In this article, we question what is an appropriate balance of ordinal and cardinal work in the early learning of number. We see an over-emphasis, in current research and practice, on the cardinal that leads, for example, to only using small numbers. We report on empirical work we have carried out in the UK and Canada that suggests the potential…

The relation between mathematical and computational aspects of recursion are discussed and some examples analyzed. Definition, proof, and construction are considered, as well as their counterparts in computer languages (illustrated with Logo procedures). (MNS)

The impact and role of social needs, including computer technology, on the secondary school mathematics curriculum are considered. Their role in the American curriculum, mathematical applications, institutionalized needs, and alternatives are discussed. (MNS)

Described are four hour-long sessions of children working with the definition and use of a procedure for triangles in Logo programming. The conclusion is that turtle geometry is not a trivial activity. (MNS)