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CERA saad chahine 2013 fuzzy clusters
 

CERA saad chahine 2013 fuzzy clusters

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Research paper on Fuzzy Cluster Analysis presented at the Canadian Education Research Association

Research paper on Fuzzy Cluster Analysis presented at the Canadian Education Research Association

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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
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CERA saad chahine 2013 fuzzy clusters CERA saad chahine 2013 fuzzy clusters Presentation Transcript

  • Embrace the Fuzz ofDifferentiated InstructionSaad Chahine, PhDJune 2, 2013CERA | Victoria, BC13-04-30
  • Differentiated Instruction• Huge push for teachers to provide DifferentiatedInstruction (DI)• Many publications are oriented to different ways ofattempting to “do” DI in the classroom• There is a great deal of speculation on the ways inwhich you do “DI” in the classroom• In practice, the attempt to be more differentiated isoften intuitive rather than evidence-based
  • Purpose- It is almost impossible for teachers to provide studentswith individualized attention for prolonged periodsduring the day- It is possible to create smaller groups of student froma pedagogical perspectiveBig Questions:Can we use mathematical algorithms to identify groupsfrom students response patterns?ππ33
  • Fuzzy Logic• Introduced in 1965 by Lotfi A. Zadeh• Questions the crisp boundaries thatwe form that may be artificial• Is becoming more widely used inengineering, computer science andmachine learning etc…ππ44
  • Some Interesting Applicationsππ55
  • Algorithm1. K “means” are randomly generatedbased on the data2. Clusters are created with data pointsclosest to these means3. The centroid of each clusterbecomes the new mean4. Repeat steps 2 & 3 until convergenceFUZZY C-Means:For each point, calculate theCoefficient of being in the clusterhttp://home.deib.polimi.it/matteucc/Clustering/tutorial_html/cmeans.htmlππ66MountSaintVincentUniversityMountSaintVincentUniversity
  • Traditional GroupingGroup 1SallyRobinStudentsBobSallyJimRobinGroup 2BobJim
  • Fuzzy GroupingGroup 1BobSallyJimRobinStudentsBobSallyJimRobinGroup 2BobSallyJimRobin40% 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” ππ99
  • Trading Card Itemsππ1010MountSaintVincentUniversityMountSaintVincentUniversity
  • Trading Cards Item 1ππ1111MountSaintVincentUniversityMountSaintVincentUniversity
  • Trading Cards Item 2ππ1212MountSaintVincentUniversityMountSaintVincentUniversity
  • Trading Cards Item 3ππ1313MountSaintVincentUniversityMountSaintVincentUniversity
  • Soccer Tournament Item 4ππ1414MountSaintVincentUniversityMountSaintVincentUniversity
  • Resultsππ1515Group 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
  • Resultsππ1616Group 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 97
  • ππ1717
  • Response Patterns• Really good at identifying Groups2 & 3• Difficulty with Group 1• Percentages are more importantππ1818MountSaintVincentUniversityMountSaintVincentUniversity
  • ππ1919Group 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 97Group 3:-Answered all items wrongor partially correct onitem 2Group 2:-Answered items 1, 2, & 4correctly (or partially onItem 2)Group 1:-Answered all itemscorrect-Answered items 1 & 2correctly-Answered item 3 correct-Answered item 4 correct
  • ππ2020Group 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 97
  • Fuzzy Clustering for DI- May be useful in identifyingresponse patterns for students- Is not fully informative on its own- Needs support of educator- Current format of analysis is notuser friendlyππ2121MountSaintVincentUniversityMountSaintVincentUniversity
  • Future• Intelligent Tutoring/Testingprograms• Possible alternative to statsmethods that arecomputationally heavy• FCA can easily be programedinto a software program foreducators’ useππ2222MountSaintVincentUniversityMountSaintVincentUniversity
  • Thank Yousaad.chahine@msvu.caππ2323MountSaintVincentUniversityMountSaintVincentUniversity