Communicating Ideas through Writing

1
Communicating Ideas through Writing

• ACUMEN Language of Mathematics
• Summer 2006
• Presented by
• Tiffany S. Powell

2
NCTM Process Standards

• Communication
• The communication standard points to the
  importance of being able to talk about, write
  about, describe and explain mathematical ideas.
  Learning to communicate in mathematics fosters
  interaction and exploration of ideas in the
  classroom as students learn in an active, verbal
  environment.Mathematical expression is part of
  the process and not an end in itself.
• (Van De Walle, 2004)

3
Writing Exercise

• Describe how addition and multiplication are
  similar.

4
Effective Instructional Planning

• In order to incorporate written communication
  skills in the mathematics classroom, there are 5
  principles to consider.
• (Information taken from Pugalee, 2005)

5
5 Principles to Develop Mathematical
Understanding

• Principle 1 The Writing Process has Three
  Phases
• Principle 2 Writing Has Different Purposes and
  Goals
• Principle 3 Writing Has Different Formats
• Principle 4 Writing Has Different Audiences
• Principle 5Writing Should Be Done Often

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Principle 1 The Three Phases of the Writing
Process

• The Writing Process Problem Solving

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Principle 1 3 Phases of Writing

• It is important for students to see the parallel
  between the thinking processes used in writing
  and those in approaching a mathematics problem.
• These are not additional thinking processes to
  develop, but known processes that need to be
  reinforced in a different setting.
• This is important for teachers to consider when
  planning mathematics lessons.
• (Pugalee, 2005)

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Questions to Guide Students

• Planning
• Do I understand what I am being asked?
• Composing
• What concepts and ideas support the statements I
  am making?
• How can I describe my thinking concisely and
  clearly?
• Revising
• Have I answered the question fully?
• Are my conjectures and ideas supported?
• Is my work clear and understanding?

9
Planning

• Tasks that are authentic and open-ended allow
  students to demonstrate their understanding and
  make conceptual connections.
• Key words and phrases help to communicate clear
  expectations for the assignments.

10
Planning

• The directions and information related to those
  tasks must contain enough structure so that the
  students writing provides meaningful information
  related to the mathematics being considered.
• Student Question Do I understand what I am
  being asked?
• Teacher Question Are my writing assignments
  stated clearly and are the expectations
  communicated?

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Key Terms for Clear Writing Tasks

• Compare and/or Contrast
• Write about what is different and/or alike.
• Describe
• Provide step-by-step details using key terms,
  graphs, charts, diagrams and other illustrations.
  Make sure the illustrations and diagrams are
  referred to in the description.
• Explain
• Elaborate on solutions, steps, ideas, concepts
  and conjectures using numbers, symbols,
  illustrations and examples when it helps to make
  your explanations clear.

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Key Terms for Clear WritingTasks

• Interpret
• Provide mathematical reasoning to describe
  relationships (e.g. mathematical information
  contained in data tables or charts, graphs,
  illustrations, models, diagrams, symbolic
  representations, and other ways of representing
  information and interactions).
• Provide Reasoning and Justification
• Give supporting evidence from mathematics to
  support your thinking, including examples,
  mathematical concepts and definitions, theorems,
  and other reasons that support what you say.

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Key Terms for Clear Writing Tasks

• List
• Provide ideas in a numbered or bulleted format.
• Show All Work
• Include all calculations, steps, and ideas that
  you thought about and used to reach your
  conclusion-all information that shows your
  thinking.

14
Composing

• Most time time-consuming of the three phrases.
• Requires the writer to produce text that moves
  toward completing the understood goal.
• Access important mathematical concepts and ideas
  and construct various written statements that
  concisely and clearly communicate their ideas.
• Teachers needs to identify the important
  mathematics that students must know in order to
  successfully complete the task.

15
Composing

• Students are encouraged to incorporate diagrams
  into their writing, properly label the diagrams
  and refer specifically to the diagram in their
  writing.
• Student Question What concepts and ideas support
  the statements I am making? How can I describe my
  thinking concisely and clearly?
• Teacher Question What is the important
  mathematical content that must be accessible to
  the student? How can the written content reflect
  good mathematical thinking? What strategies can
  be emphasized for organizing and communicating
  that information?

16
Revising

• Revising should not be underemphasized in content
  area writing.
• Research indicates that students routinely fail
  to verify the reasonableness or accuracy of their
  work (Lester, 1898 Pugalee, 2001aSexton
  Ballew, 1988).
• Encourage students be sure that they addressed
  the question being raised in the task or
  assignment.

17
Revising

• Teachers should provide opportunities for
  students to develop an understanding of clear and
  understandable writing.
• Student QuestionsHave I answered the question
  fully? Are my conjectures and ideas supported? Is
  my work clear and understandable?
• Teacher Questions Do students adequately justify
  and support their ideas? What instructional
  strategies will encourage and support clear and
  understandable writing?

18
Summary

• These principles provide some key ideas and
  serves as a framework for instructional
  activities in mathematics with a writing focus.
• These ideas become a way of thinking about the
  relationship between writing and mathematics.
• How teachers view that relationship will have an
  impact on how writing is designed, used, and
  assessed in the classroom.