom category
  • The largest group for all three musical attainment categories was made up of those who had studied secondary school music for one year or more excluding Year 12 — but the percentage grew steadily as the level of teacher qualification declined (high 38%, moderate 47%, low 55%)
  • The mirror image of the "no secondary school music undertaken" is the percentage of those who did. It was highest for the moderate group (90%) followed by the high group (79%) and the low group (69%). There may be good reasons for this somewhat unexpected result but none has been identified as yet.

Musical Performers

Alt=Table 11
A huge majority of primary school teachers played an instrument or performed as singers (Table 11). Furthermore, of the very few who didn't play an instrument, four teachers responding to the survey sang solo or in choirs, or both. Taking these into account (see footnote in Table 11), the number of non-performers declined to only 18 of the total sample of 258 (7%). Only one member of either of the high and moderate musical attainment groups did not perform music — 99% of each group did. The ratio for the least qualified group was 79%, including the two teachers who performed vocally only.

Petrova's detailed tables (10.10 to 10.14, pp 260-264) showed in summary:

  • Keyboard was the most commonly mentioned group (75% of all those who played an instrument). All but 14 of the 193 players (93%) played the piano as either the only keyboard instrument or in combination with other instruments such as (mentioned in decreasing frequency) electronic keyboard, organ and harpsichord (Petrova Table 10.10).
  • 140 (54%) played one or more string instruments. Guitars (various types but not all specified) were played by 125 (89%) either as only instrument or one of two or more string instruments. Violin was a distant second, played by 21 (15% of those playing any string instrument) (Table 10.11).
  • 132 teachers or just over half (51%) played one or more brass/woodwind instruments. The most commonly mentioned were flute, clarinet, recorder, trumpet, and saxophone. The following were played as only instrument or in conjunction with other brass and woodwind instruments: flute by 49 (37% of those playing any of these instruments), clarinet by 46 (35%), recorder by 26 (20%), trumpet by 25 (19%), and saxophone by 19 (14%). Although this group is more diverse than the previous ones, only nine (7%) played other brass and woodwind but not any of the five main ones. They included bassoon, didjeridu, french horn, Irish whistler, oboe (2), trombone (2), and tuba (Table 10.12).
  • A minority of 14% played percussion (35 observations). This group was highly diversified. What is assumed to be conventional drums and drum kits were mentioned by an estimated 13 (37%), djembe and other African drums by eight (23%). The two groups didn't overlap — it was either "conventional" or "African" (Table 10.13).
  • The number of teachers performing as vocalists was second only to the number of keyboard players (183, 71% of those surveyed).
    Alt=Table 12
    They can be divided into three groups: 104 singing in choirs only (57%), 20 singing solo only (11%), and 59 performing in choirs as well as solo (32%).

The vast majority of teachers had played their major musical instrument, or sung, for more than five years (Table 12). This was particularly the case for those with high or moderate qualifications, but 64% of the bottom group also stated that they had played their major instrument for more than five years.

Teacher Confidence

Alt=Table 13
Alt=Table 14
Alt=Table 15
One of Irina Petrova's main themes is the crucial link between a music teacher's qualifications and his or her confidence in delivering to the students. Table 13 shows the connection that was identified through the survey of primary school teachers. Only 3% of the highly qualified primary school teachers did not feel confident when teaching, compared with 6% of moderately qualified teachers and 23% of those with low or non-existing musical attainment — plus another 4% who felt unsure or didn't answer the question.

The general degree of confidence across gender and age groups does not appear low, at least on paper (Table 14). This could be partly due to the survey approach including the fact that teachers were asked to fill in a mail survey with their self-assessed expression of whether or not they felt confident about their teaching. Males appear, for what it is worth, to be more confident about their music teaching than females. Likewise, teachers in the oldest age group (50+) assess themselves as generally more confident than the younger age groups. However, the proportion of any group feeling confident never falls below 86% of the total in Table 14.

