Further Maths Unit 5 Professional Learning

WhatFurther Maths Unit 5 Professional Learning (Further Statistics)
WhoKS5 teachers
WhenSeptember 2023 – April 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 FMU5 and is aimed at teachers who currently deliver AS-level Further Maths and would like to deliver A-level Further Maths, or teachers who currently teach FMU5 and would like a refresher.

Course Structure: 4 Sessions. This course will be spread over the whole academic year.

Session 1
Combining Normal Distributions and Central Limit Theorem

Sept-Oct 2023
Linear combination of independent normally distributed random variables.
Distribution of the mean of a random sample.
Use of the Central Limit Theorem.
Session 2

Nov-Dec 2023
Use of unbiased estimators and the variance criterion for choosing between unbiased estimators.
Unbiased estimators of a probability and of a population mean and their standard errors.
Unbiased estimator of a population variance.
Session 3
Hypothesis testing (parametric and non-parametric)

Jan – Feb 2024
Hypothesis tests for:

(a) a specified mean of any distribution whose variance is estimated from a large sample.
(b) difference of two means for two independent normal distributions with known variances
(c) a specified mean of a normal distribution with unkown variance.

Non-parametric tests: Mann-Whitney and Wilcoxon signed-rank tests.
Interpret results for all these tests in context.
Session 4
Confidence Intervals

Mar-Apr 2024
Use of confidence intervals for:

(a) the mean of a normal distribution with (i) known variance and (ii) unknown variance
(b) the difference between the means of two normal distributions whose variances are known.
Approximate confidence limits, given large samples, for a probability or a proportion.
Interpret results in practical contexts.

Each module will consist of two online, weekday early evening, zoom sessions, seperated 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 2 and 3 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.

Module 1Autumn Term Week 4
Autumn Term Week 6
Module 2Autumn Term Week 8Autumn Term Week 9
Autumn Term Week 10
Module 3Spring Term Week 2Spring Term Week 3
Spring Term Week 5
Module 4Spring Term Week 7
Spring 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.