young children’s mathematical development is related to their students’ achievement (Carpenter et al., 1988; Peterson, Carpenter, and Fennema, 1989). In one study, the few teachers that actually led in-depth discussions in reform mathematics classrooms saw themselves not as moving through a curriculum, but as helping students move through levels of understanding (Fuson, Carroll, and Drueck, 2000). Furthermore, research suggests that professional development focused on developmental progressions increases not only teachers’ professional knowledge but also their students’ motivation and achievement (Clarke, 2004; Clarke et al., 2001, 2002; Fennema et al., 1996; Kühne, van den Heuvel-Panhulzen, and Ensor, 2005; Thomas and Ward, 2001; Wright et al., 2002). Thus, teaching-learning paths can facilitate developmentally appropriate teaching and learning for all children (see Brown et al., 1995).
A few words of caution are in order in interpreting findings about mathematics curriculum research. In the early childhood context, randomized control trials in mathematics may tend to overstate effect sizes because teaching some mathematics will always be more effective than teaching no or almost no mathematics (which is usually what the control classrooms are doing). Comparing the large effect sizes of the mathematics PCER study (Starkey et al., 2006) with the results of no significant differences for most of the literacy PCER studies does not mean that mathematics curricula are effective while literacy curricula are not. Preschools have had a decade of focus on literacy, so the control groups in those studies were doing a lot of literacy as well as the experimental groups. Curricular research does have great potential to advance understanding of effective instructional strategies, but only if this research is conducted with this explicit goal in mind. The inclusion of observational measures, both of fidelity to the curriculum and generalized instructional processes, greatly enhances the ability of the research to speak to specific teaching strategies that may be most important for student learning.
For example, Clements and Sarama (2008a) included extensive observation using the Classroom Observation of Early Mathematics Environment and Teaching (COEMET) and Fidelity of Implementation during a randomized control trial of two mathematics curricula—Building Blocks and Preschool Mathematics Curriculum (PMC; Klein, Starkey, and Ramirez, 2002)—and a control condition. The results indicate that research-based mathematics preschool curricula can be implemented with good fidelity, if teachers are provided ongoing training and support.
Using data from the COEMET the researchers identified instructional strategies that significantly predicted gains in children’s mathematical knowledge over the course of the year: (1) the percentage of time the teacher was actively engaged in activities, (2) the degree to which the teacher built on and elaborated children’s mathematical ideas and strategies, and (3) the degree to which the teacher facilitated children’s responding. Examples are provided