As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

Number and operations serve as the "cornerstone" of the K-12 mathematics curriculum in many countries. Solving problems in the mathematical domains of algebra, geometry, measurement, and statistics is often closely connected to student knowledge of number and operation (Griffin, 2005). Although considerable knowledge exists regarding the…

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on pre-kindergarten and kindergarten students' ability to rote count, read two-digit numerals, model two-digit numbers, and identify the…

A design research study was conducted over two years with 20 second grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked to count in multiple bases. After doing so, they were asked how they knew when to go to a new place value and why it was necessary. All 20…

Schools following the Montessori philosophy use individual and small-group teaching methods and hands-on, concrete materials. This study investigated the understanding of place value concepts and abilities of Montessori students by comparing interview task responses of 93 students in grades 1-3 in a Montessori school (n = 47) and in a mostly…