Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

Discussions about transfer have mainly dealt with how people manage to do something in a situation thanks to having done something similar in a previous situation. From an educational point of view, however, it appears more fruitful to consider the case when the learner, having learned to do something in 1 situation, might be able to do something…

Comments on four articles in a special issue of the Journal of the Learning Sciences on methodology in learning sciences. Analyzes the articles within a general model seeking to analyze human activity across multiple time scales. (Author/MM)

Introduces a special issue of the Journal of the Learning Sciences on methodology in learning sciences. Focuses on how one begins to account for learning and the potential of a learning context to support learning. (Author/MM)

Advances a methodology for capturing and tracing the emergence, evolution, and diffusion of a practice, conceptual understanding, resource, or student-constructed artifact. Presents the Constructing Networks of Action-Relevant Episodes (CN-ARE) methodology which allows researchers to identify relevant data from a complex, evolving environment, and…

Analyzes two classroom episodes using a classroom mathematical practice together with students' diverse ways of contributing to its continual regeneration as the unit of analysis. Asserts that a classroom mathematical practice is composed of three interrelated types of norms: a normative purpose, normative standards of argumentation, and normative…

Introduces a special issue on the ways in which symbolic tools enable, mediate, and shape mathematical thinking while being themselves a product of these processes. (Author/MM)

Presents a cultural-developmental framework for the analysis of children's mathematics in collective practices and illustrates the heuristic value of the framework through the analysis of videotaped episodes drawn from a middle-school classroom. Discusses the promise and limitations of the framework as a method for furthering understanding of the…

Analyzes two classroom episodes guided by the assumption that thinking can be conceptualized as an activity of communication and learning can be regarded as modifying and extending one's discursive ways. Aims to uncover the ways in which the discursive uses of such new symbolic tools were interactively constructed by the students. Concludes that…

Considers individual students' progress as they use tools, discuss data distributions, and interact with teachers and their peers. Suggests that data display tools provide a partial context for discussions but do not constrain the students' interpretations or the way they reason about the data. (Author/MM)

Describes a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. In developing the rationale for this approach, grounds the discussion in work of mathematics educators who conduct classroom-based design research. Frames sample analysis as a paradigm case in…

Describes what a methodology for situated action should do for students given problem solving in school settings. Proposes that a methodology for understanding situated action should afford the instructional designer, the methodologist, and the problem solver opportunities to co-construct coupling dynamics that operate on multiple space and time…

Describes the provenance of the data used in this issue. Includes design of the instructional sequence, instructional activities, classroom structure, and classroom episodes. (Author/MM)

Investigates not only the influence but also the confluence of students' and teacher's understandings of the quality of whole class discussions. Focuses on the communication between students and the teacher in the classroom. Considers the role of tools in both supporting and constraining communication in the classroom. (Author/MM)

Describes an epistemological framework and an associated research method. The framework focuses on the structural relations of individual and setting as experienced by the individual. The analysis consists in zooming to identify patterns that simultaneously occur at multiple levels. Uses data from a physics classroom where students learn to…