Pattern

1
Pattern

• By Lynn Arthur Steen

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Patterns in Mathematics

• Mathematics is an exploratory science that seeks
  to understand every kind of pattern
• patterns that occur in nature,
• patterns invented by the human mind,
• even patterns created by other patterns. p.8

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Why Patterns?

• To grow mathematically, children must be exposed
  to a rich variety of patterns appropriate to
  their own lives through which they can see
  variety, regularity, and interconnections. p. 8

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Fundamental Mathematics

• Mathematical Structures
• Attributes
• Actions
• Abstractions
• Attitudes
• Behaviors
• Dichotomies

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Why the Fundamentals?

• Preparation for more advanced study in
  mathematical fields
• Real-life applications

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Traditional School Mathematics

• Few strands
• Horizontal arrangement
• Lack of connection between topics/strands
• Tendency to have each course meet prerequisites
  of next course
• Narrowing of each successive layer

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Preferable School Mathematics

• Multiple parallel strands vertical continuity
• Show interconnections
• Base on appropriate childhood experiences
• Provides for different interests and talents

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Direction of Mathematics Today

• Increased use of computers and computer graphics
  has allowed mathematicians to find new ways to
  see patterns, both with the eye and with the mind
  (p. 2)

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Deep Mathematical Ideas Areas Studied in Your
Text

• Dimension Time and 3-D Geometry
• Quantity Numeration
• Uncertainty Probability and Statistics
• Shape Geometry
• Change Algebra

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Interconnections

• Measurement
• Symmetry
• Visualization
• Algorithms
• And more. . . .

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Gaining Perspective

• Newton said, If I have seen farther than others,
  it is because I have stood on the shoulders of
  giants.
• Why include different strands of mathematics?