Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

Mathematical knowledge for teaching (MKT) measures have been widely adopted by researchers. Critics have debated the value of such measures and questioned the type of knowledge that these access. This article reports on a study where the challenges in measuring teachers' knowledge were illuminated through investigating relationships between the…

The purpose of this article is to explore student-generated connections among counting problems. The literature indicates that such problems pose difficulties for students, who struggle to detect common structures and identify models of underlying problem types. A case study is presented here, in which students elaborate upon connections they make…

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and…

University graduates in China are viewed as the new mandarin class in China. University entrance examinations are seen as the modern counterpart of the long tradition of civil service examinations. It is noted that China's 630 universities and colleges only accommodate four to five percent of those seeking admission. (Author/MP)

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)