A Paired Think Aloud Model for Solving Mathematical Word Problems

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A Paired Think Aloud Model for Solving
Mathematical Word Problems

• Julie Horn
• Deer Park ISD

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Aattempted
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Types of writing

1. Journal writing
2. Creative writing involving math
3. Writing solutions to math problems
4. Writing about their thinking processes

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National Council of Teachers of Mathematics (1989)

• Learn to value mathematics,
• Become confident in ones own ability,
• Become a mathematical problem solver
• Learn to communicate mathematically
• Learn to reason mathematically

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NCTM

• Students gain insights into their thinking when
  they present their methods for solving problems,
  when they justify their reasoning to a classmate
  or teacher, or when they formulate a question
  about something that is puzzling them. (NCTM,
  2000)

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Texas Essential Knowledge and Skills

• (6) Underlying mathematical processes. Many
  processes underlie all content areas in
  mathematics. As they do mathematics, students
  continually use problem-solving, computation in
  problem-solving contexts, language and
  communication, connections within and outside
  mathematics, and reasoning, as well as multiple
  representations, applications and modeling, and
  justification and proof.

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Think Aloud
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Objectives

• Model the Think Aloud strategy
• Show how it can be used to help students solve
  word problems
• Show how to expand the Think Aloud strategy to
  include a written solution

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What is the Think Aloud strategy?

• Think Aloud is a strategy which includes
  vocalizing all of your thoughts, decisions,
  analyses, and conclusions when trying to solve a
  problem or read a text.
• (Whimbey, 1999)

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Meaning

• The Think Aloud strategy helps readers think
  about how they make meaning.
• (Beers, 2003)

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Golf
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Brain
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My students?

• Poor problem solvers frequently remark, either
  you know the answer to a problem or you dont
  know it you might as well give up or guess.
• (Whimbey, 1999)

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Pair Think Aloud

• The THINKER must vocalize very step in her
  reasoning, and the LISTENER must listen and
  understand every step the the problem solver
  takes.
• (Whimbey, 1999)

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Subvocalize

• All the evidence indicates that you should
  subvocalize freely when you read. It can produce
  better comprehension of technical material and a
  fuller appreciation of literary writing where
  alliteration and other poetic devices depend on
  hearing the words.
• (Whimbey, 1999)

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Prediction

• Challenging students to predict the question
  makes them more curious about what the question
  will be. When students make predictions they pay
  closer attention to details and nuances of
  meaning, which sharpens their thinking and
  improves their comprehension. For years, experts
  have advocated the practice of making predictions
  while reading (Stauffer, 1969 Britton, 1970
  Weaver, 1988). The latest research supports
  prediction-making as an effective learning
  strategy in any subject area (Nystrand, 1997
  Marzano, 2001).
• (Nessel, 2003)

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THINKER

• Predict
• Verbalize
• What?
• Why?
• Visualize
• Accuracy
• How?

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LISTENER

• Listen to the predictions
• Listen to what the thinker says
• Keep the thinker talking
• Ask questions
• Point out any errors
• Check for accuracy
• Jot down notes

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Feedback

• Every time you are a listener you are learning
  about problem solving by paying careful attention
  to what the problem solver does and does not do.
  Every time you are the problem solver you are
  indirectly observing the listener who is
  listening to you. The process has built into it
  all the feedback you need.
• (Whimbey, 1999)

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Make it your own

• Writing is a way to work yourself into a subject
  and make it your own.
• (Zinsser, 1993)

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• Just like writing, mathematics requires
  gathering, organizing, and clarifying thoughts.
• (Burns, 1995)

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Writing in math class

• The writing students do in math class, however,
  differs in several ways from much of the writing
  they do for language arts assignments. Their
  math writing is typically not creative writing,
  and having a final product suitable for
  publication isnt the goal. Rather, what they
  write in math class is a way for students to
  reflect on their learning and communicate their
  ideas about mathematics.
• (Burns, 1995)

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Goals

• Help students make sense of mathematics
• Help teachers understand what children are
  learning

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Correct answers arent everything

• Correct answers can hide a lack of
  understanding, but writing about the
  problem-solving strategies used can reveal levels
  of conceptual understanding.
• (Goldsby, 2002)

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Creating Word Problems

• Devising problems based on other problems allows
  you to see them from the inside out.
• (Whimbey, 1999)

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ESL

• Pair with another ESL student and allow them to
  Think Aloud and write with each other in their
  native language.
• Let them observe a Thinker-Listener pair first,
  then move into one of the roles.

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Learning Challenged

• Allow the student to draw a picture rather than
  verbalize, and then, also, draw their solution.
• Do the Think Aloud with the teacher as Listener.
• Record their solution on a tape recorder.

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Gifted and Talented

• Assign more complex and thought provoking
  problems.
• Encourage original and independent problem
  solving.
• Let them be the Listener for a struggling Thinker.

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• Next year is going to be a great year for writing!

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Resources

• Beers, Kylene, (2003). When Kids Cant Read,
  What Teachers Can Do, A Guide for Teachers 6-12.
  Portsmouth, NH. Heinemann.
• Burns, Marilyn, (1995). Writing in Math Class, A
  Resource for Grades 2-8. Math Solutions
  Publications.
• Goldsby, Diane S. Barbara Cozza, (2002).
  Writing Samples to Understand Mathematical
  Thinking. Mathematics Teaching in the Middle
  School, v.7, no. 9, p. 517.
• National Council of Teachers of Mathematics
  (1989). Curriculum and Evaluation Standards for
  School Mathematics. Reston, VA. NCTM.

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Resources

• Nessel, Denise Newbold, Ford (2003). 180
  Think-Aloud Math Word Problems. New York
  Scholastic Professional Books.
• Richardson, Judy S. (2000). Read It Aloud!
  Using Literature in the Secondary Content
  Classroom. Newark, DE International Reading
  Association.
• Tierney, Richard J., Readence, John E.,
  Dishner, Ernest K. (1995). Reading Strategies
  and Practices, A Compendium. MA Allyn and
  Bacon.
• Whimbey, Arthur Lochhead, Jack (1999). Problem
  Solving and Comprehension. Mahwah, NJ Lawrence
  Erlbaum Associates, Publishers.
• Zinsser, William K. (1993). Writing to Learn.
  Harper Collins.