31 Replies to “Secret 2024 Foundation Business: Exam Discussion”
Just had a quick look at the exam. Only one minor thing stuck out to me and that is regarding the wording of question B2a. Specifically I feel the use of “would” is not correct. Though doubt it would have caused any problems. As I said only minor, though for some reason I found it particularly irritating. Also B2c seems a little difficult in comparison the rest of the exam; I’d be interested in seeing how students answered it.
Hi, James. Yes the “would” is a little odd. I’d go with “might”, but perhaps that was considered a little proper. And yes, (c) seems heavy for Foundation, although I’m not a good judge.
Had a bit of a longer look and noticed something else. Would students taking Foundation be expected to know that the width of a hexagon is twice the side length? If not then MCQ 20 could be quite problematic. If students know that the width is 8cm then they should get the correct answer of 21 without too much trouble. However the question gives the height of the hexagon as 6.92cm (they seem to have rounded down from the actual value of approximately 6.928). If students use this value along with Pythagoras (which students should know given it’s in the formula sheet) to find the width then they’ll get a value slightly larger than 8 and therefore a final answer of 18, which isn’t one of the options. If they’d given the height as 6.93 this wouldn’t be a problem.
Or perhaps students were meant to realise that only four hexagons fit vertically and so the hexagonal pattern is 4, 3, 4, 3… and therefore the only answer can be 21. Although I doubt this would’ve been the expected approach and if it was am not sure why the side length is given.
Anyway only a minor problem that I doubt would’ve led any students to answer incorrectly but could’ve been avoided had the height been rounded up to 6.93.
Hmm. I think the question is much worse than you suggest. I *think* I understand what it is asking, but, really, the question is meaningless as written. The question is also familiar: I’m sure I’ve seen a very similar question in my blog travels, and I remember disliking it then as well, even when better phrased.
EDIT: Yes, I WitCHed the question, when it appeared in VCAA’s sample materials for FM.
Yeah, the more I consider it, the worse it seems. Certainly there are other problems with the question, all addressed in the WitCH you link to. I do think it’s fairly obvious what the question is asking though. Why they can’t simply ask how many regular hexagons of size X fit in a rectangle of size Y I’ll never understand. This insistence on giving everything some “real world” context, no matter how ridiculous, is a problem the plagues all the maths subjects. This whole exam seems to be testing students literacy as much as it does any mathematics. I also wonder how students are even meant to get through the exam in 2 hours. Simple as it is, there’s a lot of reading and a lot to do.
In my previous comments I was simply focusing on the bad mathematics of it. Which, to me, is still by far the biggest problem. Even if the problem had been worded better, the problem still remains that a valid mathematical approach, using the information given and knowledge/skills a Foundation student should be expected to know (I think anyway, you’d have to ask a Foundation teacher) leads to an “incorrect” answer.
Thanks again, James. I haven’t looked carefully at the exam beyond the questions you flagged. But, like last year, it seems longer than War and Peace. I really don’t understand the purpose of such an exam, particularly for such a cohort.
MCQ 10: due to rounding, it is possible that exactly 260 students got news from their teacher, making both A and B possibly correct (but A is obviously the expected answer and is definitely “more correct”)
Nice catch. Is A obviously the expected answer though? I would’ve thought B is the expected answer. Either way I think the mistake is bad enough that both should be accepted.
EDIT: Yeah, this one’s bad. If a student calculates 259/1064 since the question asks for fewer than 260, they’ll get 24% and probably choose B. If they calculate 260/1064 they’ll also get 24% but probably choose A. Or maybe still even choose B since 24% percent is still less than 24.4 the calculator will give.
Thanks, Jay. No question that in a proper mathematical world the answer 3/2 should not be acceptable. But this is Foundation, so I think it is reasonable and good for VCAA to accept the fraction form.
During recent weeks I have had the opportunity to look at the examination for Foundation Mathematics 2024, although I have not worked through it. However I offer the following general observations.
Foundation Mathematics has only one examination rather than two examinations. I approve of this.
Students need only a scientific calculator rather than a CAS calculator. I approve of this.
Students who had passed this (whatever “passed” means) have demonstrated that they are reasonably numerate.
It is odd that some parts of the examination are not available due to copyright restrictions. This problem can be easily avoided.
Report and marking guide only stated that one question and the wording of the exam was ambiguous to the point that both responses should have been accepted.
