How can you break the pattern of children counting all to add?

Edward C. Rathmell
University of Northern Iowa

It is natural for children to count all as they begin adding. By helping them learn more efficient ways to think, you can help them make sense of adding with the harder basic facts and mental computation with larger numbers. Helping students move beyond counting is one of the first steps in building their competence and confidence in mathematics.

Why do children continue counting from one to solve basic addition fact problems? From the time children begin to learn about numbers, they have been encouraged to count to find out how many. Furthermore, they have had success with counting to find these answers. As long as they can see the objects or directly model the problem on their fingers, they will tend to use the same counting patterns. This is one of the reasons that students using a manipulative activity program sometimes continue to count all for an extended time. If the counters are right there in front of them, why not count them? The children are confident that they can correctly answer the question using that procedure.

In order to break this pattern of behavior, teachers need to structure experiences where it is much easier to use a different thinking strategy. For example, if you create a situation where the students can not count all, they will try to find different ways to solve the problem.

Two teaching strategies tend to encourage children to look for ways other than counting all to solve the problems. Hiding the large part that is to be added, then showing the small part encourages children to count on. Similarly, using situations where one of the numbers is much larger makes it very difficult to count all. For example, if you have 34¢ in your piggy bank and put another 2¢ in the bank, how much is there now. Counting from 1 to 34 is not efficient, so students try counting on.

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