I’m not even sure what this is, but I guess we should discuss it.

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# Secret 2023 Foundation Mathematics Discussion

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75 Replies to “Secret 2023 Foundation Mathematics Discussion”

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I’m not even sure what this is, but I guess we should discuss it.

Brave of you Marty to assume that anybody teaching/completing Foundation Maths would be visiting your website. I’d be pleasantly surprised if someone actually comes along and comments!

Maybe that’s just me being a cynical MM/SM teacher who also has no idea what this “Foundation” maths is. Is it even maths? That remains to be seen…

Yeah, I know. But I figured I’d give it a shot.

Very much commendable Marty.

Unfortunately, the type of person that takes Foundation or teaches it, would give less than two hoots about what mathematics actually is and how to properly study it (not that MM or SM are too much better but you know what I mean)…

As far as I’m aware, Foundation was constructed to be an “alternative” and “real-world” application style mumbo jumbo or whatever that crap is, fuelled by CAS bashing I’d imagine. The type of people that want to become tradies or kick around a ball all day etc etc… (which reminds me of most of the dropkicks at my school but that’s a different story for a different day).

Hang on a sec Some MM/SM Guy – you may not have meant to but this came across to me as saying that teaching kids of lower maths ability isn’t great.

I teach Year 9 Remedial Maths and it has been one of the most satisfying experiences. They have a general ability of about Grade 3/4 (need to consult Singapore Curriculum as too hard to tell from Oz curriculum!).

I have learnt so much along the way, including about dyscalculia and dyslexia etc and have gained some techniques that will help with other classes (I even discovered algebra tiles). And I understand multiplication and addition algorithms myself better! It’s not that they don’t want to learn, but they’ve found it so so hard in the past and it still is hard (which is a life lesson in its own right).

I get that CAS bashing isn’t clever and the task of working out a Foundation Maths curriculum is really hard (I’ve had the luxury of no curriculum so I could teach conceptual and practical – whatever they really needed).

Maths is everywhere in the modern world and actually teaching the basics is interesting work.

And the tradies I know are really smart people who often need and understand maths.

0-15.

Foundation doesn’t use CAS. Scientific calculators only.

Which is a tick in the “pro” column.

0-30.

“…the type of person that takes Foundation or teaches it, would give less than two hoots about what mathematics actually is and how to properly study it…”

Notwithstanding the apparent comparison between tradies/athletes and ‘dropkicks’, I think that’s a very unfair comment.

0-40.

Hopefully 15-40, if I manage tomorrow to get a hold of the exam.

I think your “hopefully” would make it 30-40.

Any subject that encourages students (or adults) to learn or have an interest in more mathematics, or at least consolidate basic numeracy, is a good thing. Even a prospective hairdresser needs to understand the sort of stuff taught in Foundation.

The danger (and tragedy) is when a stigma gets attached to subjects like this due to an attitude of academic elitism. It’s fine to say it’s not our cup of tea, it’s not OK to sneer at it from our Specialist/Methods Ivory Tower.

Thanks, JJ, Javert, BiB, for saying it more politely than my immediate response.

Let’s not make it even easier to hate on mathematics than it already is.

Thanks, Ron.

The Foundation teachers at my school do read this blog, and did see your comment. The more students we have doing any level of maths, the better off we all are. Very toxic commentary from you Some MM/SM Guy. Shame on you.

It’s done. Leave it.

Are students who take specialist maths allowed to also take foundation maths?

A good and very funny question.

Technically yes, but a maximum of two subjects from the “Mathematics” group can be counted towards the ATAR in the top 4 so I would expect it to be highly unlikely.

There are a few students each year who take Specialist, Methods and General so it is not such a stretch to imagine Foundation as well.

Of course, the number of schools offering Foundation 3&4 is less than the number offering General 3&4 so…

There is a statistical bulletin released by VCAA yearly (you have to hunt for it) that may give some clues.

Off the top of my head roughly a quarter of the people in my specialist class did further (mostly in year 11.) I suspect that a large proportion, if not most of those people would elect to do foundation instead, since you’d be competing against an even weaker cohort.

Would a bunch of SM kids taking FM effectively kill FM?

Well, further maths is still going strong, so I doubt it.

I wonder though if foundation maths will kill further maths. Most of the people doing further maths are doing it either so they can do some maths in VCE, or because it’s an easy subject they can score high marks in. Foundation maths fills both those niches, and further kind of seems pointless now.

Interesting. I wonder if that would then drag down MM, and then SM.

Well most (or at least a large proportion of) people doing MM are doing it because its a prerequisite for their course, and SM because of the scaling or because it’s the most advanced mathematics subject. I don’t think MM or SM would be affected at all by foundation maths, except maybe by students who choose to do foundation/further/methods instead of further/methods/specialist.

