In 2006, NCTM released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (hereafter Curriculum Focal Points). These were developed in response to inconsistency in placement of topics by grade level in the United States and the lack of focus (“a mile wide and an inch deep”) typical of U.S. mathematics curricula. Although much shorter than PSSM (and developed over a much shorter time), this report gives grade-level recommendations for each individual grade from pre-K to grade 8. These grade-level recommendations do not specify a full curriculum but rather describe the most significant mathematical concepts and skills at each grade level. There are three focal points at each grade level, each of which is a coherent cluster of skills and ideas, sometimes cutting across NCTM’s five content strands. Curriculum Focal Points recommends that instruction at a grade level should devote the vast majority of attention to the content identified in the three focal points (p. 6). At pre-K and kindergarten, the three focal points concern number and operations, geometry, and measurement.
In addition to the three focal points at each grade level, Curriculum Focal Points describes connections, which consist of related content, including contexts and material to receive continuing development from previous grade levels. At pre-K, the connections concern data analysis, number and operations, and algebra. At kindergarten, the connections concern data analysis, geometry, and algebra. Collectively, these previous reports form the basis for the descriptions of foundational and achievable mathematics content in this report. The current report provides guidance on the two most critical mathematical areas during early childhood: number and operation and geometry and measurement, and as will be discussed later, number and operations is the area where young children need to spend the most time. Meaningful learning experiences in these content areas provide young children with the foundation that is necessary for them to be successful in later mathematics.
Our view of children is one of powerful and intrinsically motivated mathematics learners who, in a supportive physical and social environment, spontaneously learn some aspects of mathematics and make connections and extensions. However, children need adult guidance to help them learn the many culturally important aspects of mathematics, such as language and counting. In preschools and care centers, all children will bring to each mathematical topic area some initial competencies and knowledge on which to build. The major teaching challenge is to build a mathematical learning and teaching environment in which children will learn at least the basics of each topic area. This will enable them to practice and build on their own knowledge, with guidance from adults, peers, and family members, and