dictions.” Although preschoolers are often unfamiliar with these scientific terms when first introduced, it is not long before they understand the meaning of the terms in this context and use these words themselves, feeling very pleased with the air of sophistication this language bestows on their own mathematical activity. By encouraging problem solving and communication, this activity, like all activities in the program, makes children’s thinking visible, and in so doing provides the basis for ongoing assessment that is the hallmark of assessment-centered classrooms.

The rationale that was created for this activity is as follows: “In this activity, a giving pup icon is used to give children a meaningful mental image of the addition operation. This image will serve as a conceptual bridge and help children build strong connections between an increase in quantity in the real world and the +1 symbol that describes this increase in the world of formal mathematics” (Object Land: Lesson #7). Although children are not expected to make explicit use of the +1 symbol in either the preschool or kindergarten program, it is available for those who are ready to take advantage of it. To our delight, children who have been exposed to this activity in their preschool or kindergarten year spontaneously remember Plus Pup when they encounter more complex addition problems later on, providing evidence they have indeed internalized the set of connections (among name, icon, and formal symbol) to which they were exposed earlier and are able to use this knowledge network to help them make sense of novel addition problems.

Once children have become familiar with Plus Pup and what Plus Pup does, they are introduced to Minus Mouse (see Figure 6-4). The format of

FIGURE 6-4 Minus Mouse—an Object Land activity used to provide opportunities for children to understand subtraction problems.