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Basic maths: the brutal reality

By Rhonda Farkota - posted Wednesday, 31 August 2005

Parents’ worst educational fears were confirmed last month in articles appearing in two of Australia’s leading daily newspapers, the Sydney Morning Herald (Doherty 2005) and the Herald Sun (Clark 2005)

Not only do many of our children have a literacy problem, but many students have a mathematics problem also. Indeed, it seems, that more than one-third of Australia’s Year 8 students have such a low level of basic mathematical skills, they would “struggle to read a train timetable”.

While it is heartening to see the federal government funding a national set of mathematics teaching aids (to be developed by the International Centre of Excellence for Education in Mathematics), one may be forgiven for not getting too excited.


In addressing a problem of such enormity the first important question for the centre is: what are to be the guiding forces behind these new teaching aids? Are they to be based on the same philosophies that have brought us to the present situation? While noting the project hopes to bridge the transition between primary and secondary school, one sincerely hopes the problem is not being treated as largely a transitional one. Blaming our students’ lack of basic mathematical skills on the transition years has long enabled us to hide from the brutal reality that mathematics teaching in Australian primary schools is in a state of crisis and confusion.

In this writer’s long and varied experience, our teenagers’ lack of basic mathematical skills is inarguably an export from primary school. The fact these problems become glaringly obvious only when students reach secondary school doesn’t mean they have suddenly appeared out of nowhere. Even though this sorry plight has existed in our primary schools for many years now, we are still nowhere near reaching consensus on how it should be addressed.

The one point on which academic agreement can be said to exist, however, is that the vast bulk of the problems associated with student learning can be directly related back to the nature of the curriculum or the method of teaching, and are not due to any lack of requisite intelligence or innate inability on the part of our students.

The obvious deduction to make from all this is that if children still lack basic mathematical skills by the time they reach the transition years, then how they have been taught hasn’t worked: which, of course, leads us to the old student-directed versus teacher-directed learning debate. Without going down that hoary path, it is safe to say consensus is now building within the academic community that in the field of mathematics, there is a place for both teacher-directed and student-directed learning, and a balance should be struck between the two, by acknowledging that some skills are better acquired through one approach and some through the other.

It is generally accepted that a student-directed approach is more suitable when it comes to the employment and cultivation of higher order skills where reasoning and reflection are required. However, for the acquisition of basic mathematical skills, the research clearly shows that teacher-directed learning is better suited. Needless to say, these basic skills must be firmly in place before students can approach problem-solving questions with any degree of competence.

Any comprehensive comparison of the literature and research on student-directed approaches to learning, alongside teacher-directed learning, will show that the empirical data heavily favours the latter as being the more effective method yet almost every teacher-education program in Australian universities is based on a student-directed approach. Indeed, some academic advocates of student-directed learning reject the whole idea of teacher-directed instruction, arguing that mathematical ideas must be personally constructed by the students themselves.  With all due respect, this is nonsense: it’s totally unrealistic to expect children, unaided, to learn theories and concepts that have taken mathematicians millennia to put together.


It seems to this writer that there is a dire urgency for the academics of the education world to put less emphasis on the ideology they feel most comfortable with, and instead, to have a long hard look at the evidence.

Fortunately there has been a whiff of change in the air recently with some academics arguing that the method of instruction best suited to the type of lesson should be adopted and in deciding this, a variety of factors such as age and ability need to be taken into account. In a move appealing to common sense, the legal concept of fitness for purpose (which requires vendors to warrant that the goods they are selling are reasonably fit for the purpose for which they are being sold) has been brought into the educational equation.

In the light of the research, it is impossible to deny the need for structured teaching in certain important areas, just as it is impossible to deny the potential benefits to be had from student-directed learning in appropriate circumstances. If we are to provide the children of this nation with the best possible education, clearly, a balance must be achieved between teacher-directed learning and student-directed approaches - and, for our children’s sake, it must be achieved soon. Further, it is submitted that the “fitness for purpose” principle should be the guiding light when it comes to finding that balance.

When it comes to the acquisition of basic mathematical skills, the empirical data clearly shows that teacher-directed learning is the better suited approach. Unfortunately, the teachers of today have neither the time nor the training to sit down and design complex maths curricula, and then go through a comprehensive evaluation process. Fortunately, there are already highly effective, research-based, teacher-directed programs out there, requiring no preparation and no mathematical expertise to implement. Incorporating straightforward explanations and built-in diagnostic tools, they adequately fulfil the task of laying foundational mathematical skills. It is hoped the International Centre of Excellence for Education in Mathematics will cast its net wide enough to find them.

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About the Author

Dr Rhonda Farkota is a Senior Research Fellow at the Australian Council for Educational Research.

Creative Commons LicenseThis work is licensed under a Creative Commons License.

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