This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we…

Six classes received problem-centered mathematics instruction for two years in second and third grade. Results indicate that students in these classes scored significantly higher than students in traditional classes on standardized measures of computational proficiency and conceptual understanding. (TO)

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…

The study reported in this article examined relations between ethnicity, out-of-school activities, and arithmetical achievements in Latin American and Korean American children in first, second, and third grades. Three types of data were collected: parents' educational attitudes and beliefs, parents' reports of children's everyday activities with…

Analyzes one third grader's participation in mathematics class discussions, his beliefs about class discussion, and his arithmetical development throughout a school year in a problem-centered learning classroom. Concludes that a fruitful classroom discussion both necessitates and, conversely, is facilitated by the negotiation of social norms and…