portunity to learn them as the ideas become increasingly sophisticated and interconnected over these years. Relationships among the ideas as well as some of children’s common errors are also discussed. Vital ideas for Grade 1 are briefly overviewed to indicate how younger children’s knowledge is developed and extended into Grade 1.

As noted in Chapter 2, we are building on earlier efforts to articulate appropriate mathematics content for young children. In 1989, the National Council of Teachers of Mathematics (NCTM) issued Curriculum and Evaluation Standards for School Mathematics. This document described 13 curriculum standards for the grade band K-4 (as well as for the grade bands 5-8 and 9-12). Although these standards have been influential, they do not describe the mathematics to be learned in detail and did not give guidance by grade level, nor for children younger than kindergarten.

In 2000, NCTM released Principles and Standards for School Mathematics (PSSM) after an extensive process of revision of the 1989 standards. Prekindergarten (pre-K) was included this time, in the grade band pre-K–2. PSSM described five content standards—number and operations, algebra, geometry, measurement, and data analysis and probability—and five process standards—problem solving, reasoning and proof, communication, connections, and representations—for each of four grade bands (pre-K–2, 3-5, 6-8, 9-12), covering all of school mathematics from pre-K through the end of high school. Although PSSM discussed the mathematics to be learned at the grade bands in greater detail than the 1989 standards did, it still did not specify what was to be learned at individual grade levels.

Recognizing the need for more in-depth attention to prekindergarten, early childhood educators and mathematics educators convened in 2000 and publish a conference report on the development of mathematics standards for young children. The resulting book, Engaging Young Children in Mathematics: Findings of the 2000 National Conference on Standards for Preschool and Kindergarten Mathematics Education (Clements, Sarama, and DiBiase, 2004), contains 17 recommendations for early childhood mathematics education. They concern equity, programs, teaching, teachers and their development, assessment, appropriate mathematics for young children, and broader efforts to inform stakeholders and encourage collaboration in early childhood education and addressing the need for age/grade level standards. That report grouped the mathematics content for early childhood into four topic areas: number and operations, geometry, measurement, and algebra, patterns, and data analysis.

In 2002, the National Association for the Education of Young Children (NAEYC) and NCTM approved a joint position statement, “Early Childhood Mathematics: Promoting Good Beginnings.” The statement includes 10 research-based recommendations to guide practice and 4 policy recommendations. The statement includes sample charts of learning paths related to a number goal and a geometry goal with activity examples.

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