Transcript A Paired Think Aloud Model for Solving Mathematical Word

A Paired Think Aloud
Model for Solving
Mathematical Word
Problems
Julie Horn
Deer Park ISD
A=attempted
Types of writing:
1. Journal writing
2. Creative writing involving
math
3. Writing solutions to math
problems
4. Writing about their thinking
processes
National Council of Teachers
of Mathematics (1989)
• Learn to value mathematics,
• Become confident in one’s own
ability,
• Become a mathematical
problem solver
• Learn to communicate
mathematically
• Learn to reason mathematically
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)
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.
Think Aloud
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
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)
Meaning
• “The Think Aloud strategy helps
readers think about how they
make meaning.”
(Beers, 2003)
Golf
Brain
My students?
• Poor problem solvers frequently
remark, “either you know the
answer to a problem or you don’t
know it – you might as well give
up or guess”.
(Whimbey, 1999)
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)
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)
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)
THINKER
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Predict
Verbalize
What?
Why?
Visualize
Accuracy
How?
LISTENER
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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
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)
Make it your own
• “Writing is a way to
work yourself into a
subject and make it
your own.”
(Zinsser, 1993)
• “Just like writing,
mathematics requires
“gathering, organizing,
and clarifying
thoughts.”
(Burns, 1995)
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 isn’t
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)
Goals
• Help students make
sense of mathematics
• Help teachers understand
what children are
learning
Correct answers aren’t
everything
• “Correct answers can hide a
lack of understanding, but
writing about the problemsolving strategies used can
reveal levels of conceptual
understanding.”
(Goldsby, 2002)
Creating Word Problems
• “Devising problems based
on other problems allows
you to see them from the
inside out.”
(Whimbey, 1999)
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 ThinkerListener pair first, then move
into one of the roles.
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.
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.
•Next year is going
to be a great year
for writing!
Resources
• Beers, Kylene, (2003). When Kids Can’t 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.
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.