Tony Gardiner appears not to care if the results of the Third International Maths and Science Study were used inappropriately. Let me spell it out for him. If we wish to make meaningful comparisons then we must compare like with like.
At least two of the assumptions made must be challenged.
The first is that the students were all around the same age. This was not true. In the "13-year-old" age group the mean age of the children from Scotland was approximately 13.2 years, that from Germany was 14.3 years. In other words the children from Germany were over a year older than those in Scotland. England was midway between.
One reason for the age difference is that students in some countries on the Continent do not go up to the next class until they have reached the required standard so all low-attaining 12 and 13-year-old students would not have reached the classes sampled.
The second assumption is that a non-calculator, mainly multiple-choice, test of a mixture of both mathematics and science questions will allow a judgment of our students' mathematical attainment in comparison with those from other countries.This is open to debate. Our students did better on the science questions.
Is this because they concentrated on them? We will never know. How did the lack of a calculator affect students on questions designed to test things other than basic numeracy?
We should only emulate the methods of other countries if we are sure it is the methods themselves that produced higher scores. We must also be sure that, as we improve the numeracy of our students, we do not do so at the expense of a deeper understanding of maths.
Chair of general council Association of Teachers of Mathematics Derby