![]() ![]() ![]() ![]() |
|
|
|
|
NSW |
VIC |
QLD |
WA |
SA |
TAS |
ACT |
NT |
(AUS) |
|
1995 |
18.9 |
11.4 |
12.6 |
12.6 |
11.8 |
4.6 |
12.2 |
5.8 |
(14.1) |
|
2004 |
15.0 |
12.6 |
8.4 |
8.2 |
9.1 |
5.5 |
11.9 |
3.2 |
(11.7) |
Intermediate mathematics students, as a percentage of Year 12
|
|
NSW |
VIC |
QLD |
WA |
SA |
TAS |
ACT |
NT |
(AUS) |
|
1995 |
30.0 |
24.4 |
33.7 |
18.8 |
23.6 |
15.3 |
27.6 |
9.7 |
(27.2) |
|
2004 |
20.1 |
24.2 |
31.7 |
13.4 |
16.0 |
14.3 |
28.0 |
9.9 |
(22.6) |
Source: Australian Academy of Science, Mathematics and Statistics: Critical Skills for Australia's Future: The National Strategic Review of Mathematical Sciences Research in Australia, December 2006, p. 54.
Year 12 Mathematics Students in Australia 1995-2006

Source: Professor Hyam Rubinstein and Jan Thomas, National Numeracy Review – Draft Submission, AMSI, 18 July 2007, Attachment 1 p. 12.
5.35 There are various reasons for the decline in mathematics enrolments: poor career advice, a plethora of subject choice, inadequate maths options, and the need to maximise university entrance scores. One witness estimated that only 64 per cent of secondary schools were actually in a position to offer the most advanced Year 12 mathematics subjects.
The decline in the number of students taking advanced and intermediate level courses at Year 12 shows that many students are not equipped with the mathematics they need for further study.[21]
5.36 Inadequate teaching in the early years of secondary school prevents some students from attaining their full potential in mathematics. This means that students disengage from mathematics because their experiences are disappointing.
5.37 Another factor is often a disincentive to study the subject at the highest level because it is not required by the university in the course which the student is aiming to enter following matriculation. The committee regards this policy on the part of university faculties of engineering and science to be perverse, but it is explained by the competition that exists between universities for engineering and science enrolments. Academics and teachers alike told the committee that universities must share a significant part of the blame for the demise of school mathematics.
A particularly damaging action by the universities has been to remove the higher-level high school mathematics courses [Maths C in Queensland] from the list of prerequisites especially in engineering...This was done mainly because maintaining student numbers is central to the very survival of university faculties and lowering prerequisites is one way to get more students...With the removal of Maths C as a prerequisite subject for any university subject, there was no longer any compelling reason for students to do this subject in the schools and the numbers dropped rapidly.[22]
5.38 The Australian Mathematical Sciences Institute agreed:
If universities drop pre-requisites as they have done universally, and accept students into engineering who have not even studied calculus, who can blame schools for dropping advanced courses and permitting their students to hunt for TER points by taking soft options? Failure to reward students for taking more advanced subjects in TER calculations often exacerbates this.[23]
5.39 The committee believes that this is likely to have a serious effect on quality teaching over time. Universities are taking a very short-sighted view of their responsibility to achieve the highest standards. This is one instance where market forces are having an adverse effect on both efficiency and quality.
5.40 In the committee's view, the elimination of university course prerequisites, coupled with students' concern to maximise their university entry scores, has substantially contributed to the weakening of senior school mathematics. The effects on university courses must also be considerable, with a great deal of remedial work required to be done, and possibly the elimination of some of the more challenging material that was once offered in the first two years of the degree.
