Articles recently in the TES and Mathematics Teaching have
debated whether or not the standard of A-Level Mathematics is declining. In
detail, it is being said that
- A-Level standards are falling.
- Modular A-Levels are easier to pass
- Examination papers are less demanding
As an A-Level teacher of some 16 years experience, I have
to give a resounding Yes to each and every one of these hypotheses. The trouble
is, this may not be PC (politically correct not personal computer) to openly
admit. Make no mistake, I am no supporter of the British Government. Far from
it. My problem, as a socialist, is am I a supporter of New Labour?
Research
published in the TES (6 December 1996) says, according to SCAA/OFSTED, the E
grade has become easier. I don't mind that. I've known students over the years
who have worked very hard indeed over the two year course and should have
earned their pass grade, but the examination system was too tight to
permit it.
Apart from this, it seems blindingly obvious to me every day I
teach Year 12 and 13 students that it's getting easier. Just when a topic is
beginning to get interesting, then you discover you have already overshot the
outer reaches of the syllabus by a light year. Topics seem to float according
to the whims of the Syllabus-makers between Mathematics, Further Mathematics
and nowhere. Currently, the trapezium rule for approximate integration is
considered a Further Mathematics topic. Why? Complex numbers are similarly
deemed "hard". What a pity with the growth in interest in fractal mathematics.
The fact that Modular papers are easier to pass (easier
than what?) may not be a criticism at all. There may be many explanations, the
simplest of which is the ability to re-sit a modular paper as many as three
times during a 2-year course. This is not to say that any paper is easier in
itself, but rather, as with the driving test, it would be much harder to pass
if you were allowed only one chance.
What about the examination papers themselves? I subscribe
to the view that, more or less, over time, teachers and students change very
little, and those changes are very difficult to measure. On the other hand,
syllabi and examination papers change much more and surely those changes are
quantifiable. A paper sat last January 1996 included one question that asked
students to find 5 numbers that had mode 3, median 4 and mean 5. Here are some
questions from exam papers over the last 25 years. Read them and judge for
yourself. They are all Question 1 on the respective paper. |
1971
(a) If a + b +
c=a2+b2+c2=a3+b3+c3=2,
find by considering values of (a+b+c)2 and (a+b+c)3, or
otherwise, the values of (i) ab+bc+ca, (ii) abc.
Hence find the equation
whose roots are a, b and c.
(b) If y={F(x)}f(x), find the value
of dy/dx in terms of F(x), f(x), dF(x)/dx and
df(x)/dx. |
1976
(a) Solve the simultaneous equations
log2x + log2y=3, logyx=2
(b) A man
borrowed £1000 on 1st January 1973 at an interest rate of 1% per calendar
month., the interest being added on the last day of each month. The man repayed
the load in 30 equal installments each of £x, made on the first day of...
|
1981
When f(x), where
f(x)=x4-2x3+ax2+bx+c, is divided by x-2 the
remainder is -24. When f(x) is divided by x+4 the remainder is 240. Given that
x+1 is a factor of f(x), show that x-1 is also a factor. |
1986
Solve the equation
4x3+8x2+x-3=0,
given that one of the roots is an
integer. |
1991
It is given that 4x=8
2x+1. By expressing each side of this equation as a power of 2, or
otherwise, find the value of x. |
1996
The points A, B and C have coordinates (5,
-3), (7, 8) and (-3, 4) respectively. The midpoint of BC is M.
(a) Write
down the coordinates of M
(b) Find the equation of the straight line which
passes through the points A and M. |
  Comments
by Neil Zammit (NeilZammit@aol.com) April 1998
|
"I was reading your article on maths
A-level standards becoming lower. I have to say that I think that the exams are
as hard to pass as they always have been.In my experiance the teaching is
becoming worse. I am just about to take P1 and M1.I got an A grade in my GCSE
with EDEXCEL and I have to say that I was completely unprepared for A-level
maths. I have found that the teaching style that I am exposed to now is
extremely different to that which was found at GCSE. I think that students now
are unprepared for the amount of work that is involved. The amount of work that
is needed to find out what the student needs to know. I find that my teachers
either work through problems solving them quickly and without proper
explanation of how to answer a question of the type in the exam or they go into
the principles behind the maths.I feel that the purpose of the teacher is to
help you get a highest grade as possible, not to give you a complete knowledge
of the mathematical science.
Today I tried to work through a past exam paper(Jan 1998)
and I was not surprised that with over half of the questions, I didn't know
where to start. I admit that I haven't tried my absolute best at maths but in
my opinion, my teachers haven't taught to the fullest ability.
You say that the E grade is becoming easier to achieve.
Maybe so but as I now do AS level, what use is one point for university
applications? It probably would be better to repeat the year.
Maths has a major problem in education. The government
has promised to tackle it but this promise is too general in it's present form
and unless something is done, there may well be excellence up to the age of 16
but the present government will probably fail hundreds of students at a time
when they will blame poor education on another administration." |
by J Lees (jlees@btinternet.com) April 2000
|
"I wouldn't know. I've never taken
them before. But I'm doing maths and further maths A'levels, STEP Maths II and
III and hold a place to read maths at Cambridge in October... and find a lot of
the mathematics hard. The single maths A'level is, admittedly, easy in my
opinion - I took it at the end of my Lower Sixth year, in modules - but further
maths is a different matter altogether. P4 (Edexcel) is very difficult and
conceptual in parts, although topics like proof by induction are not hard per
se but build on previous work to introduce hard trig, algebra, complex numbers,
etc. STEP is impossible in places.
If the single maths A'level were harder
it would put many capable students off. Let the able and enthusiastic do
further maths as well - it will stretch them, believe me.
Maths is not so
much getting easier as getting accessible. Hopefully the new AS system will
help this. " |
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