Designing and Facilitating Ways to Advance IBL

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Designing and Facilitating Ways to Advance IBL
Kyeong Hah Roh Arizona State University khroh_at_math
.asu.edu

• This study was supported by the National Science
  Foundation (NSF) under a grant (0837443).

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The Class

• Introductory Real Analysis
• Junior Level
• BA in Math or Secondary Math Education Students
• No Textbook
• Worksheets provided in class
• Class-note provided after topics are covered in
  class
• Definitions Theorems without proofs
• Inquiry-Oriented Class
• Small groups (34 members per group)
• Students were asked to make and justify
  conjectures and to evaluate arguments.

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Benefits of IBL

• Deep Understanding of Materials
• Promoting students mathematical thinking
  reasoning
• Active Engagement in Learning Process
• Constructing creating (or reinventing)
  knowledge by students themselves
• Collaboration Communication

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But

• Designing and facilitating IBL is not a trivial
  task!

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Challenges in Designing Facilitating IBL

• Deep Understanding of Materials
• Promoting students mathematical thinking
  reasoning
• Active Engagement in Learning Process
• Constructing creating (or reinventing)
  knowledge by students themselves
• Collaboration Communication

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Questions might be

• What how to design tasks/curricular materials
  for IBL classrooms?
• How to facilitate student discourse in IBL
  classrooms?
• Issues with building up classroom norms
• Issues with dominating students
• Issues with shy students
• How to assess student work in IBL ?

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This presentation is about

• What how to design tasks/curricular materials
  for IBL classrooms?
• How to facilitate student discourse in IBL
  classrooms?
• Issues with building up classroom norms
• Issues with dominating students
• Issues with shy students
• How to assess student work in IBL?

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Designing Tasks/Curricular Materials

• Design Experiment Approach

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Teaching, Student Thinking, Design of Tasks

• Without the experiences afforded by teaching,
  there would be no basis for coming to understand
  what students understand or construct, or even
  for suspecting that students conceptions or
  construction may be different from those of
  instructors (Steffe Thompson, 2000).
• What is students current understanding to given
  tasks?
• How do the tasks influence students learning?
• How does students understanding progress?

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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Iterative Nature of Designing Tasks
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Cohort Semester of Students of Groups Sessions
1 Fall 2006 6 2 (2) Three 50-minute classes for 15 weeks
2 Spring 2007 22?20 5 (3) Two 75-minute classes one 50-minute recitation for 15 weeks
3 Fall 2009 2 1 (1) One 60-minute sessions for 10 weeks
4 Spring 2010 11 3 (3) Two 75-minute classes one 50-minute recitation for 15 weeks
This study was supported by the National Science
Foundation (NSF) under a grant (0837443).
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Cohort 4 (Spring 2010)
Week 1 Week 15
Chapter 1 Chapter 2 Chapter 3 Chapter 4
Properties of Real Numbers Limits of Sequences Limits of Functions Continuous Functions
Chapters 12 Exam Follow-up Interview 1
Chapters 3 4 Exam Follow-up Interview 2
Pretest
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Cohort 4 (Spring 2010)

• The Participants (11 undergraduate students)
• Completed calculus and a transition-to-proof
  course
• Volunteered to participate and were willing to
  work in an inquiry oriented class
• Worked with the same group members for the entire
  semester
• Data Sources
• Written tests (photo-copied)
• Individual interviews (pen-casted video-taped)
• Class Observation (field-note from Group 1 taken
  by a graduate student pen-casted in spring 2010,
  video-taped from all three groups)
• Homework (photo-copied)
• Content logs from Group 2 taken by a graduate
  student (Michael McAllister) in summer 2010

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Examples of Tasks from the Project

• Roh, K. (2008). Students understanding of the
  equivalent relationship to conditional
  statements. Paper presented at the annual meeting
  of American Educational Research Association ,
  New York, NY.
• Knapp, J., Roh, K. (2008). Students notion of
  convergence in advanced calculus courses.
  Proceedings of the 11th Conference of the SIGMAA
  on Research in Undergraduate Mathematics
  Education (SIGMAA on RUME), San Diego, CA.
• Roh, K. (2009). The nature of visualization and
  its impact on the teaching and learning of the
  notion of continuity of functions. Proceedings of
  the 12th Conference of the SIGMAA on Research in
  Undergraduate Mathematics Education, Raleigh, NC.
  
• Roh, K. (2010). How to help students
  conceptualize the rigorous definition of the
  limit of a sequence. Problems, Resources, and
  Issues in Mathematics Undergraduate Studies.
• Roh, K., Lee, Y. (in press). The Mayan
  activity A way of teaching multiple
  quantifications in logical contexts. To appear in
  Problems, Resources, and Issues in Mathematics
  Undergraduate Studies.
• Dawkins, P., Roh, K. (in preparation).
  Mechanisms for scientific debates in real
  analysis classrooms.

