In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for…

This article describes how teachers in a professional development course responded to what they noticed about children's participation in elementary mathematics classrooms and how what they noticed was connected to the teachers' positionality toward equitable mathematics pedagogy. Findings suggest that a lens of participation supported…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

This study is a longitudinal look at the different mathematics placement profiles of Black students and White students from late elementary school through 8th grade. Results revealed that Black students had reduced odds of being placed in algebra by the time they entered 8th grade even after controlling for performance in mathematics. An important…

Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used…

The release of the Common Core State Standards for Mathematics and their adoption across the United States calls for careful attention to the alignment between mathematics standards and assessments. This study investigates 2 models that measure alignment between standards and assessments, the Surveys of Enacted Curriculum (SEC) and the Webb…

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…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

Amid debates about the continued salience of gender in mathematics, this report summarizes an IES-funded investigation of gender-related patterns in the Early Childhood Longitudinal Study-Kindergarten Class of 1998-99 (ECLS-K). Girls' and boys' mathematics achievement, confidence, and interest were examined, along with experiences at…

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…

Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The authors applied the constructivist's participatory-anticipatory stage distinction as a tool for fine-grained assessment. Among solutions given by…