School is out

A bifurcation of views about maths:

Those who can and those who can’t?

Or those who can, and those who can’t YET?

My own schooling occurred at the tail end of an era when schools functioned largely to sort students according to future work paths; for example, to identify and prepare the relatively small cohort of people headed to university, students who would be given access to special privilege in the professions. Mathematics curriculum was divided up into sub-disciplines (geometry, trigonometry, and algebra were taught as separate subjects). In retrospect this now seems bizarre, since it removes or undermines the possibility of seeing mathematics as a connected, interrelated and unified set of ideas and methods. It certainly was not designed to emphasise the idea of bringing different kinds of mathematical analysis to bear on real-world problems.

I must have been right in the vanguard of the explosion of mass secondary schooling, when class sizes and retention rates really began to climb. Government policy was clearly aimed at rapidly increasing the number of teachers (e.g. introduction of education department studentships to supplement the commonwealth scholarship program) to cater for the increase in student numbers. Training for secondary school teachers had earlier not been particularly rigorous, involving for the lucky ones a degree and then a post-grad diploma, but new integrated teacher ed courses were also established. Teacher unions were working very hard to ensure new teachers were properly trained (the 'control of entry' industrial campaigns) and international recruitment was in full swing, with many new teachers arriving from the USA and UK.

In the late 1960s and early 1970s, new secondary schools were starting up everywhere to accommodate the increasing school population (perhaps mostly reflecting the reality of baby boomer population growth but recognising that these kids needed to be in school, and to be there for as long as possible). Some mathematics teachers were exploring different ways of pursuing their craft. Curriculum changes meant integrated mathematics courses up to Year 10 level became the norm. There was an explosion of teachers infected by the progressive education movements of the 60s and 70s who began thinking about the importance of promoting conceptual understanding through activity-based teaching approaches. But the textbook industry acquired and retained a tight grip, trying to provide teachers with a script for which they (schools) would pay.

Two pedagogical strands emerged -- one with an emphasis on traditional mathematical content, sticking to text book exercises as the main activity, and this seemed particularly relevant to the well-motivated students who seemed able to cope with the status quo, connecting to the older idea about there being a small group deserving of the ripest fruits; and another strand that looked to programs and approaches typified by Reality in Mathematics Education (RIME) materials that were in part a response seen as appropriate or necessary for students not particularly well-motivated, and those needing more active guidance to further their learning. Commonwealth Innovations Grants flowed freely to support the introduction of change in teaching and learning. Task Centres were established in several Victorian Primary Schools. The Victorian Ministry of Education employed squadrons of mathematics consultants who provided professional development programs around the State. This 'more progressive' strand saw conceptual understanding, practical application of mathematics, using the environment to source mathematics and to motivate an interest in applying mathematical ideas, as central elements of the effective performance of teaching duties. This same bifurcation persists.

One important philosophical division underpins these two strands (it infects both to some degree - it might even be an independent division) namely, whether or not people believe there are 'maths people' and 'not maths people' when it comes to school-level mathematics. One of the most damaging attitudes held by one side of this division is the idea that some students are essentially incapable of developing their mathematical capabilities. The alternative to this is the view that everyone is capable of learning anything they turn their minds to -- the question is what will be an effective teaching/learning algorithm for that individual to learn that thing.

With the dramatically increased Year 12 retention rates making themselves evident in the 1980s, and with increasing numbers of back-door approaches to giving kids not in the traditional top university-headed streams access to that path, several Australian States (Victoria in particular) invested money and effort in reviewing the structure and arrangements of senior school curriculum. Separate technical schools were abolished as part of a rearrangement that removed structural divisions within the State education system, and that aimed at providing all students with an education (including a mathematics education) that would give them access to the fullest possible range of post-school options. The senior mathematics curriculum was redesigned in a particularly creative way that attempted to achieve two fundamental things: first, it provided new pathways for a wide range of students; and second it introduced into the formal high-stakes assessment system assessment arrangements that put problem solving and modelling, and investigative projects, front and centre. This supported the generation of a host of new teaching and learning materials and resources, and an explosion of professional development activities for mathematics teachers that helped them explore their craft in new ways. These developments had big spin-off benefits at the earlier levels of schooling where teachers saw the need to prepare students for the kinds of mathematical thinking and activity that would be required when they reached the last two years of secondary school. 

ROSS TURNER
January 2015