Further posts are also available on this theme.
See also GCSE Mathematics and Heading for High GCSE Grades.
For this first post – just some initial notes having marked the mock examination papers for my Year 11 class (UK age 15-16). This class is studying for AQA GCSE Mathematics and also the AQA Level 2 Further Mathematics qualification; they have completed the AQA specification and have taken a complete set of Practice Papers (Set 3) for their mock examination. (Teachers who offer, or are considering offering AQA maths qualifications can register for AQA’s All About Maths). AQA recommend the use of these papers as mock exams as they reflect the balance and expected standard of their new assessment. The papers have been trialled with over 6000 students. Detailed mark schemes and further marker training material is available to support teachers. Many of the points here apply for any specification.
Assessment Objectives
It is time consuming but provides a really valuable analysis and I feel time well spent on this new specification – For each paper, I am entering the marks for each question or part of a question into an Excel spreadsheet. I have used AQA’s Higher Papers AO grid so I and my students can see a breakdown of marks for AO1, AO2 and AO3. The grid is available with the Practice Papers.
AQA Higher Papers AO Grid
This type of analysis clearly shows which topics and/or question types were more problematic for individual students as well as for the class as a whole. Using Excel with conditional formatting makes the information easy to interpret.
Some AO1 marks have been lost simply because students have forgotten material or misread a question, perhaps reading too quickly and not noticing key words. Continuing to use mini-tests should help with this. It also strikes me that we can sometimes display some flashcards as a starter. We can also use starters for GCSE revision. Links to Flashcards from Tanner Maths and other high quality GCSE revision questions are in this post on Mathematics for Students. Last time I taught a year 11 class having done a similar analysis I made sure that questions on the most problematic areas from their mock examination featured regularly in our mini tests. We used Corbettmaths 5-a-day regularly which they found very helpful.
An understanding of graphs is crucial, it seems to me we should take every opportunity to provide a graphical representation where possible for all year groups. Multiple choice questions where students have to identify a graph could be used in KS3; students simply need a common sense approach: for example “if x is 0 what is y?” They need us to help them be confident that they can work it out – work it out, not everything is a memory test. Many students who were successful in identifying an exponential graph simply took a moment to work out a small number of coordinates. Encourage graph sketching in Key Stage 3.
On notation – something I have often seen before – students confuse notation for inverse functions with a reciprocal.
Naming angles and sides, it is so much clearer when students use what use what is given in the question – if an unknown side is BD then call it BD – certainly don’t call it c when there is a C elsewhere in the diagram! Encourage students to mark angles on diagrams – it provides very clear evidence.
Whilst the laws of indices may be understood, students can be thrown with algebraic examples, (32x)3 for example.
Constructions – one of my favourite quotes from a Principal Examiner, “No arcs, no marks!”
Some facts turn up so often, for example: 2 is the only even prime number, if you square a number it’s always a positive result – watch out for these – they turn up is so many different questions!
The value of a sketch: eg reflect a quadratic with a negative coefficient of x2 in the y axis and you’ll get another quadratic – also with a negative coefficient of x2.
I train my students in the ways of marking! They all understand isw – ignore subsequent working. So a harmless extra bit on the end of their answer may not matter. However there are times when extra information will lose you marks – for a question specifically asking about the spread of marks – don’t mention the median!
On my To Do list for my Year 11s and I’ll comment further on these in blog posts to come:
- What are the most common things they have struggled to remember?
- Plan the flashcards to display
- Providing some model answers – annotating the questions, highlighting key words, clear explanations
- Using the analysis of the papers, with other assessments to write helpful reports for Year 11 this term
See also GCSE Mathematics and Heading for High GCSE Grades.