GRADUATE SCHOOL OF EDUCATION
PGCE Mathematics
SUBJECT KNOWLEDGE AND ICT AUDIT BOOKLET
2012-2013
NAME: ………………………………………………

Introduction

Completing the Subject Knowledge Audit tasks set out below will help you to become familiar with the structure and content of the National Curriculum for Mathematics and to identify the aspects of subject knowledge that you will need to develop at Key Stages 3 and 4 and at post-16 level. In addition to the self audits of science subject knowledge please complete the audit of Information and Communication Technologies (ICT) competence.

Please begin to address those aspects of Mathematics that you are not familiar with before beginning the course. Do not try to cover too many topics – we would like you to develop depth of understanding in a few areas rather than breadth of understanding across many areas. Create a ‘subject knowledge development record’ using a strategy that you feel comfortable with e.g. summary notes, revision lists, concept maps, completing tasks set in the texts, answering revision questions. This will form an important part of your Individual Development Portfolio (IDP) that you will build up over the course of the PGCE and will inform discussions about the issues it raises with respect to covering all your subject knowledge needs. Use GCSE Mathematics textbooks or other appropriate sources of information to help you develop your understanding. Once you have completed the self audit tasks construct a plan to begin the process of addressing your subject knowledge needs.

Mathematics Subject Knowledge at Key Stages 3 and 4

You will need to become familiar with the structure and content of the National Curriculum for Mathematics. This task is designed to help you understand how the curriculum is organized and to identify aspects of subject knowledge that you will need to develop.

When completing this section please refer to statements in the ‘Range and content’ section of the National Curriculum for Mathematics at Key Stage 3 and 4. This outlines the breadth of the subject on which teachers should draw when teaching the key concepts and key processes. The National Curriculum can be found in the schools section of the DfE website:

http://www.education.gov.uk/

Please tick the box which you think gives the best indication of your level of knowledge for each of these areas using the following codes:

Level 0 = no knowledge - Level 3 = very secure knowledge

Key Stage 3

Number and algebra / 0 / 1 / 2 / 3
a / rational numbers, their properties and their different representations
b / rules of arithmeticapplied tocalculations and manipulations with rational numbers
c / applications ofratio and proportion
d / accuracy and rounding
e / algebra as generalised arithmetic
f / linear equations, formulae, expressions and identities
g / analytical, graphical and numerical methods for solving equations
h / polynomial graphs,sequences and functions
Geometry and measures / 0 / 1 / 2 / 3
a / properties of2D and 3D shapes
b / constructions, loci and bearings
c / Pythagoras’ theorem
d / transformations
e / similarity, including the use ofscale
f / points, lines and shapes in 2D coordinate systems
g / units,compound measuresand conversions
h / perimeters, areas,surface areas and volumes

Statistics

/ 0 / 1 / 2 / 3
a / the handling data cycle
b / presentation and analysisof grouped and ungrouped data, including time series and lines of best fit
c / measures of central tendency andspread
d / experimental and theoreticalprobabilities, including those based on equally likely outcomes

Key Stage 4

Number and algebra / 0 / 1 / 2 / 3
a / real numbers, their properties and their different representations
b / rules of arithmeticapplied tocalculations and manipulations with real numbers, including standard index form and surds
c / proportional reasoning, direct and inverseproportion, proportional change and exponential growth
d / upper and lower bounds
e / linear, quadratic and other expressions and equations
f / graphs of exponential and trigonometric functions
g / transformation of functions
h / graphs of simple loci

Geometry and measures

/ 0 / 1 / 2 / 3
a / propertiesandmensuration of 2D and 3D shapes
b / circle theorems
c / trigonometrical relationships
d / properties and combinations oftransformations
e / 3D coordinate systems
f / vectors in two dimensions
g / conversions between measures and compound measures

Statistics

/ 0 / 1 / 2 / 3
a / the handling data cycle
b / presentation and analysisof large sets ofgrouped and ungrouped data, including box plots and histograms, lines of best fit and their interpretation
c / measures of central tendency and spread
d / experimental and theoreticalprobabilitiesof single andcombined events.

It is not only straightforward exercises that will help you with your subject knowledge. Here are some investigations that are commonly used with pupils up to GCSE. Try to complete them neatly and thoroughly. Remember to ask your own questions and take the investigation further. You will have the opportunity to compare your ideas with others on the course, during the first few days, so come prepared!

  1. Max-box
    An open box is made using a square sheet of paper (any dimensions) Squares are cut from each corner of side x. For what value of x is the volume of the resulting box a maximum? (You can use a spreadsheet, trial and improvement, algebraic methods, graphical methods or calculus.)
  2. The farmer’s field
    A farmer has 100 metres of fencing to make a grazing area. Advise him on the best shape to maximise the area.

(Is this a sensible context for such a question?)

3.  The painted cube
Unit cubes are put together to make larger cubes. (Example: 27 unit cubes make a 3x3x3 cube) The larger cubes are dipped in paint. How many of the unit cubes will have no paint on them? One side painted? Two sides painted?

4.  Equable shapes
An equable shape is one that has the same numerical value for its perimeter as its area. Investigate 2D equable shapes. Extend to 3D.

Subject Knowledge at AS and A level

Please go to the Edexcel website to find specifications for AS and A2 in Mathematics. These can be found by clicking on ‘GCE from 2008’ in the ‘Qualifications Finder’ drop down menu. Then select Mathematics and go to the specification.

Edexcel home page http://www.edexcel.com/Pages/home.aspx

Print the content of the units C1, C2, C3 and C4 and then rate your understanding of each of the topics by writing a number (0 = no knowledge up to 3 for very secure knowledge) next to each of the statements.

Self Assessment of Competence in the Use of Information and Communication Technologies (ICT)

Please rate your knowledge of the ICT skills listed in the table below.

Level 0 = no knowledge - Level 3 = very secure knowledge

Aspect of ICT / 0 / 1 / 2 / 3
Basic word processing: keyboard skills; font formatting; saving files etc
Advanced word processing: e.g. tables; text wrapping; importing graphics
Desktop publishing: e.g. using Microsoft Publisher
Email: sending and receiving emails; using attachments
Internet: accessing known sites; searching; saving text and images to files
Databases: setting up and using database
Spreadsheets: using software such as EXCEL
Digital technology: using digital images (video and still)
Data logging
Presentation software: e.g. Powerpoint
Using an Interactive White Board (IWB)