ABSTRACT
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 problems and in understanding more about the difficulties they meet. It also provides a framework for understanding the meaning of different symbolic representations of addition and subtraction, and a coherent basis for designing experiments on these mathematical processes. The theoretical reasons for the distinctions in the classification scheme are both psychological and mathematical. Let me illustrate with three examples of problems:
Problem A.
There are 4 boys and 7 girls around the table. How many children are there altogether?
Problem B.
John just spent 4 francs. He now has 7 francs in his pocket. How much did he have before?
Problem C.
Robert played two games of marbles. On the first game, he lost 4 marbles. He played the second game. Altogether, he now has won 7 marbles. What happened in the second game?
