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Resolving Differences: Twists and Resolving Differences: Twists and Turns in a Quasi‑Synchronous Turns in a Quasi‑Synchronous
Online Collaborative Mathematics Online Collaborative Mathematics Problem-Solving SessionProblem-Solving Session
Ramon Prudencio S. ToledoRamon Prudencio S. ToledoAlan R. ZemelAlan R. Zemel
Gerry StahlGerry StahlThe Virtual Math Teams &The Virtual Math Teams &
College of Information Science and TechnologyCollege of Information Science and Technologyat Drexel University, Philadelphia, USAat Drexel University, Philadelphia, USA
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
ProblemProblem
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
DataData
AIM® log of PoWwow 10AIM® log of PoWwow 10 Participants: self-selected, self-described Participants: self-selected, self-described
middle-school studentsmiddle-school students Problem available before the sessionProblem available before the session Moderator available to assist in the Moderator available to assist in the
technology but not in problem solvingtechnology but not in problem solving Excerpt: 010 – 077 of roughly 580 linesExcerpt: 010 – 077 of roughly 580 lines
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
An An excerptexcerpt from VMT chat from VMT chat010 Alice (7:01:05 PM): Is this everyone?011 MFPowwow (7:01:15 PM): If you create a picture that you would like to share with your group, you can mail it to powwow or you can make a direct connection with me.012 MFPowwow (7:01:24 PM): This is everyone tonight.013 Alice (7:01:36 PM): ok014 Alice (7:02:04 PM): so…..015 MFPowwow (7:02:12 PM): So you’ve all seen the problem. If you’ve got any ideas, now’s the time to start. :-) 014 Alice (7:02:29 PM): Ok017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the problem statement019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the base030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is033 Alice (7:06:40 PM): Lets not 034 Mario (7:06:46 PM): What's your idea?035 Alice (7:07:01 PM): It states that something is wrong with the pic. 036 Alice (7:07:08 PM): so we can't find what BV is037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be something not possible
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How do participants in an online How do participants in an online quasi-synchronous collaborative quasi-synchronous collaborative
mathematics problem solving mathematics problem solving resolve their differences?resolve their differences?
How are resources achieved?How are resources achieved? How are choices and order of approach How are choices and order of approach
determined in problem solving?determined in problem solving? How is the validity of an approach collaboratively How is the validity of an approach collaboratively
assessed?assessed? How is the appropriateness of a proposed How is the appropriateness of a proposed
solution collaboratively assessed?solution collaboratively assessed?
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are resources achieved?How are resources achieved?
Resources are situational: they have to be brought into the problem Resources are situational: they have to be brought into the problem solvingsolving020 Mario (7:03:25 PM): Should we label some points?020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the base029 Mario (7:05:20 PM): You name where the green line meets the base030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong 031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong
with the pic.with the pic.
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are resources achieved?How are resources achieved?
Resources are situational: they have to be Resources are situational: they have to be brought into the problem solvingbrought into the problem solving shapesshapes
069 Mario (7:12:14 PM): Otherwise, the red lines 069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an and the base are almost an equilateral triangleequilateral triangle
070 Alice (7:12:32 PM): I think this requires trig 070 Alice (7:12:32 PM): I think this requires trig
071 Mario (7:12:50 PM): So, one possible wrong 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a thing is, this is really a hexagonhexagon
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving?
Cooperation vs. collaborationCooperation vs. collaboration Participant invitationsParticipant invitations Participants choose:Participants choose:
Collaborating participantsCollaborating participants Which approaches are to be usedWhich approaches are to be used The order in which the approaches are usedThe order in which the approaches are used
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Collaboration vs. cooperationCollaboration vs. cooperation
Management of collective as a collaborative group which Management of collective as a collaborative group which will work together instead of subdividing the problem will work together instead of subdividing the problem among its membersamong its members017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the problem statement018 Mario (7:02:58 PM): Just the one with the problem statement019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should we label some points?020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
For co-participantsFor co-participants Non-directiveNon-directive DirectiveDirective
However, there can be self-selectionHowever, there can be self-selection
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
Participant invitation: non-directiveParticipant invitation: non-directive Non-directive = invitation does not prescribe a task for Non-directive = invitation does not prescribe a task for
invited participantinvited participant010 Alice (7:01:05 PM): Is this everyone?010 Alice (7:01:05 PM): Is this everyone?011 MFPowwow (7:01:15 PM): If you create a picture that you 011 MFPowwow (7:01:15 PM): If you create a picture that you
would like to share with your group, you can mail it to would like to share with your group, you can mail it to powwow or you can make a direct connection with me.powwow or you can make a direct connection with me.
