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…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

The purpose of this paper is to investigate the relationships between adult students' mathematical micro-identities (informed by positioning theory) and their mathematics (informed by radical constructivism). I used positioning theory to conduct a detailed turn-by-turn analysis of students' micro-identities, and to inform my models of students'…

This paper introduces the LIDO, or the Low-Inference Discourse Observation tool, that captures discourse moves produced by students and teachers in whole-classroom discussions. Coding methods are described, followed by analyses that explore validity of the LIDO through correlations among LIDO-coded discourse moves and between LIDO scores and…

Is it possible to identify instructional practices that have an impact on student learning in mathematics? The study described here is part of ongoing efforts to understand and characterize effective instruction. We drew on the work of several recently developed frameworks for understanding teaching effectiveness to develop a protocol for studying…

Research Findings: Conversing abstract concepts boost children's language learning. Despite the numerous studies on the linguistic environment of early childhood education settings (ECE), most of this work disregards contextual factors that may influence abstract conversations and omits characteristics of children's verbal participation in these…

Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children's perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a…

The field of mathematics education has seen an increase in research focused on the concept of identity, with many researchers focusing on the role of teacher pedagogies in shaping learners' identities and their participation in and engagement with mathematics. In this paper, the actual and narrated practices of two teachers, which incorporate…

This study explores the relationship between students' perceptions and teachers' discourse practices in mathematics classrooms. It reframes the sequence of Initiate-Response-Follow-up (IRF) with a renewed discourse structure that focuses on teachers' follow-up actions including listening, thoughtful questioning, and effective talk moves.…

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion,…

Although mathematics standards have changed dramatically in recent years, teaching mathematics is as complex as it has always been. Some would argue that mathematics teaching has become even more complex, with the implementation of the Common Core State Standards for Mathematics (CCSS-M) (NGA Center & CCSSO, 2010), as teachers are being asked…

This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of…

Background: This study considers the moment-bymoment mathematics discourse of teachers and students and the relationship of these discourses to student learning. I focus on the discursive constructs of responsiveness to students' mathematical thinking and the intellectual work in teacher and student discourse. Responsiveness to students'…

In this article we present a reflection about the meaning attribution to the mathematical object "exponential function" that emerges from two mathematical modeling activities. The theoretical framework of the text contemplates considerations on Mathematical Modeling and elements of semiotics as theorized by Charles Sanders Peirce. The…

This study seeks to understand the emotional connection of teachers' academically productive talk (APT) with student learning from the students' perspective. Using a sample of 2,225 students (N[subscript 7th grade] = 1,146 and N[subscript 8th grade] = 1,079) from 16 middle schools in a city of China, we investigate the relationship between…