5.41 Some would respond by arguing that there is only a very small need for pure mathematics courses, and senior secondary schools need to cater for the majority rather than the minority. The committee notes that the anecdotal and unequivocal evidence presented from academics was that there is a high-end need, which is not being satisfied. As the committee heard:
During the period 1987-96, we saw a significant reduction in the preparation of our undergraduate students to undertake a science or engineering degree. This occurred despite a progressive increase in our TER cut-off scores during that period.[24]
We are seeing a substantial reduction in the mathematical ability of students entering universities relative to a decade ago, and that this weakness has implications both to the individuals betrayed by the education system and to the development of Australia’s scientific capabilities.[25]
5.42 It is vital that Australian students' mathematical needs are met. While there is no benchmark testing to support Professor Stephen Kessell and Dr Richard Rowe's comments, the committee notes the Trends in International Mathematics and Science Study (TIMSS) results in lower levels of schooling, and the evidence that students do not always undertake further mathematics, much less pure mathematics studies in senior school. On balance, the committee believes that there is a serious problem with senior school standards in mathematics. Part of the problem is the curriculum.
5.43 The Australian Mathematical Sciences' Institute (AMSI) submitted that senior school mathematics courses vary significantly across the country. It found that the mathematical content and assessment variations were so wide that no two Year 12 courses could be described as equivalent.[26] According to the International Centre of Excellence for Education in Mathematics (ICEEM), the current content and assessment differences stem from separate perceptions of the mathematical topics and skills developed by the various boards of studies. The differences that have developed are striking and cannot be explained by the geographical location of the states and territories.[27]
5.44 This was contrary to the views expressed in the Year 12 Report. That report concluded that there was very high consistency in the 27 tertiary level mathematics courses: approximately 90 per cent consistency in high level (pure) mathematics and about 75 per cent consistency in social mathematics or mathematics for living (applied mathematics).
5.45 AMSI argued that the Year 12 Report did not include any contribution from academics who dealt with first year undergraduate students, nor data collected by the ICEEM. ICEEM described various jurisdictions as having considerable deficiencies in their senior curricula but admired the outstanding New South Wales curriculum, whose four-unit mathematics course was the best in the country, being both demanding and of extremely high quality.
5.46 The Australian Association of Mathematics Teachers (AAMT) also had concerns about mathematics curricula and standards in senior secondary school, though probably from a quite different perspective, being less concerned with standards and more concerned with whether it meets the needs of average students:
Standards at this level should include more than content standards, in particular, employability skills, meta-cognitive skills, skills in application and transference of mathematics to problem-solving and real-life contexts, including in the workplace.[28]
5.47 The committee finds the discrepancy between information provided in the Year 12 Report and by AMSI interesting. It suggests that the difference may lie in the fact that the apparent degree of commonality in maths curricula across states is based on a reading of the documents alone. The AMSI information puts emphasis on assessment. As the committee makes clear elsewhere in this report, what is set down in a curriculum document may not necessarily be taught, and if it is the assessment results may vary significantly, depending on the degree of difficulty in tests.
5.48 There appear to be clear differences of opinion between educators in the field of mathematics in regard to curriculum philosophy. Some flavour of it is picked up in the Hansard transcripts for this inquiry. This should not be a matter of any concern: rather, it is a measure of the intellectual engagement in the profession. But there are real concerns. It is also clear that there appears to be a lack of consultation within universities regarding mathematics knowledge needed by trainee teachers. There is also a concern that collaboration between universities and state curriculum agencies, which was so strong and productive in the past, may now be weakening. As one academic noted in regard to the English curriculum:
Curriculum councils and their counterparts in other states, who would not be known to a single bureaucrat in the Department of Education because they do their own thing and interact with their own little clique, see university input as the dean of the faculty of education from four or five universities, full stop.[29]
5.49 These problems should be relatively easy to fix with the application of some firm leadership and goodwill. The committee encourages a more serious climate of co-operation in the common interest of mathematics teaching and learning. There are some encouraging signs that this need is recognised. As Professor Margaret Britz of Queensland University of Technology told the committee:
It is time to stop pretending and it is time to actually look at the interface between the secondary education system and the tertiary system in a very complex matrix which varies across each State.[30]
5.50 And later:
Closer links between the tertiary and secondary sectors, and a concurrent review of what universities can deliver, and how, is needed in the short-term while the issues of curriculum design across the primary and secondary sectors are in focus.[31]
5.51 The Year 12 Report found that physics and chemistry curricula have a very high degree of national consistency, estimated at 85 per cent and 95 per cent, respectively. Unlike mathematics, science appears to be relatively untouched by any standards debate.[32] However, there was evidence provided to the committee about the decline in science enrolments. It suggests that weaknesses in both teaching and in the curriculum are disengaging students in the middle to senior school years.
