1. In-Service Teacher Training
Assessment in IGCSE Mathematics 0580/0581
Session 2: Question papers and mark schemes

2. Welcome Introductions Background Aim of training
1. It is important that you introduce yourself and outline your experience. The delegates should then introduce themselves and outline their experience. (It is often a good idea to get the delegates to write this information down as it is unlikely you will remember it - unless you already know the delegates, in which case you may wish to skip this slide.)
2. Explain the background to the training, such as:
who requested it;
where the training is from (a pack acquired from CIE for self
delivery, adapted for your own needs);
why the delegates are taking part.
3. Explain that the aim of the training is to give teachers a greater understanding of the assessment process so that they will feel in a better position to prepare their students for the examination. By improving teachers’ understanding of the process they will be able to guide and prepare students, thus helping to ensure that candidate performance is maximised.

3. Session 2 looks at: How question papers are set
The construction of questions
Grade Descriptions
Developing and applying mark schemes
Analysis of candidates’ scripts and creating mark schemes
Explain what session 2 will cover and that some work such as a lengthier analysis of questions papers and creation of mark schemes will have to be done outside the sessions. Delegates will need access to the current syllabus.

4. How question papers are set (1): Assessment Objectives
Questions set with reference to Assessment Objectives
Topics for the structured papers set first
Balance is maintained across the four areas of Number, Algebra, Shape and Space and Statistics and Probability.
Questions set across a range of grades
The list of 37 topics within the syllabus is the starting point for setting questions. Assessment Objectives are addressed through these topics – already looked at in Unit 1.
Papers 3 and 4 are set first and Centres should be aware of regular topics on those papers each year.
Papers 1 and 2 are then set addressing syllabus content not tested in papers 3 or 4.
Paper 4 often contains questions on the following topics:
extended graph drawing and analysis, probability, statistics , trigonometry, mensuration, number based – ratio, currency, percentage, algebra – verification, manipulation of expressions, solution of equation and interpretation of answer, extended transformations with vectors/matrices
These topics are suitable to develop in longer questions on Paper 4.
Activity 2.3 (could be carried out for homework)
Ask delegates to make a similar analysis of which topics regularly appear on Paper 3 and which Assessment Objectives they address.

5. How question papers are set (2): Levels of difficulty
Questions are written so that each follows a logical pattern
Answers in earlier parts of questions may be needed to help with later parts in the question
In general, easier questions are put at the beginning of a paper
Within a question there is usually a graduation of increasing difficulty, being the most difficult at the end
Point out that, where questions need an earlier answer to make an attempt at a later part, the mark scheme always allows follow through marks so that students who have got a wrong answer earlier do not get penalised again. We will see examples of this when we look at actual mark schemes.

6. Setting internal summative assessments
Setting tests in the style of IGCSE assessments
Decide on a ‘department house style’ that is similar to IGCSE style
Using command words in questions in IGCSE style
Benefits to students – they get used to this one style and the language used
Discuss how internal summative assessments can be developed to support students.
See Handout 2.5 on developing IGCSE-style test papers.

7. Devising mark schemes
For any question, the mark scheme must allow all of the marks available for the question to be achieved
Mark scheme must take into account different methods used by candidates
Mark schemes are always amended to take into account the ways that candidates answer particular questions
Before writing a question the examiner should have some sort of idea as to what he or she requires as a target answer in order to relate particular questions to particular grades.
Mark schemes may be altered at a meeting of examiners to take into account the answers of the candidates.
In general, marks are awarded for positive achievement in answering the question (within certain confines).
A mark scheme can be ‘freed up’ to allow for a wider spread of answers than originally proposed, or it can be ‘tightened up’ to allow a more specific range of answers if it is felt that the question is required to discriminate between higher grades. Any correct answer which is not on the mark scheme will be given credit.

8. Types of marks used on mark schemes (1)
M marks for method
A marks for accuracy - cannot be given unless M marks gained
B marks - independent of method marks
Together, look at examples of mark schemes for particular questions to identify these marks. (This will be done in detail at the end of Unit 2 and in Unit 3.)

9. Types of marks used on mark schemes (2)
On graphs: S - scale, P - points, C - curve, L - line
SC marks (Special Case)
Other letters as appropriate
Together, look at examples of mark schemes for particular questions to identify these marks. (This will be done in detail at the end of Unit 2 and in Unit 3.)
Correct answers without working usually score full marks.

