Overview of the new GCSE (9-1) Mathematics Specification.
The training which Edexcel is offering will help teachers to:
Understand the assessment requirements of the new specification.
Explore the paper structure and new types of questions, focusing on problem-solving
and reasoning aspects.
Review student responses to questions and understand how to accurately apply the mark
scheme.
Be able to ask questions and share good practice.
Understand how we can support you.
The session will examine assessment objectives 2 and 3, looking at questions that assess
these objectives and student answers to these questions.
In this presentation we will look at: Assessment objective 2.
Assessment objective 3.
Both assessment objectives will be examined by studying answers to source questions taken
from Specimen 1 Papers.
We will have a look at how marks have been awarded to student's responses for each question
or questions part and the commentary provided by the examiner.
Assessment Objective 2: Reason, interpret and communicate mathematically.
Students should be able to: Make deductions, inferences and draw conclusions
from mathematical information from mathematical information.
Construct chains of reasoning to achieve a given result.
Interpret and communicate information accurately Present arguments and proofs.
Assess the validity of an argument and critically evaluate a given way of presenting information.
These five strands have been broken down into elements which you can see detailed on the
slide.
The weighting for the assessment objective 2 is 25% in Foundation Tier and 30% in Higher
Tier.
Question 17 from Specimen set 1, Paper 2F is set to assess Geometry and measure content
(specification points G1, G3 and G4) testing students' knowledge and understanding of properties
of angles in a triangle.
This question tests assessment objectives 2.1a (make deductions to draw conclusions
from mathematical information) and 2.4a (present arguments).
In many geometry questions it is important to be clear which angles are being referred
to.
In most cases this can be achieved by writing found angles on the given diagram, or providing
annotation to such a diagram.
Greater familiarisation with the standard 3-letter notation for angles would be of benefit.
In geometry questions requiring a proof, or reasons to be given for each stage of working,
it is important that full explanations are given.
Many students lose marks by paraphrasing, or leaving out essential detail, such as triangles
add up to 180 without making reference to angles.
As is currently the case, students would be well advised to learn these statements by
rote.
However, it is essential that students only give those reasons relating to their solution
and not quote a list of random known facts.
Student attempt.
The value given for the angle is correct.
All necessary reasons are given.
4 out of 4 marks awarded.
Student attempt.
The answer is written by angle AQP and is correct.
One correct reason is given but the candidate has not explained why angles AQP and APQ are
equal so only 3 of the 4 marks can be awarded.
Student attempt.
The value given for angle AQP is correct.
However, there are no correct reasons given so only the first two marks can be awarded.
This is a common question between Paper 1F and Paper 1H (Question 24 and Question 5 respectively)
from Specimen set 1.
It is set to assess Ratio, Geometry and Number content (specification points R1, R10, G16
and N2).
This question tests assessment objectives 2.2 (construct chains of reasoning to achieve
a given result), 3.1b (translate problems in mathematical contexts into a series of
processes) and 1.3a (accurately carry out routine procedures).
In the question, that phrase Show that Sally is wrong indicates that working must be shown;
a correct answer with no working will score no marks.
The mark scheme shows two possible routes through to the solution but it is possible
that there are other methods.
In the case of an alternative method seen, it would be necessary to adapt the mark scheme.
A common error from students is to write down answers to calculations without showing the
calculation.
For example, 24000 without first writing down 40 100 60.
Students are strongly advised to write down all calculations attempted as it is very common
to see arithmetic errors.
Without the working a wrong answer, for example 2400 rather than 24000 would score no marks.
It is also good practice to include a final statement in questions such as this along
the lines as Sally is wrong as the sand will cost 75.
Student attempt.
A fully correct solution with all steps is clearly seen and arithmetic is accurate throughout.
5 out of 5 marks awarded.
Student attempt.
This candidate shows a fully correct method but makes an early arithmetic error (40 100
is evaluated as 40,000).
All the method marks can be awarded as each stage is clearly seen but the final accuracy
mark is lost.
