Flexible PGCE Mathematics Course
Pre-Course Information
Congratulations on attaining a place on the Flexible PGCE Course in Secondary
Mathematics. The course is demanding, and will challenge you in a variety of ways, but will
also provide a rewarding and fulfilling entry to your teaching career.
The Course leader for the Flexible PGCE Mathematics course is Felix Obadan. His office is
located on the second floor of the MATEC building. Enquiries prior to the start of the course
should be directed to Felix on 01695 584073.
Prior to commencing the course, we would strongly recommend you begin to raise your
awareness of certain issues around general education, the role of a teacher in the secondary
sector and the new secondary Mathematics curriculum. Some suggestions are given below
on how this can be achieved.
Hopefully, most of you will already have spent some time in schools, observing lessons. If
you have not done this or your opportunities have been limited, then the best preparation
that you can do for this course is to spend some time in a school. Obviously, it is
particularly valuable to watch good teachers teaching mathematics, but there is also much to
be gained from working with good teachers in other secondary subjects or in primary
schools. These observations will provide an invaluable insight into classroom management
skills, behaviour management and assessment skills as well as other expectations required
of an education professional.
You should also begin to deepen your awareness of educational issues by reading the
Times Educational Supplement (TES) (published on Fridays), the Education Guardian
(published on Tuesdays) and visiting relevant websites such as NCETM, ATM and BBC
Education.
There is no requirement to purchase any books for this course. However, a certain amount
of pre-course reading would be very valuable. Some recommended texts are detailed
below. The text is bold is highly recommended.
Goulding M (2004)
Tanner H & Jones S (2000)
Gates P (ed) (2001)
Haggerty L (2001)
Johnston-Wilder S, JohnstonWilder P, Pimm D, Westwell J
(2005)
Nickson M (2000)
Perks P & Prestage S (2001)
Chambers P (2008)
Fleming P (2004)
Clarke S (2005)
Cowley, S. (2010)
Learning to Teach Mathematics:
Becoming a Successful Teacher of
Mathematics
Issues in Mathematics Teaching:
Aspects of Teaching Secondary Mathematics
Learning to Teach Mathematics in the
Secondary School: A Companion to School
Experience
Teaching and Learning Mathematics
) Adapting and Extending Secondary
Mathematics Activities,
Teaching Mathematics
Becoming a Secondary School Teacher
Formative Assessment in the Secondary
Classroom
Getting the Buggers to Behave
David Fulton
RoutledgeFalmer
RoutledgeFalmer
RoutledgeFalmer
RoutledgeFalmer
Cassell
David Fulton
Sage Publications
David Fulton
Hodder Murray
Continuum
Publishing
Corporation
The links below are organisations that offer a wealth of useful resources for mathematics
teaching.
http://www.m-a.org.uk (Mathematical Association site)
http://www.ncetm.org.uk (National Centre for Excellence in the Teaching of Mathematics)
http://nrich.maths.org.uk/ (An online mathematics club)
http://www.stemnet.org.uk/ (Science, Technology, Engineering and Mathematics Network)
Historically students have been extremely positive about their experiences on the Flexible
PGCE Mathematics course - both in university and in school. Partnership arrangements
with local schools are strong, and students value highly the help and support that they
receive during the year from a wide range of professionals.
The PGCE course offers further opportunities for you to develop your subject knowledge.
Included below is a list of the ‘Core content for AS and A2 level’. Try to audit your own skills
against the statements listed. It will help you to identify gaps in your knowledge, which you
can then work on prior to starting the course. Again, any AS / A2 Mathematics textbook
would help with this.
Core content material for AS and A2 examinations is listed here.
No
furthe
r
work
Proof
Algebra
and
Functions
a) Construction and presentation of rigorous
mathematical arguments through appropriate
use of precise statements and logical
deduction
b) Correct understanding and use of
mathematical language and grammar, in
respect of terms such as “equals”, “identically
equals”, “therefore”, “because”, “implies”, “is
implied by”, “necessary”, “sufficient”, and
notation such as   and 
c) Methods of proof, including proof by
contradiction and disproof by counter
example.
a) Laws of indices for all rational exponents
b) Use and manipulation of surds
c) Quadratic functions and their graphs. The
discriminant of a quadratic function.
Completing the square. Solution of quadratic
equations.
d) Simultaneous equations: one linear and
one quadratic, analytical solution by
substitution
e) Solution of linear and quadratic inequalities
f) Algebraic manipulation of polynomials,
including expanding and collecting like terms,
and factorisation; simplification of rational
expressions
including
factorising
and
cancelling, and algebraic division.
g) Domain and range of functions.
Some
furthe
r
work
A lot of
further
work
Co-ordinate
geometry in
the (x, y)
plane
Sequences
and series
Composition of functions. Inverse
functions.
h) Graphs of functions and their inverses;
curves defined by simple equations.
Geometrical interpretation of algebraic
solution of equations. Use of intersection
points of graphs of functions to solve
equations.
I) The modulus function.
j) Knowledge of the effect of simple
transformations on the graph of y = f(x) as
represented by y=af(x),y=f(x)+a,y=f(x + a),y =
f(ax)
and
combinations
of
these
transformations.
k) Rational functions. Partial fractions
(denominators not more complicated than
repeated linear terms)
l) The Remainder Theorem (including the
Factor Theorem).
a) Equation of a straight line in the forms y –
y1 = m (x-x1) and ax + by + c = 0. Conditions
for two straight lines to be parallel or
perpendicular to each other
b) Co-ordinate geometry of the circle.
Equation of a circle in the form (x-a)2+(yb)2=r2
c) Cartesian and parametric equations of
curves and conversion between the two
forms
a) Sequences, including those given by a
formula for the nth term, and those generated
by a simple recurrence relation of the form
xn+1 = f(xn).
b) Arithmetic series, including the formula for
the sum of the first n natural numbers.
c) The sum of a finite geometric series; the
sum to infinity of a convergent geometric
series.
d) Binomial expansion of (1+x)n for positive
 n
integer n. The notations n! and  
r
 
