Appraisal
last updated:February 2010
Robustness
Evidence was gathered and analysed in order to answer three research questions:
- How can we design teaching so that mathematics learning will become more effective?
- What are the effects of applying such principles to the design of teaching GCSE re-take classes in FE mathematics classrooms?
- What conceptual tools facilitate the construction of collaborative cultures in these classrooms?
The research was carried out in two phases. During the first phase lasing two years, the main researcher interviewed teachers and visited four classrooms to look at existing practices and monitor their effects. Baseline data were collected on approaches used by the teachers and common difficulties and misunderstandings by students. The researcher designed a collection of classroom discussion activities using the diagnostic teaching approach. These were trialled and tested. Lessons were observed and recorded and students’ levels of understanding were monitored through pre and post testing.
For phase two, the main part of the study, 64 teachers from 44 FE and sixth form colleges in England were involved. The researchers created a one year professional development programme. Algebra was chosen as the topic for three reasons:
- it was considered fundamental to all mathematical work and one which lower- achieving students find hard to grasp as a general concept
- algebra was a topic that had not shown much improvement during the first phase of the project
- the teachers in phase one agreed that algebra is often taught in an unimaginative, transmission orientated way.
Relevance
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. This book is relevant for teachers of all phases and not just for practitioners in the FE sector.
The discussion and reflection approaches have been subsequently developed for use with all post-16 students, with adult learners and with 11-16 year old students in schools. The DFES initiative ‘Success for All’ has resulted in the development of a set of resources for teaching mathematics to all post-16 students that are based on the principles of this research.
Applicability
This research shows how collaboration and discussion in mathematics is important for learning. 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, and
- more student-centred practices used by teachers.
The new lessons also stimulated different kinds of classroom talk, including:
- students giving more reasoned explanations
- using conflict or mistakes to improve understanding, and
- greater participation in whole class discussions.
Writing
The book provides a detailed account of the research project, but it is well-sign-posted. The book consists of two parts. The first part has three chapters focusing on the purposes, theories and metaphors of learning and teaching mathematics. Part two examines how to implement the design principles, such as the design of the research tools, the programme and its effects. The language is accessible. Despite its length, the writing is lively and the inclusion of examples and diagrams adds interest. There is also a compact summary and conclusions chapter which helps the reader to immerse themselves in the substance of the work.
