Developmental Framework for Critical Thinking

Developmental Framework for Critical Thinking

Developmental Framework for Critical Thinking Foundation Knowledge Performance Patterns Observation Interpretation Judgment Planning Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation Confused Fact Finder Interventions Biased Jumper Distinguish relevant & irrelevant Information Perpetual Analyzer Relate assumptions & biases Read

conflicting opinions Analyze pros & cons Step 1 Step 2 Pragmatic Performer Prioritize issues and information Justify assumptions Step 3 Steps in Critical Thinking Strategic Re-visioner Articulate vision Reinterpret information Step 4 Steps for Better Thinking Performance Patterns, http://www.wolcottlynch.com Computer Sketch Recognition Foundation Knowledge Observation Interpretation Judgment Planning 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? Computer Sketch Recognition Foundation Knowledge Observation Interpretation Judgment Planning 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 US Foundation Knowledge Observation Interpretation Judgment Planning 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? Recognizing a Line Foundation Knowledge Observation Interpretation Judgment Planning

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: Least-square error with best fit line: + In theory, can be compared to other shapes - Confusing - Value not apparent ? Smaller range ratio: euclidean length/stroke length: + Find best-fitting line - Doesnt necessarily use perceptually important start & end points + Can remove non-perceptually important tails

feature area: + Uses endpoints - Endpoint tails not removed - Error may be larger than true error + Easy to calculate + Uses perceptually important start & end point - Endpoint tails not removed Doesnt differentiate between one point being far away and several points being near - Bigger range so harder to figure out a good threshold Least-squares error using best fit, but then use endpoints - Error not same as what is chosen + Error is more representative of line + Perceptually important endpoints Recognizing an Arc Foundation Knowledge Interpretation Judgment Planning Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation

Foundation Knowledge: Method to find sample arc as part of a circle: Observation 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: Feature area + Uses endpoints + Easy to compute - Not actually an arc + Uses real arc + Faster ? - Need the line of the arc, because takes the feature area

- Difficult polygons could be above or below Idea: Add threshold to radius for comparing against line Least squared error with arc itself + Uses real arc - Harder to compute + Faster? Compute distance of each point to the center subtract from radius 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: Slope of the direction graph == 2pi/n Doesnt handle tails Overtracing difficult because have to split Direction graph is linear Circle least squares Circle feature area 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 Center of bounding box Center of longest line Center of mass Area of Ellipse Fit a line to the ellipse To find center point 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 X^2 / a^2 + y^2 / b^2 = 1

Perpendicular bisector is minor axis (where it intersects stroke) Should points also intersect a calculated center point? A = major axis, b = minor axis Focal point is the point on the major axis that is distance A from where minor axis intersects ellipse Options: Slope of the direction graph ~2pi/n Ellipse least squares need foci Ellipse feature area Small triangles to center vs actual ellipse area Recognizing a Ellipse, Part 2 Length of Major Axis Fit a line Longest distance Length of Minor Axis Rotate Ellipse to find height of BB Average distance of stroke points that intersect minor axis from the major axis Calculate from perimeter formula (p = strokelength = pi * sqrt(2*(s^2 + b^2) (a-b)^2/2) Calculate distance from every point to the major axis: Minor axis = average distance * pi / 2 Eigenvector method Closest point to center Helix Recognition Find major, minor axis (rotated b b) Find number of rotations (direction graph from circle) Combine n helix components Rotate, scale and translate X = cos(t) + change in x at t Y = sin(t) + change in y at t

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