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…

Different methods of subtracting are described; the equal additions and the decomposition methods are discussed in detail. (DT)

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

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

Observations of students working with subtraction and division are reported. The instructional situation and goals of the teacher are discussed. (SD)

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

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)

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)

Children are asked to describe the subtraction process or to describe a context in which subtraction may be used. (JLH)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)