WhatFurther Maths Unit 1 Professional Learning (Further Pure)
WhoKS5 teachers
WhenSeptember 2023 – July 2024
HowHybrid- Primarily online, with live sessions held to cover the more complicated topics in South and North Wales
To bookfmspwales@swansea.ac.uk

More information

This course will give a comprehensive coverage of FMU1 and is aimed at teachers who currently deliver A-level Maths and would like to deliver Further Maths, or teachers who currently teach Further Maths and would like a refresher.

Course Structure: 5 Sessions. This course will be spread over the whole academic year.

Session 1
Complex Numbers

Sept-Oct 2023
Development of complex numbers, arithmetic and algebra of complex numbers.
The argand diagram.
Connection between transformations of 2D space and complex number arithmetic.
Modulus and argument and their properties. Complex number proof of compound angle formulae.
Loci in the argand diagram.
Functions of a complex variable.
Session 2
Polynomials and Matrices

Nov-Dec 2023
Roots of Polynomials.
Informal appreciation of the fundamental theorem of algebra.
Complex roots of a real polynomial appear in conjugate pairs.
Properties of roots of polynomials.
Introduction to arithmetic and algebra of matrices (particularly 2×2) an the use of 2×2 matrices to describe transformations.
Session 3
Matrices and Transformations

Jan – Feb 2024
Formalising earlier work on 2×2 matrices and their use with linear transformations of two-dimensional space.
Use of 3×3 matrices to describe non-linear transformations of two-dimensional space.
Use of 3×3 matrices to describe linear transformations of three-dimensional space.
Session 4

Mar-Apr 2024
Vector equation of a line.
The scalar product
Vector equation of a plane.
Use of vectors to calculate distances and angles in three-dimensional space.
Session 5
Proof and Series

May-June 2024
Introducing proof by induction
Using proof by induction in a wide range of examples
The sum of the first n terms of a series using induction, properties of Σ notation and the difference method.

Each module will consist of two online, weekday early evening, zoom sessions, separated by 7-14 days. In these sessions, the tutor will consider the major concepts of the topic. Video recordings of these sessions will be made available so that participants who are not able to attend can view the session that was missed.

Sessions 1 and 4 will include the possibility of you attending a face-to-face session with a tutor. These sessions will be on a weekday and held in both South Wales (Swansea) and North Wales (Wrexham or Bangor). These sessions will take place before the two zoom sessions. They will not only cover the material of the two on-line zoom sessions but also give you the opportunity to meet a member of the tutor team and exchange ideas and experiences with some of your fellow participants.

A full resource pack of learning materials, including the materials used in the zoom and face-to-face sessions, will be made available and it is hoped that you will work through the resources and attempt some exercised provided. During this period of self-study, you will have email access to your tutor.

Participants are expected to attend as many online sessions as possible.

Course Dates:

A face-to-face or online session will be held in each of the weeks indicated. Dates will be set as soon as possible.

Session 1Autumn Term Week 3Autumn Term Week 4
Autumn Term Week 6
Session 2Autumn Term Week 10
Autumn Term Week 12
Session 3Spring Term Week 4
Spring Term Week 6
Session 4Spring Term Week 8Spring Term Week 9
Spring Term Week 10
Session 5Summer Term Week 7
Summer Term Week 8

Sessions will be presented in English; materials will be available bilingually

This course will be certificated.

Each session has a short assessment task which participants will be encouraged to complete and send to their tutor. Each task will contain two or three exam style questions for participants to answer. In addition, participants will be asked to reflect upon the knowledge students will need to tackle such questions and possible teaching approaches that might be used in the classroom. It is hoped that each task should require less than 90 minutes to complete.

Certification will be based on satisfactory completion of these tasks and evidence of attendance at the sessions or independent work through the resource material.

The deadline for certification will be August 2024.