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We examine the case of a lesson planning session within the context of professional development for dialogic instruction, and the lesson enacted following this session, which was intended to provide opportunities to 11th and 12th grade algebra students to explore polynomial functions in terms of their roots and linear factors. Our goal was, through the close analysis of the planning and enactment of the lesson, to gain deeper understanding of how the two participants were framing mathematical learning and how such different frames may explain the disparity between the planned lesson and its outcome. The analysis and discussion point to the complexities of supporting teachers in transitioning from a "doing" frame to an "exploring" frame.

About two decades ago, Donald Stokes published "Pasteur's Quadrant" (Stokes, 1997). Stokes proposed that the motivations of different research projects can be understood as a two-dimensional system, with higher or lower concern for improving technology and practice on one dimension and higher or lower concern for improving fundamental understanding on the other dimension. Stokes provided concrete examples in the four quadrants of this two-dimensional system. He called the quadrant defined by low aspirations for improving technology and practice but high aspirations for improving fundamental understanding "Bohr's quadrant," typified by Niels Bohr's development of the standard model of atoms in physics. He called the quadrant defined by high aspirations for improving technology and practice and low aspirations for improving fundamental understanding "Edison's quadrant," typified by the research and development, led by Thomas Edison, that resulted in the invention of the electric lightbulb and the grid systems that distribute electrical energy in cities and societies. Stokes called the quadrant of high aspirations for both improving technology and practice and improving fundamental understanding "Pasteur's quadrant," typified by the research and development, led by Louis Pasteur, that resulted in development of the theory of disease transmission and fermentation based on hypotheses about microorganisms and revolutionized medical practice and policies in public health. In this commentary, James Greeno examines how the articles in this issue on cultural-historical activity theory (CHAT) and design-based research (DBR) relate to Stokes' (1997) characterization of research and development. Greeno concludes that the research and development represented in these articles meets the criterion of being in Pasteur's quadrant; that is, these studies qualify as use-inspired basic research.

The development of scientific concepts and methods that supported analyses of individual cognition and learning occurred during the 1950s, 1960s, 1970s, and 1980s, with outstanding contributions by Newell and Simon (1972), van Dijk and Kintsch (1983), and others, providing an impressive and rapid scientific advance. At the same time, another research program was developing in departments of anthropology, sociology, and linguistics (e.g., Garfinkel, 1967; Mehan, 1979), focused on patterns of interaction, especially in discourse. The term "situated" came into prevalent use with publications by Suchman (1987/2007; "Plans and Situated Actions: The Problem of Human-Machine Communication") and by Lave and Wenger (1991; "Situated Learning: Legitimate Peripheral Participation"). Here, author James Greeno asserts that he observes a consensus in the field that concepts and methods of both the individual-cognitive and the situative perspectives are needed in developing satisfactory explanatory accounts of human learning and cognition. Although there is agreement that some combination of resources from the individual-cognitive perspective and from the situative perspective is needed, the field has not settled on a single way in which the resources from these programs relate to each other. Greeno agrees with a philosophy argued by Sandra Mitchell that it is a mistake to assume one best theory exists in a domain, and differing theories provide alternative and productive conceptualizations. Thus the contributions to this special issue of "Educational Psychologist" advance the field's explanatory capabilities by extending the range of concepts and methods to include processes and causal factors at the level of activity systems, organizations, and cultures. Each of the contributions to this issue can be understood as providing integrative connections across these levels.

We present a view that conceives of conceptual learning as changes in discourse practices. This view focuses on interactions in which people construct understanding collaboratively, either as deliberate conceptual inquiry or to facilitate accomplishing something else. Our analysis combines concepts and methods from ethnography (e.g., Jordan & Henderson, 1995), linguistic discourse analysis (e.g., Lemke, 1990), cognitive analyses of conceptual growth (e.g., Keil, 1994), and theories of information structures in comprehension and reasoning (e.g., Kintsch & van Dijk, 1978). In this view, conceptual understanding is considered mainly as an interactional process. The view focuses on how concepts are created and built up when people engage in activity, especially when they communicate about the things they are doing and trying to understand. Participation in a community includes using its concepts according to practices in which members communicate, coordinate their action, and achieve mutual understanding. Our view of concepts is illustrated with examples drawn from a study of two FCL science classes.

