Apples and Oranges

by Burkard Polster and Marty Ross

The Age, 12 September 2011

Many years ago, one of your Maths Masters was lucky enough to be studying at a prestigious American university. While there, he landed the prestigious job of operating the mathematics department’s 16mm projector. 

At the time, the American Mathematical Society had a vast library of educational films, ranging from primary school material to high-level presentations by great mathematicians. And so, one pleasant afternoon, the mathematics department gathered to watch a filmed lecture on fractals.

Alas, there was a mix-up: instead of being on fractals, the film that had been sent was An Introduction to Fractions.  So, your youthful Maths Master found himself in charge of a roomful of brilliant mathematicians, who watched in bemusement as it was patiently explained to them why half an apple is not equal to half an orange.

These memories came back while contemplating a recent decision by VTAC, the Victorian Tertiary Admissions Centre. VTAC is responsible for converting a student’s VCE results into an overall score, their ATAR. The ATAR determines the university programs for which a student is eligible. 

The methods used to calculate the ATAR are complicated, involving as much art as mathematics. The fundamental problem is to compare the performances of students undertaking subjects of dramatically different style and difficulty. See here for the ABC (and DEF) of calculating the ATAR. 

VCE students may also undertake university-level subjects, known as enhancement subjects. Under this scheme, Melbourne and Monash universities offer versions of their first-year mathematics; though not without serious flaws (a story for another day), these subjects are mathematically richer than VCE offerings, definitely worth considering for a strong student.

An enhancement subject cannot count as one of the VCE student’s four “primary” subjects, only as a fifth or sixth subject. As a consequence, the contribution of an enhancement subject to a student’s ATAR is necessarily about 10% of that of a primary subject. 

That is a significant disincentive, but in other ways enhancement subjects have been treated generously. The maximum “increment” for an enhancement subject is 5.5, compared to the maximum of 5 for a non-primary VCE subject. Moreover, it is pre-determined that 20% of students in an enhancement subject will receive that maximum increment. 

This generous weighting is consistent with the original idea of enhancement subjects being difficult and intended for the brightest and most diligent of students. However, that is less true than it was: there are now weaker enhancement subjects and subjects accepting weaker students, for which the current scheme is overly generous.

So, last year VTAC sat down to fix things. They made a mess of it. Responding to the subsequent complaints, VTAC went back to the drawing board, and their newly revised scheme is an improvement. However, it is still misguided and clumsy. 

Beginning in 2012, there will be two major changes to the evaluation of enhancement subjects; first, the maximum increment will be lowered from 5.5 to 5, identical to the maximum increment for a non-primary VCE subject; second, a student will have to score 90 or above in the subject to receive the maximum increment. These changes are significant and regrettable.

The reduction of the maximum increment is small, and it seems that VTAC regard the change as inconsequential. Having discussed the matter with teachers, and with current and potential students, we very much doubt it.

For most VCE students, the lowering of an increment by 0.5 is unlikely to be of any consequence. However, many of the students in enhancement subjects are very strong, having their eyes on the most competitive courses, and on Dean’s Lists and scholarships. These students tend to perceive the 0.5 increment reduction as important, and we suspect that they are correct. 

In any case, the basic fact that such students believe the reduction to be important will make it that much more difficult to sell an enhancement subject. 

As for the new method to determine which students will receive the maximum increment, it strikes us as simply absurd. Scoring 90 in a subject has no objective meaning, varying dramatically across universities and subjects. 

Furthermore, if the rationale for the change is the existence of weaker students in weaker enhancement subjects, VTAC’s new scheme will only exacerbate the problem: it is exactly the weaker subjects that will be more inclined to award inappropriately high scores.

Together, VTAC’s changes will likely be a significant disincentive for mathematics enhancement. At present, only about 10% of Melbourne University mathematics enhancement students score above 90. So, perhaps the university will adjust its grading. 

If not, the large majority of  its students, who typically score in the high 40s in their VCE subjects, will receive an increment of 4.5 or less for maths enhancement. On top of which, maths enhancement cannot be counted as a primary VCE subject. Why would a student bother?

Of course, there can be good academic reasons to take an enhancement subject: the material tends to be more interesting, the subject can reinforce the material in a student’s preferred discipline, and it can enable a student to jump-start their university studies.  

However, VCE is an extremely important year and is not the ideal time for idealism. Students play the game to maximise their ATAR, exactly as they should. For VTAC to so misunderstand enhancement subjects from these strong students’ perspective demonstrates a remarkable lack of empathy.

The fundamental problem is that VTAC has simply refused to evaluate or compare enhancement subjects. Confronted with apples and oranges, they have simply declared them all equal: a 90-grade apple equals a 90-grade orange; 10% of an apple equals 10% of an orange. It is lazy and obtuse.

We sincerely hope that VTAC will reconsider their decision. In the event that  they do so, we think we can help: we can show them a 16mm film about fractions that just might clarify things.

Beginning in 2011, Burkard took over the administration and teaching of Monash University’s mathematics enhancement subject. Marty teaches the University of Melbourne’s mathematics enhancement subject at Ivanhoe Girls’ Grammar School.

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator. 

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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