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Teaching Children How to Use Language to Solve Maths Problems

Introduction

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This study looked at effective ways of using class discussion to improve the teaching of maths and science. The research suggested that children can be helped to use talk more effectively as a tool for reasoning.  But if this class discussion is not organised well then the talk can be unproductive, uncooperative or off task.

The researchers used set lesson plans and taught skills in British primary schools to compare students' use of exploratory talk (an explicit, collaborative style of reasoning) and discussion. This builds upon earlier research by the same authors which showed that exploratory talk led to individual improvements in pupils' test results.

What did the researchers discover about teaching and maths?

The researchers used 'thinking together' lessons to explore whether this approach would enhance pupils' abilities in maths and science. Their study showed that the methods used led to an increase of 44% in standard SAT test results compared with 26% in a control group. There were also improvements in the quality of class discussion and of small group work, with more active inclusion of all pupils involved.

The researchers also found that improving the quality of pupils' use of language for reasoning together improved their individual learning and understanding of mathematics. Their research showed that the teacher was an important model and guide for pupil's use of language and reasoning. When teachers provided children with an explicit, practical introduction to the use of language for collective reasoning, the children learnt better ways of thinking collectively and better ways of thinking alone.

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What did the thinking together lessons involve?

Each teacher was provided with 12 detailed lesson plans, and given training in how to apply them. The first five were designed to raise awareness of how talk could be used to work together and established a set of ground rules which could generate talk of an exploratory kind. The following seven lessons were designed to enable pupils to apply these talking skills to the year 5 maths curriculum.

Each of the lessons was split into three:

• a teacher led, whole class introduction
• a group discussion activity, and
• a final, whole class session in which ideas were shared, and there was room for reflection on the class as a whole.

In the final seven lessons, the discussion was focused on a specific talking skill and a particular curriculum concept such as reasoning about number relations. These lessons were also used to reinforce the skills learned in the earlier classes.

The researchers included samples of class interaction in this study, to illustrate the strength of these methods:

Teacher:	So if I walk around the classroom while everybody is talking together in their groups I wonder what kind of things might I hear people saying?
Asif:	'What do you think?'
Teacher:	That's a good one. Why is that an important question Carl?
Carl:	Because you ask someone else their opinion.
Sarah:	'I think this because.'
Teacher:	Why did you add 'because' at the end of that sentence?
Girl:	Because then they know why you made that remark.
Teacher:	Well done. Brilliant. You need to explain so that everybody understands what you think.

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What teaching methods worked well?

The study found that pupils felt that the group discussion approach allowed them to pool ideas, and reach conclusions they could not have reached individually. However, whole class discussion worked well only when teachers had received effective training. Training involved discussion of underlying principles, teachers' engagement in group problem solving activities (and a reflection on how they did so) and a group analysis of the talk of children working in groups, based on videos and transcripts. They were also asked to discuss and reflect on the ways in which they explored, guided and modelled talk for children, and how they set up children's participation in working groups.

Whole class discussion in this approach sometimes involved simple techniques, such as allowing the pupils to lead discussion and the use of 'reasoning words', such as 'what', 'how', 'if' and 'why'. It was also important, when using whole class discussion all students take part as the skills learned in this way can also be applied to group work. The following is an extract from a transcript of a small group activity:

Kylie:	No 'cos I think like Rebecca, I think it's halving because we had 6, and it ended up 3. Now we've got 4 and it ended up in 2. Do you think half the number or subtract? Do you want to check? Do you want the reveal thing?
Tony:	No, I think it's what Maya said.
Rebecca:	What did you say?
Maya:	I said try 4 and it would come out half.
Kylie:	Tony, do you want to try a different number, try once more?
Rebecca:	Let's see if we put in an odd number and see what happens.
Kylie:	Yeah, an odd number. (Short interruption while they adjust the seating to make sure that Tony has enough room and remains included in the group) Do you want to all try 5?
Rebecca:	Try 5 yeah?
Kylie:	Do we all agree?
Tony:	Yeah.
Maya:	Nought... 2.5
Kylie:	We thought it was half the number (To teacher, who has joined the group).
Rebecca:	Half the number.