012 MFPowwow (7:01:24 PM): This is everyone tonight.012 MFPowwow (7:01:24 PM): This is everyone tonight.013 Alice (7:01:36 PM): ok013 Alice (7:01:36 PM): ok014 Alice (7:02:04 PM): so…..014 Alice (7:02:04 PM): so…..015 MFPowwow (7:02:12 PM): So you’ve all seen the problem. 015 MFPowwow (7:02:12 PM): So you’ve all seen the problem.
If you’ve got any ideas, now’s the time to start. :-) If you’ve got any ideas, now’s the time to start. :-) 014 Alice (7:02:29 PM): Ok014 Alice (7:02:29 PM): Ok
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
Participant invitation: non-directiveParticipant invitation: non-directive Non-directive = invitation does not prescribe a Non-directive = invitation does not prescribe a
task for invited participanttask for invited participant034 Mario (7:06:46 PM): What's your idea?034 Mario (7:06:46 PM): What's your idea?
035 Alice (7:07:01 PM): It states that something is 035 Alice (7:07:01 PM): It states that something is wrong with the pic. wrong with the pic.
036 Alice (7:07:08 PM): so we can't find what BV is036 Alice (7:07:08 PM): so we can't find what BV is
037 Mario (7:07:31 PM): Yeah, and I think if we 037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be something not possible'found' BV, it would be something not possible
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
Expected response to non-directive invitation: Expected response to non-directive invitation: availabilityavailability
010 Alice (7:01:05 PM): Is this everyone?010 Alice (7:01:05 PM): Is this everyone?
011 MFPowwow (7:01:15 PM): If you create a picture that you 011 MFPowwow (7:01:15 PM): If you create a picture that you would like to share with your group, you can mail it to would like to share with your group, you can mail it to powwow or you can make a direct connection with me.powwow or you can make a direct connection with me.
012 MFPowwow (7:01:24 PM): This is everyone tonight.012 MFPowwow (7:01:24 PM): This is everyone tonight.
013 Alice (7:01:36 PM): ok013 Alice (7:01:36 PM): ok
014 Alice (7:02:04 PM): so…..014 Alice (7:02:04 PM): so…..
015 MFPowwow (7:02:12 PM): So you’ve all seen the problem. 015 MFPowwow (7:02:12 PM): So you’ve all seen the problem. If you’ve got any ideas, now’s the time to start. :-) If you’ve got any ideas, now’s the time to start. :-)
014 Alice (7:02:29 PM): Ok014 Alice (7:02:29 PM): Ok
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
Participant invitation: DirectiveParticipant invitation: Directive Directive = expects a particular form of Directive = expects a particular form of
participation from other participantsparticipation from other participants017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the 018 Mario (7:02:58 PM): Just the one with the
problem statementproblem statement019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should we label some 020 Mario (7:03:25 PM): Should we label some
points?points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Participant invitationsParticipant invitations
Participant invitation: DirectiveParticipant invitation: Directive Expected response: follow through of directiveExpected response: follow through of directive
017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?
018 Mario (7:02:58 PM):018 Mario (7:02:58 PM): Just the one with the Just the one with the problem statementproblem statement
019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol
020 Mario (7:03:25 PM): Should we label some 020 Mario (7:03:25 PM): Should we label some points?points?
021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O
022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Self-selectionSelf-selection
Self-selection = Self-selection = participant volunteersparticipant volunteers through repetitions through repetitions of claims or proposalsof claims or proposals017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?
* * ** * *028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.
* * ** * *031 Alice (7:06:19 PM): I have an idea that might help us find 031 Alice (7:06:19 PM): I have an idea that might help us find
whats wrong with the pic.whats wrong with the pic.* * ** * *
035 Alice (7:07:01 PM): It states that something is wrong with the 035 Alice (7:07:01 PM): It states that something is wrong with the pic. pic.
* * ** * *062 Alice (7:11:28 PM): I know whats wrong with the pic062 Alice (7:11:28 PM): I know whats wrong with the pic
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving? Constitution of the problem as a shared problemConstitution of the problem as a shared problem
Identification of resources, approaches and solutionsIdentification of resources, approaches and solutions017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the problem statement018 Mario (7:02:58 PM): Just the one with the problem statement019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should we label some points?020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the base029 Mario (7:05:20 PM): You name where the green line meets the base030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is033 Alice (7:06:40 PM): Lets not 033 Alice (7:06:40 PM): Lets not
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving? Revelation of some strategyRevelation of some strategy
Produce steps which describe the strategy.Produce steps which describe the strategy. Build on the formulation of the problem.Build on the formulation of the problem.
