Spoken mathematics as an instructional strategy: the public discourse of mathematics classrooms in different countries

This chapter examines the use of spoken mathematics in the public discourse of eighth-grade mathematics classrooms internationally. By “spoken mathematics” we mean the recognizably mathematical terms used in spoken interaction in the classroom. Our principal focus was the relatively sophisticated terms by which each lesson’s central concepts or procedures were named. In our analysis we addressed the question(s): “What is the occurrence of publicly spoken mathematics in the different classrooms studied and what efforts do the teachers appear to make to promote students’ use of technical mathematical terms in their public classroom talk?” A companion chapter examines the question of students’ private spoken mathematics in the classroom and the possible learning that might result.

Spoken mathematics as a distinguishing characteristics of mathematics classrooms in different countries

This paper reports research into the occurrence of spoken mathematics in some well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA. The analysis distinguished one classroom from another on the basis of public “oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Our concern in this analysis was to document the opportunity provided to students for the oral articulation of the relatively sophisticated mathematical terms that formed the conceptual content of the lesson. Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. The contribution of student-student conversations also varied significantly. Of particular interest are the different learning theories implicit in the role accorded to spoken mathematics in each classroom.

Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation : public oral interactivity and mathematical orality

The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study (LPS) documented the voicing of mathematical ideas in public discussion and in teacher-student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation are central to the development of any theory of mathematics instruction.

O rádio e as matemáticas: um estudo sobre o Projeto Minerva

According to our conceptions, to study the so called Projeto Minerva (PMi) – an action of Brazilian Military Dictatorship, implemented in the 1970s, which intended to provide access to Primary and Secondary Schools for thousands of Brazilians throughout the country, using a cheap, and at that time a widely -spread medium, the radio – implies to study not only a unique education strategy, but a variety of circumstances that allows it to be created and developed throughout its 10 years of existence in various Brazilian locations. Each circumstance, each region, each way of doing of each person involved in its development constitutes a different Minerva – that’s why we choose the plural to treat it: the Minerva ProjectS. In this paper we present one of the many possible histories about such project. Synthetically, we present some historiographical aspects of its creation, development and extinction and, based on a study about one of its lessons (related to Analitic Geometry), we try to evidence differences between a spoken mathematics and a written mathematics. According to the the oretical framework used in this text, inspired by the Wittgenstein's language philosophy, the Project articulates various mathematics, what is different of saying that the project deals with the "usual" Mathematics merely changing the way of communicate it.

Student speech as an instructional priority: mathematics classrooms in seven culturally-differentiated cities

Student spoken use of mathematical terminology in public and private classroom discourse distinguishes one mathematics classroom from another. While student-student spoken interactions were frequent in the classrooms studied in Berlin, Melbourne, and San Diego, and non-existent in Shanghai and Seoul, student use of mathematical terminology varied significantly. The variation between the practices of the mathematics classrooms studied in Seoul, Shanghai, Hong Kong and Tokyo problematizes any simplistic characterization of “the Asian classroom.” Our results demonstrate that student spoken facility with the technical language of mathematics requires deliberate scaffolding and, interestingly, this can be achieved through either public or private discourse.