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New Further Maths A/s And A`level Will Cause Panic In The World Of Maths Teaching

The affects of the changes to the A`level Further Maths syllabus

Date : 24/08/2017

David

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Uploaded by : David
Uploaded on : 24/08/2017
Subject : Maths

Needless to say, even before I stat writing, I am able to support all the subjects at the foot of this blog post. I also welcome comments about the post.

The new further Maths syllabus, set for first teaching in September 2017 and first exam in 2018 (A/S) and 2019 )A`Level) will send many teachers into panic mode and some into retirement. The syllabus is toughest syllabus for more than 30 years. With the introduction of a large number of new subjects and negligible support from the examining boards, this new change is sure to cause wide spread panic amongst teachers.

I was very interested to note about the books being written to support the new topics. They aren`t ready yet! They are expected to be ready by September but I doubt it! I tend to kind of think (for all the further maths topics only) that you will be looking at October/November at the earliest. I very strongly suspect that some of the advanced topics (*) won`t appear in print for a year.

I am sure we`d all agree that mathematics back in the 1960s and 1970s was the toughest A`level ever. And ever since this time, maths has only been getting easier and easier. Almost to the point of being rediculous. I remember that when I went to university in 1999, the directors of studies were up in arms over the inabilities of students being unable to long division of both numbers and simple polynomials. They were considering introducing a foundation year to bring students up to the required standard.

Many people have the deluded opinion that all maths teaches know everything about the subject. The fact is, that simply isn`t true. It is true that those teachers just leaving university will be best place and probably not affected by the new changes. There is an old saying: “If you don`t use it, you lose it”. The fact is if a teacher has been graudually deskilled over a number of years because of eroding standards. You cannot just roll the clock back and expect a teacher to know it all. The older teachers will have an advantage of having text books from the 1960s and 1970s when things were so much tougher but not all the topics are in there.

Be aware of the internet! The internet, whilst it is a wonderous source of information. It can also be a place of misinformation. In the world of maths, you will find a lot of complicated documents that support what you want but they will often come along with something else or be written in a complicated way, because they are intended for a different audience.

All is not lost though! I believe teachers have 1 year to catch up. The first year subjects aren`t likely to test any teacher at all. So they have a year to get exercised in the 2nd year subjects. If the school has a good maths department then I am sure there will be plenty of lessons to help bring everyone up to speed.

The new changes only really affect the pure maths part of the further maths syllabus. The new subjects include:-


The Euclidean Algortithm

Strictly speaking, this is quite a simple topic that said, it is still something teachers will need to prepare a lesson plan for. Beneath it`s simplicty there is a lot of use for this subject in the first year of the degree. It`s important for “Elementary Number Theory


The theory of equations: cubics and quartics

For the last 30 years only quadratics have been part of the syllabus. The cubic equation was last on the syllabus over 30 years ago, back in the 1970s. There is little or no ready-to-hand information on this topic. The topic isn`t a particularly difficult one but it is one in which it is easy to make mistakes. Cubic and quartic relations can be complicated and messy. Many students who have poor algebraic skills will find this topic a real challenge!


Matrices and Transformations

Matrices and geometric transformations were last on the syllabus up to the 80s, maybe even into the 90s. Even then, eigenvalues and eigenlines were on the syllabus only in the 1970s.


Functions of a complex variable*

Whilst complex tranformation and loci on the complex plane has never left us, this topic is a big step for A`level students. I do believe it was on the syllabus back in the 1970s.


Solving parametric differential equations

These were never on any syllabus that I know of but they used to appear on the old S papers from time to time. I don`t think this is a particlarly difficult topic


Differentiation from first principles

I believe most A`level tutors teach from this perspective, so this isn`t a big ask at all. When differentiation appears on the GCSE papers only the rules ar taught, but when you migrate to A`level I believe most teachers would take the backward step and teach it from first principles.


L`Hospital`s rule (La Hop-ital)

This is a wonderful, advanced topic The only concern I would have is that it is very likely students will get confused over this rule and the quotient rule. It`s this kind of rule that gets mathematician`s interested because it`s all about where things go wrong.


Groups*

This used to be on the syllabus up to the middle of the 1980s and then it disappeared. This is a facinating subject. I only wish they would add Rings and Fields too. It will take some getting used to.


Reduction formulae and difference equations

Reduction formulae dropped out for a long time whereas difference equations have never left us albeit only in the decision maths syllabus. So reduction formulae have come back and difference equations have been made a little more challenging. I don`t expect this to cause too many issues.


Leibniz`s Theorem

Oh yes! This is a rule about differentiating an expression n tims and generating a general formula. This has very very strong ties with the bionomial theorem for a positive index. Once again, this hasn`t been on the syllabus since the 1970s but it used to appear on the S papers in the 1980s. The rule wasn`t specfically required, you just had to be develop the expressions that the rule would have made obvious.


Multivariable Calculus (Differentiation and Integration)

This isn`t actually on the syllabus, but it should be!
In simple situation for 2 and 3 independent variables.

It`s important to learners used to all the terminology before they get to the degree.

This should be extended to vector calculus

This topic used to be on the old extended A`level back in the 1960s.


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