According to Table 15, confidence improves with experience at least in the second five-year period of music teaching. The table focuses on teachers with low qualifications and shows how confidence is particularly low among new teachers (one to five years of experience). It then increases to a peak among the small number of teachers with six to 10 years' experience but deteriorates thereafter. Among teachers with 16 years or longer experience, 22% were still not confident.

Irina Petrova reports that many teachers added concerns to the formal survey response that affected their confidence (pp 270). Factors that deterred their confidence included (brackets show number of observations):

  • Experience in teaching classroom music (63)
  • Training in music during per-service (44)
  • In-service training (21)
  • Support from principals and music specialists; support at start of teaching (17)
  • Knowledge of the subject (14)
  • Passion for music (10)
  • Ability to play musical instrument (9)
  • Understanding the value of music for child development (5)

A group of 19 non-confident teachers (p 271) mentioned factors such as not having any training, not playing an instrument, lack of qualifications in music, limited knowledge of music, lacking support, lacking resources, and that their training as teachers did not cover teaching methods — hardly statistically significant but the sort of supplementary material that any good survey should be alert about.

Challenges

Alt=Table 16
Primary schools devote between 30 and 120 minutes per week to music lessons (Table 16), apart from a few without regular music lessons. The average period was 53.5 minutes but the median period (middle observation) across all schools was only 43.5 minutes because the average was boosted by some schools who devoted considerably more time to music than the typical school — especially in government schools of which 11.5% devoted two hours a week to music. Average and median periods were roughly similar in government and independent schools but lower in Catholic schools, of which only 4% provided more than an hour per week. The time devoted to music in primary schools is part of the challenge facing teachers — how to fit in the best teaching program in the limited time available.

The survey form contains 13 questions (most requesting ratings for several items as in Charts 1 and 2 below, where the items are teaching tasks), to which the teachers were asked to indicate their response on a scale from 1 to 7. The scale above each set of questions in the form was marked "1: not very much; 4: not sure; 7: a lot". A score of 4 is considered the midpoint between positive and negative response.

Alt=Chart 1
Chart 1 paints a clear picture of how challenging teachers found seven defined teaching tasks, depending on their qualifications or level of musical attainment. In all cases, highly qualified teachers found these tasks less challenging than their moderately qualified colleagues, while teachers with low musical qualifications (or none) found each task more challenging than the two other groups.

The other dimension on Chart 1 depicts the similarity with which the seven tasks ranked by their average extent of challenge is reflected by each of the three qualification levels — ranging from "planning music lessons" and "teaching listening" at the least challenging end to "teaching organising sound" at the higher end.[11] For highly qualified teachers, the average challenge score ranged from a low 2.46 for "planning music lessons" to 3.60 for "teaching organising sound", which is not very far below the midpoint "not sure" level.[12]

Alt=Chart 2
At the other end of the qualification range, no average was less than 3; the tasks of "performance suggestions", "listening suggestions" and "evaluating progress" came fairly close to the "not sure" level of 4 and the gap widened between the "high" green and "low" red bars in Chart 3; and the average for "teaching organising sound/composing" went beyond the "not sure" midpoint of 4.

This is a good example of how strong the message of the Petrova thesis can be.

Teachers of different age groups appeared to find some tasks more challenging as they age, but not all tasks (Chart 2). For the planning of music lessons, which was the least challenging task in the overall analysis, there was probably little challenge which could be related to age (given the inherent sampling error). The same probably applies to performance and listening suggestions. The oldest age group of 50+, which like the 40-49 group is larger than the younger age groups, seems to be relatively highly challenged on teaching listening, and perhaps evaluating progress. The most consistently age-related challenge ratings, however, were for teaching performing and teaching organising sound/composing, both showing a continued increase from young to old.

