Subject Knowledge Enhancement Course - Mathematics

The Mathematics Enhancement Course (MEC) at the University of Chester is a six month* pre-Initial Teacher Education (pre-ITE) course. It is for graduates who wish to train to teach secondary school mathematics, but have a degree in a subject other than mathematics.

Campus Riverside Campus, Chester
Length 24, 20, 16, 12 and 8 week courses available,flexible start dates from January. Full-time
Start date March 2020

Why study the Mathematics Enhancement Course at Chester?

The course is designed for gradates who have a background in mathematics (A Level or equivalent), but a degree in another subject. The programme allows graduates to gain a deeper understanding of mathematics within the 11-19 secondary curriculum and beyond. Graduates should leave the course with confidence in their mathematical ability, with a 'big picture' of relationships between mathematical concepts and having been inspired to motivate children to learn mathematics through their own expertise and enthusiasm. There are seven main course modules including Algebraic Generalisation and Proof, Calculus, Functions and Graphical Representations, Applied Mathematics and the History of Maths.


This course includes opportunities for peer teaching, observations in school and small group intervention teaching in a Chester secondary school.

Programme Structure:


Initial Audits; GCSE papers and investigations; how do you learn mathematics?; advice on study skills; reading lists; Further Mathematics Network resources; introduction to Autograph, Cabri and Excel. Initial stages of Subject Knowledge Audits.

Phase 1

Core Mathematics 1 (CM1)
Number systems; primes; proof (by exhaustion, deduction, contradiction, induction); algebraic processes (including partial fractions, the factor and remainder theorems); functions (including graphs of rational functions); logarithms and exponentials; trigonometrical functions; differentiation (including the chain rule); basic integration; series (arithmetic, geometric and binomial).

Applied Mathematics 1 (AM1)

  • Statistics and Probability
    Representation of data; measures of location and dispersion; elementary probability; discrete random variables (including mean and variance); discrete distributions (Uniform, Binomial and Poisson distributions); continuous random variables (pdf's and cdf's); continuous distributions (Uniform and Normal Distributions); hypothesis testing using the Binomial and Normal Distributions.
  • Decision Mathematics
    Algorithms; discrete graphs; networks (minimum connector and shortest path algorithms); the Route Inspection problem; Critical Path Analysis (including Cascade charts, scheduling and resource allocation); linear programming.

Problem Solving, Enrichment and Research 1 (PSER 1)

  • Problem Solving Unit
    You will study models for mathematical problem-solving, through direct participation in problem-solving activities. This unit will enable you to gain insight into 'mathematical thinking', allowing you greater understanding of how you learn as a mathematician, as well as how effective learning models are constructed. This unit will build on some of the activities from the induction phase.
  • Mathamagic
    You will collaborate with Secondary Mathematics PGCE and some Primary PGCE students to plan and teach a two day mathematics enrichment event for school pupils from Year 6 and 7. This will enable you to gain further insight into mathematical problem-solving and mathematical modelling, as well as establishing important links with the 2008-9 Mathematics PGCE students.
  • School Based Subject Knowledge Enhancement
    You will spend time observing higher-tier GCSE, AS and A Level lessons in a partnership secondary school. During this time you will update your subject knowledge audit in the context of GCSE and A Level Mathematics lessons and record how you resolve gaps in your subject knowledge. You will be encouraged to keep a reflective journal during this time.

Phase 2

Core Mathematics 2 (CM2) Core and Extension

Classical geometry (including a sample of Euclid's proofs); transformational geometry; matrix algebra; vectors; parametric equations; polar equations; calculation of areas and volumes by integration; series (binomial, power, Taylor and Maclaurin series); complex numbers (including Euler's equation and De Moivre's theorem).

Applied Mathematics 2 (CM2)

  • Mechanics (M)
    Kinematics; forces and Newton's Laws; vectors; projectiles; general motion in 2- and 3-dimensions; work, energy and power; impulse and momentum in 1 dimension; moments; rigid body statics (including centres of mass of discrete systems).
  • Differential Equations / Numerical Methods
    Solution of equations (change of sign, interval bisection, linear interpolation, Newton-Raphson, fixed-point iteration); numerical differentiation; numerical integration (mid-ordinate and trapezium rules); 1st order differential equations.

Problem Solving, Enrichment and Research 2

  • ICT Effective use of Mathematics Software
    You will solve classical and co-ordinate geometry problems using Autograph and Geometers Sketch Pad. You will use Excel spreadsheets to solve problems involving repeated calculations. You will have the opportunity to use Autograph to develop your understanding of Probability and Statistics.
  • Research Assignment
    You will research the historical background and international context of a topic within the Key Stage 3, 4 or 5 curriculum. You will be given the opportunity to include social and functional contexts in your exploration of your chosen topic. These assignments will be shared with a view to enriching your teaching of these topics during your initial teacher training.
  • Peer Teaching
    You will be given a learning objective and asked to prepare a 45 minute lesson for your peers. Your lesson objective will be chosen from your areas of weakness identified in your initial subject knowledge audit during the induction phase of the course. This unit will be assessed by you, your tutor and your peers.
  • Further School Experience
    You will build upon your school experience from phase 1 to further enhance your insight into mathematics in the secondary school setting.

The six main course modules will be assessed in a number of ways including tests, projects, presentations and a subject knowledge enhancement portfolio. There are re-assessment opportunities for all modules if you do not pass the first attempt.

This is a pre-initial teacher education course for graduates with conditional offers of a place on a Postgraduate Secondary Mathematics ITE course.

You must meet the entry requirements for the secondary mathematics course, together with a Level 3 (A Level or equivalent) mathematics qualification.