This document discusses using fuzzy clustering algorithms to group students for differentiated instruction. It describes how fuzzy c-means clustering was used to analyze student responses to math problems and assign each student percentages of belonging to different groups based on their response patterns. Three groups were identified: students who answered all problems correctly, students who answered some problems correctly, and students who answered all problems incorrectly or partially. The document concludes that fuzzy clustering shows potential for identifying student groups but has limitations and requires teacher support to be useful for differentiation. Future applications in intelligent tutoring systems are suggested.
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CERA saad chahine 2013 fuzzy clusters
1. Embrace the Fuzz of
Differentiated Instruction
Saad Chahine, PhD
June 2, 2013
CERA | Victoria, BC
13-04-30
2. 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
3. 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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4. 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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6. Algorithm
1. K “means” are randomly generated
based on the data
2. Clusters are created with data points
closest to these means
3. 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
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9. 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
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18. Response Patterns
• Really good at identifying Groups
2 & 3
• Difficulty with Group 1
• Percentages are more important
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21. 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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22. 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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Before we can begin to answer that question – we actually need to understand the thought processes of educators in two main areas 1. Statistical Literacy & 2. Score Report Interpretation. Together I describe these as data habit of mind