I Know What I Believe; Do I Believe What I Know?

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believe that all these perceptions of the usefulness of mathematics arise from the fact that mathematics provides a means of communication which is powerful, concise and unambiguous (Committee of Inquiry into the Teaching of Mathematics in Schools, 1982). Thus begins the latest report, the Cockcroft Report, on the state of mathematics in British schools. Needless to say, the picture is not one of pride and satisfaction but more of the should do better variety. report quotes other such exercises from a century, a half-century, and a quarter-century ago, and each in turn has the flavor of should do better. American National Academy of Sciences' Report of a Convocation (1982) carries a similar message with the added note: to do better. history of teaching mathematics in Britain fails to support this contention. Prior to 1836 there was no teaching of mathematics at Eton, although some arithmetic appeared in the curriculum. At Harrow mathematics was compulsory by 1837, and by 1868 we already have a government report saying, The teaching of mathematics in English schools is rarely satisfactory. One wonders whether we have ever managed to match the subject to the child. We do now have some research in mathematics education, but have we used the results of such research to maximum advantage? Is there evidence to show that the results of research have significantly changed practice in schools? Have we in fact been engaged in research that would help the teacher?