Abstract

Mathematical thinking in children: Numbers and operations

A.     J. Baroody & A. R. Johnson,

(University of Illinois at Urbana-Champaign)

Over the last 50 years, psychologists' perception of young children's number development has changed significantly in two ways. One concerns preschoolers' ability to represent and operate on numbers. Refuting the pessimistic assessment of earlier scholars such as Edward Thorndike and Jean Piaget, nativists have claimed that research over the last three decades indicates infants can count without number words and can even do simple mental arithmetic, such as recognizing that one item added to another makes two. However, some recent research suggests these claims are overly optimistic-that children may not have an innate concept of the "intuitive numbers" (one to three). The key instructional implication is that collections as small as three may be perceived as overwhelmingly large to young children and may cause them to melt down. When teaching (and testing), then, teachers should take care not to exceed children's often extremely narrow zone of comfort. The second major change in perspective concerns the role of language in number development. Recently, some researchers have proposed that learning the first few number words is a catalyst that enables toddlers to construct a concept of numbers. The key instructional implications are as follows: (a) Parents and teachers should help children develop an ability to verbally recognize the intuitive numbers by labeling a wide variety of examples and non-examples and (b) this ability is a critical basis for number, counting, and arithmetic instruction. Indeed, verbally labeling small collections should be accomplished before trying to teach children the complex and otherwise confusing process of object counting.