Overview

last updated:February 2010

Learning mathematics through collaboration and discussion
How powerful is teaching and learning which emphasises collaboration and discussion by pupils? This RfT explores how mathematics lessons can be designed to stimulate such a classroom culture.

Why is the issue important?
Despite schools and teachers constantly looking for ways to improve the teaching and learning of mathematics, there remain groups of students who struggle to achieve in mathematics and who find particular concepts difficult to grasp. This research provides evidence that altering the style of teaching and the classroom culture towards collaboration, discussion and student-centred practices can be beneficial to the learning of mathematics.

What did the research find out?
The study concluded that student-centred, collaborative and discussion based approaches to learning were more effective than traditional transmission methods in which the teacher explains a topic and asks students to repetitively complete exercises. The lessons were particularly successful at assisting the development of conceptual understanding of mathematics. 

Specific impacts included:

• improved pupil scores in algebra tests
• increases in pupil motivation and reduction in anxiety around mathematics
• more student-centred practices used by teachers

After the project those students who experienced the discussion based lessons were more active in their learning and reported being more actively engaged with people (ie. classmates and teachers) and with tasks.

The new lessons stimulated different kinds of classroom talk, including:

• students giving more reasoned explanations
• using conflict or mistakes to improve understanding
• greater participation in whole class discussions

Use of the new lessons also stimulated a shift in the beliefs of teachers. After the project may more teachers supported a more ‘connectionist’ style of teaching which is characterised by teachers emphasising links between topics, valuing students’ own methods and encouraging learning through dialogue between teacher and student.

How was this achieved?
The teachers involved took part in a one year professional development programme including several workshops which challenged their beliefs and practices, allowed them to test out the use of discussion and collaboration in teaching and learning and gave them the resources required to deliver a series of new algebra lessons to try out on their GCSE re-take mathematics classes.

In the new lessons traditional practices, including students being asked to practise calculations repetitively with the same methods, gave way to discussions about concepts and differing methods. Features of practice which were shown to have a particularly beneficial effect on student performance and learning were:

• viewing mistakes as positive – identifying them and using them in subsequent discussions
• allowing students to develop and justify their own varied methods, and
• encouraging students to set each other problems to solve.

The classroom materials made use of three general types of activity:

• evaluating the validity of statements – is a statement ‘always, sometimes, or never true?’
• interpreting and classifying multiple representations of mathematical objects, and
• creating and solving new problems.

The research based the design of the new lessons on several key principles, including:

• lessons were conducted in supportive social contexts, with plenty of opportunities for feedback to students
• lessons consisted of rich, challenging tasks and questions
• teaching emphasised methods and reasons rather than answers, and
• students created links between mathematical topics.

How was the research designed to be trustworthy?
The research was rigorous, using a large sample and a variety of tools to measure impact of this set of lessons. 64 teachers from 44 FE colleges in England took part in the project. They were all teaching 16-21 year old students who were re-taking mathematics GCSE, having previously gained a grade D or below. The teachers were provided with a guide and resources for ten lessons and a diary to record the algebra lessons, track student attendance and progress throughout the project. Many of the lessons were observed by the researcher.

Several elements were measured before and after the project, using well tested tools, several developed specifically for this project. These measures included:

• students’ performance in algebra tests
• students’ attitude to learning mathematics, confidence and motivation
• students’ views of differing teaching style
• teachers’ beliefs, and
• teachers’ practices.

What are the implications?
The research showed that:

• students are engaged and enthused by mathematics when they are given opportunities for active learning through discussion with peers and when they are encouraged to explain their thinking.
• learning of mathematics can be enhanced by encouraging students’ mistakes to be seen as learning points, and by students setting each other problems to solve.
• teachers learned best in the same way as students, through discussion and reflection.

What do the case studies illustrate?
The case studies included in the RfT show, for example, how:

• a school incorporated discussion and collaboration into its new mathematics curriculum after trialling new practice and consulting key stage 4 students.
• retention rates improved when one school decided to make its ‘A’ level teaching more active and collaborative.
• the quality and depth of student mathematics talk in pairs improved in one school when the talk was modelled by teachers.