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Visualization
¨ Displaying information in a meaningful fashion
Week 6 Video 1 Visualization Learning Curves Visualization - - PowerPoint PPT Presentation
Week 6 Video 1 Visualization Learning Curves Visualization - - PowerPoint PPT Presentation
Week 6 Video 1 Visualization Learning Curves Visualization Displaying information in a meaningful fashion Visualization Should (Tufte, 1983) Show the data Induce the viewer to think about the substance Avoid distorting what the
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Visualization Should… (Tufte, 1983)
¨ Show the data ¨ Induce the viewer to think about the substance ¨ Avoid distorting what the data have to say ¨ Make large data sets coherent ¨ Encourage the eye to compare different pieces of
data
¨ Reveal the data at several levels ¨ (And other stuff too)
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Visualization
¨ A big area ¨ Worthy of a course in its own right ¨ Rather than discussing standard visualizations ¨ I’ll discuss a few visualizations that are particularly
important with educational data
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Learning Curves
¨ One of the most important visualizations in
education
¨ Briefly discussed in Week 4 ¨ I’ll go into more depth today
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The Classic Learning Curve
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Assumptions
¨ The student is practicing the same skill several times
in (approximately) the same fashion
¨ Completing a physics problem set ¨ Reading the same word in several stories ¨ Learning to complete an assembly line procedure
¤ Early application! (Crossman, 1959)
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Assumptions
¨ Similar methods and considerations apply to
situations where the student is recalling the same knowledge several times
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Assumptions
¨ We have some way to measure student
performance over time
¤ Speed or accuracy
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Learning LISP programming in the LISP Tutor (Corbett & Anderson, 1995)
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Learning in Cognitive Tutor Geometry (Ritter et al., 2007)
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A certain characteristic pattern
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Power Law of Learning*
¨ Performance (both speed and accuracy) improves
with a power function * -- May actually be an exponential function rather than a power function (Heathcote, Brown, & Mewhort, 2000)
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Called Power Law
¨ Because speed and accuracy both follow a power
curve
¨ Radical improvement at first which slows over time
towards an asymptote
¨ Passing the asymptote usually involves developing
entirely new strategy
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Passing the Asymptote
¨ Famous example: Fosbury Flop
- http://www.youtube.com/watch?v=Id4W6VA0uLc
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Power Law of Learning proven to apply across many domains
¨ Simple domains
¤ Pressing correct button on stimulus
¨ Complex problem-solving domains
¤ Math ¤ Programming
¨ Real-world domains
¤ Cigar-making in factories (Crossman, 1959)
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Real-world data
¨ Are rarely perfectly smooth… ¨ (At least not without hundreds of students or more)
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Example from a minute ago
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Making inference from learning curves
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Making inference from learning curves
¨ Via visual inspection of the curve form
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“Normal learning”
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No learning going on
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What might this graph mean?
0.5 1 1.5 2 2.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
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Insert Pause-Continue Quiz Here
0.5 1 1.5 2 2.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
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Student has already learned skill for the most part
0.5 1 1.5 2 2.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
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What might this graph mean?
5 10 15 20 25 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
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Insert Pause-Continue Quiz Here
5 10 15 20 25 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
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Student learned a new strategy and “broke through” the asymptote
5 10 15 20 25 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
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What might this graph mean?
5 10 15 20 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Insert Pause-Continue Quiz Here4
5 10 15 20 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Two skills treated as the same skill (Corbett & Anderson, 1995)
5 10 15 20 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Uses
¨ To understand how (and whether) a skill is being
learned across students
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Uses
¨ To study and refine item-skill mappings in
educational software
¨ As discussed in week 4, Pittsburgh Science of
Learning Center DataShop (Koedinger et al., 2010) is a common tool for doing this
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