The dissection (and opinions!) of the 2018 mathematics papers have begun. This blog provides an analysis of the key themes across all three papers.
It is worth noting that Year 6 pupils this year are the first cohort of pupils to have had the complete 2014 KS2 curriculum taught to them. Hence one could have assumed that this set of papers would have been the hardest yet. Now that the tests have been taken, opinion on this is divided however. Some have thought it was a fair assessment of the Key Stage 2 content in a range of contexts, with others thinking problems were trickily worded and the complexity of the mathematics involved was the highest yet. Third Space Learning carried out a survey with 200 teachers and reported similar mixed findings about the level of demand across all three papers.
How can we prove if the 2018 papers are more challenging than previous years or not?
One way of making a strong case as to whether the papers are more, less or of a similar challenge to previous papers is to drill down and compare the mark schemes over the last three years. As many of you will know, each question that appears within the Key Stage 2 papers is given a code from the KS2 Test Framework. This code defines the year group pitch but also content being assessed. For example, in this year’s Paper 2, Q1 assessed a Year 4 Geometry objective (and therefore coded 4G2c). It is also probably worth mentioning that many were surprised to see that the first reasoning question for 2018 was not number based!
The charts below show the analysis of the mark scheme coding for the year group composition of the 2016, 2017 and 2018 papers.
Interestingly, we see that the content drawn from each year group is balanced year on year with approximately 26% drawing on Years 3 and 4; 28% Year 5 and 45% drawing on Year 6. It is therefore important to reiterate the tests are not ‘Year 6 tests’ but are rather ‘Key Stage 2 tests’. As such, planned opportunities to consolidate and revise learning from previous year groups are paramount.
Another crucial factor to consider is how the papers are weighted with regards to curriculum content. The charts below show how much of the total 110 marks available were allocated to each content domain over the last three years.
Again, it is apparent that the content domain weighting is fairly consistent year on year with approximately 47% drawing on Number & Calculation; 22% on Fractions; 11% on Ratio & Algebra; and 19% drawing on Measures, Shape and Geometry. Hence, it is essential that curriculum maths plans across the school - not just in Year 6 - reflect a greater focus on securing Number, Calculations and Fraction within each year.
Other variables that can help with comparing the level of difficulty of the papers is to consider the number of marks available from where the questions are either:
Out of context - questions which have no ‘real -life’ context and involve filling in tables, writing missing digits, or ordering a set of numbers. For example, 2018 Paper 2, Q13.
- Show your method - questions which involve two or more steps and pupils are required to show the process of their calculation to gain up to 2 or 3 marks. For example, 2018 Paper 3, Q13:
- Selected response – questions which involve matching or selecting the correct answer from a list. For example, 2018 Paper 3, Q5:
- High Level constructed response – questions which require pupils to ‘explain how you know’. For example, 2018 Paper2, Q9:
Below shows the percentage of marks allocated to each of these different question types over the last three years.
Looking carefully at all this evidence, together with the consistent distribution of the year groups and content coverage over the past three years, it can be strongly argued that the papers have been of a similar demand year on year.
Why though might it be argued that the papers are more challenging?
In spite of robust analysis of the mark schemes showing that over time the papers are balanced, it does not come as a surprise that some deem the papers to be more challenging than previous years.
This year we saw for the first time pupils being assessed on their place value knowledge of numbers up to 10,000,000 in Paper 1, Q15 (2018), whereas in previous years pupils were only assessed on their place value knowledge to 1,000,000.
Similarly, the level of challenge when calculating fractions definitely appears to be ‘ramped up’ this year. Paper 1, Q35 (2018) asked pupils to subtract two mixed numbers with different denominators.
This is without doubt more challenging than the fraction subtraction question that appeared in the 2017 Paper 1 (Q32) test.
Interestingly, both these questions (2018, Paper 1, Q35 and 2017, Paper 2, Q32) were in their respective years coded 6F4!
Although it could be argued that some questions are more difficult than have been the case in the past, this is somewhat of a moot point given that pupils’ scores are standardised. It will be interesting to learn the standardised conversion scores when results are published on the 10th July.
However, what is the essential information about the analysis of the 2018 papers?
