We theorize about ambiguity in mathematical communication and define a certain subset of ambiguous language usage as imprecise. For us, imprecision in classroom mathematics discourse hinders in-the-moment communication because the instance of imprecision is likely to create inconsistent interpretations of the same statement among individuals. We…

Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher…

In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that…

In this paper we consider how mathematics instruction that values, attends to, and builds on students' mathematical ideas is realized through discourse. We describe interactions that build on students' thinking and in which students help to determine the direction of mathematics lessons as responsive. Using a framework we developed to characterize…

Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in…

The goal of the authors' ongoing research is to better understand how student mathematical thinking that becomes public in a classroom can be used to support the learning of mathematics content and practices (e.g., Stockero & Van Zoest, 2011). Although there are often instances of student thinking that the teacher has intentionally cultivated…

This paper presents a model of numeracy that integrates the use of digital technologies among other elements of teaching and learning mathematics. Drawing on data from a school-based project, which includes records of classroom observations, semi-structured teacher interviews and artefacts such as student work samples, a classroom-based vignette…

The author has recently been experimenting with having students work at a set of six blackboards mounted on the walls of a maths teaching space. In this article, he describes this project which he started because he had become impatient with, and aggravated by the usual setup of a maths teaching space. He had started to question why there are…

The challenges of learning statistics, particularly distributions and their characteristics, can be potentially monumental for vision impaired and blind students. The authors provide some practical advice for teaching these students.

What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

In this article, the author presents a discussion of how mathematics teacher educators model school mathematics teaching in initial teacher training colleges, as they prepare the student teachers to teach mathematics in multilingual classrooms in Malawi. In particular, the article examines the instructional practices that mathematics teacher…

The National Council of Teachers of Mathematics (NCTM) has consistently recognized communication as essential to reform-oriented mathematics teaching (NCTM 1991, 2000). In this article, the authors propose a strategic mix of univocal and dialogic discourse that, when used in conjunction with an "inductive model of teaching," can promote…

In this paper I will explore three contrasting teaching and learning environments, including one in which students engage in a "dance of agency". I will move from a consideration of classroom practices to a contention that our work as researchers of mathematics education should pay more attention to teaching practices. Further, that understanding…

In an effort to present important research results in readable form for elementary and secondary teachers of mathematics, this publication reviews a model and ways of effectively teaching mathematics. The model of instruction proposed by Good and Grouws is based on teacher-centered whole class instruction. Perspectives and guidance are offered in…