Proposed directions for new NSW Calculus based courses (1 Viewer)

[anomalousdecay]

matrices are actually taught at the equivalent of year 10 level in many countries, not to mention that some keen students here self-learn it, it is by no means too complex for the course

Well if learning it in HSC, it would be quite an incomplete topic without knowledge of vectors imo. I was referring to it being a step up from vectors if you were to learn them properly.

And by properly, I don't mean just finding REF or solving a system of linear equations, I mean as in being able to do matrix multiplication, knowing the basic laws about matrices, etc.

It's not too complex but for a course like 4U it doesn't really fit in well with the rest of the content imo.

A basic understanding of matrices also would be quite superficial and would leave many students questioning "why are we doing this?"

Proves my point.

The problem with matrices is that you have to learn a term of methods (multiplication, Gaussian elimination, etc.) before you can start actually doing interesting stuff with them. Also, it's difficult to motivate them. Complex numbers can be used for awesome unrelated proofs and students still complain about their perceived lack of practical applications.

Any graph theory in a high school course would be 60% definitions and 30% algorithm memorisation. However, I agree that the ability to abstract problems into graph theoretical terms is one of the most useful devices in one's mathematical bag of tricks. No joke, I encountered a problem at work today involving popping elements off queues over a network, and the solution was to model each queue as a weighted path graph with common source and run Dijkstra's algorithm on it.

I hope statistical inference includes Bayes' theorem.

Its not until you hit some areas of engineering (possibly science too but not sure) that you start to see some real applications of using complex numbers.

 

[Axio]

 

[tywebb]

There is a theory going around at the moment that the intent is to just implement the draft syllabuses that were written in 2008. That may or may not be true because writing briefs and draft syllabuses will be written for this again. So it will be interesting to compare the new ones with the ones from 2008 which you can get here: http://www.boardofstudies.nsw.edu.au/archives/syllabus_hsc/mathematics-advanced.html

Unfortunately if the theory is true it may not be well received. Read Bill Pender's critique of the 2008 version to see why: http://www.angelfire.com/ab7/fourunit/0806BOSSubmission.pdf

 

[GoldyOrNugget]

Pender is such a legend.

 

[Carrotsticks]

There is a consultation on the proposed directions in North Ryde next Tuesday if anybody is interested.

https://www.eventbrite.com.au/e/con...yllabuses-north-ryde-registration-12088586287

 

[sepseminar]

Does this mean they are cutting conics out of the syllabus? Conics contain a number of fundamental graphs and are an essential part to the advanced high school mathematics syllabus. Moreover, it's one of the best topics in the 4u course since it can showcase a number of nice results that are reasonably accessible. Proving the fundamental properties of the ellipse such as the 'rubber band' property are very worthwhile exercises and really shouldn't be abandoned.