10. Important marking issues
Other marking issues
Deleted work is marked, provided it is not replaced by another answer
If a choice of solutions is offered, the last is marked
Consistent misreads can score full marks with a misread penalty of one mark only throughout the question
The final two points are very important to candidates. Students must select an answer and not leave the examiner in any doubt as to the solution offered.
The misread issue is when candidates misread figures given on the question paper, for example, “324” read as “423” and then use the misread figure correctly and consistently throughout the question. Method marks will always be given for this sort of slip but accuracy marks are also allowed when the slip is consistent throughout the question – a penalty of one mark overall is applied in these cases.

11. Setting questions in context
Can increase the level of difficulty
Brings relevance to the mathematics being tested
Assesses the candidates’ ability to use and apply knowledge when confronted with new situations
Examiners will try to set questions in context, not to make them inaccessible to students but to give meaning to the mathematics being tested.
Advice to students is to read the text of a question and then analyse the key command words within the text to decide on the method and answer required.

12. The construction of questions - Command words
Command words are key words used in questions
Candidates should work on their understanding of the command words to improve their exam technique
Knowledge of command words greatly assists language interpretation in context-rich questions
Activity 2.10
Using Handout 2.10 ask delegates to carry out the activity looking at command words and their meanings on selected papers.

13. Grade Descriptions (1): Why have Grade Descriptions?
Make clear the level of performance required for different grades
Help examiners set questions of the appropriate difficulty and to balance exam papers
Help teachers assess the level of their students
Explain that Grade Descriptions are not only useful to Examiners for setting the levels of questions in a paper, but are also useful for teachers because they can be used as a general guide for what students can and cannot do in general (rather than specific) terms. Many teachers find Grade Descriptions useful for writing student reports, because they cover areas of student achievement.

14. Grade Descriptions (2): Analysing Grade Descriptions
See syllabus page 10 for descriptions of grades A, C and F
Only a selection of syllabus items are listed
Using the topics from pages 6-9 of the syllabus, pick a topic or selection of topics and write Grade Descriptions for that topic
The activity on this slide is intended to help colleagues get a feel for different levels of difficulty within topics and across the syllabus. It is not intended to be a precise activity.
Discuss how ideas within the mathematics department can be shared and a list of additional Grade Descriptions produced – this will help when setting balanced assessments in the future.
For example:
Grade B – Trigonometry in two dimensions, transformations with vectors, rearrange a simple formulae;
Grade D – divide a quantity in a given ratio, enlarge a shape with a given scale factor and centre;
Grade E – convert from one currency to another, reflect or rotate a shape.
The above are suggestions only and can be added to.

15. Grade Descriptions (3) What other topics / questions would be grade A?
What about grade B?
Where would matrices be graded?
What about averages?
These are questions which may come out of the previous activity and can be added to if necessary.

16. Grade Boundaries for IGCSE Mathematics Approximate grade boundaries (%)
Extended
Core A* 85 A
70-75 B 60 C 45 70 D 35 E 25 50 F 40 G
For grading purposes on examinations, however, a numerical scale is used, based on the student’s raw mark in the examination. The Grade Descriptions have already been taken into account when setting the exam paper.
This can vary slightly from session to session but the table gives a general picture of where the grade boundaries are set. Although there can be variations from session to session, these figures can be taken as a rough guide.

17. Strategies for marking questions: Core questions
Look at the examples of Core / Extended questions along with mark schemes and student responses
Activity 2.15
The activity looks at some Core and Extended questions from past papers, along with the mark schemes.
Handouts 2:15(a) and 2:15(b) look at sample questions, a mark scheme and students’ responses. Ask delegates to mark the responses using the mark schemes.
There are two parts to each worksheet and the second part (with the answers on) should not be given out until the marking stage is completed.

18. Creating a mark scheme for a question
Activity 2.16
For the question given, create a mark scheme in the style of those on Handout 2.16
Consider the student responses to the question and adjust the scheme if necessary to take these answers in to account
Activity 2.16
This is an opportunity for delegates to create a mark scheme to a question, and apply it to some specimen answers.
Handouts 2:16(a), 2.16(b) and 2.16(c)
Let delegates attempt 2.16(a) before seeing 2.16(b), and then finally 2.16.

19. Closing comments Closing comments
Discuss with delegates that they should now be familiar with the syllabus and have started to consider how they will use this knowledge to enhance their teaching and assessment methods. Emphasise that teaching methods should develop the skills as outlined by the Assessment Objectives. For example, teaching methods should develop the skills of application and formative assessment methods should assess the extent to which this skill has been developed.