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Classroom Management

• How to facilitate student discourse in IBL
  classrooms?
• Issues with building up classroom norms
• Issues with dominating students
• Issues with shy students

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The Role of an Instructor

• Rephrasing Taking student ideas and makes them
  concise or reinterpret them.
• Repeating Repeating student utterances
  word-for-word.
• Clarifying Attempts to make clearer what student
  utterances mean.
• Informing Providing information by defining a
  term or procedure.
• Provoking Creating students cognitive conflicts
  by directing or arranging interventions such as
• Debugging Steps Processes of testing student
  conceptions or beliefs across instances
• Contrasting Prompts A pair of statements which
  sound similar to, but are not logically
  equivalent to, each other
• Pivotal-Bridging Examples Examples that
  contradict students conceptions or beliefs
• Devils Advocate Incorrect or atypical arguments
  to evaluate
• Roh Halani (in preparation)

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The Role of Facilitators

• If you are the facilitator of your group, you are
  empowered by role and opportunity to enable all
  members of your group to share information freely
  with one another and help them attend fully to
  one another's perspectives.
• You must make an effort to promote participation
  of your group members in discussion as well as
  make sure that everyone is on the same page.
• You, as a facilitator, should promote
  participation, ensure equity, and build trust
  during group discussion.

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The Role of Note Takers

• If you are the note-taker of your group, you are
  responsible for taking notes on the notebook that
  is provided to your group.
• You need to write down a copy of the final
  version of  the proofs that your group come up
  with. However, the group notebook can also be
  used as a scratch paper.
• If someone needs a scratch paper when describing
  his/her idea, please pass the notebook with the
  pen the notebook to the person.
• Please be sure that the notes written down
  contain enough information so that it is clear to
  the group members which exercises you are working
  on and include identifying information such as
  function definitions and equations.

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eg. Cohort 4

• Regular Sessions
• Tuesdays Thursdays
• 75 min. each
• 15 weeks

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Regular Sessions

• Individual exploration a couple of minutes
• All Purpose Go Around Each student is given
  about one minute to share initial thoughts/ideas
  without interruption from others.
• Group discussion (the duration was depending on
  tasks)
• (Exchange Group Regroup so that a couple of
  students from each group is in a new group as the
  representatives" of their original group.)
• Class discussion (the duration was depending on
  tasks)
• Some contents were provided by a traditional
  lecture style

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Protocol All Purpose Go Around

• To the group Facilitator
• If nothing else is mention in exercise in
  instructions, please initiate your group
  discussion by giving the group members a short
  time to think about the problem individually
  before sharing ideas. Then, you, as a
  facilitator, give your group members about 30
  60 seconds each to present their ideas and
  thoughts. Please present your idea after everyone
  else in your group has chance to present their
  ideas.
• You should make sure that every group member has
  a chance to express their ideas and also ensure
  no one dominates the time given.
• You should distribute time properly as well as
  promote everyone's participation.
• Once everyone presents his/her idea, you can
  initiate group discussion by asking students to
  compare and contrast ideas suggested within your
  group.

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Protocol Exchanging Groups

• After discussion in your group, send two students
  in your group to two other groups. One student
  from each of the other groups join your group as
  well. You then ask those from other groups to
  present their  ideas, thoughts, and opinions.
  Once they present their work, you, and perhaps
  one od your original group member, share your
  group's ideas, thoughts, and opinions with them
  as well. You may ask questions to them or receive
  question from them to clearly understand the
  ideas. This is an opportunity to share ideas, not
  to debate the validity of your argument.
• After sharing different ideas, send people from
  other groups back to their original groups. At
  this moment, your group members will return to
  your group as well. This is the time to compare
  and contrast your ideas and the other ideas
  presented from the other groups. This is also the
  time to debate the validity of all the ideas.
• Consider those from other groups as representing
  their groups. The idea of regrouping is to share
  different ideas. Therefore, you, as a
  facilitator, should give everyone a chance to
  present their groups' work to others when
  regrouping is made. Also, before regrouping, your
  group members should understand your groups' idea
  because each member in your group have to present
  your group's idea to those in other groups after
  switching members.

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eg.Cohort 4

• Recitation
• Fridays
• 50 minutes
• for 15 weeks
• Collaborative proof writing

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Example Collaborative Proof Writing during a
Recitation

• Final Proof Writing

• Ex. Prove or disprove
• (-1)n1/n converges to 1.

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The classroom environment that empowers students

• Time for individual thinking followed by All
  Purpose Go Around enabled the students to share
  various answers to the task in the group and
  recognize the incompatibility among students
  conceptions.
• Group discussion after All Purpose Go Around
  helped students adjust their understanding of the
  given tasks.
• The group exchange allowed students to view the
  task in terms of other groups explanation and
  adjust their conception to fit that expressed by
  their original group mates previously.
• The final exchange with the original group
  affirmed the sense of mutual fit in their
  understanding and thinking of the given task.
• Dawkins Roh (in preparation)

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• The students achieved acceptable compatibility in
  their conceptions relative to the task.
• The students heard a variety of explanations of
  the same task. Thus they reached a conclusion
  without instructor intervention beyond setting up
  the parameters and responsibilities of group
  discussion.
• Dawkins Roh (in preparation)

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Assessment of Student Work

• Peer Evaluation

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• Midterm 30
• Final 30
• Assignment 20
• Classroom Participation 10
• Recitation Participation 10

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Evaluation of Participation

• Attendance 35
• Instructor Evaluation 35
• Peer Evaluation 30

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Peer Evaluation

• List ALL names of your group members including
  your own name. Give a score (0 as lowest to 10 as
  highest) for each member based on his/her
  contribution to your group during the group
  discussion of the day. Explain your evaluation.
• If you think nobody else contributed to the group
  more than you did during the group discussions,
  explain what difficulties you experienced while
  working in your group.
• Otherwise, please nominate one of your group
  members as one who contributed the most of the
  day. You should NOT nominate yourself. Explain
  why you nominate this student.

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Questions?

• Kyeong Hah Roh
• Arizona State University
• khroh_at_math.asu.edu