The Transition from A Level to University – a comparison
This report looks at the differences that students will experience during the transition from A Level
to University Mathematics courses. It is written to inform university staff about the mathematics and
experiences of learning mathematics that students are likely to have encountered prior to starting a
degree. There are two key issues that this report will focus on:


How A Levels are structured, what exams are like and how they are marked
Observing lectures and discussing the different teaching styles used at A Level and at
university
Section 1: How A Levels are structured, what exams are like and how they are marked
This report focuses on the four main exam boards: Edexcel, AQA, OCR and WJEC.
Qualifications are made up of:



A Level Maths – 6 modules
A Level Maths plus AS Further Maths – 9 modules
A Level Maths plus A Level Further Maths – 12 modules
AS modules
Core 1
Core 2
Statistics 1
Decision 1
Mechanics 1
Further Pure 1
A2 modules
Core 3
Core 4
Further Pure 2
Further Pure 3
Statistics 2
Decision 2
Mechanics 2
*
*Mechanics 3,4,5 and Statistics 3,4 are also available
There is a wide variety of modules available and different combinations are allowed with certain
restrictions:
Qualifications
A Level Maths
Compulsory modules
C1,C2,C3,C4
AS Further Maths
FP1 plus 2 other modules
(not C1-4)
FP1 and either FP2 or FP3
Any that have not been
previously studied
A Level Further Maths
1
Optional modules
M1 and S1 or
M1 and D1 or
S1 and D1 or
S1 and S2 or
M1 and M2 or
D1 and D2
As part of the A Level in maths students must study the four modules Core 1 – Core 4. There may be
slight differences between the locations of topics within the modules, but all Core 1 and Core 2
modules cover the same topics, as do Core 3 and Core 4. The detailed specification for each exam
board
is
available
on
the
exam
board
websites
(http://www.ocr.org.uk/qualifications/type/gce/maths/maths/). The overall content of these
modules is standard across the exam boards with the exception of:
Core module
titles
Numerical
Integration
Integration by
substitution
Using the
Modulus function
Differentiation of
simple functions
defined
parametrically
Volumes of
revolution
Expressing
rational functions
as partial
fractions
Edexcel
C1, C2, C3, C4
Trapezium Rule
all but the
simplest
substitutions are
given
modulus
equations only
first derivative
only
Rotation about x
axis only
degree of
numerator can be
less, same or
higher than
degree of
denominator
AQA
MPC1, MPC2,
MPC3, MPC4
mid-ordinate rule,
Simpson’s Rule
substitutions may
be given
OCR
C1, C2, C3, C4
WJEC
C1, C2, C3, C4
Simpson’s Rule
Simpson’s Rule
substitutions may
be given
substitutions are
given
modulus
inequalities
first derivative
only
modulus
inequalities
first derivative
only
modulus
inequalities
including second
derivatives
Rotation about
either x or y axis
(unspecified)
Rotation about
either x or y axis
degree of
numerator is less
than that of the
denominator
Rotation about x
axis only
degree of
numerator is less
than that of the
denominator
Exam preparation
Students have access to the previous exam papers and their mark schemes as provided by the exam
board, and will have completed many of them as practice. Students are likely to have been set exam
papers as homework and also had the opportunity to work through them in class and during support
sessions. The amount of time spent on revision in class will depend on the individual school/college,
but it would be typically around 1-2 weeks, which is significantly less that the amount of revision
time at GCSE. Students are also likely to have been set exam-style questions throughout the course.
Exams
For all exam boards assessment is by exam. Each module is of equal weighting and the exam is 1hr
30 mins. Exams may be sat in January or June, and students may resit an unlimited number of times
and the best mark will count. A calculator may not be used in the Core 1 unit of any exam board.
Scientific and graphical calculators may be used in the other modules, except those with the facility
