# 3 Effectiveness of Thinking Maths

Research carried out by CAME over two 2-year periods (1993-5 and 1995-7) monitored the effects of teaching the Thinking Maths lessons to a total of 78 classes. In the first study, pupils were tested using the Thessaloniki Maths test at the beginning of Year 7 and at the end of Year 8. This test focuses on three areas of mathematical activity (use of the 4 operations, algebra, and proportionality) covering a wide range of cognitive levels from middle concrete (2A/2B) to mature formal (3B).

The results showed improvement in test scores with 64% of the classes taught the Thinking Maths lessons making substantial gains.These results are in part dependent on the level of the support the teachers received from CAME. Only one in five of the teachers conducting the lessons had any direct contact with researchers over the two years.They used photocopied drafts of the activities in this book.The results have been analysed using a measure known as effect size, which looks at the difference between the mean results of the CAME schools and the control schools divided by their standard deviation. An effect size of 0 indicates no difference between the distributions of the scores, whereas an effect size above 0.8 indicates a large gain, equivalent to the average score being at the 79th percentile of the scores of the control schools.

- The 13 classes taught by teachers who had thoroughly mastered the new teaching skills required showed considerable improvement (median of 0.87 SD)
- 37 classes showed worthwhile effects (middle median of 0.47 SD)
- 28 classes showed no effect at all.

In intervention research, initial strong effects are often found to fade away over subsequent years. A second study looked at the pupils’ GCSE results three years after their Thinking Maths lessons. Their results were compared with the results of pupils from control schools, who had not used Thinking Maths.

The line on the graph plots an average through the control schools’ results, so the vertical distance of each CAME school above the line gives its added-value. The results show that the pupils’ ability to learn mathematics was permanently affected by Thinking Maths.

Figure 5 Added-value for Thinking Maths schools in GCSE 2000 Maths

The Thinking Maths schools’ GCSE results for science and English also showed similar improvement when compared with the control schools. It could be argued that the improvement in science was in part due to improved mathematical competence, but this argument cannot be offered for the English results. This study showed that the pupils’ general learning ability had been boosted by Thinking Maths, resulting in improved exam results three years later. Similar results for CASE intervention (similar to CAME, but in science) indicate that for maximum effectiveness Thinking Maths teachers should attend Professional Development courses run by CAME tutors, in order to develop the CAME approach.This emphasises the role of the teacher in the development of mathematical reasoning in pupils as opposed to acting as a technician providing the fragmentary teaching of skills.Teachers who attend the course can then conduct a similar programme in their own department. Alternatively the full report has been accepted for publication in Educational Studies in Mathematics.