Yes, but the mathematical standard of MM might drop (further).

“I wonder though if foundation maths will kill further maths”. A major factor will be whether, and if so how broadly, Foundation maths is accepted by universities as a maths prerequisite for courses / subjects.

If it’s accepted for Engineering, I’ll swim instead of using the bridge. If it’s accepted for Medicine, I’ll operate on myself with a spoon and fork. If it’s accepted for Law, … meh.

I think a lot of engineering courses (eg. RMIT, VU, Latrobe…) now list any of General, Methods, Specialist as their maths prerequisite, with a minimum study score of 20.

Can’t single cell organisms generally score a 20?

All facetiousness aside, I think a study score of 20 means about 93% of the cohort performed better in that subject in that year. So of course some students have to get that study score. Judging by the grade distributions from last year (and they don’t change much year to year), getting about 30% on the General Mathematics exams should result in a study score of 20.

But seriously, it mostly means people who gave up, doesn’t it?

Yes, I think that would apply to the overwhelming majority of students who receive a study score of 20 or below in General Maths.

(The giving up / not caring might occur earlier or later in the year, of course)

OK, so requiring a score of 20 as a prerequisite is in the ballpark of “didn’t give up”.

Pr(Study Score less than 20) is the same as Pr(Study Score greater than 40). About 8%.

(Mean = 30, standard deviation = 7).

Most universities regard medicine as a post-graduate course and what a student does in VCE is not relevant. Monash offers an undergraduate course in medicine but does not require that students have studied mathematics at VCE.

I have taught just the one student in my career who did Further and Methods in Yr 11, and Specialist and Uni Maths (through Monash) in Yr 12. All four subjects contributed to the ATAR of this student.

So now they could do five maths subjects?

I suppose they could do five, including Foundation.

But all five subjects would not contribute to the ATAR. If Foundation was used in calculating the ATAR, a contribution from Methods and Specialist would be precluded, I’m uncertain whether the increment from Uni maths would also be precluded. But I think General would get included in the calculation.

It’s a wacky world, I’m sure there are students and schools investigating how they can game the system. I have some thoughts which I hope never see the light of day.

No.

(Actually, yes. But they can’t both be included in the ATAR. Neither can Methods and Foundation both be included).

Well I just saw a copy of Foundation paper from some kind colleagues…

A bit exausted today.

Will give it a shot in a day or two.

That is, before jumping into any judgemental calls, I will need to physically sit this paper…

Foundation Mathematics replaced VCAL Numeracy which I taught at two schools. I learned three things from this experience. First, there were some good students in the class – capable, enthusiastic, and a pleasure to teach. Second, it was a mistake to think of these students as a homogeneous group as I was led to believe by other teachers. Finally, their enthusiasm for games led me to develop an interest in mathematical games (see Ferguson, “A course in game theory”) and use interesting games in the classroom.

I look forward to seeing the examination in Foundation Mathematics.

Really? People doing foundation maths had an interest in mathematical games?

I’m surprised that game theory has any relevance to any school mathematics, let alone further maths (if that is what you were insinuating.)

Joe,

Thanks for your comment.

I was using the term “game theory” in the sense used by Ferguson rather than von Neumann and Morgenstern.

My numeracy students enjoyed games so much that I set aside one hour/week for this. Dots-and-boxes (known in Australia as Paddocks), Nim, Sudoku are examples of games that appeal to people at all levels. I complied a list of games, with notes. Of course, students enjoyed the games, but the basic question to ask is: What is your strategy?

Your point about relevance is well taken. Some years ago, I offered a paper at a mathematics education conference on Dots-and-boxes (Paddocks). The game has an interesting history; developed by the French mathematician; Édouard Lucas (1842-1891), and has associated still unsolved problems. My numeracy students loved it. However, the organisers of the conference agreed with your sentiments about relevance to the curriculum.

You’re saying that they vetoed your paper? And are we permitted to guess which august mathematical association located in Victoria might have been responsible for this?

The paper was not accepted. You can guess if you wish – I will neither confirm nor deny your guess.

You are way, way too considerate to inconsiderate people.

I have just sat down to attempt this exam, it took me way longer than the General Maths exams consistently take me. Every question is an application question, heaps of information to process, I don’t think any student will get it properly finished. The instruction for almost all questions is “Calculate” and alot of questions have multi-step calculations and conversions to be used, unsure if any calculation will have to be shown or only the answer. Maybe a little more algebra required than in General! I do not think the exam is fit to purpose and it of course has errors. The sample exam was poor in roughly the same way.

Also a lot of implicit unstated assumptions are necessary from the context and the accuracy required in answers does not match the accuracy of the initial information.

