How can we break the pattern of take away and count what is left?

Edward C. Rathmell
University of Northern Iowa

As children first begin learning to subtract, they typically will directly model the problem by showing the whole, counting to take away the number being subtracted, then counting what is left. This procedure is expected initially, but it is very inefficient for larger numbers and students and students tend to rely on counting instead of the parts and the whole. Consequently, this procedure does not promote learning the subtraction facts nearly as well as some of the more efficient thinking strategies. Students need to be encouraged to learn new ways of thinking.

Counting what is left, after you have taken a part from the whole, provides a way of solving subtraction problems that is comfortable for children. They already know how to count. And they are usually confident in their ability to count what is left to get the answer. Consequently, you need to create situations where the students can not easily count what is left. Teaching strategies to encourage new thinking are similar to those used to encourage students to use something other than count all for addition. In other words, hide the part that is left so the students can not count it and/or use larger numbers where counting is obviously not efficient.

Hiding the part that is left can be accomplished by showing the whole, covering it and removing a part, then asking how many are still covered. For example, ask how many bears there are on the overhead projector. Show them all going into a cave (under your hand). Then have a part come out of the cave. Ask how many are still in the cave. Structure other situations where the part that is left is still hidden.

Counting what is left to subtract often continues to be an inefficient strategies that is used by students who have access to manipulatives too long. Some manipulative programs encourage teachers to let the students use these manipulatives. That is fine while the children are learning the concept of subtraction--what it is, how you represent it, and when you would use it. But, when you begin to want students to learn efficient ways to solve fact problems, the use of manipulatives should be structured so the students can not count what is left.

Return to Questions