Guest Post: Analysis of HSC Scaling

This is a guest post from Martin Mulcare. Thanks Martin for taking up my challenge! And it is nice to see that ours isn’t the only family that finds this an interesting enough topic for the dinner table.

studyingJennifer’s latest Actuarial Eye blogpost caught my attention and I have taken up her challenge to submit further analysis – although “analysis” may be an exaggeration. I share her concern about the reduction in the number of maths students in NSW, especially challenging maths. My concern is not just from the perspective of the actuarial profession but as a member of society.

I am not an expert on the HSC scaling process but I have some familiarity through the experiences of my three children who have finished school. This response relies on the quantitative input from my son Chris (2008 HSC), the qualitative input from my son Ben (2010 HSC) and the peer review of my daughter Sarah (2013 HSC)…

 The Scaling Concept

The primary source for this response is the “Report on the Scaling of the 2015 NSW Higher School Certificate”, a 64 page report (PDF), which Jennifer referred to in her blogpost. It is important to understand that the purpose of “scaling” is, as per the Report, “to estimate what students’ marks would have been if all courses had been studied by all students and all courses had the same distribution of marks.”

To illustrate, imagine that the HSC introduces a new course, Rocket Science, for the first time and only five students study it. The scaling outcome will be very different if the five students perform exceptionally well in all of their other subjects compared with mediocre performances in their other subjects, irrespective of the perception of the difficulty of Rocket Science.

It is also important to understand that the scaled marks for each subject apply only* to the ATAR and are not disclosed. The published HSC marks are a function of the assessment mark and the exam mark, both of which are subject to complex redistribution of, respectively, the school’s assessment mark and the student’s raw exam mark.

*When I write “only” I am being simplistic because the ATAR is a very big deal to many students and many schools.


Chris thinks that the impact of scaling is best reflected in the distribution of the scaled marks. Students may think about their target mark and, as a function of their perception of their peers, ask “How lucky am I feeling?”

The graph below is based on Table 5.5 of the Report and shows the % of students who achieved in excess of a scaled mark (out of 50) for each maths subject:


If a capable maths student was aiming for a scaled mark of 40/50 for their HSC then they could assess the likelihood of finishing in front of 97% students sitting General Maths, 80% of Maths students, 48% of Extension 1 students and 20% of Extension 2 students. I know what I would choose but maybe I am underestimating the quality of students sitting the Extension courses. If I was an average maths student and was happy to achieve a scaled mark of 25/50 then I would weigh up the likelihood of finishing in front of 62% students sitting General Maths or 24% of students sitting Maths (and I wouldn’t be game to think about Extension 1 or 2).

What About English?

Chris was interested in Jennifer’s suggestion that relatively poor performance in English was adversely affecting the scaling uplift for maths. He looked at it the other way – is there a potential uplift in the scaling of English as a Second Language (ESL) due to good maths scores from those students?

Here is the corresponding graph for ESL and English Standard:


Applying the same thinking and imagining that you weren’t confident with your English, let’s say you were aiming for a scaled mark of 30/50. Would you be more likely to finish in front of 89% of English Standard students or 75% of ESL students? I know what I would choose on that basis.


Ben works in a maths tutoring business with about 150 high school students from different schools, of different ages and with different abilities. Here are his insights on their perspectives based on their comments and behaviour….

  1. It’s very much a scaling thing. There’s less emphasis on “you should do this subject because it’s important” and more on “how can I maximise my ATAR?” Ben’s impression is that students feel that “the HSC isn’t about learning, it’s about getting the biggest number”.
  2. The feeling from a lot of students is “well at least I can use General Maths in everyday life”, whereas the higher levels are much more abstract. It’s harder for the students to engage with the concepts because they have no frame of reference. (Ben did acknowledge said that there are some students who prefer algebra to “all that money stuff” and actually enjoy the harder topics.)
  3. It’s a significant change in the syllabus from years 7-10 where 60% of the work is revision with gradual introduction of new content compared with the higher maths courses, where an increased proportion of the content is “new”. Students who had been coasting on last year’s knowledge and picking up a few new ideas are now forced to actually learn new ways of looking at problems and that may be a challenge.
  4. Another reason for the decline may be that the exams for the higher level maths subjects are set too hard and students become discouraged. After all they’ve got enough on their plates in the HSC without voluntarily taking on more maths stress!

Overall, it is easy to see why students are not excited about taking on harder maths subjects, despite the rational case for enrolling to maximise their ATAR. Perhaps there is a two tier system emerging where selective schools are successfully encouraging higher maths while other schools are unsuccessful? The clear message at my sons’ private school was: “If you are not good at a subject then scaling won’t save you. But if you have any capability for more challenging subjects then please stick with them because the scaling will benefit you.” I wonder if that is still the message?