Kindergarten

Before kindergarten, many children lack measurement rules such as lining up an end when comparing the lengths of two objects, although they can learn about such ideas. At age 4-5 years, however, many children can, with opportunities to learn, become less dependent on perceptual cues and thus make progress in reasoning about or measuring quantities.

In kindergarten, children can leam to extend and create patterns. Furthermore, children learn to recognize the relationship between patterns with nonidentical objects or between different representations of the same pattern (e.g., between visual and motoric, or movement, patterns). This is a crucial step in using patterns to make generalizations and to reveal common underlying structures. Through kindergarten and the primary grades, children must learn to identify the core unit (e.g., AB) that either repeats (ABABAB) or "grows" (ABAABAAAB), and then use it to generate both these types of patterns.

What is the nature of a high-quality prekindergarten mathematics curriculum? The trend to push the present kindergarten mathematics to preschool is not the answer. Too often, that curriculum is not even appropriate for kindergarten. Too many U. S. curricula teach skills, but do not build on children's sense-making ability. Teaching and learning are most effective if they build on children's existing concepts. Present textbooks predominate mathematics curriculum materials in U. S. classrooms and to a great extent determine teaching practices, even in the context of reform efforts . Publishers attempt to meet the criteria of a multitude of national, state, and local curriculum frameworks, and thus the educational vision of any one is, at best, diluted. Moreover, teachers' reliance on textbooks minimizes any effect of such visions.

The standards-based accountability movement that has dominated elementary and secondary education reform for the last decade has now reached preschool and kindergarten. The most obvious manifestation of this trend is the requirement for child-outcome-based accountability in the 1998 reauthorization of Head Start. Other evidence is readily available as increasing numbers of states develop guidelines for prekindergarten learning. Professional organizations are also extending their learning standards down to preschool, while technical reports such as the National Research Council's Preventing Reading Difficulties in Young Children include statements of literacy accomplishments for children, even below the age of 3. In its revised standards, the National Council of Teachers of Mathematics for the first time includes prekindergarten mathematics standards.

Historically, early childhood educators have been resistant to specifying learning goals for very young children for several reasons. Their frequently voiced concerns mirror the basic disadvantages of having specific mastery goals for young children's learning. A major concern has arisen from the fact that children develop and learn at individually different rates so that no one set of age-related goals can be applied to all children. A specific learning timeline may create inaccurate judgments and categorizations of individual children. Early childhood educators are wary that outcomes will not be sensitive to individual, cultural, and linguistic variation in young children. These concerns are not without basis in reality given that readiness testing for preschool and/or kindergarten entrance and exit are common, and negative consequences are more frequent for certain groups of children.

A concerted effort needs to be made to come to consensus among early childhood educators and mathematics educators about what the standards should be for preschool and kindergarten. Then an implementation plan is needed to move the standards into practice by reeducating teacher educators and making sure classroom teachers have the materials and knowledge they need to implement well-designed curricula.