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Combining Methods at Two Levels in Learning Research

James Greeno

University of Pittsburgh

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Strategies/methods at two levels of research activity

• 2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.

• 1. Developing and evaluating hypotheses: Progressive refinement.

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1. Developing and evaluating

hypotheses: Two (extreme) strategies • Experimental (strict form): Hypothesizing must

precede empirical testing, which gives binary answers.Hypotheses are modified, but only between experiments

• Ethnographic (strict form); Minimize hypotheses in advance of empirical study (= avoid preconceptions); hypotheses emerge in experience of field work; evaluate with field notes. Hypotheses happen, at least in the form of organizing concepts, but they are kept general

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Examples of Ethnographic Research

• A classic: Jean Lave’s study of math in grocery shopping. JPF shoppers nearly always picked the product with the lowest unit price, although their performance on paper-and-pencil math tests was much poorer.

• Nunez, Schliemann, & Carraher, and Saxe, studied young Brazilian street merchants. They managed the math of wholesale purchases and setting prices, and didn’t do as well on paper-and-pencil tests.

• Current research at the LIFE Learning Sciences Center is studying family math and activities involving science at home, finding capabilities that exceed performance in school, e.g., a girl who successfully mixes chemicals for cosmetics at home, but is low-performing student in school science.

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Combining these complementary strategies

• Progressive refinement; enabled by video records.• Start with a general issue or type of process; select

and analyze some relevant episodes; formulate hypotheses; reconsider analyses and consider more episodes; reformulate hypotheses, usually more specific, toward (hopefully until) convergence.

• (e.g., Engle, Conant & Greeno, 2007)

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2. Analyzing dynamics and contents of subject-matter discourse

• Method of information-processing analysis —> hypothetical information structures, attributed to individual mental activity.

• Method of interactional discourse analysis —> hypothetical patterns of participation and coordination, attributed to groups, with material and informational resources (activity systems).

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Combining these complementary methods

• Interaction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.

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An Example

• Analysis by Carla van de Sande of videos recorded by Melissa Gresalfi, Victoria Hand, and Greeno (supported by the Spencer Foundation)

• Setting: an 8th-grade algebra class; the teacher emphasized cooperative problem solving and sense making.

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Some hypotheses we carried into this analysis

• General topic: growth in conceptual understanding through discourse interaction (since 1991)

• Analytical scheme: Information structures constructed as contributions to discourse (Clark & Schaefer)

• Hypotheses of supporting conditions: ° distribution of authority, authorship, accountability and ° practices of problematizing, resolving subject-matter issues (Engle & Conant; Engle); ° dispositions toward collaboraative mathematical engagement (Gresalfi)

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Selecting episodes for analysis

• From field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be.

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Two findings to be explained

• Episodes in which new understanding was achieved had a characteristic structure, with one (or more) of the participants providing an explanation to the other(s).

• The process of reaching mutual understanding can be difficult, requiring sustained attention and effort.

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Hypotheses we have developed in this study

• Participant functions of inquirer and explainer organize interactions of (effortful) constructive listening. This need not correspond to who leads the conversation.

• Cognition is fundamentally perspectival (from MacWhinney, Fauconnier)

• Success in communication requires alignment of perspectives, and reorganizing a perspective can be very hard (cf. gestalt theorists)

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Our questions, then, in studying an episode:

• Does the episode provide evidence supporting or disconfirming these new hypotheses? (That is, do the hypotheses support an interpretation of the episode that accounts for important aspects of the interaction)?

• Do our current more general hypotheses provide a useful framework for analyzing this episode?

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Specifically:

• Look for evidence of the explainer/inquirer participant structure in constructing contributions

• In cases of difficulty in reaching mutual understanding, formulate and evaluate hypotheses involving perspectives that differed initially, with eventual alignment.

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A scheme for summarizing contributions:

• Cognitive function (what they accomplished, or got into common ground)

• Participation (positioning in the interaction)

• Task information (contents of information structure in the interaction)

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4:07 - 5:13

• Cognitive function: Settle that the answer to S10 for Function 1 is 21

• Participation: D enacted her solution, G and J followed and accepted D’s enactment and the result, the G and D corrected their earlier answers

• Task information: D counted the segments of S5, then iteratively enacted adding 2 for each member of the sequence from S6 6o S10.

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>5:13 - 5:59

• Cognitive function: Determine that the formula 2n+1 is correct

• Participation: G’s presentation was not picked up; J’s presentation was responded to negatively by G, but J did not accept G’s objection and they did not resolve their difference. D took the lead in the interaction to present her support for 2n+1

• Task information: Candidate patterns were presented … 2n+1 was verified in examples by D, agreement was given by G

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>6:10 - 6:38

• Cognitive function: Complete the work sheet for Function 1 (graph, answer for S17) and reconfirm the formula 2n+1sd

• Participation: Interaction between D and G. G presented tentative answers, D provided candidate answers, G accepted.

• Task information: D and G attended to graphing Function 1 by points (3, 5, …) and to the answer for S17 (34? No, 35) and wrote 2n+1 as the pattern

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7:34 - 8:42

• Cognitive function: Settle that both 3n+2 and 5+3(n-1) “work.”

• Participation: D and G presented different patterns (again); D didn’t disagree with G but repeated her pattern with examples. G presented and explained her pattern again and D accepted it with stronger evidence.

• Task information: D presented 3n+2, G presented 5+3(n-1) D demonstrated 3n+2 for S1, S2, and S3. G presented 5+3(n-1) again demonstrating it for S3.

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Evidence for perspectives?

• Task information: D presented 3n+2, G presented 5+3(n-1)

• D’s perspective: pattern of numerical progression; G’s perspective = pattern of change in diagrams?

• D demonstrated 3n+2 for S1, S2, and S3. G presented 5+3(n-1) again demonstrating it for S3.

• G shifted perspective to numerical evaluation of the formula?

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8:48 - 8:52

• Cognitive function: determine that S10 - 32

• Participation: D and G participated jointly

• Task information: Evaluated 3(n-1)+5 for S10.

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A couple of summary notes

• Aspects of positioning interacted with aspects of information content throughout. For example, J’s proposal to solve for S10 in Function 1 (2 times 11) could have been resolved, but J was reticent and D took over the conversation

• The adjustment of perspective we hypothesize for G in Function 3 might indicate a stronger commitment by G to achieving mutual understanding than D had.

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Something that didn’t happen

• Reconciling the two patterns (cf. Bass & Ball)