for symbolic algebra manipulation or symbolic differentiation/integration. Each exam consists of 712 questions of different lengths and mark allocation. A short question would typically be 2 marks,
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and a long question anything up to 16 marks. Long questions are generally broken down into several
parts. Students attempt all the questions. There are 75 total marks available (72 for OCR). Past exam
papers and mark schemes are freely available on the exam board websites and students are
encouraged to access these. Questions are fairly standard in format and solvable using methods
seen in the module, sometimes incorporating methods seen in a previous module, with a small
proportion of parts of questions designed to challenge and extend the most able students.
There are three types of marks awarded – M, A and B.
M marks are awarded for ‘knowing a method and attempting to apply it’
A marks are awarded for accuracy. These can only be awarded if the relevant method (M) marks are
earned.
B marks are unconditional accuracy marks awarded for stating something which is correct e.g. giving
the formula for calculating the gradient given two points, or knowing the general shape of a cubic
graph.
The vast majority of marks on any paper are M and A marks.
Mark schemes are applied positively. Students are given credit for what they have shown they can
do, rather than being penalised for omissions. Answers without working may not gain full marks.
Exam papers are sent to the exam board to be marked.
Students are provided with a formula book in the exam, and the information contained in it is
common across all exam boards. Copies of the formula books can be viewed from the exam board
websites (http://www.edexcel.com/quals/gce/gce08/maths/Pages/default.aspx). It is worth noting
that students are expected to use these standard results and formulae, not to remember them. In
general they contain formulae for sequences and series, trigonometric identities and standard
differentiations and integrations for a range of trigonometric functions. In the statistics section there
are formulae for correlation and regression, and tables for Normal, Binomial and Poisson
distributions. In Mechanics no formulae are given for M1 or M2 (students are unlikely to study any
more Mechanics modules, even though they do exist).
At least 20% of the questions in modules C2, C3 and C4 are designed to provide synoptic assessment,
whereby the knowledge, understanding and skills from a previous module are required. For
example, in C1 students will be asked to find the equation of a straight line. In Core 2 they will need
this knowledge to find the equation of a tangent to a circle.
Between 32-40% of the exam paper for all modules is designed to assess a student’s ability to write
mathematical arguments with precise statements and logical deduction, with the rest of the paper
focusing on applying and interpreting mathematical facts and using calculators and statistical tables
correctly. This means that students are not necessarily penalised for omissions or mathematically
incorrect working. At first glance this seems a very low proportion for a subject as precise as maths,
but one needs to take into account the fact that at GCSE level the exams are marked very differently.
At GCSE a correct answer implies a correct method therefore full marks will be given even if the
method is not shown. Therefore the requirement to write a complete solution at A Level is a
significant difference that many students struggle with. It is interesting to note that there are only
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two proofs in the whole A Level Maths course that students are required to learn: the Sum of an
Arithmetic Progression and the Sum of a Geometric Progression.
There is a list of standard mathematical notation which is used by all exam boards and published in
the specification (http://www.wjec.co.uk/uploads/publications/3665.pdf) (page 42)
Examples of the allowances made at A Level:

Students are advised to state the general formula first then substitute in values. They are
not penalised if they omit the general formula.

When differentiating 𝑦 = 3𝑥 4 with respect to 𝑥, students will not lose marks if the




= at
the start of the next line of working is omitted.
A missing 𝑑𝑥 (or similar) after an integral sign is not penalised.
When factorising quadratics the = 0 can be omitted without penalty, e.g.
𝑥2 + 𝑥 − 6 = 0
(𝑥 + 3)(𝑥 − 2) the mark is awarded for factorising into two brackets,
even though the = 0 is missing.
𝑥 = −3 𝑜𝑟 𝑥 = 2
For a large majority of questions, conditions such as 𝑥 ≥ 0 or 𝑥 ∊ ℝ can be ignored.
Incorrect additional notation is ignored, for example when differentiating implicitly students
may start the next line with

𝑑𝑦
𝑑𝑥
𝑑𝑦
𝑑𝑥
= … even though it is incorrect.
Unsimplified answers are accepted, for example a gradient of
−6
8
Any subsequent working after the required answer is ignored, for example solving (or trying to solve)
a factorised quadratic when not required.
Examiners will mark any solution that has not been crossed out, even if there are multiple attempts,
and the highest mark from any attempt is awarded. If a student crosses out an attempt and replaces
it with second attempt then only the second attempt will be marked, even if the first attempt is the
correct solution. If a student makes only one attempt and then crosses it out, but does not give an
alternative, then the attempt is marked.
It is acceptable for students to use a graphical calculator instead of probability tables, but the mark
scheme is such that where students have used a calculator and written the correct answer only
without any method, they may not gain full credit. (However, they may gain full credit, depending on
the question)
It is common for diagrams to be given, particularly in recent years where graphical calculators are
allowed in exams. This is to prevent students without graphical calculators being disadvantaged.
Alternative but less efficient methods are tolerated at A Level.
Solutions to ‘show that…’ questions are required to give every step, although they can be answered
by starting with the assumption that it is true and verifying that it works.
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Exam papers are marked out of 75 (72 for OCR) and the scores are converted into UMS (Uniform
Mark Scale) marks which are out of 100. The actual grade boundaries are set after candidates have
sat each exam, but generally they are very similar to percentage marks. For example, a raw mark of
61/75 has a percentage of 81.3̇ but may be converted to a UMS of around 79- 83 depending on the
perceived difficulty of the paper. The UMS scores relate to grades in the following manner:
80 = A, 70 = B, 60 = C, 50 = D, 40 = E
Each module carries an equal weighting. If students are studying AS Further Maths or A Level
Further Maths then the module scores are arranged to give the highest possible grade for A Level
Maths. For example, a student may have enough UMS marks to achieve AC or BB across both A
Levels depending on the combination of modules, but the exam board will combine the modules to
award AC because the A is the higher grade for A Level Maths.
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Section 2: Observing lectures and discussing the different teaching styles used at A Level and at
university
Teaching styles used at A Level
Teaching styles seen at university
Teacher specifies what to write down, and
ensures it is written.
Students directed to take notes, but actual notes
taken depended on individual students, and
quality may vary.
A lot of content was given verbally, rather than
in any written format, either printed, displayed
or hand written during the lecture for students
to copy
Greater emphasis on written explanation and
notation rather than working through examples
although the proportion of this depended on the
individual lecture
Facilities dependent on room used
Teacher-led examples
Classrooms with whiteboards/chalkboards, and
commonly a data projector/interactive
whiteboard
Group work, investigations, posters, matching
exercises, true or false statements
In some lectures students worked through
examples
Individual whiteboards used to assess all
students’ learning
Assessment depended on individual lecturers,
but almost impossible due to large group size
Starter activity and plenary
Introductory real world examples were used in
some lectures
Opportunities to ask questions in lectures
varied according to lecturer
Regular tutorials, staff office hours
Opportunities to ask questions in class
Opportunities to get additional help with the
work set including individual help at lunchtimes
Homework is regularly set and marked.
Non-submission is challenged. Achievement is
monitored and students are given feedback to
help improve their understanding.
Homework is regularly set and marked.
Non-submission is challenged. Achievement is
monitored and students are given feedback to
help improve their understanding.
Students are likely to have experienced a range of teaching styles during their A Levels. The most
significant difference between A Level teaching and university teaching is that at A Level learning
maths is a very interactive experience, whether it is the teacher interacting with the students or
students working with other students, and there is always the opportunity to ask questions. During
every lesson there will be a mixture of teacher-led discussion, copying down notes, and students
practicing questions with support available from the teacher.
Students will copy down the information written by the teacher. They will be given some examples
and the teacher will ask questions as the solution unfolds to assess understanding. The teacher may
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write on the board and students copy down the information, or they may complete a gapped
handout. The emphasis is on making an accurate copy of the information provided; it is unlikely that
students will be asked to select information and make their own notes.
Some teachers may present the information electronically, for example, using Microsoft PowerPoint
or similar. There are many teaching resources available on the internet, usually by paying a
subscription. In our college we use www.mymaths.co.uk. In this particular resource the explanation
is revealed one step at a time. The advantage of this is that students can see the solution being
constructed, rather than the full solution being presented at once, such as in a textbook. We use it in
class as a teaching resource, and also for students to refer to outside of lessons.
Students may be asked to complete questions from a textbook or worksheet. This will involve short
questions designed to practice skills, such as simple differentiation, then lead on to exam-style
questions where the students have to select the process required, such as identifying turning points.
Other tasks may include matching activities where questions and solutions are printed on separate
cards and students have to match them up. Another way of using cards is to print statements on
them and students sort them into ‘true’ or ‘false’, or even ‘always true’, ‘sometimes true’ and ‘never
true’.
Students may design posters, making their own selection as to the key aspects of a topic. This is
particularly used as a consolidation or revision task.
In recent years there has been a greater emphasis placed on assessing learning throughout the
lesson. A teacher is likely to:



