The title is deliberate; it will be argued there are severe difficulties with constructivism as an account of the nature of know ledge, and in particular of scientific know ledge, that carry over to aspects of constructivist teaching and learning. (This is not to say that there are not useful things to be obtained from some constructivist accounts of learning and teaching). What is constructivism? This is a protean doctrine; a number of varieties of which are mentioned to focus attention on some of its aspects addressed in this paper. Constructivists allege that their opponents, usually called 'objectivists', are committed to a didactic view of teaching; the mistake in this claim is set out. Then follows a discussion of the nature of knowledge to I discover truth and falsity contained in the constructivist slogan that 'pupils construct their own knowledge'. The conception of knowledge used is that first developed by Plato and still a necessary feature of present-day theories of knowledge. Constructivists talk of constructing out of experience not only knowledge but also meaning. It is argued that some accounts of the construction of meaning are wedded to an untenable behaviourism about the meaning of words; however, the general thrust of most contemporary theories of meaning since Wittgenstein and Chomsky is that meaning cannot be a construct out of experience. Finally, a rival to constructivist learning is suggested. This is an adaptation of a method employed in the sciences to the case of learning that is opposed to constructivism; instead of constructing up from experience to 'knowledge' one starts with hypotheses which are checked against experience. While it is not alleged that this rival will suit all cases of learning, it at least frees one from the single model advocated by constructivists. Whether all aspects of constructivist learning and teaching are satisfactory is not a theme addressed in this paper; instead the paper will deal with inadequacies in constructivist accounts of knowledge and the erroneous consequences which flow from it for learning and teaching.