Meeting the Demands of Teaching


Alt=Table 17


The primary music teachers were asked how adequate they felt their pre-service training had been in the tertiary teaching institutions they attended. Given that the midpoint of 4 divides the adequacy scale between largely favourable and largely unfavourable (with a score of 1 meaning quite inadequate), there was a clear difference between teachers in terms of musical qualifications. The "high" group rated 4.37 on average, which is not tremendous when the maximum possible score is 7 but compared favourably with the average for the "moderate" group (3.00) and especially with the group of least qualified teachers (2.48, tending towards "quite inadequate").[13]

By age group, both groups under 40 showed average scores above 4, and the two older groups showed much lower averages (3.16 and 3.31, respectively). Male music teachers (average score 4.32) were significantly more positive than female teachers (3.37). Males were also better educated as music teachers (Table 6).[14]

Alt=Table 18


In contrast to pre-service teacher training, all groups were dissatisfied with the adequacy of their in-service training. Teachers with high musical attainment showed an average adequacy score of 3.38, a full point below the 4.37 for pre-service training. The adequacy scores for those with moderate and low qualifications both averaged around 2.8, which indicates considerable dissatisfaction.

Professional development (PD) workshops rated better among primary music teachers. As many as 87% had attended such workshops though the percentage was lower for teachers with low or no formal qualifications in music. These workshops were generally rated as beneficial (average score around 5 on a 7-point scale for five criteria)., but even those in the low group returned average scores between 3.90 and 4.54, generally above the midpoint of 4.[15]

The four age groups showed average scores ranging from 2.87 to 3.36, and the average was similar for women and men (3.10).

Alt=Chart 3
Alt=Chart 4
Alt=Chart 5
Alt=Chart 6
The final presentation consists of two sets of charts, based on a score of sufficiency using the usual seven-point scale (insufficient = 1). The first set deals with staff resources, the second with teaching resources. Each set starts with a distribution by the five mainland states, followed by a chart showing type of school (government, Catholic, independent).

Chart 3 shows the average sufficiency score of each of five staff and related resources (teaching staff, time allocated in the timetable, support staff, specialist staff, and available facilities). For Australia as a whole, the average score was best for facilities (4.47), time in timetable (4.39), and teaching staff (4.26) — all above 4 as distinct from specialist staff (3.87) and support staff (3.69).[16] The pattern, however, differed considerably among these states.[17] Chart 3 shows that Western Australia led the field on three of the five staff and related resources, Victoria on one, and Queensland on one. Victoria and Queensland clocked in as number 2 on two of the resources, South Australia on one. Third position went to Western Australia and Victoria (twice each), and Queensland. South Australia scored three number four positions, Queensland one and NSW one. NSW came in last on four criteria, South Australia on one.

We can make a crude ranking of this, giving first position five points, going down to one point for last position. The maximum total score is 25 and the minimum 5. Western Australia on this crude ranking model scores 21 points, Victoria 19, and Queensland 18 — observations that may be too close to declare an outright "winner" among the three in view of the rough and ready ranking model. Clearly, however, South Australia lags behind with 11 points, and so even more does NSW with six, only one point above the minimum.

The primary music teacher survey revealed mainly minor differences in respect of perceived sufficiency of teaching resources, between government, Catholic and independent schools (Chart 4). The only sizeable difference among schools related to specialists, led by independent schools with an average of 4.35 compared with 3.76 and 3.78, respectively, for government and Catholic schools. Independent schools may have a slight edge on the four other criteria as well, but it is quite small and probably not statistically significant.

The distribution of mainland states in Chart 5 shows that the least adequate teaching resources in Australian primary schools are computer software, video recordings, and electronic instruments (scores less than 3). They are better served with audio recordings, though only two states, Western Australia and Victoria, achieved average scores above 4. The most sufficient resources are traditional instruments (all states scoring 4 and above) and books and other written resources (all above 4 except NSW).

The pattern of mainland states is extraordinary in one respect: Western Australia has the highest scores for all six resource types, whether or not they are generally considered inadequate as for software, videos and electronic instruments.