We propose three analytic representations of collaborative problem solving. Activity nests, a generalization of goal-subgoal trees, represent functional decompositions of task activity into components, using nesting to indicate operations that satisfy task functions. Semiotic networks, an extension of semantic networks, represent meanings as refers-to relations between symbolic expressions and other signifiers, and relations in situations and situation types, along with general relations between these meanings. Contribution Vagrants, an adaptation of contribution trees (Clark & Schaefer, 1989), represent how turn sequences collectively achieve task components. W e developed these representations to analyze how pairs of middle-school students constructed tables to represent quantitative properties of a simple physical device that models linear functions. Variations between activity nests of dififerent pairs support an explanation of activity in terms of attimement to constraints and to affordances and abilities, rather than following procedures. The semiotic networks support a hypothesis that task components are completed through accomplishing alignments of refers-to relations.which is a generalization of goal satisfaction. Similarities between the contribution diagrams support a general pattern that we call the turn structure of collaborative operations, in which task information is recognized and task operations are initiated, performed, and accepted. Interaction is organized into this structure in order to support mutually aligned intentions, understandings, actions, and agreements.

This paper reports research into how mathematical explanations are constructed during conversation based on videotapes of pairs of student math teachers collaboratively writing explanations in geometry. In particular, we analyzed how disagreements about parts of their explanations were managed in these conversations. In contrast to research on disagreement in everyday conversation, explanation disagreements were more likely to overlap with preceding turns and to be stated baldly without prefaces, token agreements or qualifications. However, the observed frequencies of different kinds of disagreements were not consistent with a model favoring explicit substantive disgreement either. Instead, it is proposed that both the interpersonal concerns that would motivate a preference for agreement and the conceptual concerns for a quality explanation that would motivate a preference for substantive disagreement are being managed by participants. Disagreements are co-constructed, and conversants are seen to jointly employ complex devices for introducing and managing disagreement across turns that can satisfy both kinds of concerns with much less conflict betweeen them than might have been expected.

Two suggestions for instruction in chemical equilibrium are presented, along with the evidence that supports these suggestions. The first is to use diagrams to connect chemical reactions to the effects of reactions on concentrations. The second is the use of the majority and minority species (M&M) strategy to analyze chemical equilibrium systems. Two studies are presented in support of these suggestions.

We report analyses of the construction andinterpretation of mathematical symbols that refer toquantitative properties and relations of a physicalsystem. Middle-school students solved problems thatinvolved contracting tables, equations and graphs torepresent linear functions of a device where blocks aremoved varying distances by turning a handle thatwinds string around spools of different sizes. Previousresearch analyzed activities of reasoning aboutquantities of this system as attunement to constraintsand affordances, a characterization of students' imphcitunderstanding of concepts of variable and linearfunctions. This report concerns activities ofrepresenting quantitative properties and relations usingmathematical notations. W e are developing analysesof constructing and interpreting tables, equations, andgraphs in terms of attunement to constraints andaffordances of the represented system, the system ofnotations, and relations between the constraints of thenotations and the represented domain. W e presentexamples that illustrate concepts of semantic clumps,groups, and morphisms; descriptive and demonstrativerepresentations; multiple referent domains; andconstructions of meaning in contributions toconversational discourse.

We present a theoretical analysis of students' implicit understanding of the concept of variables and functions, and present a cognitive model of this understanding based on the idea that reasoning involves a successful interaction between psychological agents and the things and other people in a situation. In the first part of the paper, we provide evidence that middle-and high-school students demonstrate implicit understanding of functional relations among quantities when they reason about a physical model of linear functions. Implicit understanding is knowledge of concepts or principles that enables and constrains performance, but is not articulate. In the second part of the pa^r, we describe several theoretical properties of our computational model: a.) activities are modeled as interactions between a parson and a situation; b.) reasoning is modeled as a form of activity that produces new information; and c.) understanding is modeled as attunement to the constraints of conceptual activities.

We discuss the process of mathematization in science, focusing on uses that theorists make of physical representations that w e refer to as abstracted models. W e review abstracted models constructed by Faraday and Maxwell in the mathematization of electromagnetic phenomena, including Maxwell's use of an analogy between continuum dynamics and electromagnetism. W e discuss ways in which this example requires major modifications of current cognitive theories of analogical reasoning and scientific induction, especially in the need to understand the use of abstracted models containing theoretically meaningful objects that can be manipulated and modified in the development of new concepts and mathematized representations.

The articles in this special issue make valuable contributions toward a scientific understanding of concepts that is broader than the traditional view that has focused on categorizing by individuals. I propose considering concepts for categorization as a special case of concepts. At their clearest, they can be referred to as "formal concepts," or "concepts used formally," which have explicit definitions and are used in formal deductive reasoning and argumentation. A label for broader aggregations of concepts is "functional concepts," or "concepts used functionally." This distinction is nearly parallel to Vygotsky's (1934/1987) distinction between "scientific concepts" and "everyday concepts." Formal (uses of) concepts are important products and resources in subject matter disciplines, especially in science and mathematics. I suggest that the distinction between formal and functional (uses of) concepts can support a useful interpretation and organizing frame for efforts to provide meaningful instruction in disciplinary domains.

