Understanding the nexus of theorized Teaching Quality Measures (TQMs) and classroom enactments of learning goals is important. Video and student performance data for a two-year period were examined for two sixth grade mathematics teachers. Due to their importance in contributing to the development of mathematical conceptual understanding, the TQMs…

Teachers and researchers have long recognized that students tend to misunderstand the equal sign as an operator; that is, a signal for "doing something" rather than a relational symbol of equivalence or quantity sameness. Students' equal sign misconception has been researched for more than thirty years (Weaver, 1971, 1973) with little…

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…

This paper illustrates the value of applying the law of parsimony to canonical correlation analysis solutions. The primary purpose of parsimony is that the more parsimonious the solution, the more replicable the model will be. The ultimate goal is to estimate an equal or reasonable amount of variance with the smallest variable set possible. A…

This study addresses the nexus of two critical challenges for today's mathematics teacher. On the one hand, teaching for understanding for all students is the goal of most mathematics teachers. However, many teachers also must acknowledge and address the requirement that students do well on high stakes tests. This study analyzed data on 6th grade…

A sample of 134 sixth-grade students who were using the Connected Mathematics curriculum were administered an open-ended item entitled, Vet Club (Balanced Assessment, 2000). This paper explores the role of misconceptions and naive conceptions in the acquisition of statistical thinking for middle grades students. Students exhibited misconceptions…

This study analyzed how one teacher used contemporary children's literature to supplement middle-grades geometry. The teacher's students were matched to students in other classes on general reading, general mathematics, and geometry. Student and teacher interviews, observation notes, and video tape recordings provided insights into fluency and…