Doing a crude ranking as for Chart 3, Western Australia scores the maximum 30 points (all six types of resources scored the maximum of five each). Victoria, with four second places, a third and a fourth, scores 21, and Queensland (two seconds, two thirds, a fourth and a fifth) scores 17. South Australia with three third places, two fourth places and a fifth, scores 14, and NSW, with two fourth places and four fifth and last places, gets 8.[18]

Finally, Chart 6 showing teaching resources for each type of primary school did not uncover any significant differences, except possibly that video recordings and electronic instruments seem to be considered a little more adequately resourced in independent schools than in government and Catholic schools.

Conclusions

It is recommended that you peruse Major Research into School Music Education, as a reminder of Irina Petrova's own conclusions as she expressed them in Music Forum. One of her recommendations was to work quickly to address issues in time to influence the current discussion of the School National Curriculum and other public debates as effectively as possible.

The basic problem is that the majority of primary schools in Australia (63%) do not receive classroom music teaching. Irina Petrova's point which is amply supported by her thesis is that inadequate primary teacher training impacts on the quality of secondary school music education because many students enter secondary ill-equipped for further education in music. In primary schools the lack of quality is exacerbated because music teachers with inadequate music skills are more likely to lack confidence to teach students. Unsatisfactory in-service training and other factors do not improve the situation.

The analysis of Petrova's research in this series of knowledge base papers supports her conclusions and we hope at the same time makes them more accessible beyond academia. It is important to expose these issues to a wider public, and the knowledge base is designed to do just that.

There is a host of issues to overcome to revive the quality of primary school music teaching. They include:

  • Making classroom music more available, ultimately to all primary schools in Australia — a conclusion that has now been reinforced by "Creative Australia" putting music and the other creative skills firmly into the national curriculum.
  • Improving the qualifications to high standards for all primary school music teachers, in all states and territories. Currently, Queensland has the highest proportion of highly qualified teachers according to the survey (69%), and NSW the lowest (27%). The proportion in Victoria, South Australia and Western Australia was about 57%, and in Tasmania 53% (small sample of 19).
  • Improving the qualifications and standards in all primary schools: government, Catholic, and independent. The differences were not as great between these schools as might have been expected, according to the survey.
  • Boosting the confidence of teachers to deliver quality classroom teaching in primary schools — basically through improving their competence and qualifications
  • Overcoming specific problems such as the provision of qualified music teachers in NSW, currently lagging behind other states, especially Western Australia, Victoria and Queensland
  • Also overcoming issues associated with lack of understanding among school principals and policy makers of the role of music (and arts generally) in primary school education.[19]

The paper on Secondary School Music Teaching follows with more general conclusions.

Author

Hans Hoegh-Guldberg. Entered on knowledge base 9 March 2013.

