A contest of ideas about maths in Victoria

A selection of newspaper headlines from 1987-1990

Public debate about controversial issues usually challenges all participants, whatever side of the debate they occupy.

I recently came across a trove of old newspaper clippings that caused me to sit down and relive a period in my professional life that was, to say the least, fraught. Traumatic even. It gave me pause and I immediately began reflecting on the period.

This question presented itself: Why did introduction of the Victorian Certificate of Education (VCE) in the early 1990s, especially the mathematics components of the VCE, cause such a strong negative reaction? My answer to this question goes both backwards and forwards from around 1990 when the major fights occurred.

Ancient history

I have been interested in mathematics education for much of my life: first, as the recipient of some highly effective remedial teaching early in my primary school education (thank you Marie Norrish); and second as a diligent and successful student of mathematics through my later primary school years and through secondary school. Then as I undertook a science degree with a major in pure mathematics, followed by a year of teacher training that included a focus on teaching mathematics to secondary school students. During that year I was obsessed with finding solutions to the problem of how to teach mathematics more effectively to those many students who struggle and are turned off by maths.

Once I hit the workforce, I had the very good fortune of being posted to a Victorian secondary school that had a new mathematics coordinator who became a significant role model and mentor (thank you Charles Lovitt). I became part of a team that worked hard to develop new teaching and learning materials and an approach to teaching designed to promote understanding, and to engage students actively in their mathematical experiences and learning. These ideas became popular, and we found audiences of teachers eager for professional development in using the ideas and materials we were pursuing, as well as soon-to-be teachers through the mathematics education program of Monash University where for a period I became a part-time tutor.

The 1960s, 70s and 80s

The skills I was developing, and the profile I was building, became important in the broader context of education in Victoria as my work as a secondary school maths teacher took off. As a member of the ‘boomer’ generation, I was in the middle of an epoch that saw massive increases in the numbers of students staying on to the end of secondary school. Many new schools were built to accommodate them, teacher training institutions were burgeoning, and overseas recruitment of teachers was in full swing as part of the government’s strategy to meet the growing need for an expanded teacher workforce.

Prior to that period, the Matriculation certificate (re-named in 1970 to the Higher School Certificate) was the pinnacle of secondary schooling, marking the successful completion of Year 12 (then known as Form 6). The certificate was primarily geared to the needs of the university sector. The curriculum, and the end-of-year examinations, were designed and controlled by university people, through the Victorian Universities and Schools Examination Board. However, as the number of students staying on to the end of high school increased, and became more diverse, the need to expand the pathways available to senior secondary students became increasingly evident. The extra students were not necessarily all headed towards university. Certainly, the increased range of levels of engagement with schooling observed in this cohort meant that a narrow academic curriculum designed to service the needs of students headed for careers in the sciences, medicine, law, engineering, economics, and various branches of the arts, was no longer suitable. Even for those students aspiring to university study, most had experienced a broader secondary education than had been the case for previous generations.

Various responses to these pressures emerged during the 1980s, including a proliferation of alternative pathways for students, and of alternative schools and forms of schooling. Even the ‘solution’ of retaining the high schools as the preferred pathway for potentially academic students, and the technical school system as the preferred pathway for those heading to the trades and other more practical endpoints, was breaking down. Reviews of educational provision, most significantly the Ministerial Review of Post-compulsory Schooling headed by Jean Blackburn, which reported to the government in 1985, lead to a decision by the then Labor government to design curriculum and assessment arrangements for a completely new senior school certificate, The Victorian Certificate of Education (VCE). It was to span the last two years of secondary schooling, to embody a wide range of curriculum options that would attract and be meaningful to the widest possible cohort of young learners and would articulate through its new assessment arrangements with revised processes for entry to post-secondary education.

My role

In late 1986 I was recruited to be part of the team developing the curriculum and assessment details for the new VCE mathematics study. The task of developing the new curriculum, across each different ‘field of study’ including mathematics, presented interesting challenges. The bones of the new certificate, and the basic arrangements and design principles to be implemented within each study area, were determined by the Victorian Curriculum and Assessment Board (VCAB) that was responsible for implementing the Blackburn recommendations as adopted by government. The aim was to provide a broad range of students access to high quality Years 11 and 12 courses that would prepare them for any post-school destination they might contemplate.

The design framework represented quite substantial change from the previous situation, and some aspects proved quite controversial. For example, award of the VCE as a credential was to be based on the satisfactory completion by students of prescribed ‘work requirements’ in each unit of each study. If students did the work, and their teachers deemed it satisfactory in accordance with standards defined in each study design, they were awarded credit for that unit towards their VCE. Completing the required range of units of study led automatically to award of the VCE. The assessment of the level of achievement attained by students was to be treated separately, through externally defined and assessed ‘common assessment tasks’ associated with each pair of ‘Units 3 and 4’ (equivalent to ‘Year 12 level’) within each study. Students would no longer be deemed to have ‘passed’ or ‘failed’ according to their performance on end-of-year external examinations. Rather, if they completed the work of their chosen VCE courses they could emerge with a universally recognised credential, together with a set of grades that they could use in any subsequent selection processes (for example, for entry to post-secondary courses).