5.52 According to Megan Motto of the Association of Consulting Engineers Australia:
Learning about science is a matter of experiencing its effects, doing rather than reading and listening. Encouraging science, engineering and technology (SET) skills at a young age in primary school provides the impetus for interest in the enabling sciences. For most secondary school students science involves learning facts for an exam, remembering formulae, plugging the right number in to get the correct answer, and the need to perform some short experiments that hopefully produce the result required by the teacher. Many, if not most, students who spend four or six years going through this system become both somewhat naive and disenchanted about the role and process of science.[33]
5.53 Professor Bray also told the committee that the experiential nature of science requires the kind of teacher who is 'a little bit out there' and who loves the discipline: many students are attracted to science when they pick up on a teacher's passion for the discipline. For Ms Motto, this clearly involved an element of quality teaching:
If you are not fully conversant with your subject area, you are very unlikely to teach it with confidence, much less passion and enthusiasm. This is what translates into students liking the subjects, therefore trying in the subjects and wanting to go further in those subject areas.[34]
5.54 Science qualifications, as in other specialist discipline areas, were another relevant factor in the quality of science teaching. The committee noted statistics quoted from a recent study conducted by the Australian Council of Deans of Science that:
5.55 If boring curricula and uninspired, unqualified teaching are turning students off the study of the enabling sciences, the committee is alarmed. Not only will students fail to realise all available study opportunities, it would also endow them with a weak foundation for further education, training and employment in scientific areas. This could be remedied at university, as it is with mathematics, but the committee's comments applying there apply equally here.[36]
5.56 The committee notes that while senior school science enrolments were said to be in decline, there does not appear to be a crisis of the same magnitude as in mathematics. This was certainly apparent in the smaller number of submissions. Nonetheless, the issues were remarkably similar, with minor variations.[37]
5.57 Dr Rowe and his colleagues from James Cook University put forward a case for 'competence' in the enabling sciences in first year undergraduate students. Without such critical competence, university training is a difficult, inefficient and frustrating process.[38]
5.58 The submission from Professor Britz and her colleagues was one of the few which directly addressed the issue of whether there is an actual decline in academic standards for senior school science:
The tertiary science sector is expected to deliver many outcomes building on the knowledge, skills and experience of high school graduates who are increasingly recognised as poorly prepared to acquire the professional and generic attributes during a three- or four-year degree.[39]
5.59 At the committee's Brisbane hearing, Professor Britz elaborated:
We have problems in both a lack of hard wiring in the basic knowledge of the disciplines and a diversity of experience that students walk in with—sometimes with subjects that we may call ‘soft science’ and often with minimum qualifications in English and one form of mathematics. That means that we face the challenge of remedial action in the first year in trying to catch students up.[40]
5.60 This is not to say that all science undergraduates, or even mathematics, law or education undergraduates, are inadequately prepared for further education by the senior school system. In fact, academics were keen to note that they do teach some brilliant and enthusiastic young people.
5.61 The committee is concerned about the serious skills shortages in the areas of mathematics, the sciences, and engineering. It is in Australia's economic interests to encourage all students, but most especially those at senior secondary level, to maintain an interest in, choose to study and reach their full potential in these areas.
5.62 There is increasing discussion about the need for more innovative curriculum in science. The Chief Scientist is lending weight to this argument, although it probably has more relevance to science teaching in the lower secondary school. This issue was referred to earlier in this report. In Year 12 the committee considers the challenge to be to encourage students to undertake and perform at high levels in mathematics. That requires having teachers with degrees in subjects like physics and chemistry, and such graduates are now hard to recruit into the teaching profession. Thus the issue of standards and examination performance, and certification are closely tied up with factors that are less under the control—if at all—of governments or regulatory bodies.
5.63 The committee considered the idea of students across the country being issued with a common senior school certificate at the end of Year 12 and believes that the principle has some attraction.
