Achieving Alignment of Perspectival Framings in Problem-Solving Discourse

Abstract

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.]

ACKNOWLEDGMENTS

This research was supported by a grant from the Spencer Foundation. We are grateful for extensive conversations with Robert Glaser, who provided comments on previous drafts; with Brian MacWhinney about perspectives in language and reasoning; with David Hammer and Edward Redish about framing; and with Peter Machamer and Jim Bogen about mechanistic explanation. We also thank Jeremy Roschelle, Cindy Hmelo-Silver, Rogers Hall, and Anna Sfard for helpful editorial advice and Ellice Forman, Michael Ford, Robert Hausmann, and Jodi Davenport for a discussion of reviewers' comments on a previous draft.

Notes

¹We agree with Kirsh (2009) that analyses of problem solving in cognitive science have neglected important aspects of cognitive framing, and we hope that our analyses contribute toward remedying that.

²The concept of constraint that we use is very general, developed in situation theory (Barwise & Perry, 1983). Attunements to constraints include cognizance of requirements (e.g., in Case 2, discussed later, it was relevant that solving an algebra problem with two unknown variables requires two equations) and knowing regularities in the environment (e.g., in Case 3 it was relevant that the shape and direction of one arrow in the display was programmed to coincide with a change in another arrow, also in the display).

³An example by Rommetveit (1980) illustrates framing with significant positional and cognitive aspects: Mr. Smith is mowing the lawn at his and Mrs. Smith's house on a Saturday morning. Rommetveit (1980) discussed two hypothetical phone calls, both of which ask Mrs. Smith “Is he working?” Although the two callers ask questions using the same words, Mrs. Smith would answer them with different responses. If the caller was Mr. Smith's frequent golfing partner, Mrs. Smith would correctly frame the question as asking whether Mr. Smith was working at his office and answer “No, he's mowing the lawn.” But if the caller was a nosy neighbor known to disapprove of late-night partying, Mrs. Smith would correctly frame the question as asking whether Mr. Smith was working rather than still sleeping and answer “Yes, he's mowing the lawn.” To answer “Is he working?” correctly Mrs. Smith would adopt a conceptual framing that is determined by the caller's positional relationship with Mr. Smith, which, epistemologically speaking, makes different information about Mr. Smith (no, he is not working at his office; or yes, he is awake and active) relevant to answering the question informatively.

⁴As Goldstone and Gureckis (2009) put it, “Indeed, one might go so far as to say that groups of people themselves can be interpreted as information processing systems” (p. 415). We also include other material and informational systems that are in the groups' environments, along with groups of people, as components of the systems that process and construct information.

⁵<> indicates unintelligible talk.

⁶We infer that Jacinda was assuming that if f(5) = 11, then f(10) = 11 + 11.

⁷On page 2 of the homework assignment students were asked to draw graphs of the three functions and were given tables with blanks to fill in, including the value of each function for Diagram 17, which Gillian and Dani discussed in turns 48–49.

⁸The ambiguity results from indeterminacy of what “the same thing” was. It is possible that they meant that Dani's and Gillian's formulas were “the same,” presumably mathematically equivalent, which they were. However, if this is what they (or either of them) meant it is surprising that there was no reference to formulas being equivalent for Function 3, which we discuss as Episode 1e. We infer then that “the same thing” more likely referred to the similarity between Dani's formulas for Functions 1 and 2. On this latter interpretation Gillian's action can be understood as acceptance of Dani's formula for Function 2 on the same basis as she accepted the answer Gillian constructed for Function 1.

⁹We expect that Scherr and Hammer (2009) might characterize the difference between Gillian's and Dani's framings as epistemological, involving the relevance of different kinds of knowledge—knowledge of numerical properties and operations in Dani's framing and knowledge obtained from observing properties of the diagrams, with knowledge of numerical operations secondarily, in Gillian's framing. We also consider it valid to characterize this difference as misaligned conceptual framings that differ in which aspects of the situation were foregrounded. In either interpretation there were significant aspects of epistemological framing for which Dani and Gillian were aligned. For example, they were satisfied to conclude that their equations both “work,” and they did not take up the question of whether their equations were mathematically equivalent. We explain this by hypothesizing that their epistemological framing did not extend to issues beyond being convinced that written answers were correct.

¹⁰This case was also discussed by Greeno and van de Sande (2007).

¹¹The concept of framing is central in some discussions of comprehension of literary texts (e.g., MacLachlan & Reid, 1994), which hypothesize that there is one or more intended framing(s) of a text that make(s) it comprehensible, and successful comprehension of the text involves a reader interacting with the text in a framing or framings that are sufficiently aligned with one or more of the intended framings. Our interpretation of Carol and Dana's learning is analogous to these discussions of literary interpretation. After they reframed their understanding of the program their framing was aligned with Roschelle's (1992) intended framing regarding the mediating role of the thin arrow in the relation between the thick arrow and the particle's motion.

¹² Roschelle (1992) also included other features of the process of convergent conceptual change achieved in interaction. These were interplay of metaphors; an iterative cycle of displaying, confirming, and repairing situated actions; and application of progressively higher standards of evidence for convergence. We believe that these features are present in the episodes that we analyze; they may be general features of discourse that qualifies as dialogic or exploratory talk as discussed by Mercer (1995, 2008) and others.