This article investigates the coconstruction of student identity and engagement in the case of a 9th grader in a project-based algebra classroom that afforded students a great deal of autonomy. The focal student, Terrance, utilized classroom resources to serve both project-related and social functions as he interacted with his peers during…

Seeking the right level of help at the right time can support learning. However, in the context of online problem-solving environments, it is still not entirely clear which help-seeking strategies are desired. We use fine-grained data from 38 high school students who worked with the Geometry Cognitive Tutor for 2 months to better understand the…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

Descriptions of faculty practice that illuminate nuances of how course planning and classroom instruction occur in specific contexts are important to inform pedagogical interventions. The study reported in this article draws on systems-of-practice theory to focus on the dynamic interplay among actors, artifacts, and tasks that constrains…

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based…

In this article, we describe the design principles undergirding "productive failure" (PF; M. Kapur, 2008). We then report findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability. In the 1st…

As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

In this article we describe and illustrate an analytical perspective in which educational policies are viewed as designs for supporting learning. From the learning design perspective, a policy comprises 3 components that we term the what, how, and "why of policy": the goals for the learning of members of the group targeted by the policy, the…

The concept of "intrinsic motivation" lies at the heart of the user engagement created by digital games. Yet despite this, educational software has traditionally attempted to harness games as extrinsic motivation by using them as a sugar coating for learning content. This article tests the concept of "intrinsic integration" as a way of creating a…

This article reports on an ethnographic study of a 10-year-old's pursuit of school-based mathematics across school and home to suggest that participating in school-based mathematics is a cross-setting phenomenon in at least 2 ways. First, I illustrate how accomplishing school-based mathematics literally extends into the home and how individuals…

Rich-media representations of teaching using animated cartoons can be effective at stimulating teachers' discussion about practice and hence help them learn productively from one another about their profession. Our research aims to design web-based interactive rich-media virtual settings for teachers to learn to do the practice of teaching. For…

Providing instruction on spatial geometry, specifically how to calculate the surface areas of composite solids, challenges many elementary school teachers. Determining the surface areas of composite solids involves complex calculations and advanced spatial concepts. The goals of this study were to build on students' learning processes for…

Eighth grade students in Australia (N = 60) participated in an experiment on learning how to solve percentage change problems in a regular classroom in three conditions: unitary, pictorial, and equation approaches. The procedure involved a pre-test, an acquisition phase, and a post-test. The main goal was to test the relative merits of the three…

It is commonly suggested to mathematics teachers to present learners different methods in order to solve one problem. This so-called "learning with multiple solution methods" is also recommended from a psychological point of view. However, existing research leaves many questions unanswered, particularly concerning the effects of…