The purpose of this chapter is to present and explain a classification of additive relationships
helpful in interpreting the procedures students use in solving addition and subtraction …

There is a growing consensus in this country that mental calculation is different from mental
arithmetic: the latter may involve mental recall alone, whereas the former requires mental …

Four ways in which subtraction is more difficult than addition are discussed: Verbal solutions
are not always parallel to object solutions. Two correct methods exist for counting down a …

Six fifth-grade children participated in a four-day teaching experiment on complex additively-
structured problems, which was followed by in-depth interviews of individual children. The …

A tacit assumption of most school mathematics programs is that addition and subtraction are
best introduced through physical or pictorial representations of joining or separating sets of …

A model of subtraction development and the computing difficulties and research issues
suggested by the model are outlined. It is argued that, in order to mentally compute the …

Children in the third grade in a normal class and children poor in mathematics attending
special classes solved all additions with the sum of the two positive addends smaller than …

and 13-year-olds were tested with two types of tasks to test their understanding of
applications of the multiplication and division of positive numbers:(i) writing down …

One hundred twenty-eight children in Grades 1, 2, and 3 were given two multiplication and
four division word problems that differed in semantic structure. The children's solution …

The studies presented in this book should be of interest to anybody concerned with the
teaching of arithmetic to young children or with cognitive development in general …