Within that framework, the team designing the mathematics components of the VCE relished the opportunity to work from a relatively blank slate. The team’s working motto was “more mathematics for more students”. The mathematics study design that was developed, adopted, and implemented first in a pilot program that commenced in 1989, then across all VCE schools from 1990, required schools and teachers to change several aspects of their work. The set of mathematics components involved a substantial reconfiguration of content from previous courses. The mathematical content from all previous senior mathematics courses was spread across three new sets of units, each able to provide courses for high level endpoints as well as broadly accessible courses, rather than the hierarchical course structures previously available. This was perhaps the most significant change. The new structure had the potential to really challenge the prevailing view that there is some mathematical content that should be kept for just those highly capable students who were headed for technically rich post-school endpoints. By contrast, the new structure rested on the challenging notion that all students should have access to the most important mathematical knowledge available. The focus questions for schools and teachers would have to shift from ‘which students are suited to this mathematical content’ to ‘how will I teach this content to all students wanting to learn it’.

The structural features, the concept of work requirements that took some time for teachers and students to understand and manage, and the formal assessment tasks, all presented a major shift in work practices for both teachers and students.

Two elements incorporated in the new mathematics study became a compulsory part of each mathematics unit in which students enrolled. They were substantially new for most people, certainly as part of the formal assessment of a senior secondary mathematics subject: an extended project, involving a mathematical investigation, taking up to 20 hours spread over four weeks, on some area of application of the mathematics that was of interest to them, and a written report of their work; and an extended problem-solving task, taking up to 10 hours spread over one to two weeks, involving the solution of a challenging and typically novel problem, together with a written report of their analysis and solution. Both tasks involved elements that had not been a standard part of mathematics teaching and learning: relatively open-ended problem situations, expectation of serious engagement over an extended period, culminating in production of a written report.

Many students found these extended investigations and problem-solving tasks highly challenging and engaging. Many teachers saw the benefit arising from parts of the mathematics courses being more student-directed, or at least requiring (and achieving) a high level of engagement by their students who were exploring interesting and often unfamiliar situations using mathematics that often required learning a new range of skills. However not everyone was happy, and several interest groups weighed in on the new curriculum and assessment arrangements, generating a great deal of negative commentary running counter to the positive educational benefits seen by some.

Schools and teachers

Schools were at the front line of delivery of the new VCE. Teachers were the bearers of knowledge (of the requirements, and of their subject area), transmitters of information to their students, and arbiters of success of their students. Schools and teachers were faced with a steep learning curve about the new requirements and rules, the options for curriculum structure and choices, subject content and delivery, and the new assessment arrangements. A state-wide professional development program was implemented to explain and support school plans for VCE introduction. It was supported by a wonderful collection of curriculum consultants attached to each of the Education Department’s school support centres. New resources and materials were developed centrally to support the change. Textbook publishers and authors were quickly on the job and were supported by the curriculum authority to understand and respond to the new requirements within each study area. New textbooks were thick on the ground.

Nevertheless, many teachers felt overwhelmed and under-supported in the face of these changes. In particular, the requirements around the new ‘challenging problem’ and ‘investigative project’ tasks were stressful events for many teachers. Some felt ill-equipped to guide and support students, particularly when students wished to explore some problem or area that may have been unfamiliar to the teacher. One response was to impose strict limits on the nature of the project topics students were permitted to undertake, thereby limiting the range of guidance and support they needed to provide. Perhaps the most extreme reaction by a handful of schools was to abandon the VCE and shift to offering the International Baccalaureate to their senior students instead.

Equally challenging for schools and teachers was the change in mindset needed to shift from a system where separate courses were designed and implemented for learners fitting into rigid stereotypes (particularly those stereotypes that predict learners’ mathematical capabilities) to a system focusing on providing access for all learners to the knowledge deemed most important.

Parents

Adults sometimes feel that they know about schools and education because, hey, weren’t they once students? Well, many parents of VCE students were confronted with changes that they struggled to comprehend, new subject names that were unfamiliar, and daughters and sons that often reflected the stress of change they had picked up from their teachers as well as those emanating from the new work requirements. Parents’ ability to understand and support their children in developing new skills, for example in problem solving, mathematical investigations, and report writing, often presented a new source of stress and angst.

The University Sector

The interface between the school and higher education sectors was undergoing severe strain at the time of the introduction of the new VCE. The increasing numbers of students seeking entry to university courses, and their increasingly diverse levels of background preparation, had led mathematics departments, as an example, to seek new ways to prepare students for entry. Various forms of additional preparation courses were introduced, such as summer schools and preparatory courses, in their efforts to get students up to standard ready for the technical content of their courses in mathematics, statistics, engineering and others. Despite the direct involvement of technical and further education representatives, including from the universities, on the various committees and working groups undertaking VCE development, there was a view among some that the new VCE arrangements did not sufficiently help to address those challenges.

