cera saad chahine 2013 fuzzy clusters
TRANSCRIPT
Embrace the Fuzz of Differentiated Instruction
Saad Chahine, PhD June 2, 2013CERA | Victoria, BC
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Differentiated Instruction • Huge push for teachers to provide Differentiated
Instruction (DI)
• Many publications are oriented to different ways of attempting to “do” DI in the classroom
• There is a great deal of speculation on the ways in which you do “DI” in the classroom
• In practice, the attempt to be more differentiated is often intuitive rather than evidence-based
Purpose - It is almost impossible for teachers to provide
students with individualized attention for prolonged periods during the day
- It is possible to create smaller groups of student from a pedagogical perspective
Big Questions:
Can we use mathematical algorithms to identify groups from students response patterns?
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Fuzzy Logic • Introduced in 1965 by Lotfi A. Zadeh
• Questions the crisp boundaries that we form that may be artificial
• Is becoming more widely used in engineering, computer science and machine learning etc…
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Some Interesting Applications
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Algorithm 1. K “means” are randomly generated
based on the data2. Clusters are created with data points
closest to these means3. The centroid of each cluster
becomes the new mean 4. Repeat steps 2 & 3 until convergence FUZZY C-Means: For each point, calculate the Coefficient
of being in the cluster http://home.deib.polimi.it/matteucc/Clustering/tutorial_html/cmeans.html ππ
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Traditional Grouping
Group 1
Sally
Robin
Students
Bob
Sally
Jim
Robin
Group 2
Bob
Jim
Fuzzy Grouping
Group 1
Bob
Sally
Jim
Robin
Students
Bob
Sally
Jim
Robin
Group 2
Bob
Sally
Jim
Robin
40% 60%
20%80%
25%
80%
75%
20%
Methods• TIMSS 2011 Math Number -
Reasoning Items - Book 1• Random selection of 30 students • Items coded:
– “2” for correct– “1” for partially correct – “0” for incorrect
• Analysis conducted using R “fannyx”
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Trading Card Items
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Trading Cards Item 1
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Soccer Tournament Item 4
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Results
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Group 1 Group 2 Group 3Student 1 43 40 17Student 2 20 71 8Student 3 44 33 23Student 4 20 71 8Student 5 20 71 8Student 6 43 41 16Student 7 43 41 16Student 8 22 69 9Student 9 22 69 9Student 10 22 69 9Student 11 45 35 20Student 12 45 35 20Student 13 34 47 19Student 14 43 22 35Student 15 35 18 47Student 16 35 18 47Student 17 42 33 24Student 18 35 18 47Student 19 2 1 97Student 20 2 1 97Student 21 2 1 97Student 22 47 23 30Student 23 42 36 21Student 24 43 22 35Student 25 39 30 30Student 26 2 1 97Student 27 2 1 97Student 28 2 1 97Student 29 2 1 97Student 30 2 1 97
Results
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Group 1 Group 2 Group 3Student 1 43 40 17Student 2 20 71 8Student 3 44 33 23Student 4 20 71 8Student 5 20 71 8Student 6 43 41 16Student 7 43 41 16Student 8 22 69 9Student 9 22 69 9Student 10 22 69 9Student 11 45 35 20Student 12 45 35 20Student 13 34 47 19Student 14 43 22 35Student 15 35 18 47Student 16 35 18 47Student 17 42 33 24Student 18 35 18 47Student 19 2 1 97Student 20 2 1 97Student 21 2 1 97Student 22 47 23 30Student 23 42 36 21Student 24 43 22 35Student 25 2 1 97Student 26 39 39 30Student 27 2 1 97Student 28 2 1 97Student 29 2 1 97Student 30 2 1 97
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Response Patterns
• Really good at identifying Groups 2 & 3
• Difficulty with Group 1 • Percentages are more important
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Group 1 Group 2 Group 3Student 1 43 40 17Student 2 20 71 8Student 3 44 33 23Student 4 20 71 8Student 5 20 71 8Student 6 43 41 16Student 7 43 41 16Student 8 22 69 9Student 9 22 69 9Student 10 22 69 9Student 11 45 35 20Student 12 45 35 20Student 13 34 47 19Student 14 43 22 35Student 15 35 18 47Student 16 35 18 47Student 17 42 33 24Student 18 35 18 47Student 19 2 1 97Student 20 2 1 97Student 21 2 1 97Student 22 47 23 30Student 23 42 36 21Student 24 43 22 35Student 25 2 1 97Student 26 39 39 30Student 27 2 1 97Student 28 2 1 97Student 29 2 1 97Student 30 2 1 97
Group 3:
-Answered all items wrong or partially correct on item 2
Group 2:
-Answered items 1, 2, & 4 correctly (or partially on Item 2)
Group 1:
-Answered all items correct -Answered items 1 & 2 correctly -Answered item 3 correct -Answered item 4 correct
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Group 1 Group 2 Group 3Student 1 43 40 17Student 2 20 71 8Student 3 44 33 23Student 4 20 71 8Student 5 20 71 8Student 6 43 41 16Student 7 43 41 16Student 8 22 69 9Student 9 22 69 9Student 10 22 69 9Student 11 45 35 20Student 12 45 35 20Student 13 34 47 19Student 14 43 22 35Student 15 35 18 47Student 16 35 18 47Student 17 42 33 24Student 18 35 18 47Student 19 2 1 97Student 20 2 1 97Student 21 2 1 97Student 22 47 23 30Student 23 42 36 21Student 24 43 22 35Student 25 2 1 97Student 26 39 39 30Student 27 2 1 97Student 28 2 1 97Student 29 2 1 97Student 30 2 1 97
Fuzzy Clustering for DI
- May be useful in identifying response patterns for students
- Is not fully informative on its own
- Needs support of educator- Current format of analysis is not
user friendly
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Future
• Intelligent Tutoring/Testing programs
• Possible alternative to stats methods that are computationally heavy
• FCA can easily be programed into a software program for educators’ use
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Thank You
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