The VCAA is reportedly planning to introduce Foundation Mathematics, a new, lower-level year 12 mathematics subject. According to *Age* reporter Madeleine Heffernan, “It is hoped that the new subject will attract students who would not otherwise choose a maths subject for year 12 …”. Which is good, why?

Predictably, the VCAA is hell-bent on not solving the wrong problem. It simply doesn’t matter that not more students continue with mathematics in Year 12. What matters is that so many students learn bugger all mathematics in the previous twelve years. And why should anyone believe that, at that final stage of schooling, one more year of Maths-Lite will make any significant difference?

The problem with Year 12 that the VCAA *should* be attempting to solve is that so few students are choosing the more advanced mathematics subjects. Heffernan appears to have interviewed AMSI Director Tim Brown, who noted the obvious, that introducing the new subject “would not arrest the worrying decline of students studying higher level maths ā specialist maths ā in year 12.” (Tim could have added that Year 12 Specialist Mathematics is also a second rate subject, but one can expect only so much from AMSI.)

It is not clear that anybody other than the VCAA sees any wisdom in their plan. Professor Brown’s extended response to Heffernan is one of quiet exasperation. The comments that follow Heffernan’s report are less quiet and are appropriately scathing. So who, if anyone, did the VCAA find to endorse this distracting silliness?

But, is it worse than silly? VCAA’s new subject won’t offer significant improvement, but could it make matters worse? According to Heffernan, there’s nothing to worry about:

*“The new subject will be carefully designed to discourage students from downgrading their maths study.”*

Maybe. We doubt it.

Ms. Heffernan appears to be a younger reporter, so we’ll be so forward as to offer her a word of advice: if you’re going to transcribe tendentious and self-serving claims provided by the primary source for and the subject of your report, it is accurate, and prudent, to avoid reporting those claims as if they were established fact.

I am interested to see more detail. What is the purpose of this innovation?

And I offer a comment on a less important issue about the article. The photo of mathematics being written on the blackboard annoys me. Don’t get me wrong – I love blackboards and chalk. But you would have to search far and wide to find a classroom in an Australian school with a blackboard.

Furthermore, what is written on the board does not look like what will be in the curriculum for Foundation Mathematics. (I realise that the journalist may have no control over the photo.)

Journalists would object to a photo that depicted a journalist as a man, hunched over a typewriter, tie askew, hat on his head, smoking a cigarette with a half bottle of scotch next to him.

Similarly, is it possible to find a realistic picture of an Australian mathematics classroom?

Best wishes to everyone for Christmas and 2020.

BTW, I read of a nerdy fellow who sends his Christmas cards out on 31 October because 31 Oct = 25 Dec.

Thanks, Terry. I think the “purpose” is to get those students who have learned no maths up to Year 11, and see if they’ll learn some in Year 12. As for the photo, newspapers typically use stock photos: you can see the same photos reused. And yes, they could use a stock photo of a more realistic classroom, but are you sure that’s a good idea?

I thought that Further Maths was meant to do (and not do) what it is now claimed Foundation Maths will do (and not do). And we all know how adding Further Maths ultimately turned out ……

I thought otherwise, JF: I thought that Further Maths was intended to be preparation for tertiary studies that require mathematics skills / knowledge beyond Year 10, but not at the level of calculus / functions of a single real variable. I agree that Further Maths is not achieving this aim, although I think the main culprit here is not the syllabus, but (in decreasing order of culpability) (i) the overwhelming presence of CAS; (ii) the exams; (iii) incentivising strong maths students to choose the subject. I’m not aware of any information about this, but if these errors are repeated with Foundation, then the subject is doomed to failure.

Notwithstanding all the problems pointed out thus far (which I agree with, but have nothing to add), I think one silver lining to the introduction of Foundation 3&4 could be that some students who aren’t suited to Further Maths will pick Foundation. Whether or not it is reasonable, there are many low achieving students who pick Further Maths because (i) they think it is important to have completed a 3&4 maths subject, or (ii) they need to pick another subject to fill out their timetable, and maths is a “safe” option. I hope this will yield higher standards for Further Maths, but that’s probably unreasonably optimistic.

Hi SRK.

I agree with all your comments. However, I can’t think of too many tertiary courses that in practice “require mathematics skills / knowledge beyond Year 10, but not at the level of calculus / functions of a single real variable”. The fact that Further Maths Unit 3&4 is a minimum prerequisite for nursing (for example) is a damning indictment on the education system up to Yr 10. (This comment does not absolve the VCE of its crimes).

Thanks, SRK. It seems to me the majority of Further Maths is no higher than Year 10, and much is much lower.

As is my habit at this time of year, I’ve worked through the NSW HSC Mathematics papers. They are not perfect, I will admit, and the IB papers just seem “nicer” to me in a way I cannot really explain, but geez, the amount of content in these papers that couldn’t be given to a graduate of VCE is quite remarkable. So, VCAA, there IS a solution of sorts and it is not that far away…

Thanks, Rf. Yes IB is so, so much richer and more coherent than VCE. If we weren’t governed by idiots it would be trivial to put in place a massively superior curriculum.

It is also the style of assessment. I’m not as keen on the new IA style in IB, I feel the multiple portfolio tasks were a good idea, but the exams are way, way better.

The curriculum documentation also makes a lot more sense!

…and by “not perfect” I don’t mean content, just some of the wording is on occasion open to interpretation. Much like the phrase “show that” in VCE…

Hi,

I agree with RF in that the IB Maths curriculum as at 2018-19 appears to cater for most standards with Math Studies ,Math SL and HL ,Further Mathematics with a reasonable project based assessment on a topic selected by the student and moderated by the school assessor with standardised marking moderated by the IB

For those who dislike pre programmed algorithms their is no CAS assistance on the calculator

It also allows all students to compete against themselves rather than the relative abilities of their cohort ?

That said the IB curriculum is being modified into analysis and application options at SL and Hl

https://www.ibo.org/university-admission/recognition-of-the-ib-diploma-by-countries-and-universities/latest-curriculum-updates/mathematics-curriculum-changes/

https://www.ibo.org/programmes/diploma-programme/curriculum/mathematics/

Steve R

Thanks, Steve. Yes, the whole world is getting dumber. But IB is getting dumber slower.

https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/foundationmathematics/Pages/Index.aspx

If you scroll down to the Study Review Plan, you will see that Foundation Mathematics 1-4 will be reviewed in 2021.

Thanks, Terry. This fits in with the Age report.

Is there any official documentation that sheds more light on Foundation Mathematics 3-4?

Very good question. The Age article weirdly fails to indicate either a person or a document. I took a quick look, but couldn’t find anything.