In this mixed-methods study, we introduce an activity-based perspective on mathematical authority that considers who leads mathematical activities in a classroom. Our framework for mathematical authority extends existing research that focuses primarily on Authoring mathematical ideas to include the activities of Visualizing and Speaking. Using…

The goal of this article is to examine students' mathematical development that occurs as a teacher works within each of 2 zones of learning: students' zones of proximal development (ZPD) and students' zones of potential construction (ZPC). ZPD, proposed by Vygotsky, is grounded in a social constructivist perspective on learning, whereas ZPC,…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh's actions, this article…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…