activities over the year, is needed to ensure that all children have a chance to learn the topics in the learning path. Such systematic opportunities are needed to help improve mathematical outcomes for all young children.

Mathematics Curriculum

A limited amount of research is available on the effectiveness of specific mathematics curricula or curricular approaches. As described earlier, most early childhood programs do not include primary mathematics experiences or focused mathematics time but rather rely on integrated mathematics experiences in which mathematics is a secondary goal and often incidental (Preschool Curriculum Evaluation Research Consortium, 2008). However, incidental mathematics instruction appears to be less effective than activities with a primary focus on mathematics, although this evidence is only correlational (Starkey et al., 2006).

In addition, reliance on incidental or integrated mathematics may contribute to the fact that little time is spent on math. For example, in the Preschool Curriculum Evaluation Research (PCER) Study, conducted by the U.S. Department of Education, a literacy-oriented curriculum (Bright Beginnings, available at http://www.brightbeginningsinc.org/) and a developmentally focused one (Creative Curriculum, available at http://www.teachingstrategies.com/) engendered no more mathematics instruction than a control group (Aydogan et al., 2005). Other research (Farran et al., 2007) found a negligible time devoted to mathematics in a literacy-oriented comprehensive curriculum.

It is important to note, however, that in response to changing standards and current research, the developers of Creative Curriculum have recently added a mathematics component to their approach (Copley, Jones, and Dighe, 2007). In addition, the High/Scope curriculum (Hohmann and Weikart, 2002) is developing a more challenging focused mathematics component (Schweinhart, 2007).

Large effect sizes support the strategy of designing a mathematics curriculum built on comprehensive research-based principles, including an emphasis on hypothesized teaching-learning paths (Clarke, Clarke, and Horne, 2006; Clements and Sarama, 2007b, 2008a; Thomas and Ward, 2001; Wright et al., 2002). Most of these studies also emphasized key developmental milestones in the main teaching-learning paths, promoting deep, lasting learning of critical mathematical concepts and skills.

Teaching-learning paths or learning trajectories are useful instructional, as well as theoretical, constructs (Bredekamp, 2004; Clements and Sarama, 2004; Simon, 1995; Smith et al., 2006). The developmental progressions—levels of understanding and skill, each more sophisticated than the last—are essential for high-quality teaching based on understanding both mathematics and learning. Early childhood teachers’ knowledge of



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