References

  1. It would be useful to have information on the absolute number of primary schools reached by Petrova in each category in each state and territory, as this is an important indicator of differences between types of schools and across Australia.
  2. The source of this description is Australian Bureau of Statistics, Australian Social Trends, 2006, ABS cat 4102.0.
  3. Catholic schools may be more diverse than the other categories, ranging from a large number of local schools to schools that cater for similar markets as the major independent schools.
  4. The survey form, on which the rest of this article is based, is reproduced in Irina Petrova's thesis (pp 1114-1121). It has five parts: A: About you. B: About your teaching. C: Your pre-service training. D: Your in-service music training and support of music advisers/consultants. E: About your school.
  5. Petrova's observation would be influenced by her extensive general research as well as the surveys. However, we note from Table 6 in the next section that the level of formal qualifications was highest among 30-39 year olds and also somewhat higher in the 20-29 group than among people aged 40 and over. But there were also relatively many males in the 30-39 group (which may be attributed to sampling error as discussed above) and males according to Table 6 included a higher proportion of highly qualified persons. In a complex situation, Petrona's warning remains relevant.
  6. The estimate is made from total population statistics and estimated workforce participation rates, and assumes the teaching workforce falls exclusively or almost so into those age brackets.
  7. Musical qualification or level of attainment is defined in the 2012 thesis, pp 247-248, as follows: High: Musical Degree or Diploma, Bachelor’s Degree with a music specialty, Master’s Degree in Music or Music Education. Moderate: Bachelor’s Degree with no music but supplemented by Grade 5 or higher in musical instrument playing, or completion of a Diploma of Associate in Music in Australia. Low: Bachelor’s Degree with no music and Grade 4 or lower in musical instrument playing, or no formal music education.
  8. "Although teachers with a high level of music education dominated in Victoria and South Australia, there was also a large percentage of teachers who achieved a low level of musical attainment or none at all." (Petrova, p 425). We don't know whether the explanation has to do with city versus country, age of teachers, type of school, or something else. We would like to know more, and invite any reader to communicate.
  9. This suggests that "none" comprised one-third of the "low" group, and that the remaining two-thirds did not get through formal training beyond Grade 4 of the 8-grade system needed to qualify for entry to higher study at tertiary level.
  10. However, Table 9 showed that every member of the moderate group had undertaken musical training before their teacher training course. Maybe these people were motivated differently from those who trained more intensively to become music teachers, perhaps by pursuing a career or hobby as popular musicians? Again, there is more to this complex subject than meets the eye through statistical samples.
  11. Chart 1 abbreviates some of the original descriptions, including "teaching organising sound/composing".
  12. Petrova's tables also include a standard measure of consistency: the variance which is defined as the average of the squared differences from the mean, where the latter is the expected value shown as the average on Chart 1 and similar graphs. The magnitude of the variance indicates the degree of agreement or disagreement among respondents. For "teaching performing", to take an example, there was an inverse relationship between average score (increasing to indicate greater challenge) and the variance: high average 2.96, variance 3.38; moderate average 3.25, variance 3.19; low average 3.56, variance 2.36. In other words, there was more agreement among the "low" group that the challenge was significant, than there was among the "high" group that the challenge was less significant. The pattern across Petrova's Table 10.20, however, is not consistent and can be hard to interpret. This also applies to many of her other tables, but we have explored each for any significant patterns. In the interest of simplifying the presentation, the references to variance are shown in footnotes, and only those findings that I found provided additional insights into the statistics have been quoted.
  13. The associated variance measure also showed a consistent pattern: "high" group 3.88, "moderate" group 3.02, and "low" group 2.25. In other words, the spread of responses was far wider in the "high" group, whereas the "low" group was in much more agreement about their adequacy ratings. To illustrate, the vast bulk of the "high" group may have rated the adequacy of pre-service training between, say 7 and 2, whereas few if any in the "low" group might have voted above 4.
  14. Men were also more in agreement about the adequacy of their training. The variance for males was 3.02, compared with 3.97 for females (Petrova Table 10.34). In contrast, there was no consistent variance pattern across the four age groups (Petrova Table 10.33).
  15. Petrova Table 10.92, p 295).
  16. The overall variance pattern for these resources varied from 5.21 for support staff, 4.88 for specialist resources, 4.37 for teaching staff, 4.30 for time in timetable, to 3.89 for facilities. It was difficult to detect any consistent patterns in the individual states. The variances in the total sample were higher than for the teaching resources in the second set of charts: audio equipment 4.16, traditional instruments 3.46, computer software 3.43, books and written resources 3.30, electronic instruments 3.23, and video equipment 3.06 — indicating greater agreement among teachers on these resources than on teaching and related resources.
  17. If Tasmania had been included in Chart 3, it would have ranked fourth or fifth on all scores. However, there were only 19 Tasmanian primary schools in the sample.
  18. Tasmania, if it had been included regardless of its sample of only 19 teachers, would have ranked about as well as Queensland, that is, much better than for staff resources where it would have achieved only fourth and last places.
  19. The high refusal rate that Petrova met when presenting her survey should serve as an indictment to the school community. Petrova was attempting to create a major piece of original research into a neglected area and this rate of non-cooperation should be cited as a major example of how efforts have been damaged to expand essential knowledge in the interest of genuine community progress.
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