Secondary school mathematics

This book reports on a study conducted in England between 1992 and1995 that was first published in 1997 in the UK, and in 2002 in the US. 

The study is an evaluation of two different naturally occurring approaches to teaching mathematics, characterised respectively as traditional and progressive (called ‘reform’ in the US).  The study took place during a period of change in England    including the introduction of the mathematics national curriculum and changes to the mathematics GCSE examination. The researcher reviewed research literature about mathematics that covered studies of how individuals used mathematics outside the classroom in a range of real-life contexts. The researcher also considered studies showing that students who were taught using open or activity approaches performed better on tests.

The research tracked a cohort of students in two secondary schools in England over three years.  During this period the cohort progressed through Year 9 (n=305 13-14 year olds), Year 10 (n=268 14-15 year olds) and Year 11 (n=290 15-16 year olds).  The two schools were similar in terms of sex, ethnicity, socio-economic composition, and abilities of students. The schools were chosen because they had two different philosophies – one (traditional) where the mathematics department mainly used a text book approach with pupils set in ability groups, and the other (progressive) in which mathematics was taught to mixed ability classes using open ended activities differentiated by outcomes. 

A good range of data was collected.  The researcher used standardised NFER tests from Year 8, pupil questionnaires and tests administered for each year of the study and GCSE mathematics results for Y11 in order to assess changes in attainment, and in students’ attitudes towards mathematics teaching and learning over the period of the study.  These data were complemented by a number of other data sources, which together provided a rich description of mathematics teaching and learning in the schools. They included 100 lesson observations, interviews with 32 students in Y10 and 44 pupils in Y11; interviews with thirteen teachers of Y8 and Y11 students and researcher designed tests of mathematical problem solving from a sample of students in Y9 and Y10.

The findings relating to open-ended approaches which were linked with improvements in students’ understanding, in their confidence about using mathematics and in their performance in GCSE examination results should prove interesting to schools and teachers of mathematics. Whilst focused on the 14-16 years age range, the messages from the research are also relevant to teachers in other phases.  Although the study reported on students’ experiences in the mid 1990s, and some practitioners today may find the context of the study dated, the findings should help to inform current thinking about the curriculum and approaches to teaching and learning.

There was a clear focus in the study on teaching and learning that appeared to have influenced learning gains in mathematics.  The findings are illustrated with a range of material relating to mathematics teaching and learning in contexts familiar to teachers of mathematics in mainstream schools in England. Teachers will find it helpful to consider their own teaching strategies and activities in the light of those described in the study including the use of open-ended approaches, setting problems in the context of real-life situations, allowing students to work at their own pace, the preferred teaching and learning styles as expressed by boys and girls, and the impact of different ways of grouping students. The findings relating to underachievement should prove useful to schools and policy-makers.

In revising and updating this study for an audience of US practitioners the author has had to explain terminology used in England and Wales, but this does not detract too much from the essence of the report.  The study is written in a way that is likely to engage many readers and provides a great deal of thought provoking evidence and analysis that could help teachers to reflect on their own practice today.