Combining Methods at Two Levels in Learning Research

1. Combining Methods at Two Levels in Learning Research James Greeno University of Pittsburgh

2. 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.

3. 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

4. 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.

5. 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)

6. 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).

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

8. 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.

9. 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)

10. 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.

11. 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.

12. 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)

13. 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?

14. 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.

15. 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)

16. 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.

17. >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

18. >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

19. 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.

20. 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?

21. 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.

22. 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.

23. Something that didn’t happen • Reconciling the two patterns (cf. Bass & Ball)