School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners' proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are…

To achieve ambitious and equitable mathematics education, districts will likely have to extend their efforts beyond the bounds of classroom teaching and learning, and also address the social and political aspects involved in improving mathematics education. However, the literature has yet to explore the underlying boundaries that determine which…

This paper explores the affordances of mobile learning in developing frameworks for discourse analysis. Specifically, this paper examines the commognitive analysis of classroom discourses in virtual learning environments (VLEs) and how it resolves the challenges of discourse analysis in face-to-face (F2F) settings. With the ongoing social turn of…

This study attempted to develop a literature-informed discourse-based instructional approach and evaluated its effects on eleventh-grade students' conceptual and procedural understandings in probability and statistics. To this end, a quasi-experimental study that involved two control groups and one experimental group was used. One-way analysis of…

Mathematics curricula are often the primary resource used in the teaching and learning of mathematics--in particular, they represent mathematical knowledge for teachers and students. Yet, there seems to be a discrepancy between the curricular materials written for teachers and students (e.g., more variety in the semiotic choices in text provided…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

In this study we applied a discursive perspective of learning (Sfard, 2008) to a sequence of 21 geometry mini-lessons taught in a fourth grade classroom. From this perspective, learning is defined as changes in mathematical discourse. We first characterize and then compare discourse from the beginning and the end of the mini-lesson sequence. We…

Teaching simulations such as scriptwriting tasks offer a novel way to support pre-service teachers in gaining diagnostic competencies and in guiding students to work through difficulties. We first report on the theory-driven development of a scriptwriting task, specifically the theoretically-founded language- and accompanying content-related…

Mathematics problems are shared rapidly across all social media platforms, and the relative anonymity granted to users can lead to unfiltered discourse. This study examined 1,046 comments from a mathematics problem posted twice to YouTube in February 2016 to determine the underlying narratives that indicate the commenters' mathematical mindsets…

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child's evolving responses to the question "Where is…

This study examined how classroom discourse evolved in a gifted class and compared it with a non-gifted class at the same year level. The following features of classroom discourse were examined: Initiation-Response-Follow up (IRF) patterns, teacher and student questions, and teacher revoicing. To conduct the study, audiorecordings of classroom…

This study aims to investigate a mathematical-metacognitive discourse model with IMPROVE metacognitive self-question prompts (What, How/When, and Why) in order to promote a deeper level of discourse in mathematics classes. The study involved 32 math teachers and 824 fifth-grade students (from 32 public schools) from one district in Israel.…

The purpose of this study is to investigate routines as guides for mathematical thinking. Four English-speaking and four Korean-speaking students were interviewed in English about the concepts of limit and infinity. Based on the communicational approach to cognition, which views mathematics as a discourse, we identified the primary characteristics…

This article focuses on the theoretical-methodological question of how to identify reform-induced changes in school mathematics. The issue arose in our project The Evolution of the Discourse of School Mathematics (EDSM), in which we studied transformations in high-stakes examinations taken by students in England at the end of compulsory schooling.…