Why do Gestures Matter?

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Why do Gestures Matter?

• Luis Radford
• Université Laurentienne
• Ontario, Canada

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A Classroom Episode

• Two children walk in opposite directions, as
  shown in the figure.
• Grade 10 students were asked to sketch a graph of
  the relationship between the elapsed time and the
  remaining distance between the children

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First Clip (33 s)
Some antecedents In Grade 9
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Two Questions What and How

• What is the role of gestures?
• How do gestures contribute to the production of
  mathematical meaning?

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Why do Gestures Matter?
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(No Transcript)
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• Man is an unfinished animal, a deficient being.
• Man is an acting being
• He acts through his senses
• Thought and imagination are versatile forms of
  action

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Bees perception
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Gestures and the tactile experience of the world
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The cooperation between hand, eye, and language

• The senses have become theoreticians in their
  immediate praxis.

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Do you see the dalmatian dog?
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Do you see the dalmatian dog?
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Objectification

• Objecttification
• Obiectare
•  to put something in front of some one
• Facere
•  to make 

• To place something in front of some one in order
  for him/her
• to perceive or
• to notice it or
• to become aware of it.

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Objectification

• Process whose goal is to show something to
  someone.
• What are the means to show it?

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Semiotic Means of Objectification

• Objects, artefacts, linguistic terms and signs
  in general which are used in order to render
  apparent an intention, to attain an awareness
  and/or to carry out an action.

For the Learning of Mathematics,
2002. Mathematical Thinking and Learning, 2003.
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A Learning Strategy for Promoting One More
Deductive Step (Fou-Lai Lin)

• The reading and coloring strategy (R-C strategy)

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GESTURES

• gestures are part of the semiotic means of
  objectification that allow the students to become
  aware of conceptual aspects that, because of
  their own generality, cannot be fully indicated
  in the realm of the concrete.

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Why do gestures matter?

• Gestures matter because, in learning settings,
  they fulfill an important function they are
  important elements in the students processes of
  knowledge objectification. Gestures help the
  students to make their intentions apparent, to
  notice abstract mathematical relationships and to
  become aware of conceptual aspects of
  mathematical objects.

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• A gesture is often a tactile movement that
  replaces the actual movement that we would carry
  on a mathematical object, were we able to
  physically handle it.

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The cooperation between hand, eye, and language
Semiotic Nodes
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Semiotic Nodes

• A semiotic node is a piece of the students
  semiotic activity where action and diverse signs
  (e.g. gesture, word, formula) work together to
  achieve knowledge objectification.

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Example of a Semiotic Node