From How Children Fail, by John Holt. This was written in 1961!
A very skillful public relations job has been done for the so-called new math. Everyone talks about it, and any school or teacher who isn't doing it seems hopelessly old-fashioned. Some of this new math is really very good. Here and there, truly revolutionary and constructive changes in math teaching are being made; children are finding out things for themselves instead of being told answers or hinted toward them with leading questions. But these places are few. Most of the New Math is just what the Bad Old Math was -- cookbookery. The difference is that the cookbooks are newer, more up to date -- which may be a good thing, if cookbookery is what you want. Some of the cookbooks are not only newer, but better; but many, including some of the most highly touted, lavishly financed, and widely used, are not. Some I have examined are unclearly written; they contain many ambiguities; their examples are often ill chosen; they assume understandings that many children don't have; they do not make sufficiently strong the bridge between the known and real and the unknown and symbolic; they have too much material in them; they are too disconnected, too linear, too answer-directed. They are, in short, not worth all the fuss that is being made over them, and some of the children I know who are using them are as confused, baffled, and frightened as ever.