Intellectual humility is an intellectual virtue where humility and the pursuit of epistemic goods intersect. As of this dissertation being written, intellectual humility had been studied in psychology and philosophy, but not from the perspective of the teacher in 6th-12th grade mathematics. Hence, this Grounded Theory study sought to develop a…

A teacher's reactions to students' mathematical contributions have critical implications for shaping both teaching and learning. We present a framework for describing reacting moves that resulted from a comparative analysis between two existing frameworks; one developed by secondary teachers for parsing instructional practice and the other…

This article presents a study that investigated potential misconceptions presented in third grade mathematics classrooms and the association of these potential misconceptions with Mathematical Knowledge for Teaching (MKT) and standards-based teaching practices (as measured by the Mathematics Scan). A sequential explanatory mixed methods model was…

This article describes the normative beliefs and the discursive claims related to mathematics and teaching mathematics made by approximately 50 middle-level and secondary mathematics teachers within four high-need local education associations participating in a Mathematics and Science Partnership with a southeastern college's Science and Math for…

This paper attempted to illustrate how a coherence instruction could be accomplished by a teacher's discourse moves. The ultimate goal of this study was to provide mathematics teachers and educational researchers an insightful view of instructional coherence which needs more attention to achieve high quality of mathematics teaching. A Chinese…

The interpretive framework for the study of learning introduced in this article and called "commognitive" is grounded in the assumption that thinking is a form of communication and that learning mathematics is tantamount to modifying and extending one's discourse. These basic tenets lead to the conclusion that substantial discursive change, rather…

Proposes that the style and format of questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. Use of questions depends on both scaffolding and fading their use in front of students so that students internalize questions for their own learning and practice of…

This project opens a conversation about the use of discourse as the basis for encouraging students' mathematical thinking in classrooms and supporting professional growth. A collaboration of teacher practitioners and Math Forum staff, it reflects an attempt to integrate practice and research, reporting on findings culled from discussions of…

Presents a study in which children in four grade 2 classrooms learned about transformational geometry and symmetry by designing quilts, while their four teachers participated in professional development focused on understanding children's thinking in arithmetic, and two of the teachers participated in additional workshops on students' thinking…

The purpose of this article is to describe Discourse Time (D.T.), a teaching practice that aims to integrate argumentative literacy, the third piece of the literacy puzzle, into math learning environments. Snapshots from a tenth grade classroom at Skyview Academy High School in Thornton, Colorado is used to paint a vivid picture of what D.T. looks…

This paper is designed to extend a dialogue on the nature of explanations to include instructional explanations. The paper explores the distinctions between specific types of explanations, (common, disciplinary, self, and instructional) with respect to specific features (problem type, initiation, evidence, form, and audience). Given this context…

Describes a professional development activity that offers a way for teachers to analyze their current classroom discourse practices and move toward the goal of dynamic and productive mathematical discourse. (ASK)

This paper examines two types of discourse in which teachers engage when discussing case studies based on classroom episodes, and the ways in which the availability of video data of these episodes may motivate a shift in the mode of discourse used. We interviewed two pairs of secondary school mathematics teachers after they had read a case study…

A third-grade teacher and a teacher educator argue that, in an elementary mathematics class in which the teacher is encouraging the children to communicate and justify their mathematical ideas, the features of a mathematical task shape the mathematical discourse. They conjecture that divergent tasks, problems with many correct answers, may…