Yaniv, I’ve looked and I don’t see any ambiguity in 10(b)(i), and I don’t see anything wrong with the calculation in the report. You’ll have to spell out in detail whatever is bothering you.
I’m tired. I appreciate your posts, but I’d appreciate them a lot more if you would spell out your concerns, rather than just posting “this sucks”.
I know you know what you’re doing, and if you say it sucks then it very probably does. But please consider your very tired blogger and say *why* it sucks.
How students likely would add up the width would be to go from left to right and add up what seems to give the total width. Here it would be 3.9 metres (bedroom) + 5.7 metres (dining room) = 9.1m
The length they would do a similar thing and go from up to down and add up what seems to give the total length. Here it would be 3m (kitchen) + 4.6m (dining room) + 4.3m (entry) + 5.5m (living room) = who knows what. EXCEPT entry is actually pointed to the left and is part of the overlap. An unnecessary trick
Very easy to miss this in an exam that would be time pressured to students
Well, I certainly don’t like Q11. Like almost all of Foundation, it seems nuts, just pseudo-application. The diagram is also certainly not great: why bother with forcing the entry dimensions if you don’t also bother with storage and bathroom, and why put the dimensions where they have? But I don’t see that the question is *that* confusing.
To get the width, for example, you look at the bedroom and dining room. So, which dimensions do you choose? There seem to me two easy ways to see that.
Just had a quick look at the exam. Only one minor thing stuck out to me and that is regarding the wording of question B2a. Specifically I feel the use of “would” is not correct. Though doubt it would have caused any problems. As I said only minor, though for some reason I found it particularly irritating. Also B2c seems a little difficult in comparison the rest of the exam; I’d be interested in seeing how students answered it.
Thanks, James. My guess is there will be more that annoys me but I haven’t seen the exam yet.
Hi, James. Yes the “would” is a little odd. I’d go with “might”, but perhaps that was considered a little proper. And yes, (c) seems heavy for Foundation, although I’m not a good judge.
Had a bit of a longer look and noticed something else. Would students taking Foundation be expected to know that the width of a hexagon is twice the side length? If not then MCQ 20 could be quite problematic. If students know that the width is 8cm then they should get the correct answer of 21 without too much trouble. However the question gives the height of the hexagon as 6.92cm (they seem to have rounded down from the actual value of approximately 6.928). If students use this value along with Pythagoras (which students should know given it’s in the formula sheet) to find the width then they’ll get a value slightly larger than 8 and therefore a final answer of 18, which isn’t one of the options. If they’d given the height as 6.93 this wouldn’t be a problem.
Or perhaps students were meant to realise that only four hexagons fit vertically and so the hexagonal pattern is 4, 3, 4, 3… and therefore the only answer can be 21. Although I doubt this would’ve been the expected approach and if it was am not sure why the side length is given.
Anyway only a minor problem that I doubt would’ve led any students to answer incorrectly but could’ve been avoided had the height been rounded up to 6.93.
Thanks, James. I see the exam is up now. I’ll look at all this soon.
Hmm. I think the question is much worse than you suggest. I *think* I understand what it is asking, but, really, the question is meaningless as written. The question is also familiar: I’m sure I’ve seen a very similar question in my blog travels, and I remember disliking it then as well, even when better phrased.
EDIT: Yes, I WitCHed the question, when it appeared in VCAA’s sample materials for FM.
Yeah, the more I consider it, the worse it seems. Certainly there are other problems with the question, all addressed in the WitCH you link to. I do think it’s fairly obvious what the question is asking though. Why they can’t simply ask how many regular hexagons of size X fit in a rectangle of size Y I’ll never understand. This insistence on giving everything some “real world” context, no matter how ridiculous, is a problem the plagues all the maths subjects. This whole exam seems to be testing students literacy as much as it does any mathematics. I also wonder how students are even meant to get through the exam in 2 hours. Simple as it is, there’s a lot of reading and a lot to do.
In my previous comments I was simply focusing on the bad mathematics of it. Which, to me, is still by far the biggest problem. Even if the problem had been worded better, the problem still remains that a valid mathematical approach, using the information given and knowledge/skills a Foundation student should be expected to know (I think anyway, you’d have to ask a Foundation teacher) leads to an “incorrect” answer.
Thanks again, James. I haven’t looked carefully at the exam beyond the questions you flagged. But, like last year, it seems longer than War and Peace. I really don’t understand the purpose of such an exam, particularly for such a cohort.
