According to the NCTM reform suggestions, when teachers are orchestrators of student interactions, students adopt a more active role in explaining and learning mathematics. This research, which mapped the nature and role of meaningful mathematical discourse, provides insights into discursive practices that lead to rich mathematical interactions. We observed, coded, and analyzed middle school algebra, number, and data lessons using a grounded theory approach. We organized the observed paths that emerged into a map depicting actual paths for mathematics discourse. The results indicated that communication pathways between the teacher and students occur in many ways, and certain student-initiated questions may trigger predictable teaching patterns. Conversation that originates with the teacher often results in dialogue that is one-dimensional, mostly provides factual information, and rarely results in rich, meaningful mathematical dialogue. However, when students engage in the teacher's conversation or they are persistent in their own questioning, teachers tended to provide more detailed explanations, and teachers often embellished with new examples and representations using nuanced solution methods. Although results seem to indicate that teaching children to be persistent with their questioning will enhance understanding, this behavior may be interpreted as threatening to some teachers. Therefore, caution is warranted when attempting to turn these findings into action. It is important that, before instructing students about being persistent with questions, teachers understand the students' intentions. Although participants did not have negative reactions to persistent student questioning, some children might experience negative responses without proper professional development for teachers.
A variety of factors contributes to student achievement in mathematics, including but not limited to student behaviors and student, teacher, and school characteristics. The purpose of this study was to explore which of these factors have an impact on student mathematics achievement. The target population for this study was North Carolina Algebra II students. Analyses of variance models were examined for group differences and aThree-level Hierarchical Linear Modeling method was employed to examine individual predictors of student achievement in mathematics. Statistically, significant differences were found between students of different ethnicities, socioeconomic statuses (SES), and parental education levels. No gender effects were statistically significant. All teacher-level variables investigated were found to be statistically significant, impacting student achievement in mathematics. School size and SES were not found to significantly contribute to student achievement. More research on the relationships between these factors shown to make statistically significant differences on mathematics achievement is needed to further explain several phenomena that this research reveals.
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 coded in the videos were probing for student understanding, encouraging curiosity and questioning, and using accurate representational forms. For each of the TQMs, graphical, time-integrated analyses were constructed and used to aid analysis and presentation of the results of coding. Although these middle school teachers generally remained consistent in their delivery of instruction, they modestly increased their enactments of the three TQMs. By the second year, both teachers demonstrated increases from their initial level of enactments, and when comparing each teacher's performance to the prior year, their increased enactments were related to improved student performance based on the learning goal of converting fractions, decimals, and percents.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.