In this book we focus on conceptual subitizing and show how this aspect of subitizing forms the basis for mental computation. In particular the two strategies of counting on, rather than counting all, and doubles develop naturally out of conceptual subitizing. So, what is conceptual subitizing?
Conceptual subitizing refers to the ability to see groups of objects, to combine the groups mentally and to know how many objects there are in the group. For example, the ability to count on by 1, 2 or 3 from a subitized group is a form of conceptual subitizing.
It is time now, to build a framework for conceptual subitizing which leads to fluency with early addition facts. Although this may sound trivial, for many students, developing ideas about the concept of altogether requires considerable support. Developmental milestones to watch for include:
- Knowing that written numbers tell how many are in a group and are not the names for the last object counted.
- Knowing that objects can be moved but that the amount in the group remains unchanged.
- Being able to break the counting sequence and count on from a given starting number.
- Combining two groups rather than naming the groups.
When students are first presented with two groups to combine they are likely to count all. If we’re not careful, counting all becomes the default strategy that is used for all later computation. The activities presented here are designed to encourage subitizing and counting on. When students can spontaneously count on they will be ready for the introduction of doubles and rainbow facts. Until that point teaching other strategies is difficult because the basics are not in place.