We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another human participant or a non-human system. Participants with these different positionings have different perspectives that shape the interpretations and functions of their contributions. We hypothesize that achievement of mutual understanding also depends on participants having "epistemological" and "conceptual framings" that are sufficiently aligned. We distinguish between cases in which the participants achieved alignment of conceptual framing by adopting a schema that was in their common ground, cases in which the participants co-constructed a coherent framing without the benefit of a prefabricated schema (by constraint satisfaction, we hypothesize), and cases in which mutual understanding involved a refinement that did not require reframing. We argue that our hypotheses qualify as explanatory mechanisms, and we explicate this in an appendix. Our general goal is to contribute to the growing body of scientific studies that include concepts and methods for understanding cognitive structures and processes integrated with concepts and methods for understanding interaction that people have with each other and with other material and informational systems. [Supplementary materials are available for this article. Go to the publisher's online edition of the "Journal of the Learning Sciences" for the following free supplemental resource: "A Mechanistic Analysis of Discourse," which presents an analysis of an episode from Case #1 of this article as a more detailed example of the kind of mechanism we have hypothesized in our more general accounts of interaction presented in the article.] (Contains 8 tables, 9 figures and 12 footnotes.)

Son and Goldstone (2009) provided orienting activities intended to increase personal engagement, and these activities reduced participants' transfer based on concepts of signal detectability theory. I offer a theoretical interpretation that differs from theirs. First, instead of assuming that activity is contextualized in some conditions and not in others, I assume that activity always occurs in some context, or framing. Second, instead of hypothesizing that generality is achieved by ignoring features of specific situation, I adopt the classical hypothesis (e.g., from Judd, 1908; Wertheimer, 1945/1959) that generality results from framing in which specific features are organized in a particular way that includes conceptual structure. Third, although I agree that an enactive positional framing, with more personal engagement, can result in a narrower depth of field, I hypothesize that what is enhanced or inhibited by enactive positioning depends on the activity, so that if activity is focused on conceptual structures (for example, in constructing explanations as studied by Chi et al., 1989) personal engagement could increase generality of learning.

We propose a bridge between cognitive and sociocultural approaches that is anchored on the sociocultural side by distributed cognition and participation, and on the cognitive side by information structures. We interpret information structures as the contents of distributed knowing and interaction in activity systems. Conceptual understanding is considered as achievement of discourse in activity systems, and conceptual growth is change in discourse practice that supports more effective conceptual understanding. We also introduce a concept of perspectival understanding, in which accounts of cognition, including conceptual understanding, include points of view. This concept generalizes the concept of schema by hypothesizing that a perspectival understanding can be constructed by constraint satisfaction when a sufficient schema is not known or recognized. We provide an example in which perspectival understanding was jointly constructed, illustrating an interactional process we call "constructive listening."

In Giyoo Hatano's passing, we have lost an esteemed colleague and a treasured friend. Among his many contributions to our field, our work, and our lives, we honor and build on his and his colleagues' work on conceptual growth. We liken the view developed by Hatano and his colleagues to Toulmin's evolutionary scheme for understanding conceptual growth in intellectual disciplines, and we briefly sketch recent studies and discussions in which our methods and conceptualizations depend upon and draw meaning from Hatano's work, findings, and insights. He contributed strongly to the evolutionary growth of conceptual understanding in our scientific field, and he was an important hub of communication and interaction among scientists around the world. We are grateful to have had the chance to interact and learn with Giyoo Hatano, and we will gratefully continue our interaction with his ideas, his contributions, and the relations that he forged across national boundaries.

Engle's (this issue) analysis of framing students' contributions in learning interactions to construct generality and Marton's (this issue) discussion of learning to discern differences make valuable contributions to the ongoing scientific effort to understand transfer. This commentary characterizes these articles as contributing to 2 valuable themes of recent and ongoing research on transfer. One involves positioning of students in activity systems where they can learn or where their transfer is assessed. The other involves characteristics of knowing in conceptual domains. Based on the contributions of Engle, Marton, and others, this commentary conjectures that positioning with authority and accountability in learning and transfer settings (cf., Engle & Conant, 2002) and learning that develops connected knowing of affordances and constraints that are broadly characteristic of a domain (cf., Belenky, Clinchy, Goldberger, & Tarule, 1986; Gibson, 1979) are probably important contributing factors in supporting positive transfer.

Offers three different interpretations for the apparent failure to transfer (learning) and suggests that cognitivistic perspectives on transfer are limited. Suggests "productivity" rather than "transfer" to refer to the generality of learning. (SLD)