Mathematics Subject Knowledge Audit Part 1
School Direct Programme
2013-2014
Name:_____________________________
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Introduction
The University of Nottingham School of Education School Direct
Mathematics Subject Knowledge Self-Assessment Audit Part 1
The purpose of this audit is to help you to make informed judgements about the subject knowledge areas you need to develop during
the course. Part 2 enables you to work through key issues in maths, see your strengths and areas for development. This audit is
given to everyone who will be taking up a place to train as a mathematics teacher on the University of Nottingham School Direct
programme. You should begin work on this audit as soon as you can - the earlier you do, the more time you will have to develop your
subject knowledge for mathematics teaching before the start of this programme.
Entrants to the School Direct programme have varied academic backgrounds and experience. Everyone has met at least minimum
subject knowledge requirements - what we generally find is that people have areas of considerable expertise and other areas that will
need to be developed further before the end of the year. At your school and university interviews, we will have begun to explore the
extent of your subject knowledge for teaching your subject. This audit is the next stage in the process, which allows you to use the last
few weeks before the programme starts to reflect on and develop your subject knowledge through accessible research, target setting
and reading tasks. You will discuss plans for further development with your tutor and mentor when you start the programme.
You might describe this as an audit of your knowledge about what to teach in Mathematics - or at least some of it. This will then form a
good starting point for considering the next level, which concerns developing your understanding of how to apply your subject
knowledge in teaching Mathematics. Throughout the School Direct programme, you will have opportunities to discuss these audits with
your fellow trainees, your tutor and mentor, and to review them regularly as part of your Professional Development File.
How to use this audit
* We would like you to read the audit before completing any of it, in order to get a sense of what is covered here. We would be
surprised if anyone had completely covered all these areas of subject knowledge at this stage, so please do not worry about any
gaps you may have. The important thing is to think about strategies for addressing these gaps.
* Against each 'area of subject knowledge', make some brief notes in the 'current expertise' column, indicating the extent of
your knowledge about the particular topics covered and where you think you may have areas to develop.
* For any areas to develop, read the 'suggestions for further development' and decide what you are going to do. You might like to
highlight suggestions you want to follow up and write in further suggestions of your own.
* Set yourself a plan for following up these suggestions between now and the start of the School Direct programme. You may need
to set priorities and regular targets.
* Enjoy finding out more about Mathematics.
* A few days before the start of the School Direct programme, fill in the final 'evidence' column showing how you have
started to develop your subject knowledge.
This audit is based on the National Curriculum (NC) for Mathematics teaching in schools which applies until September 2014, and will be
taught during your training year. These two documents contain the present Programmes of Study:
KS3 and KS4:
Download the full programmes of study:
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http://www.education.gov.uk/schools/teachingandlearning/curriculum/secondary/b00199003/mathematics
You may be aware of changes to the NC which will apply from 2014. The Draft NC Programmes of Study (PoS) starting in 2014 are
available for reference at: https://www.education.gov.uk/schools/teachingandlearning. You may notice that the draft Programmes of
Study for Key Stages 3 and 4 in Mathematics differ in many ways to the current curriculum, and to that which you may have already
experienced as a learner yourself. This audit covers general areas of the Mathematics curriculum that are practical for you to develop,
if necessary, before joining the School Direct programme, and also in the early part of the programme so that you are prepared for
teaching across all aspects of the subject, both during the coming year and beyond.
This document uses the ‘old’ KS3 curriculum for audit purposes. At Key Stage 4 this audit is based on statements in both the current
and previous National Curriculum. This audit is a detailed framework to enable you to engage with specific concepts which reflect the
way the current NC is enacted within different exam board specifications.
Please follow these instructions carefully:
You should use part one of the audit as a reference document to support you in identifying which aspects of the mathematics
curriculum you will need to work on to ensure you have the appropriate level of knowledge to teach that area effectively. Part two of
the audit should be a working document and you should follow the instructions on that document.
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√ √ very confident; √ confident; ? not sure understand; Underline - need to work on.
KEY STAGE 3/4 REQUIREMENTS
2: Key Processes
√?
Strategies
Evidence
Processes in mathematics: The key processes in this section are
clearly related to the different stages of problem-solving and the handling
data cycle.
2.1 Representing
Representing: Representing a situation places it into the mathematical
form that will enable it to be worked on. You should be able to explore
mathematical situations independently; identify the major mathematical
features of a problem and potentially fruitful paths; use and amend
representations in the light of experience; identify what has been included
and what has been omitted; and break the problem down (eg starting with
a simple case, working systematically through cases, identifying different