circulate round the classroom speaking to individuals,
ask questions addressed to the whole class which an individual will answer
pose a question and students write their answer on individual whiteboards, so that every
student has to offer an answer. This allows the teacher to assess understanding and address
any misconceptions. Students may be encouraged to work in pairs, depending on the task.
Homework will be set and marked on a regular basis. Students also have access to past exam papers
and mark schemes. We publish these on our college Virtual Learning Environment, and all are freely
available from the exam board websites. Mark schemes are used in two ways: firstly to allow
students to check their answers, and secondly to demonstrate the number of stages of working out
required. Correct answers with no working out may not gain full marks in the exam, so there is some
emphasis on being able to demonstrate a correct method.
Use of technology and environment issues:




lack of boards to write on in the Students Union Auditorium. All teachers who observed this
and several students who were asked agreed that this significantly hampered the learning.
difficult to follow a solution if the complete solution is shown on screen in one go.
at times the data projector was unhelpful. It was difficult to read indices and subscripts, and
scrolling back and forth made note-taking difficult. The laser pointer was difficult to see.
powerpoints – once a powerpoint had been moved onto the next slide the lecturer was
unable to refer back to the previous slide. This hindered the students being able to refer
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

back to previous work. At times there was too much information on each slide, and some
students had difficulty in selecting and copying down all the relevant information before it
was moved onto the next slide. Also it is difficult to get the pace of the lecture right if the
lecturer is not doing any writing.
gapped handouts, when used, were very effective. They were especially effective when the
lecturer had the notes printed onto acetate and filled in the notes at the same time as the
students, viewed on the OHP, ensuring key points were highlighted and that students had a
complete set of notes.
The document camera seen in use during the Numbers and Groups lecture was particularly
effective. Coupled with the gapped handouts that the students brought with them, it meant
that students could follow precisely where the lecturer was in the notes, and annotate and
highlight key points.
In summary, both the teachers and the students asked said that they preferred lectures in which the
lecturer wrote on the blackboards and students copied the notes. The students asked said they felt
that they did not mind not having the technology used at A Level, and in most cases the technology
hampered their learning. They said that the best lectures were the ones where the lecturer wrote
the notes on the board and students copied them down. They preferred the solution to be written
down step by step in front of them and liked that the lecturer could refer back to a key point on a
previous board that was still on display.
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Interviews with students
Informal interviews were conducted with a small number of students at two points in the academic
year – early October and March. The technology referred to in many of these interviews
encompasses the use of OHPs, data projectors and powerpoints.
October 2011
Girl: She had done Mathematics and Further Mathematics at A level and said she felt she was coping
well because of this.
She commented that she found time management the most difficult issue, as there was far more to
organise than when living at home and attending school. She liked courses that provided gapped
hand-outs, because it helped her to keep up, but also enabled her to maintain concentration so that
she didn’t miss anything. She found the differential equations and vectors and mechanics courses
straightforward because they were most similar to A level. She found the statistics and probability
courses hard, mainly due to the formal way of writing information down, and the use of different
notation to that used at A level. These were interesting comments from a student who did S1 and S2
at school. She found set-theory confusing, saying it was very formally written, with some differences
between lecturers on the meaning of some phrases.
October 2011
Students’ comments on their experience at university compared with that at A-level:
Boy: He was not overwhelmed; he said there was lots of support available and is aspiring to a 2i or
1st; had done AS Further Mathematics.
Girl: She was enjoying the course and had done Further Mathematics; she said the teaching style
was very different as she was just talked at all the time now. She wasn’t sure what to aspire to in
terms of degree classification yet.
Boy: had an AA in Mathematics and Further Mathematics; he prefers the teaching style at university
where more responsibility is placed on the student to go to the lectures and copy down the notes
and then learn independently.
9
October 2011
Talking to students they had the following comments to make:
COURSES