017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the problem statement018 Mario (7:02:58 PM): Just the one with the problem statement019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should we label some points?020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the base029 Mario (7:05:20 PM): You name where the green line meets the base030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is033 Alice (7:06:40 PM): Lets not 033 Alice (7:06:40 PM): Lets not
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving? The pronominal ‘we’ and its variants are used to solicit participation.The pronominal ‘we’ and its variants are used to solicit participation. Co-participants are solicited to participate in one’s approach.Co-participants are solicited to participate in one’s approach.
Produce steps which describe the strategy.Produce steps which describe the strategy. Build on the formulation of the problem.Build on the formulation of the problem.
017 Alice (7:02:38 PM): Anyone have a pic?017 Alice (7:02:38 PM): Anyone have a pic?018 Mario (7:02:58 PM): Just the one with the problem statement018 Mario (7:02:58 PM): Just the one with the problem statement019 Alice (7:03:17 PM): lol019 Alice (7:03:17 PM): lol020 Mario (7:03:25 PM): Should 020 Mario (7:03:25 PM): Should wewe label some points? label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): 028 Alice (7:05:16 PM): LetsLets find out whats wrong with the pic first. find out whats wrong with the pic first.029 Mario (7:05:20 PM): 029 Mario (7:05:20 PM): You name where the green line meets the baseYou name where the green line meets the base030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.032 Mario (7:06:30 PM): 032 Mario (7:06:30 PM): WeWe could use good ol' Pythag thm to see what BV is could use good ol' Pythag thm to see what BV is033 Alice (7:06:40 PM): 033 Alice (7:06:40 PM): LetsLets not not
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving? Resolution may be through tokens of agreementResolution may be through tokens of agreement
066 Alice (7:11:45 PM): The diagnol is not 4.6066 Alice (7:11:45 PM): The diagnol is not 4.6067 Mario (7:11:51 PM): Right067 Mario (7:11:51 PM): Right068 Fatima (7:12:02 PM): exactly068 Fatima (7:12:02 PM): exactly069 Mario (7:12:14 PM): Otherwise, the red lines and the base are 069 Mario (7:12:14 PM): Otherwise, the red lines and the base are
almost an equilateral trianglealmost an equilateral triangle070 Alice (7:12:32 PM): I think this requires trig 070 Alice (7:12:32 PM): I think this requires trig 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really
a hexagona hexagon072 Alice (7:12:56 PM): No072 Alice (7:12:56 PM): No073 Mario (7:13:01 PM): Right073 Mario (7:13:01 PM): Right074 Alice (7:13:09 PM): Im talking about the triangle diagnol074 Alice (7:13:09 PM): Im talking about the triangle diagnol075 Mario (7:13:11 PM): Let'sd stick with octagon075 Mario (7:13:11 PM): Let'sd stick with octagon076 Mario (7:13:24 PM): So we assume 4 is right076 Mario (7:13:24 PM): So we assume 4 is right077 Alice (7:13:32 PM): yes077 Alice (7:13:32 PM): yes
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How are choices and order of How are choices and order of approach determined in problem approach determined in problem
solving?solving? Resolution may be through accommodation to an Resolution may be through accommodation to an
alternative approachalternative approach028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the 029 Mario (7:05:20 PM): You name where the green line meets the
basebase030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats 031 Alice (7:06:19 PM): I have an idea that might help us find whats
wrong with the pic.wrong with the pic.032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see 032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see
what BV iswhat BV is033 Alice (7:06:40 PM): Lets not033 Alice (7:06:40 PM): Lets not034 Mario (7:06:46 PM): What's your idea?034 Mario (7:06:46 PM): What's your idea?035 Alice (7:07:01 PM): It states that something is wrong with the pic. 035 Alice (7:07:01 PM): It states that something is wrong with the pic. 036 Alice (7:07:08 PM): so we can't find what BV is036 Alice (7:07:08 PM): so we can't find what BV is037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be 037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be
something not possible something not possible
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How is the validity of an approach How is the validity of an approach collaboratively assessed?collaboratively assessed?
