Yesterday I was able to sit with a few of my learners to discuss their approaches to some of the reasoning questions. Whilst some of my initial hypotheses were correct about why some low scores were attained – not reading the question properly being the top one – it was a useful exercise in gaining insight about the children’s approaches.
I interviewed four pupils who all scored below ten on the KS2 Mathematics Reasoning Paper 3 2016. Their scores ranged from 1/35 to 9/35. Their procedural fluency scores were higher with a range of 12/40 to 27/40. These scores would render these children working below Year 6 standard, if they were the actual results in May.
“I read it through and didn’t get it”
This response to the above question was quite straightforward, but it made me think of the emotional response in addition to the cognitive response. Compared to the previous question, which the pupil knew he could do because he “knows time”, I wonder how a lack of confidence with this non-routine problem affected his potential to attack the question. With guidance from me prompting him to look for certain information and a scaffold for how to re-represent the problem, there were no arithmetic barriers and he was successful. This suggests that the children need a richer diet of problems to build experiences which will support them in the SATs. In addition, perhaps another pedagogic implication is to plan for individual thinking time, before collaborative working, when dealing with problems in class so that I can more easily identify which pupils rely on others more.
“Reading the protractor made it difficult”
This response showed that the pupil was confused between the different directions of the protractor. He did not score on this question at all, and yet independently defined acute and obtuse for me and was able to identify, without a protractor, which angles were acute and obtuse. This implies that he, and perhaps others, need to be build confidence in their capabilities and be more reliant on checking strategies.
“I thought the answer was too big”
The pupil achieved the correct answer in his working out but did not write it in the answer box. He explained that he thought it was too big an answer. This was an interesting response and I suggest that more experience of problems involving “larger” answers would support this pupil. Kudos to him for considering how likely the answer was – showing he is thinking about what he is doing.
“I thought smallest means the least digits”
This pupil applied the wrong strategy despite practising a very similar question days before our practice paper. He explained that the language was confusing. Given the pupil’s history, language is an issue – however, it shows that providing experience with these type of problems cannot be taken for granted that they will prepare the children for similar problems in the future. It shows for these children who score poorly, I need to have a stronger focus on them explaining or proving that they understand why they have answered the question in this way – especially if they have worked with a partner. This ‘explanation’ will be better feedback for me than the response by itself
This was a really useful task, and one which I think I should do more often. It has given me a real insight into the students’ approaches and has allowed me to get to know the pupils better. The implications for preparing these pupils for success are:
- Insist on explanations for answers in lessons
- Ensure that collaborative learning tasks are structured in ways which allow for individual assessment
- Provide a broad range of problems to build pupils’ confidence (knew this anyway, but glad to see it is important)
- Provide instruction on how to re-represent problems to support understanding – bar modelling in particular.
- Provide more opportunities for children to hear other children’s working out and then attempt strategies themselves. I am quite interesting in using the Rally Coach Kagan structure for this.