This research reports on the teacher language and gesture that contributed to shifts in thinking about the equal sign and equations observed in twenty kindergarteners who took part in an early algebra intervention. Our analysis revealed ways in which the teacher used language and gesture to support students in moving from describing and working…

This study explores high school students' and their mathematics teachers' mathematical discourses on the equal sign and variables in the classroom context. The participants in this case study were ninth graders and their mathematics teachers. The data were analyzed in terms of participants' routines, specifically ritual and explorative routines in…

Despite many studies on students' understanding of the equal sign, little attention has been paid to whole-class discourse on their conceptions of equations with two equal signs. This study analyzed the classroom discourse of 30 fourth graders in Korea who participated in a 5-week classroom teaching experiment. A series of discussions on specific…

Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the…

The aim of this study is to investigate relationships between note-taking and the orchestrating of math-talk in whole-class teaching. A lesson on (average) velocity in a Swedish Grade 6 has been observed. Taking an inferentialist stance on human understanding, the study conceptualizes teaching and learning from the perspective of how students come…

This study investigated features of instructors' classroom discourse on the derivative with the commognitive lens. The analysis focused on how three calculus instructors addressed the derivative as a point-specific value and as a function in the beginning lessons about the derivative. The results show that (a) the instructors frequently used…

This paper examines the chronotopic nature of physics discourse and instructional practices that are mediated through the integration of disciplinary spatial repertoires and mathematical symbolic systems. The paper addresses how meanings are constructed during instruction between bilingual international teaching assistants (ITAs) and undergraduate…

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

Symbols play crucial roles in advanced mathematical thinking by providing flexibility and reducing cognitive load but they often have a dual nature since they can signify both processes and objects of mathematics. The limit notation reflects such duality and presents challenges for students. This study uses a discursive approach to explore how one…

I propose that attending how symbolizing activity functions for teachers and students helps to characterize student-teacher communication, and allows for an investigation of how symbolizing activity contributes to learning. I begin this discussion by articulating four ideas-schemes, symbolizing activity, communication, and learning. Then I propose…

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be…

Analyzes the interpretations of equality and the equal symbol of third grade children who participated in a year-long, whole-class socio-constructivist teaching experiment. Concludes that children expanded their conceptualizations of equality due to an active role in class discussions and the arithmetical tasks that took into account children's…

Although mathematics can be described as a formalized language, the signs and symbols of mathematical representation are subject to individual interpretation, which, if inaccurate, can lead to inhibitions about and interferences with the mathematical learning process. The purpose of this study was to explore communication in an intermediate-level…

This paper presents the idea of multimodal teaching and learning and discusses how this perspective can help better understand the learning of students. The discussion is based on data gathered in a qualitative study of a fifth-grade bilingual classroom where at-risk students were successful in mathematics. We report on one class episode and one…

A two-part communication model for teaching elementary mathematics is proposed. Part I delineates symbols commonly used in teaching arithmetic. Parts of mathematical language (mathematical objects, relations, operations, expressions, and sentences) are compared to analogous parts of the English language. Part 2 is a conceptualization of strategies…