Although there is debate about the level of challenge of the papers, what is inarguable is that the 2018 Tests are an invaluable teaching tool to support teaching and learning for the next cohort of pupils who will take the next round of Key Stage 2 Tests. If we can dare mention 2019 SATs preparation, then SIX key areas to consider based on our 2018 analysis are:
1. Securing calculation method for the four operations
Ensuring pupils are confident with a formal written method for each operation, but also have a wealth of mental calculation strategies to draw on is still of vital importance. Pupils who are too heavily reliant on written methods and not able to apply mental calculation strategies to some questions will not have enough time to complete the papers. Remember the arithmetic paper has 36 questions to answer in 30 minutes! Similarly, pupils have a lot to get through in the reasoning papers each allocated 40 minutes.
2. Embedding the understanding of fractions
Assessing pupils’ understanding of fractions continues to be very prevalent in the SATs papers. This year we saw 22% of all marks allocated to the Fractions, Decimals and Percentages domain. There was clear emphasis on mixed numbers (in fact, 7 questions included a mixed number!) and we cannot fail to mention one of the most challenging questions this year, the final question of Paper 2, Q23, which involved pupils partitioning 58 2/3 to complete the long multiplication (58 x 24), then finding a fraction 2/3 x 24 and finally re-combine!
3. Developing fluency in number and variation in practice
The 2014 Programmes of Study for mathematics has three clear aims, one of which is that pupils are fluent in mathematics. This year SATs papers saw an increase in questions that assessed pupils’ fluency and ‘mastery’ of mathematics. For example, Paper 3, Q9 required pupils to have a firm understanding of the relationship between numbers:
4. Practising ‘show your method’ multi-step word problems
Multi-step word problems that require pupils to show their calculation method continue to have a heavy emphasis. This year a third of total marks were awarded to ‘show your method’ questions. It is essential therefore that pupils have regular opportunities to break down these more complex word problems into mini-calculation steps to gain as many marks as possible, even if they don’t always get the correct definitive answer.
5. Exposing pupils to a variety of problem solving and reasoning questions
Although there was a heavy focus on ‘word problems’, we saw a variety of problem solving question types being assessed:
Missing numbers - Paper 3, Q4 (finding three missing digits to make a correct addition).
Finding all possibilities - Paper 3, Q2 (missing colour combinations for a new team shirt).
Logic Puzzles - Paper 2, Q 21 (calculate the value of individual shapes from a design).
Visualisation puzzles - Paper 3, Q17 (sum of the dots on opposite faces of a die).
Reasoning questions - Paper 3, Q6 (identify ‘true’ statement about a big cat pie chart); Paper 2, Q9 (explaining why Cricket World Cup was not held every four years).
It is therefore essential that problems solving and reasoning is an integral part of all pupils’ daily maths diet and they are explicitly taught how to solve the rich variety of questions that are presented to them.
6. Understanding mathematical terminology and knowing key mathematical facts
It comes as no surprise that for pupils to be successful at solving the vast range of questions, they need to have a secure understanding of mathematical vocabulary and key mathematical conversion facts. The table below highlights the key terms / facts they would have needed to know in this year’s papers:
Don’t forget, coupled with these SIX essential areas outlined above are also the key two points raised earlier:
Consolidation and revision of learning from previous year groups is paramount.
Ensure there is a greater focus on securing Number, Calculations and Fraction as per the content domain weighting of the tests.
Finally, remember, the implications from the SATS is not just applicable for the Year 5 pupils who will be sitting the Key Stage 2 mathematics tests in 2019. As a short task, as a Mathematics Subject Leader or Senior Leader, use the SIX key points that have been highlighted as key implications, and RAG rate them for every year group in your school, using this free downloadable template.
The outcomes from doing this can in turn be used to support whole school next steps for robust SATs planning over time and hopefully avoid the ‘race to the end’ when pupils reach year six!
Best of luck for the results day on the 10th July!
Sarah-Anne Fernandes heads up her own consultancy company, SolveMaths Ltd, where she is highly effective at delivering mathematics consultancy support and training for schools to improve standards. In addition to in-house school support, Sarah-Anne is an established mathematics author and series editor who has worked on a range of titles for leading education publishers. Sarah-Anne has great belief that mathematics can be enjoyed and successfully learned by all!