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…

When teachers listen to, and learn from, students, they begin to see the world from a child's perspective, and this helps make what they teach more accessible to students. Thus it is important for teachers and educators to understand mathematics from the children's perspectives to help them improve their classroom instructions, by anticipating…

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)

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)