This study investigated the development of length measurement ideas in students from prekindergarten through 2nd grade. The main purpose was to evaluate and elaborate the developmental progression, or levels of thinking, of a hypothesized learning trajectory for length measurement to ensure that the sequence of levels of thinking is consistent…

The primary goal of Project M[superscript 2] was to develop and field-test challenging geometry and measurement units for all K-2 students. This article reports on the achievement results for students in Grade 2 at 12 urban and suburban sites in 4 states using the Iowa Tests of Basic Skills (ITBS) mathematics concepts subtest and an open-response…

Based on Piaget's theory of logico-mathematical knowledge, 126 students in grades 2-5 were asked 6 questions about elapsed time. The main reason found for difficulty with elapsed time is children's inability to coordinate hierarchical units (hours and minutes). The educational implications drawn are that students must be encouraged to think about…

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…

This study investigated how elementary teachers in a mathematics lesson study made sense of student learning, teaching, and content, as related to using representations in teaching multidigit subtraction, and how changes occurred over time in their talk and practice. The lesson-study process paved a group talk path along which teacher talk shifted…

A randomized controlled trial conducted in Alaska examined the efficacy of 2 second-grade modules of the reform-oriented and culturally based Math in a Cultural Context (MCC) teacher training and curriculum. The results show that the "Picking Berries" (representing and measuring) and "Going to Egg Island" (grouping and place value) modules…

This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers' specialized knowledge for teaching mathematics and illustrates how such research could be conducted. Participants completing 2 DMI modules were compared with similar colleagues who had not taken DMI.…

Recent research on mathematics reforms in the United States indicates that the reforms are not yet widely implemented. Generally, this claim results from looking at the extent to which teachers use curricular materials or engage in particular classroom practices. This article moves beyond disparate questions of use and practice to examine…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

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 provide evidence that…

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…