5.64 In 2007, the Australian Council for Educational Research (ACER) reported on possible models and implementation arrangements for a single national senior school certificate. The proposed Australian Certificate of Education (ACE) would replace the existing nine senior school certificates. The ACE report noted the many jurisdictional differences, which, in its view, were difficult to explain or justify, and which did not reflect students' needs or best interests. In some instances, such as the reporting of students' results, ACER believed that the differences actually disadvantaged students. The jurisdictional differences also resulted in significant duplication of effort, and expense, across bodies responsible for senior secondary curricula and assessment.[41]
5.65
In regard to HSC-type qualifications, all state and territory education
systems were satisfied either with what they had in place or what reforms were
anticipated. Where they were not, education departments pointed to extensive
and expensive initiatives aimed at correcting any deficiencies. Tasmania, South
Australia and Western Australia are currently revising their Year 12
certification, with particular emphasis on how final achievement gradings are
to be arrived at. A chart showing the variations in assessments across states and
territories is below.
Proportions of external and internal Year 12 assessment for matriculation
|
|
NSW |
QLD |
VIC |
WA |
SA |
TAS |
ACT |
NT |
|
External exam |
50 |
0 |
50-66* |
50 |
0-50 |
40-60 |
0 |
0-50 |
|
School-based assessment |
50 |
100 |
34-50 |
50 |
50-100 |
40-60 |
100 |
50-100 |
* this range is for core subjects only, some non-core subjects can have as little as 30 per cent or as much as 75 percent externally examined
5.66 As discussed earlier in this chapter, the lack of external assessment in Queensland has made it difficult to be confident that there can be any reliable comparison made with achievement levels in other states. The committee believes that there is a strong justification for external examinations. The most obvious advantage is in ensuring that the curriculum or the syllabus is covered as intended. It also ensures that there is comparability in the level of difficulty in the questions that are asked across states and territories. It is not necessary to have a standardised national examination paper to ensure this, but a year-by-year moderation of exam papers across states will achieve this purpose. Finally, the committee believes that there are important learning benefits to be gained from external examinations. They provide an extra incentive or motivation to learn, and give students an insight into a wider world of learning.
5.67 The committee recommends that all Australian states and territories adopt and implement a substantial proportion of Year 12 assessment to an external examination.
5.68 The committee also understands, as earlier discussed, that any proposal for an ACE would not require a national test, but would be awarded by states on the basis of agreed curriculum and assessment instruments. Each awarding body could continue to offer or accredit a variety of subjects and courses that would count toward the ACE, including vocational studies. There would continue to be diversity and responsiveness to local needs under the umbrella of the single national qualification.
5.69 Education unions argued that the need for an ACE has been overstated. While conceding that an ACE might have some advantages, the Independent Education Union of Australia agued that this is not a policy issue created by educators, state or territory ministers, parent organisations, or the community. Education unions regarded the certificate as another Commonwealth initiative inappropriately linked to funding conditions.[42]
5.70 A few schools and systems expressed concern with the proposal for an ACE. The Australian Association of Christian Schools specifically feared for the autonomy of independent schools:
Whatever advantages there might be in defining uniform standards for senior school certification across Australia, these must be carefully weighed against the disadvantages of destroying effective school-based practices that have produced strong outcomes at the senior school level. This particularly applies in the non-government sector where, for philosophical and religious reasons, learning is not necessarily pragmatic and utilitarian in its focus.[43]
5.71 With that view in mind, the committee noted that the Association of Consulting Engineers supported a national Year 12 certificate for what could be described as utilitarian reasons. These included: comparability of results across the country; nationally high and consistent curriculum standards; and more efficient use of limited resources. For instance, rather than developing seven separate syllabuses or curriculum frameworks for a particular subject, awarding bodies could share some syllabus and assessment materials.[44] In relation to these points, the committee notes that, in subjects which particularly concern consulting engineers, there is already a high degree of commonality in curricula, and some evidence of national collaboration in curriculum construction. However, this does not guarantee comparability of standards and results.
