What do YOU think should be in the HSC exams in the next few years? (1 Viewer)

[tywebb]

If the national curriculum is to replace the current HSC syllabuses, for the next few HSC exams the exam committees will focus on aspects of the syllabus which have never been (or rarely been) examined in the external examinations.

At the Board of Studies, it is assumed that all aspects of a syllabus will be examined at least once during the lifetime of the syllabus. Although many aspects of the current syllabus seem to be examined quite frequently, others seem not to have been.

You guys seem well attuned to what has been examined recently, so i'm interested in what YOU think should be examined in the next few years.

For example should there be a question on proving the reflection property of a hyperbola? This was discussed last year at the MANSW 2011 Conference and there were some representatives from the Board of Studies who confirmed that that had not yet been examined.

 

[largarithmic]

MORE GEOMETRY!

edit: should probably be a bit more specific. The syllabus has scope for some really interesting and actually quite hard pieces of Euclidean geometry near the end, which unfortunately are quite rarely touched upon. In particular I'd love to see a question where you prove a simple geometrical result, and then apply it to do some sort of construction. (e.g. the question about areas I posted on the marathon). There were some very good geometry questions in SBHS trials in the early 2000s if I recall correctly, shame they never translate into external exam questions.

 

[IamBread]

More moving away from the syllabus. Onto to questions to test understanding rather then how well someone can remember something.

 

[zeebobDD]

i honestly think they should introduce matrices into 4u

 

[SpiralFlex]

Keeping in mind there's only a year to learn the content. I think the content currently is fine but the tests need slightly challenging questions.

 

[4025808]

More probability I suppose? Put probability along with actuarial and financial problems. Probability is one of those topics where it is actually tested in uni, unlike a lot of the geometry that we learn. Probability is a topic that will actually discriminate heavily between those who are intelligent and those who aren't.

However, I do suggest that you guide through the problems instead of just telling them to do this do that.

Or alternatively, get the committee who writes the Australian Mathematical Olympiad to write the questions, provided that they follow the syllabus too.

 

[1xcv3we]

Being a university student and having done 4 unit mathematics I certainly think the 4-unit course could get rid of things like the geometry, conics, volumes modules etc and introduce linear algebra modules or methods for solving differential equations. Having spent 3 years in university already, I have never seen anything like Euclidean Geometry, conics and volumes (apart from volumes of revolutions covered for like 1 lecture in 1st year) appear in any course I have done. Why not have linear algebra topics like solving linear equations, vectors, linear independence/dependence, basis, dimension, spanning sets, linear transforms....etc. Linear differential equations when restricted to 1st and 2nd order are not overly difficult, perhaps some methods like integrating factors and undetermined coefficients would be nice. I certainly think this stuff would be far more useful to students but NSW seems to have a great emphasis on pure mathematics.

 

[Carrotsticks]

Currently, many exam questions are like this:

a) Consider XXXX

i. Show that XXX 2 marks

ii. Show that XXX 2 marks

iii. Hence deduce that XXX 1 mark

They lead you to the answer. Although I agree that there should be such questions (surely an exam can't consists of ONLY difficult questions), I think there should be a couple of questions like this:

a) Consider YYYYY. Show that YYY. 5 marks

My reason for this is because more often than not, there is more than 1 way of doing a question. Including such questions in the Extension 2 Examination would promote creativity of solutions (perhaps even elegance).

This is just regarding exam format.

Regarding actual topics, it would be nice to have questions on topics that are rarely/never been examined. A well rounded student should be able to apply their knowledge in order to do these questions, regardless of practice or not.

 

[cutemouse]

Probably wouldn't hurt to introduce statistics, like the central limit theorem and its applications.

Regression analysis and ANOVA could be useful, but I admit that they are boring topics...

 

[delian]

i honestly think they should introduce matrices into 4u

Why?

 

[seanieg89]

Some elementary number theory, it is one of the most attractive and accessible subjects for a high school student.

 

[Carrotsticks]

Some elementary number theory, it is one of the most attractive and accessible subjects for a high school student.

The last number theory question I have seen in the Ext 2 HSC was 1989 Q8.

Wasn't fun.

 

[math man]

well i think victoria's syllabus has got it right, they have vectors matrices stats and some others i cant remember. I think 4u kids should learn
vectors properly so they can do the complex number vectors properly and also are able to better resolve forces in circular motion. However, if
you look at victoria's final external exam it is the biggest joke ever. Not only are the questions straight forward but they are given a formula sheet
which is basically a textbook...very silly imo. Overall in australia the external 4u exam of nsw is the hardest by far, shame they are ruining it with MC now

 

[seanieg89]

The last number theory question I have seen in the Ext 2 HSC was 1989 Q8.

Wasn't fun.

That one wasn't particularly nice. I meant more things like basic applications of Fermat's little theorem, basic results about primes etc.

 

[cutemouse]

The last number theory question I have seen in the Ext 2 HSC was 1989 Q8.

Wasn't fun.

It was stupid too because some students who were involved in extracurricular maths clubs had seen very similar problems before and therefore were advantaged.

 

[largarithmic]

It was stupid too because some students who were involved in extracurricular maths clubs had seen very similar problems before and therefore were advantaged.

This is actually a really ludicrous complaint to make. Students are always going to be "advantaged" in subtle ways; for instance anyone who took the time to try out olympiad-like maths or just really enjoyed geometry and worked through lots of problems on their own would likely have seen every single Euclidean geometry question that can possibly be asked. Similarly with things like inequalities and polynomials, or even permutations and combinations, there are going to be a handful of students in the state that would have seen almost more of those questions than several full classes combined (and Im not joking on this by the way). Similarly, there are going to be people who went to coaching colleges, hired a private tutor outside of that, paid full attention in class and then did every single exercises from say the Cambridge textbook and remember how to do all the "hard" types of extension questions.

So yeah, such students are "advantaged". But is it an unfair advantage? An unfair advantage is when the teacher actually tells the students, "I got a secret tip off that <this question> is going to be in your exam". This on the other hand is the sort of "advantage" where the student has displayed legitimate interest in maths and has taken the time to pursue it and it doesn't matter whether this in "extracurricular" or not. And this is the sort of "advantage" that is deliberately conferred on students by the design of these examinations to reward hard work and knowledge. Exams aren't a level playing field and never were supposed to be, instead they're a heavily weighted one but where you can change the weights yourself through interest, study and ability. I don't see how going to an extracurricular maths club is then any less valid a source of knowledge helpful in an exam than working though integration drill exercises.

 

[cutemouse]

This is actually a really ludicrous complaint to make.

Haha. I thought it was an alright question until I spoke to Peter Brown. He's the one who's shaped my views about that question

But that dude seriously hates University of Sydney for some reason. He ranted on about how the 1986 paper had so many errors and it was written by USyd...

 

[Trebla]

But that dude seriously hates University of Sydney for some reason. He ranted on about how the 1986 paper had so many errors and it was written by USyd...

lol looks like someone's holding onto a grudge for a very long time

 

[Carrotsticks]

Is Peter Brown a Maths lecturer at UNSW?

 

[mnmaa]

put vectors and vector calculus into the 4u course. Maybe even some hard vector proofs to sort the men from the boys