components that need to be brought together and identifying the stages
in the solution process).
You should be able to:
a) Identify the mathematical aspects of a situation or problem. This includes
identifying questions that can be addressed using statistical methods.
b) Compare and evaluate representations of a situation before making
a choice. This includes moving between different representations in pure and
applied contexts, for example in an engineering context or assembling a piece of
flat-pack furniture.
c) Simplify the situation or problem in order to represent it mathematically
using appropriate variables, symbols, diagrams and models. This involves using
and constructing models with increasing sophistication and understanding the
constraints that are being introduced.
d) Select mathematical information, methods, tools and models to use. : This
involves examining a situation systematically, identifying different ways of
breaking a task down and identifying gaps in personal knowledge. In statistical
investigations it includes planning to minimise sources of bias when conducting
experiments and surveys and using a wide variety of methods for collecting
primary and secondary data. ICT tools can be used for mathematical applications,
including iteration and algorithms.
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√?
Strategies
Evidence
2: Key Processes Contd
2.2 Analysing
Using mathematical reasoning you should be able to:
a) Make connections within mathematics. For example, realising that an
equation, a table of values and a line on a graph can all represent the same thing,
or understanding that an intersection between two lines on a graph can represent
the solution to a problem.
b) Use knowledge of related problems
c) Visualise and work with dynamic images
d) Identify and classify patterns
e) Make and justify conjectures and generalisations, considering special
cases and counter-examples covering a range of mathematical content and
contexts in different ways (including algebra).
f) Explore the effects of varying values and look for invariance and covariance.
This involves identifying variables and controlling these to explore a situation. ICT
could be used to explore many cases, including statistical situations with
underlying random or systematic variation.
g) Take account of feedback and learn from mistakes
h) Work logically towards results and solutions, recognising the impact
of constraints and assumptions
i) Identify a range of techniques that could be used to tackle a problem,
appreciating that more than one approach may be necessary, for example,
working backwards, looking at simpler cases, choosing one or more of a numerical,
analytical or graphical approach, and being able to use techniques independently.
j) Reason inductively, deduce and prove. (Reason inductively: This involves
using particular examples to suggest a general statement. Deduce: This involves
using reasoned arguments to derive or draw a conclusion from something already
known.)
Use appropriate mathematical procedures (This includes procedures for
collecting, processing and representing data.)
You should be able to:
k) Make accurate mathematical diagrams, graphs and constructions on
paper and on screen
l) Calculate accurately, using mental methods or calculating devices
as appropriate, for example, when calculation without a calculator will take an
inappropriate amount of time.
m) Manipulate numbers, algebraic expressions and equations and apply
routine algorithms
n) Use accurate notation, including correct syntax when using ICT
o) Record methods, solutions and conclusions. This involves use of formal
methods, including algebra, and formal proofs.
p) Estimate, approximate and check working.
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2: Key Processes (Contd)
√?
Strategies
Evidence
2.3 Interpreting and evaluating (This includes interpreting data and
involves looking at the results of an analysis and deciding how the results relate to
the original problem.)
You should be able to:
a) Form convincing arguments to justify findings and general statements. This
involves using more formal arguments and proof to support cases and appreciating
the difference between inductive and deductive arguments.
b) Consider the assumptions made and the appropriateness and accuracy
of results and conclusions
c) Appreciate the strength of empirical evidence and distinguish between
evidence and proof. This includes evidence gathered when using ICT to explore
cases and understanding the effects of sample size when interpreting data.
d) look at data to find patterns and exceptions. Students should understand
that random processes are unpredictable.
e) Relate their findings to the original question or conjecture, and indicate
reliability
f) Make sense of someone else’s findings and judge their value in the
light of the evidence they present. For example, errors in an argument or missing
steps or exceptions to a given case. This includes interpreting information
presented by the media and through advertising
g) Critically examine strategies adopted. This includes examining elegance of
approach and the strength of evidence in their own or other people’s arguments.
2.4 Communicating and reflecting (This involves communicating
findings to others and reflecting on different approaches.)
You should be able to:
a) Use a range of forms to communicate findings to different audiences. This
includes appropriate language (both written and verbal forms), suitable graphs
and diagrams, standard notation and labelling conventions and ICT models.
b) Engage in mathematical discussion of results
c) Consider the elegance and efficiency of alternative solutions which might
include multiple approaches and solutions using ICT.
d) Look for equivalence in relation to both the different approaches to the
problem and different problems with similar structures
e) Give examples of similar contexts they have previously encountered and
identify how these contexts differed from or were similar to the current
situation and how and why the same, or different, strategies were used.
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3.1 Number and algebra
√?
Strategies
Evidence
Level 6

