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Arial&Monotype Typography ?-O=S04Combining Methods at Two Levels in Learning Research%James Greeno
University of Pittsburgh5Strategies/methods at two levels of research activity2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.
1. Developing and evaluating hypotheses: Progressive refinement.B1. Developing and evaluating hypotheses: Two (extreme) strategies CA$XExperimental (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
HfZFZZfFfF(Combining these complementary strategiesEProgressive 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)FF5
>2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive function: Settle that the answer to S10 for Function 1 is 21
Participation: D enacter 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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
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G@;b`B&V2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive function: Settle that the answer to S10 for Function 1 is 21
Participation: D enacter 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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.8Something that didn t happen.Reconciling the two patterns (cf. Bass & Ball)sx,, ` e(HH(dh
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>6:10 - 6:387:34 - 8:42Evidence for perspectives?8:48 - 8:52A couple of summary notesSomething that didnt happenFonts UsedDesign Template
Slide Titles#_uBrett LeberBrett LeberLDTimes,`++~1,
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Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
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Arial&Monotype Typography hnamd`
Arial&Monotype Typography ,namd$Times Roman ,namd$Times Roman ?-O=x74Combining Methods at Two Levels in Learning Research%James Greeno
University of Pittsburgh5Strategies/methods at two levels of research activity2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.
1. Developing and evaluating hypotheses: Progressive refinement.B1. Developing and evaluating hypotheses: Two (extreme) strategies CA$XExperimental (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
HfZFZZfFfF!Examples of Ethnographic Research"!$rA 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.8%
YP" ;s:(Combining these complementary strategiesEProgressive 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)FF5
>2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive function: Settle that the answer to S10 for Function 1 is 21
Participation: D enacter 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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.8Something that didn t happen.Reconciling the two patterns (cf. Bass & Ball)sx,, ` e(HH(dh ry'F(
/0LDTimes,`++~1,
`.
@n?" dd@ @@``,$dR
c$@-uʚ;2Nʚ;g4SdSdHrppp@<4!d!dpgʚ;<4ddddpgʚ; `___PPT10@8 ~___PPT9`X@h___PPT2001D<4X___PPTMac11b@f hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography hnamd`
Arial&Monotype Typography ,namd$Times Roman ,namd$Times Roman ?-O=~74Combining Methods at Two Levels in Learning Research%James Greeno
University of Pittsburgh5Strategies/methods at two levels of research activity2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.
1. Developing and evaluating hypotheses: Progressive refinement.B1. Developing and evaluating hypotheses: Two (extreme) strategies CA$XExperimental (strict form): Hypothesizing must precede empirical testing, which gives binary answers.
Hypotheses are modified, but only between experiments
" Ethnographic (strict form); Minimize hypotheses in advance of empirical study (= avoid preconceptions); hypotheses emerge in experience of field work; evaluate with field notes. Hypotheses happen, at least in the form of organizing concepts, but they are kept general
HfZFZZfFfF!Examples of Ethnographic Research"!$rA 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.8%
YP" ;s:(Combining these complementary strategiesKProgressive 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)LL5>2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive function: Settle that the answer to S10 for Function 1 is 21
Participation: D enacter 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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.8Something that didn t happen.Reconciling the two patterns (cf. Bass & Ball)sx,, ` e(HH(dh
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Arial&Monotype Typography ,namd$Times Roman ,namd$Times Roman ?-O=~74Combining Methods at Two Levels in Learning Research%James Greeno
University of Pittsburgh5Strategies/methods at two levels of research activity2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.
1. Developing and evaluating hypotheses: Progressive refinement.B1. Developing and evaluating hypotheses: Two (extreme) strategies CA$XExperimental (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
HfZFZZfFfF!Examples of Ethnographic Research"!$rA 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.8%
YP" ;s:(Combining these complementary strategiesKProgressive 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)LL5>2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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.8Something that didn t happen.Reconciling the two patterns (cf. Bass & Ball)sx,, ` e(HH(dh
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Arial&Monotype Typography hnamd`
Arial&Monotype Typography ,namd$Times Roman ,namd$Times Roman ?-O=~74Combining Methods at Two Levels in Learning Research%James Greeno
University of Pittsburgh5Strategies/methods at two levels of research activity2. Analyzing episodes of activity: Interaction analysis, including subject-matter content.
1. Developing and evaluating hypotheses: Progressive refinement.B1. Developing and evaluating hypotheses: Two (extreme) strategies CA$XExperimental (strict form): Hypothesizing must precede empirical testing, which gives binary answers.
Hypotheses are modified, but only between experiments
" Ethnographic (strict form); Minimize hypotheses in advance of empirical study (= avoid preconceptions); hypotheses emerge in experience of field work; evaluate with field notes. Hypotheses happen, at least in the form of organizing concepts, but they are kept general
HfZFZZfFfF!Examples of Ethnographic Research"!$rA 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.8%
YP" ;s:(Combining these complementary strategiesKProgressive 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)LL5>2. Analyzing dynamics and contents of subject-matter discourse?>(lMethod 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). %Combining these complementary methodsInteraction analysis, including participation structures (e.g., distribution of agency), and construction of information structures in common ground.
An ExampleAnalysis 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.
Z>-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)
ZP7+"Selecting episodes for analysisFrom field notes (by Gresalfi) we chose episodes in which a solution or method initially was not mutually understood, but came to be. j
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.
+Hypotheses we have developed in this study,+$oParticipant 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)ppP
p,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?00
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.'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)
4:07 - 5:13Cognitive 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.XXW>5:13 - 5:59PCognitive 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 GZ>6:10 - 6:38Cognitive 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|Z|7:34 - 8:42NCognitive 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.ZEvidence for perspectives?pTask 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?
F9Z9c^=8:48 - 8:52Cognitive function: determine that S10 - 32
Participation: D and G participated jointly
Task information: Evaluated 3(n-1)+5 for S10.A couple of summary notesAspects 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.8Something that didn t happen.Reconciling the two patterns (cf. Bass & Ball)sx,, ` e(HH(dh :
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