You mean you're a real high school teacher?" said an American delegate at the International Congress on Mathematics Education in amazement. Another was blunter: "ICME is not a place for teachers." In fact there were a number of genuine school teachers in Seville for the eighth international congress and quite a few from the United Kingdom. But we were a clear and quiet minority among a community dominated by the tertiary sector - researchers into mathematics education, teacher trainers, university lecturers, etc. The worlds of the teacher and the "educationist" do not link up often, and as "bashing the educationist" looks like becoming at least as much fun as "bashing the teacher" it may be worth asking what benefit we derive as a nation from our maths educationists.
If all such people were ditched tomorrow in the English Channel, would we notice? First, we would lose the most sensitive and original thinkers in the maths world. An examination of any of the magazines of the maths teaching associations shows the debt we owe them. Teacher membership of these organisations (The Mathematical Association and the Association of Teachers of Mathematics) is, however, painfully small as compared with the total population of maths teachers, so these articles are not as widely read as they deserve to be.
It is also unfortunate that such articles do not count towards the "Brownie points" of the educationists themselves. They, and their institutions, are judged by the number of refereed papers they have had published. Such papers have a narrower circulation still, so that it is doubtful if 1in 10,000 teachers reads any particular article.
One can get the impression, therefore, of a world somewhat separate from the business of teaching, where an international community exists who meet up regularly at conferences, communicate with each other on the Internet, referee each other's papers and invite each other on lecture tours. The maths teacher is oblivious to it all, except through an occasional window such as the excellent publication from the Office for Standards in Education, Recent Research in Mathematics Education 5-16.
This review also makes the comment: "It has been a sobering experience to realise how little British research there is on important issues in teaching and learning." I am in no position to pass judgment, but it is astonishing that as a teacher with 20 years' experience who has made active attempts to keep abreast of current developments I have no real idea of what research my colleagues are doing or how it might help me in the classroom day after day.
High quality research certainly does exist. At ICME-8 I was most impressed with the research of Kathleen Heid of the Pennsylvania State University on the use of computer algebra systems in the classroom. She highlighted the importance of the teacher and the culture of the classroom. Such research should be widely available and widely read. We would do well to rely on such research before introducing more "reforms".
Given the shortage of funds for education as a whole I am sure that it is right for there to be a review of research in the university sector. I hope this would not be too negative - we do need good research, both pure and applied. But we do need to disseminate this, and close the link with the classroom teacher. Perhaps university departments should be given equal credit for the dissemination as for the research itself?
I also hope that schools will engage in research themselves. One of my former colleagues, Jackie Philpott, did some research on the effect of a portable spreadsheet (Acorn Pocketbook) on maths teaching and learning. She was assisted by the department at Birmingham University and the work contributed to an Advanced Certificate in Education. This research also benefited our department as we were able to engage in being near the frontier of educational knowledge.
Educational research is an inexact science with few definite theorems. It is therefore easy to disparage it. Perhaps it sometimes deserves that disparagement. But I have seen enough to believe that we can enrich our classroom environment if we can bring these two worlds closer together. It will be well worth the effort involved.
Robert Barbour is head of mathsat Hagley Roman Catholic High School, Worcestershire