The title *Travelling* * Through Education* is slightly misleading. The author, a professor in the Department of Education and Learning of Aalborg University, Denmark, has written a book of philosophy. He refers to Derrida, Wittgenstein, Foucault, Adorno, Feyerabend, Popper and many others less well known, and a reader not familiar with their modes of discourse may be at sea, as I was.

He is an advocate of “critical mathematics education” which, as far as I am able to make out, maintains that mathematics educators should be concerned with more than the proper way to teach fractions and should take into account the social effects of mathematics.

One of my difficulties with the book is the author’s very wide idea of mathematics. Mathematics is everywhere, he says: “There is mathematics included in the process of buying bread and a newspaper on Sunday morning” (p. 22), and “Mathematics is brought into operation in all kinds of free time activities, such as planning a holiday trip, buying a sweater, cooking, or parking a car” (p. 162).

This seems to me to be carrying things too far. For me, buying a sweater does not involve mathematics. Readers of the book, if they don’t share this idea, will have to be able to suspend their disbelief if they are to get anything from it.

He has a similarly wide view of mathematics education. It too is everywhere. In any workplace that contains computers, he says, teaching and learning of mathematics is taking place. The cashier in the check-out line is using mathematics and “The persons who have taught the cashier how to operate the cash register may never have thought of this as an example of mathematics education.” (p. 22). Professor Skovsmose does, though I do not.

A parallel could be made with friction. Friction is everywhere. We use friction whenever we walk or pound a nail and without it our woven clothes would fall to pieces. A person teaching someone to drive a car is a friction educator. It might be possible to write a book on critical friction education.

I was not able to grasp the author’s ideas sufficiently to be entirely clear on how the “processes of globalisation and ghettoising become influenced by what takes place in mathematics education” (p. 210). Nor could I follow his material on aporia, the apparatus of reason, or mathemacy. This is a book for those who like to talk about education rather than for those who actually do it.

Woody Dudley’s graduate school training was in number theory, so he can deal with positive integers but finds abstraction difficult.