Trigonomet
ry
e) Binomial series for any rational n.
a) Radian measure. Arc length, area of sector
b) Sine, cosine and tangent functions. Their
graphs, symmetries and periodicity
c) Knowledge of secant, cosecant and
cotangent and of arcsin, arccos and arctan.
Their relationships to sine, cosine, and
tangent. Understanding of their final graphs
and appropriate restricted domains.
d) Knowledge and use of formulae for
sin2  +cos2  =1 and its equivalents.
Exponential
s and
logarithms
Differentiati
on
e) Knowledge and use of formulae for sin
 A  B  , cos  A  B  and tan  A  B  ; of double
angle formulae; and of expressions for
acos  + bsin  in the equivalent forms of r
cos   a  or rsin   a  .
f) Solution of simple trigonometric equations
in a given interval.
a) The function ex and its graph
b) Exponential growth and decay
c) The function lnx and its graph : lnx as the
inverse function of ex. Laws of logarithms.
d) The solution of equations of the form ax =
b.
a) The derivative of f(x) as the gradient of the
tangent to y = f (x) at a point; the gradient of
the tangent as a limit; interpretation as a rate
of change; second order derivatives.
b) differentiation of xn, ex, ln x and their sums
and differences; differentiation of sinx, cosx,
tanx and their sums and differences.
c) Applications of differentiation to gradients,
tangents and normals, maxima and minima
and stationary points, increasing and
decreasing functions.
d) Differentiation using the product rule, the
quotient rule, the chain rule and by the use of
dy
1

dx  dx 
 
 dy 
Integration
Numerical
methods
e) Differentiation of simple functions defined
implicitly or parametrically
f) Formation of simple differential equations.
a) Indefinite integration as the reverse of
differentiation.
b) Integration of xn, ex, 1/x, integration of sinx,
cosx
c) Evaluation of definite integrals.
Interpretation of the definite integral as the
area under a curve.
d) Evaluation of volume of revolution.
e) Simple cases of integration by substitution
and integration by parts. These methods as
the reverse processes of the chain and
product rules respectively.
f) Simple cases of integration using partial
fractions
g) Analytical solution of simple first order
differential equations with separable
variables.
a) Location of roots of f(x) = 0 by considering
changes of sign of f(x) in an interval of x in
which f(x) is continuous
b) Approximate solutions of equations using
simple iterative methods;
Vectors
c) Numerical integration of functions (eg
using trapezium rule)
a) Vectors in two and three dimensions
b) Magnitude of a vector.
c) Algebraic operations of vector addition and
multiplication by scalars, and their
geometrical interpretations.
d) Position vectors. The distance between
two points. Vector equations of lines
e) The scalar product. Its use for calculating
the angle between two lines.
Once again, congratulations and I wish you the very best on your chosen course of study.
Please contact me using the details below.
Felix Obadan
Course Leader,
Flexible PGCE Mathematics
01695 584073
Email: obadafe@edgehill.ac.uk