Overview

last updated:September 2005

Why is the issue important?
Students’ views of the teaching they receive can be very useful for assessing quality of teaching. Determining which aspects of mathematics teaching promote effective student learning and which tend to prevent it is an important tool for learning about effective teaching.

What did the research show?
Students at the 'progressive’ school:

• understood mathematics better
• were able to apply their knowledge better
• were more confident in new mathematics-related situations
• remembered their mathematics better
• did better at GCSE mathematics.

than students at the 'traditional’ school.

How was this achieved?
Mathematics teachers at the 'progressive’ school put students into mixed ability groups, gave open-ended tasks, encouraged students to discover and use their own mathematical methods, gave students a high degree of choice with regard to the direction of their work, asked open questions that required students to think hard about their answers as well as how they had arrived at them, and encouraged discussion between students. They aimed to give students a comprehensive mathematical understanding that would help them throughout life, rather than narrowly focussing on examination success. Students at the 'traditional’ school were placed in ability groups at the start of Year 9. Lessons typically followed a consistent pattern, were highly structured, used set approaches to problems, and required students to give only brief responses to questions.

How was the research designed to be trustworthy?
The study tracked a cohort of around 300 students in two English secondary schools as they progressed through Years 9-11. The two schools were similar in terms of the student intake and socio-economic conditions, but the schools differed markedly in their philosophy and ethos, approach to classroom organisation, and teaching methods in mathematics in Key Stage 4.The researcher collected a variety of student test data during each year of the study, surveyed and interviewed the students, interviewed teachers and observed around 100 lessons.

What are the implications?
The study showed the importance of:

• giving students opportunities to work through problems that require thought and to reward students who demonstrate careful mathematical thinking
• opportunities to discuss with each other what they can do if they get stuck
• using open-ended activities and prompting students to discuss the problem fully and to encourage them to record it in their own mathematical language
• helping teachers to be aware of their preferred teaching techniques and the effects these have on their students.

What do the case studies illustrate?
The case studies show, for example:

• a mathematics classroom was set up to enable the students to learn algebra more effectively via an open-ended, investigative style of teaching and learning
• whole class teaching can be used effectively to improve the quality of students’ learning in mathematics
• some of the difficulties students experience and the misconceptions they may adopt in algebra if the subject is taught in a way that emphasises routine skills rather than understanding, and if explicit attention is not paid to the careful use of technical language.