Meaningful Discourse in Middle School: Linking Research to Practice

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Meaningful Discourse in Middle School Linking
Research to Practice

• Diana Piccolo, Mary Margaret Capraro, Robert M.
  CapraroTexas AM University
• Adam HarbaughUNC Charlotte
• Tamara CarterOklahoma City Community College

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Classroom Communication

• NCTM recommends teachers
• should orchestrate discourse bylistening
  carefully to students ideas asking students to
  clarify and justify their ideas orally and in
  writing
• deciding what to pursue in depth from among the
  ideas that students bring up during a discussion
• deciding when to provide informationand when to
  let a student struggle with a difficulty
  (National Council of Teachers of Mathematics,
  1991, p. 35).

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Classroom Communication

• NCTMs Communication Standard recommends teachers
  and programs enable students to
• Organize and consolidate their mathematical
  thinking through communication,
• Communicate their mathematical thinking
  coherently and clearly to peers, teachers, and
  others,
• Analyze and evaluate the mathematical thinking
  and strategies of others, and
• Use the language of mathematics to express
  mathematical ideas precisely  
• (National Council of Teachers of Mathematics,
  2000, p. 60).

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Classroom Communication

• The IRE sequence and its derivatives (Edwards
  Mercer, 1987) have been the prominent in many
  studies on mathematics classroom discourse (Nardi
  Steward, 2003).

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Classroom Communication

• Teachers as orchestrators of interactions may
  give students a more active role in
  explaining/learning mathematics (Forman Ansell,
  2001).
• Teachers serve as facilitators in students
  reflective discourse practices by initiating
  discussions and taking a non-participatory
  evaluative role (Cobb, Boufi, McClain,
  Whitnack, 1997).

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QuestioningBi-directional

• Teacher
• Broadcast
• Directed
• Specific
• Pinpoint
• Student
• Teacher
• Peer
• Broadcast

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Effective Questioning

• Effective questioning combined with rich
  dialogues precipitate significant mathematical
  ideas - - between teachers and students (Thompson
  Thompson, 1996).
• Open-ended questionscan contribute to the
  construction of more sophisticated mathematical
  knowledge by students (Martino Maher, 1999,
  p. 53-54).

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Conceptual Questions

• Currently, the emphasis of mathematics reform
  encourages teachers to focus on conceptual
  approaches to learning mathematics however,
  research shows a lack of conceptual questioning
  in classrooms and verifies the need to improve
  teachers knowledge about the use of these
  questions (Belliveau-White, 2001).
• Dialogue that elicits questions can extend a
  students knowledge (Martinello, 1998).

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Disposition to Questions

• Teachers
• Probe for information
• Guide toward solutions or strategies
• Students
• Procedures
• Processes

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Questions hard to answer

• It is not how many questions a teacher can ask
  that the students will answer readily, but how
  many questions are asked that inspire them to ask
  him which he finds hard to answer (Rollins, 2006).

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Classroom Interaction and Conversation

• Five components that foster effective
  teacher-student communication
• Communicating clearly and accurately
• Using questioning and discussion techniques
• Engaging students in learning
• Providing feedback to students
• Demonstrating flexibility and responsiveness
• (Danielson, 1996)

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Evidence of quality discourse

• For students to become engaged in learning,
  they must be exposed to clear directions and
  explanations. In addition, a teachers use of
  vivid and expressive language can enhance a
  learning experience (Danielson, 1996, p. 90).

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Methodology

• Extant video
• Three Years (2001-04)
• Year 1
• 72 videos (18 Ts)
• Year 2
• 71 videos (20 Ts)
• Year 3
• 40 videos (10 Ts)

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Video Content

• (1) symbolic equations representing how a
  quantity of something changes over time or in
  response to other changes
• (2) use, interpret, and compare numbers as
  integers, fractions, decimals, and percents.
• (3) measures of central tendency

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Engaged Time

• Class Time 60 to 90 minutes
• Engaged time 42 minutes (SD 15.23)
• Range 10 - 72 minutes
• Total minutes viewed 8700

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Coding

• 10 individuals trained to identify
  teacher-student interactive discussion
• Each video coded by 4 members of team
• Reliability at 95
• 20 second window
• 210 single-spaced pages

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Results

• Little change over time in discursive practices
• Changes in lesson delivery was evident but this
  change did not seem to influence discursive
  practices.
• Persistent student questioning led to more
  in-depth teacher responses which appeared to be
  connected to improved discourse, deeper and more
  robust teacher explanation, and more persistent
  teacher inquiry into student understanding.
• Multiple questioning techniques (cloze/open) led
  to our our observation of evidence of student
  initial understanding.
• Cloze questioning also led to evidence of student
  initial understanding, albeit not as frequently
  as more open forms.

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Recommendations

• Continue teacher professional development on
  questioning to establish an atmosphere conducive
  to student initiated questioning.
• Students should be instructed in questioning
  techniques that allow them to persist until they
  acquire understanding.
• Examine the effects on classroom discourse of
  student workshops about questioning techniques.
• Examine discourse practices on student
  achievement.
• In order to help students transition toward
  asking more metacognitive questions, teachers
  should engage in problem posing (students
  providing questions to problem prompts).

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Rich Mathematics Classroom Conversations

• Robert M. Capraro, Texas AM University
• rcapraro_at_coe.tamu.eduMary Margaret Capraro,
  Texas AM University
• mmcapraro_at_coe.tamu.edu
• Adam Harbaugh, UNC Charlotte
• apharbau_at_email.uncc.eduTamara Carter,
  Oklahoma City Community College
• tcarter_at_occc.edu
• Diana Piccolo, Texas AM University
• ldp11_at_neo.tamu.edu

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References

• Ball, D. L. (1990). The mathematical
  understandings that prospective teachers bring to
  teacher education. Elementary School Journal,
  90(4), 449-466.
• Belliveau-White, P. (2001). Conceptual
  questioning in the mathematics classroom.
  Unpublished dissertation,The University of New
  Brunswick.
• Cobb, P., Boufi, A., McClain, K., Whitenack, J.
  (1997). Reflective discourse and collective
  reflection. Journal for Research in Mathematics
  Education, 28, 258-277.
• Danielson, C. (1996). Enhancing professional
  practice. Alexandria, VA Association for
  Supervision and Curriculum Development (ASCD).
• Edwards, D., Mercer, N. (1987). Common
  knowledge The development of understanding in
  the classroom. London Methuen.
• Martinello, M. L. (1998). Learning to question
  for inquiry. The Educational Forum, 62(2),
  164-171.
• Forman, E. A., Ansell, E. (2001). The multiple
  voices of a mathematics classroom community.
  Educational Studies in Mathematics, 46, 115-142.
• Martino, A. M., Maher, C. A. (1999). Teacher
  questioning to promote justification and
  generalization in mathematics What research
  practice has taught us. Journal of Mathematical
  Behavior, 18(1), 53-78.
• Nardi, E., Steward, S. (2003). Is mathematics
  T.I.R.E.D? A quiet disaffection in the secondary
  mathematics classroom. British Education Research
  Journal, 29, 345-367.
• National Council of Teachers of Mathematics.
  (1991). Professional standards for teaching
  mathematics. Reston, VA Author.
• National Council of Teachers of Mathematics.
  (2000). Principles and standards for school
  mathematics. Reston, VA Author.
• Rollins, W. (2006). Retrieved 4/1/06 from
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• Shulman, L. (1987). Knowledge and teaching
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• Wilson, S. M., Shulman, L. S., Richert, A.
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