Developmental Framework for Critical Thinking

1
Developmental Framework for Critical Thinking
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation
Steps in Critical Thinking
Confused Fact Finder
Biased Jumper
Perpetual Analyzer
Pragmatic Performer
Strategic Re-visioner
Performance Patterns
Distinguish relevant irrelevant Information Rea
d conflicting opinions
Relate assumptions biases Analyze pros cons
Prioritize issues and information Justify assumpt
ions
Articulate vision Reinterpret information
Interventions
Step 1
Step 2
Step 3
Step 4
Steps for Better Thinking Performance Patterns,
http//www.wolcottlynch.com
2
Computer Sketch Recognition
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation

• Foundation Knowledge Stroke, Sezgin Method, Yu
  Method
• Which primitive (or group) is this stroke?
• Line, Arc, Ellipse
• Precedence, Error, Tolerance
• What about a Rubine gesture?

3
Computer Sketch Recognition
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation

• Foundation Knowledge Stroke, Rubine Method,
  Sezgin Method, Yu Method
• Which primitive (or group) or gesture is this
  stroke?
• Line, Arc, Ellipse, RGesture1, RGesture2
• Precedence, Error, Tolerance
• What about combination of strokes? May change
  lower level interpretations geometric context

4
US
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation

• Foundation Knowledge Stroke, Sezgin Method, Yu
  Method
• Which primitive (or group) is this stroke?
• Line, Arc, Ellipse
• Precedence, Error, Tolerance
• What about a Rubine gesture?

5
Recognizing a Line
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation

• Foundation Knowledge Stroke, Sezgin Method, Yu
  Method, Geometry
• How do we find line tolerance error
• Options
• Least-squares error from endpoints
• Uses endpoints
• - Endpoint tails not removed
• - Error may be larger than true error
• Least-square error with best fit line
• Find best-fitting line
• - Doesnt necessarily use perceptually important
  start end points
• Can remove non-perceptually important tails
• feature area
• In theory, can be compared to other shapes
• - Confusing
• - Value not apparent
• ? Smaller range
• ratio euclidean length/stroke length
• Easy to calculate
• Uses perceptually important start end point

6
Recognizing an Arc
Observation
Interpretation
Planning
Judgment
Foundation Knowledge
Identify The Problem
Explore Interpretations Connections
Prioritize Alternatives
Envision Strategic Innovation

• Foundation Knowledge
• Method to find sample arc as part of a circle
• Connect endpoints, find perpendicular bisector of
  that line
• Find where that line intersects stroke
• Make two lines connecting center stroke point and
  endpoints
• Find perpendicular bisector of each line
• Intersecting point is circle center
• Find feature area
• A curve of order 2
• Options
• Least-squares error from endpoints with a curve
  of order 2
• Uses endpoints
• Easy to compute
• - Not actually an arc
• Feature area
• Uses real arc
• Faster ?
• - Need the line of the arc, because takes the
  feature area
• - Difficult polygons could be above or below

7
Recognizing a Circle

• Foundation Knowledge
• Method to find direction graph slope
• Direction graph Find direction of each point
• Direction vs. time since start
• Depends on time since start
• Direction vs. point number
• Depends on sampling rate
• Direction vs. stroke length
• More time computationally
• Find slope
• Fit a line to direction graph use same least
  square method
• Splitting Spilt it when change in direction
  (every) 2pi
• Circle center
• center of bounding box or
• average of all points
• Circle radius
• Bounding box / 2
• Average distance from center
• Options

8
Recognizing a Ellipse

• Foundation Knowledge
• Method to find direction graph slope
• Use endpoints
• Find best fit line of direction graph
• Major axis and minor axis not equal
• To find major axis
• Two points w/ greatest distance is the major axis
• Perpendicular bisector is minor axis (where it
  intersects stroke)
• Should points also intersect a calculated center
  point?
• Fit a line to the ellipse
• To find center point
• Center of bounding box
• Center of longest line
• Center of mass
• Area of Ellipse
• PI (length of major axis/2) (length of minor
  axis/2)
• Definition of Ellipse
• Sum of the distance from focus 1 and focus 2 is
  constant
• X2 / a2 y2 / b2 1