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Developmental Framework for Critical Thinking

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

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Developmental Framework for Critical Thinking

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  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 Read conflicting opinions Relate assumptions & biases Analyze pros & cons Prioritize issues and information Justify assumptions 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: Stroke, Sezgin Method, Yu Method • Which primitive (or group) is this stroke? • Line, Arc, Ellipse • Precedence, Error, Tolerance • What about a Rubine gesture? Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation

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

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

  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 • - Doesn’t 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 • - Endpoint tails not removed • Doesn’t 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

  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 • 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

  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: • Slope of the direction graph == 2pi/n • Doesn’t handle tails • Overtracing difficult because have to split • Direction graph is linear • Circle least squares • Circle feature area

  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 • X^2 / a^2 + y^2 / b^2 = 1 • A = ½ major axis, b = ½ 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

  9. 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

  10. 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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