Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16…

Preschoolers' patterning skills are predictive of their concurrent and later math knowledge; however, it is unclear if patterning is only a proxy for general intelligence, or how it might support specific math skills. The current study examined the relation between 66 preschool children's patterning skills and their general cognitive abilities,…

Preschoolers' patterning skills are predictive of their concurrent and later math knowledge; however, it is unclear if patterning is only a proxy for general intelligence, or how it might support specific math skills. The current study examined the relation between 66 preschool children's patterning skills and their general cognitive abilities,…

Comparison is a fundamental cognitive process that can support learning in a variety of domains, including mathematics. The current paper aims to summarize empirical findings that support recommendations on using comparison of multiple strategies in mathematics classrooms. We report the results of our classroom-based research on using comparison…

State-mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519…

State mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519…

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math…

There is a long-standing and ongoing debate about the relations between conceptual and procedural knowledge (i.e., knowledge of concepts and procedures). Although there is broad consensus that conceptual knowledge supports procedural knowledge, there is controversy over whether procedural knowledge supports conceptual knowledge and how instruction…

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…

Children's knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers' understanding of repeating patterns. One hundred…

Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development. The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development:…

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An Early Math Trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from age 4 to 11. This model includes a broad range of math…

The focus of the present synthesis reflects the research on programs, practices, and policies intended to improve mathematics outcomes funded through the Institute of Education Sciences' (IES's) National Center for Education Research (NCER) and National Center for Special Education Research (NCSER). The authors were asked to review those published…

Background: The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear.…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…