by Edward Booth, Braunstone Frith Primary School
I have chosen to carry out an action research project on the impact of exploratory talk to support mathematical reasoning on a group of students in my year 5 class who entered the year being one or more steps below Age Related Expectations (ARE). I have chosen to research this area of student learning because I wanted to find out if the skills needed to work together effectively in maths to solve reasoning problems would aid students when they are working alone. I believe that teaching children the skills to work through a mathematical reasoning problem together will create an internal voice that will support them when working alone. A previous study by Mercer, Wegerif and Dawes (1999) had shown that “the induction of children into an explicit, collaborative style of reasoning which we call Exploratory Talk led to gains in children’s individual scores on the Raven’s Progressive Matrices test of non-verbal reasoning.”
When entering my year 5 class, students displayed a preference for working individually, which meant that they gave up on reasoning problems that they could not complete on their own. The reason for this preference was, I think, due to an inability to work together and a lack of clarity on how they could support each other effectively. Neil Mercer puts forward an argument helps explain why children in my class preferred to work alone, “A possible explanation for the doubtful quality of much collaborative talk is that the children do not bring to this task a clear conception of what they are expected to do, or what would constitute a good, effective discussion” (Mercer, 2006).
My research project aimed to teach the children to use exploratory talk to work collaboratively on a range of mathematical reasoning problems. This was to be carried out through a series of 10 lessons delivered over 10 weeks to the whole class. A group of six students were to be monitored and their progress tracked. A group of six children in a different year 5 class, who are all one or two steps below ARE and would not receive these lessons, would act as a control group.
At the end of the Autumn term 2018, all children carried out Progress in Understanding Mathematical Attainment tests (PUMA) that generated a standardised score. The table below shows the students’ data before the research lessons took place. A score of 100 indicates that a child is working at ARE.
Prior to the reasoning lessons starting, I filmed the focus children working together without being taught specific group talk skills. On the opposite page is an illustrative extract from one of the problem-solving activities.
Hennessey and Rojas-Drummond (2015) developed a tool to analyse dialogic interactions in classrooms and codify them for comparison purposes (T-SEDA coding framework). I used this framework to analyse the baseline transcript.
There were a total of 28 interactions, with 11 of them being off-topic. Student C is identified here as the main disrupter of collaborative talk using strategies to disengage with the activity such as drinks and comfort breaks. This baseline transcript shows a lack of skills to work on a maths problem together and also suggests a reason why the children preferred to work independently upon entering year 5.
Intervention and intended impact
All of the students in the class took part in group talk lessons. The first two lessons did not have a maths focus, this was introduced during lesson three. They built on discussion guidelines that the students were already using elsewhere in the curriculum, as well as drawing upon their own set of guidelines. The following learning objectives were used as a result of assessing the baseline video.
- Lesson 1: I can show my group that I am listening to them
- Lesson 2: I can take it in turns to talk in a group
- Lesson 3: I can use talk ground rules to solve a maths problem
Sentence starters were supplied to help structure a collaborative discussion:
- What do you think?
- I agree with _ because…
- I disagree with _ because…
- Why do you think that?
- Do we agree? (Or shall we talk more?)
- Any more ideas to share?
My hope was that by week eight I would be able to film the focus group again and observe a much more collaborative approach to problem solving. I hoped to see a shift away from off-topic conversations to a dialogue that included the children inviting each other to build on their ideas and express their own ideas backed up with explanations.
I intended to help the children make the link between the discussion guidelines that they were beginning to use effectively elsewhere in the curriculum and how they could be applied to their maths group work.
Due to demands on the timetable within a busy primary school, the lessons had to be cut down to eight. Lessons four – eight were based around the children solving maths problems with their peers. These ranged from magic squares to online function machines (https://www.mathplayground.com/functionmachine.html).
I also hoped that the students would make six or more Target Tracker steps in five data collections between September 2018 and May 2019 (accelerated progress).
After eight lessons, a second video was analysed and the talk coded again using the T-SEDA coding framework.
The number of off-topic talk incidents fell from 11 to zero. There are significant numbers of incidents when the students expressed their ideas or guided the direction of the dialogue. During this post-teaching activity they invited each other to contribute to the conversation and built on each other’s ideas.
It was Student C who made the largest gains in his collaborative working skills. In fact, it was Student C who began the problem-solving process. Transcript 2 shows the beginning of the same three children working together, with Student C making a number of valuable contributions. All children, throughout the activity, check with each other asking “What do you think?” and express their ideas by saying “I think…” They even challenge each other by saying “I respectfully disagree because…” All of the children remained part of the group and maintained concentration for the full 18 minutes of the task. Here follows an illustrative excerpt from the post-intervention problem-solving activity:
Progress data after the eight lessons showed that three out of the six students made accelerated progress with Student B making seven rather than the hoped for six steps of progress. The remaining three students all made expected progress and remained below ARE. Standardised scores from the test data showed a significant shift in scores from three of the students, while no significant impact can be seen from the remaining three students.
The control group showed a similar picture with two students making accelerated progress and two of the students making a significant shift in their test scores.
While the results do not show a dramatically different outcome for either group, what does become clear is that by teaching the children strategies to work and think together, the children are now able to work together meaningfully on mathematical reasoning problems. While there may be a number of reasons for the accelerated progress made by half of the focus group (such as new whole school approaches in the teaching of regular maths lessons), the confidence that these students have gained from the talking approach has had a huge impact on their learning. I have witnessed these three students in particular volunteer to answer and explain maths questions using relevant mathematical vocabulary and build resilience to try again when they get answers wrong.
As my research project focussed on teaching my own students in a regular classroom setting, I did not feel the need to obtain consent at the beginning of the project. I did not want to affect the outcome of the research by informing the focus group that they were being monitored in case this changed their behaviour. I informed the control group’s teacher at the end of the project and gained consent to use a selection of his children’s data to compare with the focus group.
As the control group has been taught by a different teacher, there are many different variables that could have affected direct comparison between the two groups. I do not have data relating to how the control group work together, therefore I have no way of measuring whether the control group’s collaborative talk has improved naturally over time. If I were to carry out a similar project in the future, I would ensure I have the same qualitative and quantitative data for both the control and focus group. In addition, I would gain quantitative data through a questionnaire (pre and post research project) to assess confidence levels in solving problems as a group and the student’s own understanding of how this has supported their own reasoning skills. Due to the impact on student interactions, I intend to continue these lessons to further improve the social and emotional needs of the students with the hope that this will begin to impact mathematical reasoning ability for every student.
Mercer, N., Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20, 6, 2006, pp507 – 528
Hennessey, S., Rojas-Drummond, S. (2015) Scheme for Educational Dialogue Analysis (SEDA). Available at: https://www.educ.cam.ac.uk/research/projects/analysingdialogue.
Wegerif, R., Mercer, N., Dawes, L. (1999). From social interaction to individual reasoning; an empirical investigation of a possible socio-cultural model of cognitive development, Learning and Instruction, 9, 493-516.