Order and approximate decimals when solving numerical problems
and equations [for example, x3 + x = 20], using trial-and-improvement
methods.

Aware of which number to consider as 100%, or a whole, in problems
involving comparisons, and use this to evaluate fractions &
percentages.

Understand and use equivalences between fractions, decimals and
percentages, and use ratios.

Add and subtract fractions by writing them with a common
denominator.

Find and describe in words the rule for the next term or nth term of

a sequence where the rule is linear.

Formulate and solve linear equations with whole-number coefficients.

Represent mappings expressed algebraically, and use Cartesian
coordinates for graphical representation interpreting general
features.
Level 7

In making estimates, round to one significant figure and multiply and
divide mentally.

Understand the effects of multiplying and dividing by numbers
between 0 and 1.

Solve numerical problems involving multiplication and division with
numbers of any size, using a calculator efficiently and appropriately.

Understand and use proportional changes, calculating the result of
any proportional change using only multiplicative methods.

Find and describe in symbols the next term or nth term of a
sequence where the rule is quadratic; You multiply two expressions
of the form (x + n); You simplify the corresponding quadratic
expressions.

Use algebraic and graphical methods to solve simultaneous linear
equations in two variables.

Solve simple inequalities.
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3.1 Number and algebra (contd)
√?
Strategies
Evidence
Level 8

Solve problems involving calculating with powers, roots and numbers
expressed in standard form, checking for correct order of
magnitude.

Choose to use fractions or percentages to solve problems involving
repeated proportional changes or the calculation of the original
quantity given the result of a proportional change.

Evaluate algebraic formulae, substituting fractions, decimals and
negative numbers.

Calculate one variable, given the others, in formulae such as V =
pr2h.

Manipulate algebraic formulae, equations and expressions, finding
common factors and multiplying two linear expressions.

Know that a2 –b2= (a+b)(a – b).

Solve inequalities in two variables.

Sketch and interpret graphs of linear, quadratic, cubic and
reciprocal functions, and graphs that model real situations.
Exceptional Performance

Understand and use rational and irrational numbers.

Determine the bounds of intervals.

Understand and use direct and inverse proportion.

In simplifying algebraic expressions, use rules of indices for
negative and fractional values.

In finding formulae that approximately connect data, express
general laws in symbolic form.

Solve simultaneous equations in two variables where one equation is
linear and the other is quadratic.

Solve problems using intersections and gradients of graphs.
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3.2 Geometry and measures
√?
Strategies
Evidence
Level 6

Recognise and use common 2-D representations of 3-D
objects.

Know and use the properties of quadrilaterals in classifying
different types of quadrilateral.

Solve problems using angle and symmetry properties of
polygons and angle properties of intersecting and parallel
lines, and explain these properties.

Devise instructions for a computer to generate and transform
shapes and paths.

Understand and use appropriate formulae for finding
circumferences and areas of circles, areas of plane
rectilinear figures and volumes of cuboids when solving
problems.

Enlarge shapes by a positive whole-number scale factor.
Level 7

Understand and apply Pythagoras' theorem when solving
problems in two dimensions.

Calculate lengths, areas and volumes in plane shapes and right
prisms.

Enlarge shapes by a fractional scale factor, and appreciate
the similarity of the resulting shapes.

Determine the locus of an object moving according to a rule.

Appreciate the imprecision of measurement and recognise
that a measurement given to the nearest whole number may
be inaccurate by up to one half in either direction.

Understand and use compound measures, such as speed.
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3.2 Geometry and measures (contd)
√?
Strategies
Evidence
Level 8

You can understand and use congruence and mathematical
similarity.

Use sine, cosine and tangent in right-angled triangles when
solving problems in two dimensions.

Distinguish between formulae for perimeter, area and volume,
by considering dimensions.
Exceptional Performance






Sketch the graphs of sine, cosine and tangent functions for
any angle, and generate and interpret graphs based on these
functions.
Use sine, cosine and tangent of angles of any size, and
Pythagoras' theorem when solving problems in two and three
dimensions.
Use the conditions for congruent triangles in formal
geometric proofs [for example, to prove that the base angles
of an isosceles triangle are equal].
Calculate lengths of circular arcs and areas of sectors, and
calculate the surface area of cylinders and volumes of cones
and spheres.
Appreciate the continuous nature of scales that are used to
make measurements.
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3.3 Statistics
√?
Strategies
Evidence
Level 6

Collect and record continuous data, choosing appropriate
equal class intervals over a sensible range to create
frequency tables.

Construct and interpret frequency diagrams.

Construct pie charts.

Draw conclusions from scatter diagrams, and have a basic
understanding of correlation.

When dealing with a combination of two experiments, identify
all the outcomes, using diagrammatic, tabular or other forms
of communication.

In solving problems, use your knowledge that the total
probability of all the mutually exclusive outcomes of an
experiment is 1.
Level 7

Specify hypotheses and test them by designing and using
appropriate methods that take account of variability or bias.

Determine the modal class and estimate the mean, median and
range of sets of grouped data, selecting the statistic most
appropriate to your line of enquiry.

Use measures of average and range, with associated
frequency polygons, as appropriate, to compare distributions
and make inferences.

Draw a line of best fit on a scatter diagram, by inspection.

Understand relative frequency as an estimate of probability
and use this to compare outcomes of experiments.
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3.3 Statistics (contd)
√?
Strategies
Evidence
Level 8



Interpret and construct cumulative frequency tables and
diagrams, using the upper boundary of the class interval.
Estimate the median and interquartile range and use these to
compare distributions and make inferences.
Understand how to calculate the probability of a compound
event and use this in solving problems.
Exceptional Performance




Interpret and construct histograms.
Understand how different methods of sampling and different
sample sizes may affect the reliability of conclusions drawn.
Select and justify a sample and method to investigate a
population.
Recognise when and how to work with probabilities associated
with independent mutually exclusive events.
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