I reckon the following are straight errors (ignoring the guesses from context required). There are probably others.

Q6 MC – the total the students are expected to use for % does not fit the description.

Q13 MC – The key should say “total payment” and “total interest” or cumulative

Q 2e SA makes a mockery of the given data. Also as a sidenote the whole question switches happily between male/female and ‘identified gender’ which is not even correct use of the modern idea.

Q6 swaps between % market share and % increase/decrease of total use

Q11 diagram is surely just plain wrong, superfluous extra size rectangle which is misleading

Thanks very much, YT.

If the exam is long and hard (within reason), that is not necessarily a problem. A systemic issue with MM and SM is that too much is too easy. But, you’re suggesting they have significantly overdone it. I’ll check the suggested errors later.

If you decide to take a proper look, questions 1 and 10 of the Sample Exam short answer are worth considering too.

Thanks. Very busy editing Burkard’s latest video transcript: he seems to think Mathologer is more important than spotting exam errors. But will try to look soon.

44 pages? Sheesh.

Hi, YT. Of course this is a new subject, with a new culture, and I don’t know the nature of the students at all. Do you have a sense, for this world, how acceptable or how problematic the errors and the context-guessing would/should be?

I have not got much experience with this group of students. I would guess a large number of the students doing this subject won’t sit the exam at all, going “School Assessed” instead as it will be a funnel for students who have learning difficulties of all kinds. I think the sheer amount of information to be processed is the major problem, particularly given the group of students. This of course hinders the ability to guess from context in a sensible manner. I guess they will just choose the questions they know how to do straight away.

Of the errors I identified there is a fair chance students will not realise the error having skimmed through the question and pulling out the “right” numbers anyway. Some students will definitely be confused at least by the diagram error in Q13 MC and Q11.

Thanks. I’ll look.

Thanks again, YT.

I’ve looked very quickly at the questions you flagged (and nothing else). I’m guessing you’re right, that for most or all of these questions the students will grab the numbers and do the only thing they can reasonably do. I’m also not sure to what extent it’s sporting to be critical in the same manner as for the other subjects. I’m not convinced any are “errors” per se, although there’s definitely some clumsiness. (Q1 and Q6 seem the most errorish to me.) But perhaps I’ve been so mean the last couple weeks, I’m just too tired to keep it up.

For what it’s worth, here are my quick thoughts.

MCQ6. What is wrong with this? I couldn’t see.

MCQ13. Yeah, it certainly seems like bad wording and I would have thought, at minimum, momentarily confusing for some students. I wonder if there is some semi-convention being followed.

Q1. What worried you here? The one thing that concerned me is there are two ways to work out the percentage increase in part (c), and I’m not sure the answers agree. (I only calculated quickly.) Admittedly, the second method takes an extra preliminary computation, so probably no one will do it.

Q2. Part (a) is trivial, but why “mockery”? Also, I couldn’t care less about the gender thing, but would there be a problem if the preamble referred to “gender” rather than “identified gender”?

Q6. Yes, this seems genuinely bad. It probably won’t affect how students answer, but it’s definitely teaching Not Maths.

Q10. What is the problem here? I’m not sure what would be expected for the 1-mark “show that” in (d)(i), but other than that I’m not sure of any issues.

Q11. Yeah, that is one crazy rectangle. Like I speculated for MCQ13, could this be some weird convention, which the kids would be used to?

MCQ6 – “The approximate percentage of Instagram accounts following the natgeo account” is the question and the students only have the “total number of followed Instagram accounts” which is a subset of total accounts and not the same thing unless my ignorance of Instagram is tripping me up.

MCQ13 – I’m not sure about a convention, I would think that “Payment” by itself would have always referred to the single period value.

2e. was the one that bothered me, tagged on the back of all the data looking at participation and now all participating females are categorised simply as “ball sport” or “non-ball sport” when the students have probably been assuming people can do more than one thing seems odd. The gender thing I was just noting, doubt it will bother students. Edit: Also the graph surely implies that the non-ball sport % column is no more than 30

Q11 – Having a quick look at a textbook (Nelson) and asking the subject teacher from this year I couldn’t see any evidence of a convention for this extra rectangle, pretty sure it’s just an error. It would seem they were going to add some extra concrete and changed their mind.

Q1 and Q10 I was actually referring to the VCAA Sample Exam which can be looked at here https://www.vcaa.vic.edu.au/assessment/vce-assessment/past-examinations/Pages/Foundation-Mathematics.aspx.

Adding picture for the house plan

Sorry, YT, I overlooked your reply. Quick re-replies.

MCQ 6: I think this is ok. I think we’re clearly only talking within the world of Instagram accounts, and then it’s fine. But I only looked quickly. Feel free to say it again.

MCQ13. Yeah, I agree. Bad error.

