William Brownell had a distinguished career as a mathematics educator, arithmetic textbook writer, and educational researcher. He was an active member of NCTM and many other professional organizations and served for some years as Director of the National Society for the Study of Education and as president of AERA in 1938.
In the February 1978 issue of the Arithmetic Teacher, Lichtenberg invited mathematics educators to engage in dialogue on the topic of mathematical symbolism. It is vital that we do so. Lichtenberg's suggestions belong to a doctrine of pedagogical formalism laid out in the sixties, one that has natural appeal for mature students of mathematics. But formalistic methods may not be effective with mathematically immature students. Indeed, it is likely that formalistic methods sacrifice the very goal they purportedly seek, achievement of meaning.
All four of the books reviewed here are deeply concemed with issues of equiry in mathematics education. I'll say a bit about each book in order to orient readers, and then I'll organize my remarks around the themes that arise again and again: the nature of mathematics. mathematics curriculum and pedagogy, and the philosophical and cultural factors inside and outside classroom that affect our educational efforts.