Dynamic Geometry Conference

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Dynamic Geometry Conference
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The general philosophy of Math Trailblazers

• Children best learn mathematics in contexts that
  make sense to them and are engaging. One of
  these contexts is the scientific investigation of
  accessible phenomena.

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• One of the main organizing principles of Math
  Trailblazers is the concept of a variable. In
  principle, this should make dynamic geometry
  particularly appropriate.

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Geometry related to measurement variables
length, area, volume

• 2-Dimensional
• Meaning of perimeter and area
• Relation between perimeter and area
• How does the area vary if we hold one side of a
  rectangle fixed and vary the length of the other?
• How does the area of a triangle vary if we hold
  the base fixed and vary one of the sides (is this
  a controlled experiment?)
• What if we vary the height of the triangle?
• Put N-squares together. What are the maximum and
  minimum perimeters? What values can you get for
  the perimeter?

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Geometry related to measurement variables
length, area, volume

• 2 3-Dimensional
• Volume vs. height for prisms and pyramids -
  computer builds prism of varying height from
  given a floor plan (on a grid?).
• Surface area vs. height - same as above. Perhaps
  you can paint squares and find surface area by
  counting.
• Surface area vs. volume

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Coordinate Geometry

• Scale maps (Mr. O)
• Graphing (plotting data points, best fit lines)

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Transformational Geometry

• Flips, slides, and turns
• Symmetry related to flips, slides, and turns

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3-D visualization

• Computer lets you cut a polyhedron and make it
  into a net.
• Computer constructs a sold from a net and pasting
  instructions.

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Questions

• 1. Can work with the computer take the place of
  doing the real thing (i.e. hands-on)?

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Questions

• 1. Can work with the computer take the place of
  doing the real thing (i.e. hands-on)?
• 2. Just because we CAN do this, how can we say
  that we SHOULD do this? How do we address the
  mile wide and an inch deep characterization of
  U.S. curricula. Do we need to focus on a smaller
  set of topics and cover them more deeply? If so,
  how do we decide which topic are to be covered?