4 out of 5 marks awarded.
Student attempt.
It was possible to arrive at the correct answer in this question through incorrect working.
This is the case here; the candidate has made an early arithmetic error when evaluating
100 60 40.
The wrong conversion from cm to litres has then been used.
Therefore, the mark available for the use of 1 litre = 1000 cm cannot be awarded and
neither can the final accuracy mark.
3 out of 5 marks awarded.
Assessment Objective 3: Solve problems within mathematics and in other contexts.
Students should be able to: Translate problems in mathematical or non-mathematical
contexts into a process or a series of mathematical processes.
Make and use connections between different parts of mathematics.
Interpret results in the context of the given problem.
Evaluate methods used and results obtained.
Evaluate solutions to identify how they may have been affected by assumptions made.
These five strands have been broken down into elements which you can see detailed on the
slide.
The weighting for the assessment objective 3 is 25% in Foundation Tier and 30% in Higher
Tier.
This is a common question between Paper 1F and Paper 1H (Question 20 and Question 1 respectively)
from Specimen set 1 is set to assess Algebra in context of Geometry (specification points
A21, A2 and G3) testing students ability to derive and solve an equation by using properties
of angles in a triangle.
This question tests assessment objectives 3.1b (translate problems in mathematical contexts
into a series of processes) and 1.3b (accurately carry out set tasks requiring multi-step solutions).
P(process) marks are used here rather than M(method) marks.
This is purely to alert examiners that there may be more than one way to solve the problem
so they should be on the lookout for alternative methods.
P marks work in the same way as M marks.
There is no requirement in the question to show working as a correct answer will score
full marks.
However, students are advised to show working for every question.
A common error in a question like this will be for students to give the value of x [DJ1]rather
than the size of the smallest answer as required by the question.
Student attempt.
A correct equation is formed; the candidate does then clearly show the correct method
of solution but makes arithmetic errors.
All the process marks can be awarded but not the final accuracy mark.
It is common to see arithmetic errors such as these on papers.
2 out of 3 marks awarded.
Student attempt.
It is common for candidates to fail to answer the question set.
This is the case here the candidate has correctly found the value of x [DJ2]but not the smallest
angle of the triangle as required by the question.
2 out of 3 marks awarded.
Student attempt Poor arithmetic in this response (72 12 evaluated
as 7) is the reason for the loss of a mark in this question.
It is also worth noting that it is possible from the arrow and smallest on the diagram
that the candidate has assumed that the angle labelled 7x [DJ3]is the smallest angle in
the triangle.
In this instance, with a correct value for x[DJ4] of 6, the 7x[DJ5] angle does work out
to be the smallest but assumptions should not be made from diagrams. 2 out of 3 marks
awarded.
Question 21 from Specimen set 1, Paper 2H is set to assess Ratio content (specification
point R16) testing students' abilities to set up, solve and interpret the answers in
growth and decay problems.
This question tests assessment objectives 3.1d (translate problems in non-mathematical
contexts into a series of mathematical processes) and 3.3 (interpret results in the context
of the given problem).
As the question asks for the number of bees, it is essential that the final answer is an
integer as shown in the mark scheme.
Students should be encouraged in questions like this to show full working including substitution
into the given iterative formula rather than just a list of values.
Student attempt.
The first substitution is correct but has been evaluated incorrectly.
However, the candidate has clearly shown the subsequent substitutions so both process marks
(but not the accuracy mark) can be awarded.
2 out of 3 marks awarded.
Student attempt There will be questions, as here, where candidates
will need to think about the accuracy of their answer.
Here, the question is about the number of bees and so an integer answer was expected.
For that reason, this candidate loses the final accuracy mark for giving a decimal answer.
2 out of 3 marks awarded.
Student attempt The 4th line of working shows the correct
substitution to find the population at the end of year 1 and so gains the first process
mark.
Some further figures are given but these are incorrect and no working is shown to explain
where they have come from so no further marks can be awarded.
1 out of 3 marks awarded.