Collaborative mathematics

Teachers and researchers have been concerned with how best to help pupils overcome their difficulties with mathematics for many years. This TLA research summary* describes an approach that has helped some teachers address these difficulties. The project used a student-centred, collaborative and discussion based method for learning, with some positive results.The key questions which the research set out to answer were:   How can we design teaching using lessons from other research, so mathematics learning becomes more effective? What effect do student-centred and collaborative learning approaches have on student learning and attitudes to learning, and on teachers' beliefs and practices?  What tools can be used to encourage collaborative learning in mathematics classrooms? The researcher involved in the project designed a series of algebra lessons to be used with low attaining GCSE students. The design phase took two years, using observation of four teachers. The second phase involved the new lessons being implemented in 44 different classes over one year. The lessons were designed to promote discussion as a route to learning, using activities which encouraged reasoning, improved understanding of concepts, and collaboration. The teachers attended a series of workshops to introduce them to the materials and methods which they then put into practice.The research concluded that student-centred, collaborative and discussion based approaches to learning were more effective than more traditional transmission methods, especially in 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 mathematic; andmore student-centred practices used by teachers. In the lessons designed by the researcher, traditional practices such as asking students 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 research also concluded that teachers' existing beliefs about teaching and learning are critical in determining teachers' practice, and in determining the extent to which they can be encouraged to experiment with new practices.The research focused on students who were retaking GCSE mathematics at 44 FE colleges in England, but the approach is applicable to secondary students of all ages and phases. Indeed the discussion and reflection approaches suggested by the researchers have already been further developed for younger learners in schools.This summary extends our earlier summary Raising achievement through group work which examined evaluations of classroom approaches which helped primary pupils learn to work collaboratively and improve their capacity to think into a specific curriculum area.*The summary is based on the following publication:Swan, M. (2006) Collaborative learning in mathematics: A challenge to our beliefs and practices. National Research and Development Centre for adult literacy and numeracy (NRDC) and the National Institute of Adult