Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn,…

Participants in this study were asked to report what strategies were most often used in their attempts to foster their students' problem solving abilities. Participants included 70 second through fifth-grade elementary teachers from 42 schools in a large state of the south central region in the U.S. Data analyses of the interviews revealed…

Providing students with a classroom environment that allows for meaningful learning experiences is important for students to develop deep and long lasting understanding about mathematics. This article adds to the literature on learning environments in mathematics by presenting a case study of one fifth-grade mathematics teacher and her classroom…

The aim of this study is to evaluate sixth-grade Turkish students' spatial visualization ability and to determine the strategies that students employ and the mistakes that they make while solving the problems requiring spatial reasoning. Therefore, the study examined the following achievements: visualizing different view images of…

Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this…

This paper documents how a team progressed through the five stages of team development as a result of a school-based professional development program using a laboratory class cycle. Six Grade two teachers and their administrator in a primary school in the southeastern United States participated in the study. All the teachers were interviewed at…

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…

This article discusses how communication theory is used to understand the thoughts mathematics teachers employ when creating messages intended for students. According to communication theory, individuals have different premises about the act of communicating, and these thoughts, called message design logics, guide the process of reasoning from…

The purpose of this study was to measure student attitudes toward and conceptions about statistics, both before and after an introductory undergraduate college statistics class. Relationships between those attitudes and conceptions, as well as their relationships to achievement in statistics, were also studied. Significant correlations were found…

This paper articulates a perspective on learning to discuss ways in which students develop personal sense and negotiate meaning in a middle school algebra context. Building on a sociocultural perspective that incorporates mental objects, learning is described as a mutually dependent process involving personal sense making and the public…

Pre- and posttests and interviews concerning misconceptions and alternate conceptions of rates of change were administered to (n=42) students in first-semester calculus using a conceptually-motivated curriculum. Suggests that an emphasis on visual representations through construction and interpretation in conjunction with teacher-student analysis…