Appeal to the problem formulation (Appeal to the problem formulation (appeal to the writer of the problemappeal to the writer of the problem))035 Alice (7:07:01 PM): It states that something is wrong with the pic. 035 Alice (7:07:01 PM): It states that something is wrong with the pic. 036 Alice (7:07:08 PM): so we can't find what BV is036 Alice (7:07:08 PM): so we can't find what BV is037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be something not 037 Mario (7:07:31 PM): Yeah, and I think if we 'found' BV, it would be something not
possiblepossible Appeal to a familiar method (Appeal to a familiar method (Pythagorean TheoremPythagorean Theorem))
020 Mario (7:03:25 PM): Should we label some points?020 Mario (7:03:25 PM): Should we label some points?021 Mario (7:03:56 PM): Like, center is O021 Mario (7:03:56 PM): Like, center is O022 Alice (7:04:04 PM): We could do that022 Alice (7:04:04 PM): We could do that023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?023 Mario (7:04:21 PM): Vertex where red line meets is, what, V?024 Alice (7:04:38 PM): The center?024 Alice (7:04:38 PM): The center?025 Mario (7:04:47 PM): No, down at the vertex025 Mario (7:04:47 PM): No, down at the vertex026 Alice (7:04:52 PM): oh026 Alice (7:04:52 PM): oh027 Alice (7:05:00 PM): That might help027 Alice (7:05:00 PM): That might help028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.028 Alice (7:05:16 PM): Lets find out whats wrong with the pic first.029 Mario (7:05:20 PM): You name where the green line meets the base029 Mario (7:05:20 PM): You name where the green line meets the base030 Alice (7:05:30 PM): B030 Alice (7:05:30 PM): B031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.031 Alice (7:06:19 PM): I have an idea that might help us find whats wrong with the pic.032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is032 Mario (7:06:30 PM): We could use good ol' Pythag thm to see what BV is
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How is the appropriateness of a How is the appropriateness of a proposed solution collaboratively proposed solution collaboratively
assessed?assessed?058 Mario (7:11:10 PM): With the numbers given, BV would be 058 Mario (7:11:10 PM): With the numbers given, BV would be 059 Mario (7:11:11 PM): yeah059 Mario (7:11:11 PM): yeah060 Alice (7:11:14 PM): I think thats wrong060 Alice (7:11:14 PM): I think thats wrong061 Fatima (7:11:19 PM): how so?061 Fatima (7:11:19 PM): how so?062 Alice (7:11:28 PM): I know whats wrong with the pic062 Alice (7:11:28 PM): I know whats wrong with the pic063 Mario (7:11:31 PM): base would be twice that063 Mario (7:11:31 PM): base would be twice that064 Fatima (7:11:33 PM): what064 Fatima (7:11:33 PM): what065 Mario (7:11:41 PM): 4.54 ish065 Mario (7:11:41 PM): 4.54 ish066 Alice (7:11:45 PM): The diagnol is not 4.6066 Alice (7:11:45 PM): The diagnol is not 4.6067 Mario (7:11:51 PM): Right067 Mario (7:11:51 PM): Right068 Fatima (7:12:02 PM): exactly068 Fatima (7:12:02 PM): exactly069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle070 Alice (7:12:32 PM): I think this requires trig 070 Alice (7:12:32 PM): I think this requires trig 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon072 Alice (7:12:56 PM): No072 Alice (7:12:56 PM): No073 Mario (7:13:01 PM): Right073 Mario (7:13:01 PM): Right074 Alice (7:13:09 PM): Im talking about the triangle diagnol074 Alice (7:13:09 PM): Im talking about the triangle diagnol075 Mario (7:13:11 PM): Let'sd stick with octagon075 Mario (7:13:11 PM): Let'sd stick with octagon076 Mario (7:13:24 PM): So we assume 4 is right076 Mario (7:13:24 PM): So we assume 4 is right077 Alice (7:13:32 PM): yes077 Alice (7:13:32 PM): yes
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How is the appropriateness of a proposed How is the appropriateness of a proposed solution collaboratively assessed?solution collaboratively assessed?
In this case, appropriateness is based on mutual In this case, appropriateness is based on mutual agreement(!) agreement(!)
