In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

Ever since "mental arithmetic" was updated to "mental calculation," official documents have succeeded in perpetuating several basic misconceptions and misunderstandings about this topic. This situation does not augur well for the successful teaching of mental calculation strategies to young children. In this article, the author…

Discusses a tally device using discs on a paper diagram. Instructions given for number representation, negative values, games, addition and subtraction. (RS)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)