In group discussion the key factor was to impress the clear use of ground rules on students; before this method was used, small group work in the target classes often suffered as some children were dominating, others were quiet and discussion often led to ignoring the task at hand. The researchers found that by making the ground rules clear, that small group activity was improved, and each member of the group was included.

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How was the study designed?

The target classes were in Year 5 (aged 9-10), involving 109 students over the two years with a further 121 as a control group. The researchers argued that a simple analysis of the use of language by the students would be too clumsy for real insight. They were more interested in the quality of discussion and the improvements of grades. The resulting grade improvement was an increase of 44% in the target classes compared with 26% in the control group.

The researchers measured improvements over two years, and only included students who were in the study from beginning to end. This removed the possibility of changes (children changing schools and so on) which may have let to a corruption of the result. Schools chosen were of similar standards and in a close geographical area. The effects of the intervention programme on children's talk, reasoning and learning were measured through observation and formal assessment in experimental 'target' classes, with pre- and post-intervention comparisons being made with children in matched control classes in other schools with similar catchments.

Results were analysed using the following methods:

• Key stage 2 SAT tests
• Analysis of teachers' interactions with children, particularly:
• use of 'why' questions
• use of reasoning words ('if', 'because', 'so')
• use of reason to back up statements
• checks that everyone with a relevant idea was heard
• agreement throughout the class at the end of the debate
• analysis of pupil's talk in groups, particularly:
• how pupils in all classes solved problems, and
• changes in the target classes pre- and post-intervention

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What are the implications for practitioners?

In completing this digest the author began to ask the following questions about the implications for teachers and school leaders:

For teachers:

• There is significant evidence that class discussion and group work improves pupils' maths skills, but if these classes are not well organised then discussion may turn into unfocused talk on unrelated subjects. Can you think of occasions when group discussion was going well and others when pupils have gone off topic or worked in an unfocussed way? What do you think makes the difference? Would you find it helpful to work with a colleague to compare effective ways of structuring group discussion? Do you think that structuring whole class discussion may support pupils who are often overlooked?
• In this study it was important to maintain focus by making it clear early on what students were required to do and how to do it. It was also important that this was reinforced over the course of several classes. How might you work over time to ensure that group work skills are as well understood by your class as they should be?
• The teaching style was also important; this method didn't work so well when teachers dominated class discussion. Teachers using exploratory language and questions such as 'why do you think that', 'how did you come to that conclusion' and 'what do you think' promoted good talking and discussion skills amongst students. To what extent are your classes are organised like this? Could you organise classes so that pupils are more involved in discussion?

For school leaders

• In order to develop and maintain these skills, the teachers required additional training. Evidence from the control groups made it clear that those without the right professional development were less successful in this manner. What opportunities can you see for developing teachers skills in the use of group activity? Could this feature, for example, in work with the strategies on talk for September 2008?
• Much of the professional development involved collaboration between teachers. Would it help to involve some of your staff in a group effort to achieve these goals?
  

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Where can I find out more?

Practitioners may be interested in other TRIPS digests about pupils' learning and the strategies that can be used to enhance it. The following digests might interest you:

Attitude and achievement of the disengaged pupil in the mathematics classroom. Available at:
http://www.standards.dcsf.gov.uk/research/themes/Mathematics/TueJun241346352003/

How are pupils' working memory skills linked to their mathematical abilities? Available at:
http://www.standards.dcsf.gov.uk/research/themes/Mathematics/memoryskills/

How classroom talk supports reading comprehension. Available at:
http://www.standards.dcsf.gov.uk/research/themes/speakandlisten/classroomtalk/

Raising achievement through group work. Available at
www.gtce.org.uk/research/romtopics/rom_managementoflearning/groupwork_nov06/

Reason and creativity in classroom dialogues. Available at
http://eprints.soton.ac.uk/16286/

Thinking together. Available at:
http://www.thinkingtogether.org.uk/

Effective talk in the primary classroom. Available at
http://www.gtce.org.uk/research/romtopics/rom_teachingandlearning/effective_talk_sep06/

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