Convergence is not only university work. (1 Viewer)

[buchanan]

Some people think convergence is only university work.

It isn't.

The current 1-year 4 unit course used to be a 2-year course (Level 1). Covergence was in Level 1 and used to be taught in high schools in NSW. Other countries' syllabuses for high school maths also have convergence. So it isn't only university work.

Level 1 was watered down to the 1-year course in 1981.

Many people would like the 2-year course to return.

The only excuse for why the harder Level 1 course can't be taught in high schools again, is teacher incompetence. And that's a very poor excuse.

 

[acmilan]

You know thats not what slidey meant, buchanan

 

[Riviet]

A 2 unit 4 unit course would be interesting, but wouldn't fit the 1 year HSC schedule that we currently use (although starting the 2 year course at the beginning of yr 11 could be a possibility).

 

[Trev]

*shouldn't have attempted that convergence question*

 

[Trev]

I smell lies.

 

[buchanan]

A 2-year 4 unit course would be interesting.

I spoke to Peter Osland from the Board of Studies about this when the syllabus changes and he said that it's a possibility.

Here are the topics previously in the course which have been removed, but many people want back:

Leaving Certificate (1916-1966)

• 3rd derivative test for inflections
• Substitution x=acos<SUP>2</SUP>θ+bsin<SUP>2</SUP>θ for ∫√((x-a)(x-b))dx, ∫(1/√((x-a)(x-b)))dx, ∫√((x-a)/(b-x))dx
• Euler's Formula
• Integration as a summation
• Determinants and solutions of equations
• Convergence and divergence of infinite series
• Logarithmic and Exponential series and Euler's constant
• Binomial series for fractional or negative index.

Level 1 (1966-1980)

• Euclidean algorithm
• Proof of the fundamental theorem of arithmetic
• Determinants and the solution of equations and area of triangle
• Geometry of matrices
• Geometrical transformations using matrices
• Algebra of matrices
• Rolle's theorem and mean value theorem
• Integration as summation
• Euler's formula
• Length of arc
• Group theory, isomorphism
• Applications of matrices to geometry and probability
• Work, Kinetic Energy, Potential energy
• Convergence and divergence of infinite series
• Riemann Zeta function
• Logarithmic and exponential series
• Series for sinx, cosx, tan<SUP>-1</SUP>x
• Taylor's series.

Level 2F (1966-1982)

• Mid-ordinate rule
• Change of coordinate systems - transformations
• Analytical geometry in three dimensions

Quite a lot of this stuff which used to be taught in school, is now postponed till university in Australia. However, other countries are still teaching it in school. So Australia is seen as a bit behind the rest of the world, particularly in regard to school maths and 1st year uni maths.

If we bring these topics back and make 4 unit a 2-year course again, we won't have to postpone them till university, and perhaps the uni's can then focus on what they should be doing and not have to teach what should have been done in school, as they currently do.

 

[acullen]

Convergence is actually a pretty interesting topic, it requires a bit more than regurgitating a procedure (as every integration question does), but applying a series of tests to the sequence/series based on educated "guesses"of its behaviour.

 

[acullen]

Oh and I should add that our system isn't in too bad of a state when you consider the typical mathematics a high school student in the US would learn. The majority will not do calculus until they reach university. But compared to some Asian and European countries, we're certainly lagging a bit.

 

[Raginsheep]

The only excuse for why the harder Level 1 course can't be taught in high schools again, is teacher incompetence. And that's a very poor excuse.

What are the current requirements for teaching 4u maths?