Perceptions of instrumentality (PI) are the connections one sees between a current activity and a future goal. With high PI, one is motivated to persist with quality effort because the current activity, even when difficult, is perceived as aligned with, and progress toward, the goal. Conversely, with low PI, one is motivated to relinquish effort…

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes's method of exhaustion in order to compute the number p. Working in a computer environment, students inscribe and…

The teaching and learning of mathematics in schools has drawn tremendous attention since the education reform in Taiwan. In addition to assessing cognitive abilities, Taiwan Assessment of Student Achievement in Mathematics (TASA-MAT) collects background information to help depict average student achievement in schools in an educational context.…

The United States Department of Education (USED) granted 11 states waivers (eight full waivers and three conditional waivers) to provide what the USED termed "flexibility" from meeting some of the requirements in the No Child Left Behind Act (NCLB). Much of the flexibility relieves schools from the Adequate Yearly Progress mandate that requires…

Gain a new perspective on the sharing of erroneous solutions in classroom discussions. Based on their research in grades four and six, the authors reveal how student-to-student correction of errors promotes mathematical reasoning and understanding. Tips for teachers include strategies for using students' errors to encourage reasoning during…