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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
These data show a focus on the area of number and operations; on average, states devoted 32 percent of their mathematics standards to this area, and all states had at least some standards in this area. Geometry received less emphasis than number in the early learning standards (18 percent), and measurement accounted for 16 percent of standards in mathematics. In addition, there was much greater overall emphasis on the content standards areas than on the process standards areas (see Table 7-1).
A more detailed analysis was conducted of all standards in each of the three content areas that are the focus of this report (as well as the NCTM Curriculum Focal Points): (1) number and operations, (2) geometry, and (3) measurement. Table 7-2 provides the details of the results for each area.
In the area of number and operations, states have most often addressed number sense (an average of 24 percent of the number/operations standards); however, there is considerable variation among states—from 11 states with no standards in this area, to 4 states for which number sense accounted for 100 percent of their number and operations standards. Three other core areas of number were relatively frequent—the number word list, 1-to-1 counting correspondences, and written number symbols—and each is addressed by 11 to 14 percent of the standards. Cardinality and the three basic kinds of addition/subtraction situations received minimal attention.
In the geometry early learning standards, there was an emphasis on children’s knowledge of properties of shapes (40 percent) and spatial reasoning (25 percent) (e.g., knowledge related to spatial location and direction), although, again, there was considerable variability among states. Some important aspects of geometry for young children receive little attention, including transformation and visualization of shapes.
In the measurement standards, areas most often emphasized are measurement of objects (34 percent of the standards), comparing objects (27 percent), and understanding of concepts related to time (27 percent). Again there was variability—for example, 2 states had no measurement standards at all, and 15 states had no standard related to comparisons of objects and the concept of time (see Table 7-2).
The committee also commissioned an analysis of the 10 states with the largest student populations that publish kindergarten-specific mathematics standards: California, Florida, Georgia, Michigan, New Jersey, New York, North Carolina, Ohio, Texas, and Virginia (Reys, Chval, and Switzer, 2008). These states were selected for analysis because they represent approximately 50 percent of the U.S. school population and therefore influence the intended curriculum for a substantial population of students. Given their size, these 10 states are also likely to influence textbook development and materials that are produced by commercial curriculum publishers.