Moreover, in the case of mathematics, some feared that the new assessment components were not sufficiently objective, being open to overly generous assessments by schools and teachers without suitable checks of authenticity. To some extent these views rested on a lack of understanding of the authentication and verification processes schools implemented to ensure the veracity of their assessments, nevertheless prominent academics expressed negative views loudly and publicly.

The then Vice-Chancellor of the University of Melbourne, a frequent spokesperson for the university sector at the time, apparently knew that VCE mathematics students could purchase solutions to the VCE Challenging Problem and Investigative Project assessment tasks at the local market. It is not clear whether this repeated claim was based on real information about VCE students, and reports purchased from local markets, or whether he just imagined it was a problem because his own sector was well and truly beginning to have to deal with cheating of that kind. This by the way has subsequently become a boom industry with the online availability of the most amazing array of ways to cheat university assessment requirements, and the even more ingenious range of approaches to producing and disseminating bogus assessment products.

Employer and industry groups

VCAB conducted many consultations with industry and employer groups to inform them of changes, to identify any concerns they may have had and to resolve as many of those as possible. They had a clear interest in supporting innovation that would lead to better educated students graduating from secondary school better fitted for the modern labour market. Nevertheless, the changes involved presented employers, and their peak employer and industry representative bodies, the same challenges to understand the changes that were afoot. The peak bodies had a role in mediating between their members and affiliates and VCAB, both to reflect concerns and uncertainty to VCAB and to ensure their members were informed about the likely effect of the changes. They became another voice within the community expressing views about the new Certificate.

Commercial interests

As well as these interest groups, another group had a strong commercial interest in changes to the VCE – book publishers. It is often said that it is the textbooks that determine what goes on in mathematics classes. While the authors of mathematics textbooks work hard to understand current requirements and write materials that will help students and teachers undertake their studies in accordance with the requirements, they have a strong tendency to generate a version of the requirements that militates against innovation. They facilitate an ossification of the current state.

There was a mad scramble among publishers as the new VCE arrangements were being designed, tested, and implemented, to recruit the best and brightest of available teachers and academics to quickly produce new textbooks that would reflect the new mathematics subject names, content, and assessment requirements. The new VCE ushered in a boom period for the publishing industry.

A recipe for tension soup

From 1987, and increasingly over the ensuing five or six years, the public debate among these various interest groups reflected a considerable degree of tension. Articles published in the press, responses to those articles, letters to the editor, radio interviews and pronouncements by radio commentators, as well as meetings of those involved (such as professional development meetings of teachers) all became a soup in which uncertainty, critique both positive and negative, anxiety, and outright opposition were freely expressed. These tensions were used by the then Liberal Opposition in Victoria to foment anti-government sentiment. The tensions were compounded by the political climate.

For many students a senior certificate that seemed fresh and innovative, and that provided reward for effort and engagement to all students whatever their abilities, disabilities, and previous educational experience, offered a great deal of promise. The tension swirling around them coming from especially the three major interest groups: their schools and teachers, their parents, and the universities, threatened to undermine that promise.

As time went on, the responsible authorities launched reviews, and adjusted policies and practice in response. There was a change of government. The tension gradually subsided as the players learned their new roles. A major review of the VCE mathematics study design was conducted in 1993, which recommended a very substantial reconfiguration of the structural components, returning the design to something much more like the hierarchically structured components that had existed previously, with different subjects designed to suit learners with different supposed interests and capabilities. Those changes were implemented and have essentially persisted into subsequent accreditation periods.

More students than ever before are now undertaking mathematics courses as part of their senior secondary studies. Across several subsequent re-accreditation periods for VCE studies, some of the original design innovations have been wound back, but some essential features have been retained. Most significantly, the separation of decisions about award of credit for VCE components and for the Certificate from decisions about levels of performance is still at the core of the VCE. Innovative aspects of the VCE mathematics study (extended investigative projects, and extended problem solving and modelling tasks) have also continued in some form as part of VCE mathematics assessment, indeed are referred to liberally in curriculum documents of most Australian states and territories and of ACARA, the Australian Curriculum and Assessment Authority. Whilst these components were removed from the formal assessment of levels of VCE performance, they have continued at least in theory as part of the school-assessment of coursework that leads to the award of the VCE. Indeed, these innovations laid the foundation for advances in the ongoing practices of mathematics educators, including the expanded use of technology as tools for learning, as well as the incorporation of investigations, and modelling and problem solving as regular elements of mathematics curriculum.

In 2020, about 95% of VCE students undertook some mathematics in Year 11, and over 80% included some mathematics in their Year 12 studies. In other words, more students are studying more mathematics. It seems the widely held community view about the importance and utility of mathematics is shared also by today’s learners. Further changes are needed to ensure that these learners are getting more out of their mathematical studies, so that mathematical knowledge and skills continue to build in the community. We should more strongly adopt a ‘growth mindset’ regarding the capabilities of mathematical learners, resist the channelling of learners into limiting pathways thought to suit their assumed capabilities, and reflect more strongly the view that learners can learn anything to which they apply their minds.

ROSS TURNER

October 2022