MCQ 10: due to rounding, it is possible that exactly 260 students got news from their teacher, making both A and B possibly correct (but A is obviously the expected answer and is definitely “more correct”)
Nice catch. Is A obviously the expected answer though? I would’ve thought B is the expected answer. Either way I think the mistake is bad enough that both should be accepted.
EDIT: Yeah, this one’s bad. If a student calculates 259/1064 since the question asks for fewer than 260, they’ll get 24% and probably choose B. If they calculate 260/1064 they’ll also get 24% but probably choose A. Or maybe still even choose B since 24% percent is still less than 24.4 the calculator will give.
Thanks, Jay. That is weirdly and needlessly borderline. Why do you consider A the expected answer?
Apologies, B is the expected answer. I should stop writing comments at 2am
No worries, and thanks. I appreciate the exam scrutiny.
Question 1C marking guide: the ratio 3:2 definitely shouldn’t be expressed as 3/2
Thanks, Jay. No question that in a proper mathematical world the answer 3/2 should not be acceptable. But this is Foundation, so I think it is reasonable and good for VCAA to accept the fraction form.
During recent weeks I have had the opportunity to look at the examination for Foundation Mathematics 2024, although I have not worked through it. However I offer the following general observations.
Foundation Mathematics has only one examination rather than two examinations. I approve of this.
Students need only a scientific calculator rather than a CAS calculator. I approve of this.
Students who had passed this (whatever “passed” means) have demonstrated that they are reasonably numerate.
It is odd that some parts of the examination are not available due to copyright restrictions. This problem can be easily avoided.
Thanks, Terry. It’s an odd beast, not all bad.
Q10bi should be more throughly scrutinised. Attached is VCAA’s solution
Attached is an alternative solution that WOULD NOT have been accepted. The exam report notes that this question is a 1% solve rate
Thanks, Yaniv. The question would have to be scrutinised before it could be more thoroughly scrutinised. But I will scrutinise it tomorrow.
Is it obvious from the report, or otherwise, why VCAA would have not accepted your alternative solution?
Report and marking guide only stated that one question and the wording of the exam was ambiguous to the point that both responses should have been accepted.
OK. Can you save me some work and summarise what is going on? Is VCAA’s solution wrong or is the question ambiguous? Either way, why?
All the question stated was that a 2.5m rubber wide something is to be wrapped around the pool.
Two interpretations exist. 1: VCAAs interpretation which groups the whole ‘base’ of 45m as a rectangle.
2. Alternate interpretation which groups 25m as a rectangle and the remaining 20m as part of the rounded shape
Yaniv, I’ve looked and I don’t see any ambiguity in 10(b)(i), and I don’t see anything wrong with the calculation in the report. You’ll have to spell out in detail whatever is bothering you.
This diagram is absurd – so easy to add ‘entry’ 4.3m as part of total length.
Also, barely anything in formula sheet was assessed
Yaniv …
I’m tired. I appreciate your posts, but I’d appreciate them a lot more if you would spell out your concerns, rather than just posting “this sucks”.
I know you know what you’re doing, and if you say it sucks then it very probably does. But please consider your very tired blogger and say *why* it sucks.
How students likely would add up the width would be to go from left to right and add up what seems to give the total width. Here it would be 3.9 metres (bedroom) + 5.7 metres (dining room) = 9.1m
The length they would do a similar thing and go from up to down and add up what seems to give the total length. Here it would be 3m (kitchen) + 4.6m (dining room) + 4.3m (entry) + 5.5m (living room) = who knows what. EXCEPT entry is actually pointed to the left and is part of the overlap. An unnecessary trick
Very easy to miss this in an exam that would be time pressured to students
Thanks very much, Yaniv. Your second was-anonymous comment somehow got flagged as spam, and I’ve unspammed it now.
I know Foundation has *lots* of clunkiness in it, and I appreciate your flagging stuff. I’ll look at the two questions later today.
Well, I certainly don’t like Q11. Like almost all of Foundation, it seems nuts, just pseudo-application. The diagram is also certainly not great: why bother with forcing the entry dimensions if you don’t also bother with storage and bathroom, and why put the dimensions where they have? But I don’t see that the question is *that* confusing.
To get the width, for example, you look at the bedroom and dining room. So, which dimensions do you choose? There seem to me two easy ways to see that.
Sorry the anonymous reply was by me – didn’t put in my name by mistake