5.72 All curriculum documents should specify the standards to be reached, and indicating what might be considered minimal level rising to outstanding achievement level. The ACE Report recommended that nationally agreed standards be developed in those subjects for which core curriculum is identified. The committee agrees that this is essential.
5.73 At the April 2007 MCEETYA meeting in Darwin, the states agreed to work collaboratively, and with other relevant educational bodies, to develop nationally consistent curricula setting core content and achievement standards expected of students at the end of Year 12, and at key junctures up to that point. The focus is on three subject areas: English, Maths and Science. The committee welcomes these efforts to determine minimum levels of achievement for all students, and strongly supports the process of extensive consultation.
5.74 The previous year, MCEETYA had also agreed to work toward improved consistency of reporting for senior secondary students' achievement levels. A working party has been established to investigate a common scale for reporting all senior secondary subject results, and a quality assurance process. This includes reporting on options for common scale reporting and an indicative timeline for the development of comparative procedures. The committee believes that MCEETYA's April 2007 announcement should assist the June 2006 commitment, but a year has now passed and the working party has not even announced its own investigative timeline. The committee hopes that the project commitment remains strong. In the meantime, the ACE Report has been delivered and presents one specific option which might also assist the MCEETYA working party.
5.75 The ACE Report proposed five nationally agreed standards in each subject. Standards labelled A to E were stated to be the preferred option with each standard representing a defined and illustrated level of achievement in the subject. The committee notes that this should anticipate some of the objections to that method of reporting. In states and territories which also report results on numerical scales, there would be a need for a process to interpret students’ scores in terms of the nationally agreed standards.
5.76 One of the key features of the ACE Report was a recommendation for the creation of a national standards body, including a 'subject panel'. The 'subject panel' would comprise assessment specialists and incorporate international benchmarking standards. It was argued that a single national body would be appropriate to ensure the necessary co-ordination in senior secondary arrangements, and for setting standards for the certificate.[45]
5.77 Responsibility for setting standards will be a matter for delicate negotiation. The committee agrees that a national standards body, or national subject panel, must go beyond heeding the prevailing ideology or philosophy of state and territory authorities of the day. There must be genuine consultation and consideration of the views of all stakeholders, including academics, subject associations, professional bodies and community or parent representatives. According to one parent:
Consultation does not extend to parents. One of the problems we have is that in many instances parents are used as justification for decisions, yet there has not been the consultation. In the state situation we do have that consultation. We would hope that it would occur at the federal level as well.[46]
5.78 From an academic perspective, Associate Professor Wayne Read remarked on the need to have discipline or subject experts involved in setting standards:
The first and foremost thing is that this really is a quality assurance thing. We have to be involved. Universities and genuine end users have to be involved in the process of defining the level, the quality, of these students...We have to start adopting Australia-wide, worldwide standards. There has to be some common set of core skills that everyone understands and represents...Assessment has to be independent of education faculties and basically of education departments. If you produce a fine ball bearing you can throw it out there into the marketplace and anyone can measure it.[47]
5.79 The committee notes that objections to what some see as the excessive influence of academics on curriculum content is a long-standing tradition. It appears to the committee that for a number of years academics have been in retreat from their responsibilities to advise school curriculum agencies on standards issues, in part because of work pressures. This has been an unfortunate development. Universities are a community resource and their usefulness should be seen to rise above petty jealousies, especially in education.
5.80 While the committee believes that the development and implementation of an Australian Certificate of Education should be further investigated by MCEETYA there are more important priorities. A national certificate has lesser claims for priority than the negotiation of comparable assessment practices. Without that agreement, consulting engineers and all similar occupational associations with a scientific or engineering basis, or relevant university faculties, will not be certain that matriculants will have a proper foundation of school knowledge to engage in higher education. Elsewhere in this report is recorded the experiences of academics who regularly encounter this problem. It is the principal justification for a large component of external assessment by examination.
Recommendation 6
The committee therefore recommends the Government and MCEETYA work expeditiously toward the negotiation of a comparable Year 12 curriculum that will embrace the principle of common standards and expectations of achievement at designated levels of study, and agreed common standards of assessment, including a significant component of external examination.
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