058 Mario (7:11:10 PM): With the numbers given, BV would be 058 Mario (7:11:10 PM): With the numbers given, BV would be 059 Mario (7:11:11 PM): yeah059 Mario (7:11:11 PM): yeah060 Alice (7:11:14 PM): I think thats wrong060 Alice (7:11:14 PM): I think thats wrong061 Fatima (7:11:19 PM): how so?061 Fatima (7:11:19 PM): how so?062 Alice (7:11:28 PM): I know whats wrong with the pic062 Alice (7:11:28 PM): I know whats wrong with the pic063 Mario (7:11:31 PM): base would be twice that063 Mario (7:11:31 PM): base would be twice that064 Fatima (7:11:33 PM): what064 Fatima (7:11:33 PM): what065 Mario (7:11:41 PM): 4.54 ish065 Mario (7:11:41 PM): 4.54 ish066 Alice (7:11:45 PM): The diagnol is not 4.6066 Alice (7:11:45 PM): The diagnol is not 4.6067 Mario (7:11:51 PM): Right067 Mario (7:11:51 PM): Right068 Fatima (7:12:02 PM): exactly068 Fatima (7:12:02 PM): exactly069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle070 Alice (7:12:32 PM): I think this requires trig 070 Alice (7:12:32 PM): I think this requires trig 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon072 Alice (7:12:56 PM): No072 Alice (7:12:56 PM): No073 Mario (7:13:01 PM): Right073 Mario (7:13:01 PM): Right074 Alice (7:13:09 PM): Im talking about the triangle diagnol074 Alice (7:13:09 PM): Im talking about the triangle diagnol075 Mario (7:13:11 PM): Let'sd stick with octagon075 Mario (7:13:11 PM): Let'sd stick with octagon076 Mario (7:13:24 PM): So we assume 4 is right076 Mario (7:13:24 PM): So we assume 4 is right077 Alice (7:13:32 PM): yes077 Alice (7:13:32 PM): yes
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
How is the appropriateness of a proposed How is the appropriateness of a proposed solution collaboratively assessed?solution collaboratively assessed?
The agreement is based on a result which The agreement is based on a result which neither proposal obtained, but the group moves neither proposal obtained, but the group moves on. on.
058 Mario (7:11:10 PM): With the numbers given, BV would be 058 Mario (7:11:10 PM): With the numbers given, BV would be 059 Mario (7:11:11 PM): yeah059 Mario (7:11:11 PM): yeah060 Alice (7:11:14 PM): I think thats wrong060 Alice (7:11:14 PM): I think thats wrong061 Fatima (7:11:19 PM): how so?061 Fatima (7:11:19 PM): how so?062 Alice (7:11:28 PM): I know whats wrong with the pic062 Alice (7:11:28 PM): I know whats wrong with the pic063 Mario (7:11:31 PM): base would be twice that063 Mario (7:11:31 PM): base would be twice that064 Fatima (7:11:33 PM): what064 Fatima (7:11:33 PM): what065 Mario (7:11:41 PM): 4.54 ish065 Mario (7:11:41 PM): 4.54 ish066 Alice (7:11:45 PM): The diagnol is not 4.6066 Alice (7:11:45 PM): The diagnol is not 4.6067 Mario (7:11:51 PM): Right067 Mario (7:11:51 PM): Right068 Fatima (7:12:02 PM): exactly068 Fatima (7:12:02 PM): exactly069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle069 Mario (7:12:14 PM): Otherwise, the red lines and the base are almost an equilateral triangle070 Alice (7:12:32 PM): I think this requires trig 070 Alice (7:12:32 PM): I think this requires trig 071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon071 Mario (7:12:50 PM): So, one possible wrong thing is, this is really a hexagon072 Alice (7:12:56 PM): No072 Alice (7:12:56 PM): No073 Mario (7:13:01 PM): Right073 Mario (7:13:01 PM): Right074 Alice (7:13:09 PM): Im talking about the triangle diagnol074 Alice (7:13:09 PM): Im talking about the triangle diagnol075 Mario (7:13:11 PM): Let'sd stick with octagon075 Mario (7:13:11 PM): Let'sd stick with octagon076 Mario (7:13:24 PM): So we assume 4 is right076 Mario (7:13:24 PM): So we assume 4 is right077 Alice (7:13:32 PM): yes077 Alice (7:13:32 PM): yes
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Summative findingsSummative findings Each proponent of a proposal wants the Each proponent of a proposal wants the
collective to use their proposal.collective to use their proposal. SpurnedSpurned proponents find alternate ways to proponents find alternate ways to
reallocate participation by recycling a proposal reallocate participation by recycling a proposal or presenting a new step which reorients or presenting a new step which reorients participants to the participants to the spurnedspurned proposal. proposal.
Participants use Participants use achieved shared resourcesachieved shared resources to to build competing proposals.build competing proposals.
Due to the quasi-synchronous nature of chat, Due to the quasi-synchronous nature of chat, participants may select parts of competing participants may select parts of competing proposals and append them to their own proposals and append them to their own proposals.proposals.
16 July 200716 July 2007 The VMT at Drexel UniversityThe VMT at Drexel University
Next stepsNext steps
Investigation of resolution of differences in Investigation of resolution of differences in quasi-synchronous online collaborative quasi-synchronous online collaborative environments with dual interaction spaces environments with dual interaction spaces ((shared whiteboardshared whiteboard and and chat windowchat window))