A closer focus: Different styles of question in maths

By Susan Rose, Senior Research Manager

Friday 28 August 2020

Question-level analysis of the 2018 and 2019 key stage 2 national curriculum tests, in addition to analysis of the year 6 NFER Tests during the standardisation trial, shows that the style of question and response type can impact a pupil’s ability to gain the available marks. Some of the more common issues are discussed below.

1. Demonstrating mathematical fluency

Of the three papers taken by pupils as part of the end of key stage 2 national curriculum tests in mathematics, the arithmetic paper is the most consistent in both content and style. The style of question varies very little between the years and, with practice, pupils should become familiar with the way in which questions are asked. Each year around 50% of the marks in this paper are based on content from the year 6 curriculum, meaning pupils are also required to demonstrate the skills learned in earlier years. The paper aims to test whether pupils have true fluency in their understanding of mathematical concepts: a large number of questions, particularly in the first half of the paper, can be completed without or with very limited working. Pupils need to quickly identify these questions that do not require a full written method; those who are not able to do this may find that the time taken to work through a written solution prevents them from completing the paper in the time allowed. In the latter part of the paper there are a number of questions which earn only one mark but require multiple stages of working, so will need some level of written method.

Around 50% of content in the reasoning papers is also from the year 6 programme of study, but several questions assess content from years 3 and 4. Where this is the case, it is often asked within a context and it may not be immediately obvious as to which skill is required. Pupils would benefit from revisiting work from earlier years in increasingly complex contexts so that they remain familiar with the skills and also learn to apply them in a range of different situations.

2. Questions requiring an explanation

Pupils often found questions requiring an explanation challenging as shown in the 2018 and 2019 KS2 papers. For example, in 2019, pupils were asked to explain why two numbers were not prime; only 31% of pupils could do this. Similarly, in 2018, when asked to explain why a triangle was not an equilateral triangle, only 54% of pupils were successful in gaining the mark. Similar results were seen in questions that involved a small calculation such as when asked if doubling an acute angle always resulted in an obtuse angle (2019 question), just over half (53%) gained the mark. Pupils were slightly more successful in explaining a simple sequence, such as in 2018 when asked to explain whether a competition ran every four years; nevertheless, this still proved challenging to nearly a quarter of pupils (22%). Overall, pupils struggled more with ‘explain’ questions that required recall of knowledge but did not require a calculation to be carried out. This suggests that pupils may benefit from more opportunities to explain their answers verbally, including a focus on explanations which require more than just a calculation or a diagram. They would then need practice at transferring these verbal explanations into writing.

3. Open ended multiple choice questions

In the reasoning papers, many pupils struggled when faced with a question that did not specify the required number of correct responses. For example, in 2019, when asked to tick all equivalent fractions without being told the number of responses to be ticked, only 45% of pupils could do so. However, when pupils are told the number of responses required they perform much better. For example, in 2018, in a very similar question where pupils were told that there were two correct responses, 88% of pupils were able to gain the mark. In the NFER Tests, questions which similarly did not specify the number of responses proved particularly challenging for the lower achieving pupils with over 20% giving only one answer each time. However, in a question regarding the properties of a shape, 14% of higher achieving pupils, 15% of middle achieving pupils and 29% of lower achieving pupils also only gave one of the required responses. Whilst this may be based on subject knowledge, it may also be the result of not reading the question carefully enough and realising that more than one solution may be required. When a question specifies the required number of responses, pupils may not need to look at all possible options, but in questions where this is not the case, pupils should be encouraged to consider each option carefully to determine whether or not it is a correct response.

4. Digesting multiple pieces of information

A number of questions in the reasoning paper use word problems. Often these questions also contain multiple pieces of information which pupils need to interpret in order to solve the problem. For example, in 2018, a question about the collection of eggs required some basic calculations, (4 x 11 and 57 + 44), but multiple pieces of information also needed to be processed including the number of days in a month, the number of eggs already collected and how many could be collected on other days. This led to only 39% of pupils being able to correctly answer the question. Pupils may benefit from being exposed to these types of problem more often and having opportunities to discuss the problem, identifying why certain pieces of information have been provided.

Pupils also found it challenging when the question had two parts with very similar wording but required the opposite calculation to be carried out. For example, in 2018, when faced with a question about children completing a race, pupils were told the time taken by one child, Jack. The first part of the question gave an instruction that a second child had finished the race x minutes after Jack - 54% of pupils were able to work out how long this child took. In part two of the question, the wording was identical except it stated another child had finished the race y minutes before Jack, and in this case only 22% of pupils were able to gain a mark. The year 6 NFER Tests contain a similar question, involving straightforward addition and subtraction, made up of two parts which are worded very similarly; however, the order of the words make the requirements different. This caused confusion for pupils of all achievement levels but particularly those with lower and middle achievement. Many pupils were able to gain one mark by carrying out the same calculation for both statements i.e. either increasing both or decreasing both. This type of question is important to assess pupils’ understanding of mathematical language and differences between mathematical statements. Therefore, pupils would benefit from further practice with questions of this type so that they can develop strategies in how to approach problems, such as being encouraged to translate these statements into number sentences.

5. Completing multiple stages of working out

A large number of questions, particularly in the reasoning papers require several steps of calculation and these can prove challenging to pupils of all achievement levels. The first difficulty is where it is not immediately obvious as to which calculation pupils need to carry out. Lower achieving pupils in particular can find it difficult to get into a question, even though they may have the knowledge to carry out the skill once they recognise what is needed. Pupils may benefit from practising basic skills in a range of different contexts and in identifying how problems can be broken down. Starting with a single step question and building up the number of steps required may also prove helpful. Across all three national curriculum papers, a large number of questions, despite awarding only one mark, are multi-stage and pupils (particularly those of middle and lower achievement levels) can be put off attempting the question if the required method is not immediately obvious – once again demonstrating that practice is key.

Another issue in this type of question is where the first steps are more complicated than the final step. In this instance, some pupils, having successfully completed the complicated steps, do not complete the remainder of the question. For example, in the NFER Tests, one question requires pupils to add fractions with different denominators before using this answer to state the fraction of children that had used a different method of transport. In this question, a number of pupils recognised the need to add the three fractions and did so successfully - which was the more complicated step - but then omitted to subtract their answer from 1 (the simpler step). There was a similar question in the 2018 national curriculum tests where pupils were asked to find the area of a garden used to plant carrots. The first step required two fractions with different denominators to be added. The second, simpler step required this answer to be subtracted from 1. It is possible that, as found in the NFER Test, some pupils who did not gain the full marks (59%) omitted this final, simpler step. When pupils are attempting a complex problem solving activity they need to ensure that all steps are completed and may benefit from more opportunities to focus on problem solving strategies in the classroom and ensuring they see a question through to its full solution.

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