Proposed directions for new NSW Calculus based courses (2 Viewers)

[tywebb]

BOSTES has announced proposed changes to the NSW Calculus-based courses today and are calling for feedback via the online survey ( https://www.surveymonkey.com/s/bostesstage6 ) (closing date Sept. 21) or via written submission to the Board Inspector, Peter Osland (email peter.osland@bostes.nsw.edu.au )

Here are the proposed changes in content for the calculus-based courses on page 22 of http://www.boardofstudies.nsw.edu.a...f_doc/senior-secondary-evaluation-2014-08.pdf :

Preliminary Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as real numbers, algebra, functions, graphs, geometry, trigonometry, differential calculus, sequences and series, and descriptive statistics.

A number of modelling topics focusing on applications of Mathematics from other topics in the Preliminary course and utilising techniques from other topics in the course and earlier courses, such as applications involving real functions and applications of series to finance.

HSC Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as differential calculus, integral calculus, probability, trigonometry, exponential and logarithmic functions, descriptive statistics, and random variables.

A number of modelling topics focusing on applications of Mathematics from other topics in the HSC course, and utilising techniques from other topics in the course and earlier courses, such as applications involving probability and finance, applications to the natural environment.

Preliminary Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as circle geometry, further algebra, polynomials, functions, graphs, trigonometry, series, elementary difference equations, random variables, and the normal distribution.

HSC Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as mathematical induction, binomial theorem, methods and applications of integration, further trigonometry, inverse functions and the inverse trigonometric functions, and further applications of calculus.

Mathematics Extension 2

Approximately eight topics focusing on areas of Mathematics such as further inequalities, complex numbers, polynomials, functions, graphs, vectors, integration techniques, volumes, modelling with functions and derivatives, mechanics, difference equations, and statistical inference.

 

[GoldyOrNugget]

From what I can see, the differences are:

HSC Mathematics: +random variables
Prelim MX1: +circle geom, +random variables, +normal distribution
HSC MX1: -circle geom
MX2: +statistical inference, +vectors, +difference eqns


It's been a while since I did this stuff though.

Seems good to me. I wonder how much detail the MX2 vectors topic will contain.

 

[Trebla]

Totally did not expect statistical inference to appear in Ext2

 

[Stygian]

Vectors sounds cool, statistical inference less so

Im surprised matrices hasn't been incorporated into the syllabus yet

 

[randomly_generated]

This will definitely help with university level mathematics

 

[braintic]

From what I can see, the differences are:

HSC Mathematics: +random variables
Prelim MX1: +circle geom, +random variables, +normal distribution
HSC MX1: -circle geom
MX2: +statistical inference, +vectors


It's been a while since I did this stuff though.

Seems good to me. I wonder how much detail the MX2 vectors topic will contain.

You missed Difference Equations.
Also, methods of integration seems to be in Ext 1 rather than Ext 2. Not sure if it will be handled well at that level.

 

[anomalousdecay]

Vectors sounds cool, statistical inference less so

Im surprised matrices hasn't been incorporated into the syllabus yet

To understand matrices, you'll need to know vectors in depth first. Matrices can be a whole new ball game in some respects and contain a lot more variety which wouldn't be sufficiently covered in time in MX2.

 

[faisalabdul16]

Why did they originally remove matrices?

 

[tywebb]

Originally in 1965 when the HSC syllabuses were written matrices was included in the highest level course (called Level 1). This was revised in the 1970's and renamed 4 unit but matrices remained till 1980 when the most drastic change was made. Before that it was a 2-year course. In 1980 matrices was removed and it became a 1-year course.

There is still an argument for including matrices even in a 1-year course however. Maybe not covering all the content of the old Level 1 course. But you could still do some matrices.

I would say don't do statistical inference or graph theory and do some matrices instead.

Here are the older syllabuses for you to compare:

1965: http://www.angelfire.com/ab7/fourunit/level1syllabus.pdf

1973: http://www.angelfire.com/ab7/fourunit/4usyllabus1.pdf

1980: http://www.angelfire.com/ab7/fourunit/4usyllabus2.pdf

1989: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf

 

[Drongoski]

Will be fun!



PS

Guys, look at the 1965 Syllabus document.

All typed out or handwritten and figures hand-drawn. That was the state of the art. With the amazing mathematical typesetting software (Thanks to Donald E Knuth for his TeX) and the very sophisticated textual software that we now tend to take for granted, it is hard to imagine what it was like in those days. You must say that Jim Coroneos's self-published books weren't so bad at all.

 

[faisalabdul16]

Will be fun!



PS

Guys, look at the 1965 Syllabus document.

All typed out or handwritten and figures hand-drawn. That was the state of the art. With the amazing mathematical typesetting software (Thanks to Donald E Knuth for his TeX) and the very sophisticated textual software that we now tend to take for granted, it is hard to imagine what it was like in those days. You must say that Jim Coroneos's self-published books weren't bad at all.

Old Coroneos textbooks with that weird font kill the eyes haha

 

[Stygian]

To understand matrices, you'll need to know vectors in depth first. Matrices can be a whole new ball game in some respects and contain a lot more variety which wouldn't be sufficiently covered in time in MX2.

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

 

[RealiseNothing]

I would say don't do statistical inference or graph theory and do some matrices instead.

I don't see graph theory?

(though graph theory is absolutely awesome so I hope they include it)

 

[RealiseNothing]

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

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?"

 

[Stygian]

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?"

Yeah that is true it doesn't fit in too well with the other hsc topics (it might with the vectors) but why not teach it in year 10 and begin to incorporate it into some of the other topics? For example it can be used in co-ordinate geometry to find the area of a triangle etc.

To be honest i just think it's a cool thing to learn

 

[GoldyOrNugget]

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.

 

[Trebla]

I think that statistical inference will be quite limited in it's scope and difficulty unless students properly learn about distributions other than binomial and normal. I'm also wondering whether students will be learning about probability distribution theory which is necessary for statistical inference. If so, then the concept of infinite limits in integrals must be covered.

 

[tywebb]

Timeline for implementation has not been established yet. It won't be implemented next year.

 

[Carrotsticks]

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.

Haha amazing! I've personally found Graph Theory to be the most 'immediately useful' Mathematical topic.
Although Dijkstra's algorithm is fairly intuitive, it's always nice when a bit if Mathematics can help you with things in real life.

 

[Trebla]

Statistics in 2u? Omg no, they should save that for general– feeling sorry for next year's Year 11's haha :/

lol the statistics is much more interesting and complex beyond Year 10 and into uni level. It involves probability and calculus. Way too hardcore for general.