Q2(e). Oh, geez. That question is screwed every which way from Sunday.

Q11. I agree. The rectangle doesn’t even make any sense.

S1 and S10. Doh! Can you save me some time and indicate what’s wrong?

Sample Exam 1: Very strange blend of fractions and approximations

I guess the context is cooking so it’s not so bad, I would never want a student to estimate with a fraction though.

Sample Exam 10: A hilarious context (trucker taking stops along a predefined route with rest times in a geometric sequence.)

Also students doing alot of visual guesses from images and then making oddly precise calculations with them. One of these a “show that” in part d

Sample image included

Thanks Stephen. Q1 I’m ok with, for the reason you suggest: fraction approximations in cooking is more natural than in other contexts. I agree, Q10 is pretty funny, and pretty weird.

Is there a copy of the exam or the relevant questions online anywhere? I imagine High Schools Activate might take an interest in it.

I don’t know of it, but am fine with anyone posting a reddit link or whatever.

Nearly as bad as 2016 MM2 exam the famous PDF error, on this foundation math paper, Question 6, the black percentages do NOT add up to 100% in the diagram…

Not sure what would happen if some students did subtraction of non-renewable energy percentages from 100% rather than using sum of all renewable energy percentages. Two answers were close but not matched. 40.2% and 40.3% respectively.

Should this be counted as the 8th error across all four maths subjects?

I’m not convinced it’s bad or an error.

Or it was just an “unintentional slip”?

Does the question have a disclaimer that all percentages are rounded to the nearest 0.1% and don’t necessarily add up to 100%?

Should it add up to 100%? If not, why not?

Marty, if it’s not an error, what is it? Are you saying the discrepancy is OK? If so, when does a discrepancy become large enough that it becomes an error? It’s a slippery slope.

Is it the error of the data source (EMO Quarterly), not the VCAA? (No need to fact check info before citing?) Or has VCAA not included the above disclaimer (if there was one)?

It’s Foundation, not Methods. Yeah, maybe there should be a “may not add up disclaimer”, but I don’t see it as a big deal.

It’s Methods, not 2nd year Mathematical Probability and Statistics. Maybe they should have had a disclaimer that it might not integrate to 1, but no biggie …

(Said at the risk of poking the bear).

Nah, your poke missed. The ≠ 1 situations are not much similar at all.

I understand that, at this stage, people want to kick VCAA for every half-way slip up, and I’m more than happy to put the boot in when I think it is warranted. In the dedicated Errors post, I’ve listed “errors” that are seemingly of no concern to teachers, and I’ve flagged as “major” errors that teachers seemingly regard as minor.

But this one, I’m just not that fussed. I’d consider it maybe a minor error, for there not being a “may not add to 100%” warning, but that’s the most.

To me the ≠ 1 situations are similar because this is indeed a ≠ 1 situation. If, as Centurion says, there a two different answers depending on the working, it seems that it is something that VCAA needs to explain how they will mark it.

Maybe I’m getting soft in my old age.

I agree that, at minimum, it’s needless and not great. It would have been easy enough to have added a 0.1% somewhere and included an “adapted from …” clarification in the source acknowledgment. Nonetheless it seems to me that, for a number of reasons, this ≠1 situation is way less “wrong” than the Methods distribution. I’d still call it “minor error” but no more.

The picture looks like it was copied from an official report. In such reports, it is often the case that the percentages do not add up to 100% due to rounding. Teachers of Foundation Mathematics should point this out to their students. I always check such data for this.

Of course. The question is whether this is standard practice in Foundation, and/or whether it is standard practice for such a chart to include a “may not add up” disclaimer.

Yowzer. I just attempted this exam cold, out of sheer curiosity – using the allocated reading time and writing time. Admittedly, I did the exam on a sheet of paper with a computer screen, so it wasn’t an exact replication. I also got up once to go to the bathroom – so I maybe lost about 3 minutes there.

But keeping that in mind… I, an adult, working at a reasonable but not overly rushed pace, barely finished with enough time to even think about double checking any answers. And let’s be real – I’m only human so it is entirely possible I have made some small mistakes somewhere.

There is so much reading comprehension required and I am not sure how much working out some of these questions require, which also means that if you err on the side of caution, you waste valuable time writing down enough information. As stated, every question involves some kind of application and usually more than one step – meaning lots of room for error when entering numbers into a calculator.

An average student has no chance of finishing this paper in time. Knowing the sorts of students that would choose this subject, this exam is not fit for purpose. I don’t even have the brain capacity at the moment to nitpick this any further, because my mind is still reeling that I needed almost the whole time to complete the exam in the first place.

Thanks, SMT. Not really for me to judge, but it seemed to me a pretty loony exam for such a subject.