They found some lectures more engaging than others and didn’t like just reading off a
screen. They particularly liked the lectures on Numbers and Groups as they found it more
engaging as they filled in sections in the lecture notes as the lectures took place.
 They like to do examples of questions in lectures. They found the vectors lectures engaging
for this reason.
 Some said they found the Probability and Stats lectures the hardest but wondered if that
was because they hadn’t done Statistics at A level.
 They were unsure of the role of the computer lab session for the Maple module and felt
they were just following instructions rather than learning anything. They would like a better
idea as to what the aim of using the computer was.
 They like the lecture notes to be available online.
 They were confused by different notation being used by different lecturers for the same
ideas.
TUTORIALS

They found tutorials helpful but would quite like smaller groups as sometimes they felt guilty
taking up too much time and asking too many questions.
SUPPORT IF STRUGGLING



Find the course difficult initially if they haven’t done further maths
They like knowing that they could see their personal tutor if they were struggling and
knowing that help was available.
They suggest a summer school might have been good to bridge the gap for those students
who had not done further maths.
March 2012
Girl: She hadn't done Further Maths and was finding statistics very hard. The amount of time she
spent on homework was variable. She found tutorials very similar to A-level support sessions. She
found the didactic nature of teaching very different to A-level teaching.
Boy: He was used to technology at College in Stockport however he didn't really think it was
essential. Nevertheless, he did feel that Maple would have better facilitated exemplifying how
partial derivatives related to three-dimensional curves in the lecture that day; he would have liked to
have seen this used in the lecture, though since he had access to Maple via the university he would
go and use Maple and see it for himself. Overall, he felt he received more contact time than at
College. He was happy with the teaching.
A Chinese student said that in China you were left to find the solutions yourself once you had been
shown one solution; she found the process similar at Sheffield University.
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March 2012
Two boys: They don't think that the use of technology at A-Level is vital to learning. They are left to
work on their own much more than at A Level. They felt the work is sometimes overcomplicated.
Boy: Finding the transition to 1st year university work challenging. He feels he needs more one-onone help (he had done Further Maths). He preferred the use of a blackboard and chalk as opposed
to PowerPoints where he finds the points are revealed too quickly and the pace of lectures too fast.
He felt that in some lectures he was expected to understand and use everything he learns straight
away. He feels the technology commonly experienced in Further Education is not vital to learning.
Girl: She wanted more information prior to university about how much work there would be (she
had done Further Mathematics). She would prefer more worked examples during lectures; she is
finding it challenging! She has found certain lecturers to be more effective than others, possibly due
to their natural charisma and enthusiasm, clarity of notes, and engaging and detailed explanations.
She didn’t miss the technology commonly used at A-level - overheads and blackboards she felt were
fine. Smartboards nevertheless may improve the professional impression of the presentation.
She suggested a Summer School at Sheffield University for students so that they know what to
expect.
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