I must not fear.
Fear is the mind killer.
Fear is the little death which brings total
I will face my fear!
I will permit it to pass over me and through
And when it has gone past I will turn the
inner eye to see its path.
Where the fear has gone there will be nothing.
Only I will remain.
Frank Herbert - Dune.
Why was the
mistakes - a tale of integration.
So I duly had the extra lessons, from a lovely Scottish lady who kept
me "You can do it.". To my great surprise, I
found I could! I sailed through the exam with a grade "3" ( the
grades were 1 to 6 in those days, so a "3" was quite
I thought of taking history, physics and chemistry to Advanced level,
they wouldn't let me take history (my first love) - so I took
instead. In the end, I studied double maths, physics and
I then took a (third class) B.Sc in Chemistry with Mathematics
King's College London in 1979. I was a bit ashamed of the class
my degree, but greatly enjoyed university life. Amongst other
I was secretary of the students' union and learned many very useful
and lessons. I decided to teach maths in comprehensive schools, because
I was determined that I would not write anyone off as I had been
I taught for fourteen years, and loved it, but had to take early
due to ill health (ulcerative colitis). I started studying
with that wonderful institution, the Open
University, determined to tackle the more difficult
I had run away from twenty years before. I took a BA (first class
hons) at Christmas '99 and completed my M.Math (also first class
honours) in Y2k. I am also in the process of writing a book, part
of whose introduction I reprint below.
It is very rare (in education) genuinely to apply any branch of Applied
Mathematics. For example, it
is possible, even normal to study probability and statistics without
a single experiment or analysing any real raw data.
Consequently, although some students do extremely well in examinations,
they have no intuitive understanding of what their knowledge really
The same criticisms can equally apply to the study of Mechanics.
At university, the unit I took in Numerical Analysis enabled me truly
understand much of the 16+ school syllabus, especially the
for the first time. Calculus is such a key area that I feel that
there has been a tendency for teachers and traditional syllabi to
rush into it - trying to push students into running before they can
In fact, many students of mathematics never learn to walk at all! It
seems to me that proficiency in the techniques of the calculus is to
like a mathematical virilty symbol, but I often wonder how
real understanding there is. I believe that one should
empirical, finite techniques, before going on to the analytical,
I finally became happy with mathematics in my late teens, when, if I
understand something, a friend and fellow student encouraged me to work
it out for myself from first principles. (Thank you Bob!)
I started teaching, I found my own failings and failures a great
help, in that, from painful experience, I usually understood why
were having a particular difficulty. I also understood the
feelings of inadequacy and
physical ill-being which
any lack of comprehension. To all who have suffered these
I would say this: It is
not to understand a topic the first time you encounter it.
However, with patience, experiment,
and repetition, familiarity can breed content!