ABSTRACT
This chapter suggests that an obstacle to pupils' genuine involvement in learning – through the constitutive features of their own everyday language – seems to be the way in which concepts like artesian wells, porosity, tides, dry valleys, beaches to be embodied in a kind of minimal grammar. Those who hold to an objectivistic view of knowledge will therefore be particularly disposed to look for the production of appropriate language–the correct language 'of' the subject. Clearly, like any assumption about the correct language of a subject, the belief that there is a mathematically correct language can overlook what is being done by learners in and through 'correct' or 'incorrect' language. W. Dagnall stresses the need for 'precise and correct language in the infant school', and would like 'to reserve the use of "big" and "small" for volume relations', and not use it for area. Whatever precision maths language has, its situated use by maths teachers reveals imprecision, ambiguity and conflict.
