Developing Math Foundations: Counting On

Counting on is an important strategy that we typically develop in childhood. What is counting on? Counting on is the strategy that if we have two addends, we count on after where the first addend ends.

For example, 17+3. Children who aren't automatic with numbers, haven't developed addition strategies, and haven't developed counting on as a strategy will count out 17 beginning from 1 (using their fingers or a manipulative) and then add 3 more to arrive at the answer, 20.

A child who counts on will start after where the first addend ends. Since the first addend is 17, he/she will count on 3 begining at 18; 18, 19 and 20. A child who develops a count on strategy will have typically developed the strategy after noticing that the sum remains the same using either the shorter, more efficient counting on strategy or the more laborious and time consuming strategy of individually counting out the first addend and then adding the second.

Some children figure it out on their own but others need explicit instruction and modeling to make sense of the strategy. I remember having problems with counting on up until elementary school. My main problem was uncertainty of where I begin counting on from. For example, 17+3. Do I count on beginning with 17 or after it beginning at 18? I eventually figured out the strategy by using logic and easy examples. I would do simple problems for which I knew the answer to--like 5+3. I would then experiment to figure out which was the correct strategy. Since I knew the answer was 8, only one model of the counting on strategy would give me that answer.

This is the kind of experience our kids go through to make sense of numbers and math. We should allow them to explore and make sense of it for themselves but at the same time provide activities, guidance and support for building key concepts.