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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.

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.

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)

A framework is presented for characterizing competence for cognitive tasks, with a detailed hypothesis about competence for counting by typical 5-year-old children. It is proposed that competence has three main components that are called conceptual, procedural, and utilizational competence. Conceptual competence, which is discussed in greatest detail, is the implicit understanding of general principles of the domain. Procedural competence is understanding of general principles of action and takes the form of planning heuristics. Utilizational competence is understanding of relations between features of a task setting and requirements of performance. A characterization of conceptual competence for counting is presented, in the form of action schemata that constitute understanding of counting principles such as cardinality, one-to-one correspondence, and order. This hypothesis about competence is connected explicitly to a detailed analysis of performance in counting tasks. The connection is provided by derivations of planning nets for procedures that are included in process models that simulate children's performance. It is concluded that the nature of young children's understanding reflects competence that supports the understanding of counting as well as later development, such as explicit understanding of the role of one-to-one correspondence in definitions of equivalence. (Author/JN)

Discusses situative perspective as a framework for integrating issues of theoretical assumptions, educational practices, and educational research. In this perspective, the focus of theoretical principles is at the level of interaction among people and between people and their environments. Contains three pages of references. (MMU)

Findings from a study of diverse assessment practices in a fifth-grade classroom were used to develop a framework for describing assessment system practices. The framework is used to compare different assessment activities, and new criteria for designing systemically valid assessments to support and extend classroom practices are proposed. (SLD)

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific instruction. (Author/JJK)

Teaching is characterized as a complex cognitive skill amenable to analysis in a manner similar to other skills described by cognitive psychology. A formal model of the process of instruction in elementary mathematics is presented and examined in light of empirical data from both expert and novice teachers. (Author/LMO)