Aspects of mathematical education

Abstract

Concern about certain of the difficulties encountered by undergraduate students in learning mathematics is discussed. Three attitudes of present‐day undergraduates to study are examined. These attitudes, which contribute substantially to the difficulties encountered by students, are: an expectation to assimilate new ideas without mental effort; a reluctance to devote time to study and to practice; the lack of persistence necessary to tackle exercises of a non‐trivial nature. The attitudes are related to the current trends in mathematics curricula in primary and junior schools mathematics, where depth of study is sacrificed to a broad syllabus which, of necessity, involves superficial treatments of topics. Although this trend persists up to O‐level standard, it is argued that present day A‐level syllabuses may be regarded as satisfactory although, even at this level, future reorganisation of public examinations in the UK may lead to erosion of standards. The degree of mastery of mathematics that is necessa...