 ## Introduction

Students can use counting as the basis of a range of strategies to solve problems, such as determining how many objects are in a collection or various kinds of additions and subtractions. Within these strategies, counting refers to more than producing the sequence of number words, sometimes called rote counting.

To continue the process of counting as a way of adding to the total, students need to know the sequence of number words well enough to continue counting from any number. If you ask a young student what number comes after nine, he or she will often initially count from one to find the answer. The need for facility with counting to solve problems far exceeds rote counting. A student cannot count on from seven if he or she does not know the number word that follows seven. In becoming effective users of mathematics, students develop and use a range of methods of solving problems. These solution strategies become more sophisticated as students develop better ways of determining the answer. Sometimes inefficient counting strategies persist in students’ repertoires well past the time when they may have provided a practical means of solving problems. For example, a student asked to find 8 + 3 can count out 8, then count out 3 and finally count all the objects to obtain an answer. If this strategy of counting from one three times persists in later years, the amount of mental effort needed to obtain the answer makes it difficult to achieve further learning. This Aspect of the continuum outlines a progression of efficient strategies.

One of the challenges with inefficient strategies is that, although they are slower, they still work. This means that inefficient strategies can be very persistent.